{"group":{"group":{"id":97667,"name":"The Complexity Paradigm","lockable":false,"created_at":"2026-03-20T06:14:51.000Z","updated_at":"2026-03-22T14:36:15.000Z","description":"I have no idea to say but that's my passion, It's more difficult than the first one I created. If you feel bored, why not trying to solve my problems !:D","is_default":false,"created_by":4945722,"badge_id":62,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":null,"image_id":7206,"published":true,"community_created":true,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI have no idea to say but that's my passion, It's more difficult than the first one I created. If you feel bored, why not trying to solve my problems !:D\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 359.5px 21px; transform-origin: 359.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 335.5px 21px; text-align: left; transform-origin: 335.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eI have no idea to say but that's my passion, It's more difficult than the first one I created. If you feel bored, why not trying to solve my problems !:D\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","published_at":"2026-03-22T14:36:15.000Z"},"current_player":null},"problems":[{"id":61278,"title":"Robust Huffman Decoding: The Single-Bit Error Challenge","description":"In the world of data compression, Huffman coding is a classic algorithm. However, it is notoriously fragile: a single bit error during transmission can lead to \"synchronization loss,\" causing the decoder to misinterpret the entire remaining sequence.\r\nIn this problem, you are tasked with recovering a message from a corrupted Huffman-encoded bitstream.\r\nThe Setup:\r\n1.Dictionary: You are given a cell array of binary strings (e.g., {'0', '10', '11'} ). The i-th element corresponds to the i-th letter of the alphabet (1-\u003e'A', 2-\u003e 'B', etc.).\r\n2.Bitstream: A string of '0's and '1's. This stream contains exactly one flipped bit (an error where a 0 became a 1 or vice versa).\r\n3.ValidWords: A cell array of possible original strings (e.g.,{'ABC', 'BBA'}).\r\nThe Rules:\r\nThe original (pre-corruption) bitstream, when decoded, results in one of the strings listed in ValidWords.\r\nA decoded string is only valid if the bitstream can be completely partitioned into codewords from the dictionary with no bits left over.\r\nYou must identify the single erroneous bit, flip it back, and return the corrected decoded string.\r\nInput:\r\nDictionary: 1 x N cell array of bit strings.\r\nBitstream: A string of '0's and '1's.\r\nValidWords: A cell array of strings.\r\nOutput:\r\ndecodedWords: The corrected string (must be an element of ValidWords).\r\nExample:\r\nDictionary = {'0', '10', '11'} (A = '0', B = '10', C = '11')\r\nValidWords = {'ABC', 'BBA', 'ACC'}\r\nBitstream = '00011'\r\nAnalysis:\r\nIf we flip the 1st bit: '10011' -\u003e 'B' + '0' + '11' = 'BAC' (Not in ValidWords)\r\nIf we flip the 2nd bit: '01011' -\u003e '0' + '10' + '11' = 'ABC' ( Matches ValidWords! )\r\nResult: 'ABC'","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 722.633px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 361.317px; transform-origin: 468.5px 361.317px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the world of data compression, Huffman coding is a classic algorithm. However, it is notoriously fragile: a single bit error during transmission can lead to \"synchronization loss,\" causing the decoder to misinterpret the entire remaining sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this problem, you are tasked with recovering a message from a corrupted Huffman-encoded bitstream.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eThe Setup:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e1.Dictionary:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e You are given a cell array of binary strings (e.g., \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e{'0', '10', '11'}\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ). The \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ei\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-th element corresponds to the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ei\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-th letter of the alphabet (1-\u0026gt;'A', 2-\u0026gt; 'B', etc.).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e2.Bitstream: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA string of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e'0'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003es and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e'1'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003es. This stream contains \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eexactly one \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eflipped bit (an error where a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e became a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or vice versa).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e3.ValidWords: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA cell array of possible original strings (e.g.,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e{'ABC', 'BBA'}\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eThe Rules:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 30.65px; transform-origin: 451.5px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe original (pre-corruption) bitstream, when decoded, results in one of the strings listed in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eValidWords.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA decoded string is only valid if the bitstream can be completely partitioned into codewords from the dictionary with no bits left over.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou must identify the single erroneous bit, flip it back, and return the corrected decoded string.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 30.65px; transform-origin: 451.5px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDictionary: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1 x \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e cell array of bit strings.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBitstream: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA string of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e'0'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003es and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e'1'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003es.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eValidWords:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e A cell array of strings.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 10.2167px; transform-origin: 451.5px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003edecodedWords: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe corrected string (must be an element of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eValidWords\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 30.65px; transform-origin: 451.5px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDictionary = {'0', '10', '11'} \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(A = '0', B = '10', C = '11')\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eValidWords = {'ABC', 'BBA', 'ACC'}\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBitstream = '00011'\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eAnalysis\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 30.65px; transform-origin: 451.5px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf we flip the 1st bit: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e'10011'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e -\u0026gt; 'B' + '0' + '11' = \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e'BAC'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (Not in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eValidWords\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf we flip the 2nd bit: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e'01011'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e -\u0026gt; '0' + '10' + '11' = \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e'ABC'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ( Matches \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eValidWords\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e! )\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eResult: 'ABC'\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function decodedWord = solve_huffman(Dictionary, Bitstream, ValidWords)\r\n  decodedWord = 1;\r\nend","test_suite":"%% Test Case 1: \r\ndict1 = {'0', '10', '11'}; \r\nbits1 = '00011';           \r\nvalid1 = {'ABC', 'BBA', 'ACC'};\r\nassert(isequal(solve_huffman(dict1, bits1, valid1), 'ABC'));\r\n\r\n%% Test Case 2: \r\ndict2 = {'1', '01', '00'}; \r\nbits2 = '11001';\r\nvalid2 = {'BCA', 'AAA', 'CCC'};\r\nassert(isequal(solve_huffman(dict2, bits2, valid2), 'BCA'));\r\n\r\n%% Test Case 3: \r\ndict3 = {'00', '01', '10', '11'}; \r\nbits3 = '111101';\r\nvalid3 = {'DDA', 'DDB', 'DDD'};\r\nassert(isequal(solve_huffman(dict3, bits3, valid3), 'DDD')||isequal(solve_huffman(dict3, bits3, valid3),'DDA'));\r\n\r\n%% Test Case 4: \r\ndict4 = {'0', '11', '100', '101'}; \r\nbits4 = '111';\r\nvalid4 = {'AB', 'CC'};\r\nassert(isequal(solve_huffman(dict4, bits4, valid4), 'AB'));\r\n\r\n%% Test Case 5:\r\ndict5 = {'00', '01', '10', '11'};\r\noriginal_word = repmat('ABCD', 1, 25); \r\noriginal_bits = repmat('00011011', 1, 25);\r\ncorrupted_bits = original_bits;\r\ncorrupted_bits(157) = '0';\r\nvalid5 = {original_word, 'BCDA', 'AAAA'};\r\nassert(isequal(solve_huffman(dict5, corrupted_bits, valid5), original_word));\r\n\r\n%% Test Case 6: \r\nalphabet = 'ABCDE';\r\ndict6 = {'0', '11', '101', '1001', '1000'}; \r\nsecret_idx = randi([1, 5]);\r\nwords6 = {'ABCDE', 'EDCBA', 'AAAAA', 'BBBBB', 'CCCCC'};\r\ntarget_word = words6{secret_idx};\r\n\r\nbits_encoded = '';\r\nfor char_val = target_word\r\n    bits_encoded = [bits_encoded, dict6{char_val - 'A' + 1}];\r\nend\r\n\r\nflip_idx = randi([1, length(bits_encoded)]);\r\ncorrupted_bits6 = bits_encoded;\r\nif corrupted_bits6(flip_idx) == '0'\r\n    corrupted_bits6(flip_idx) = '1';\r\nelse\r\n    corrupted_bits6(flip_idx) = '0';\r\nend\r\n\r\nassert(isequal(solve_huffman(dict6, corrupted_bits6, words6), target_word));","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":4945722,"edited_by":4945722,"edited_at":"2026-03-21T03:42:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2026-03-21T03:42:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-17T14:31:50.000Z","updated_at":"2026-03-30T13:07:27.000Z","published_at":"2026-03-17T14:31:50.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the world of data compression, Huffman coding is a classic algorithm. However, it is notoriously fragile: a single bit error during transmission can lead to \\\"synchronization loss,\\\" causing the decoder to misinterpret the entire remaining sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, you are tasked with recovering a message from a corrupted Huffman-encoded bitstream.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe Setup:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1.Dictionary:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e You are given a cell array of binary strings (e.g., \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e{'0', '10', '11'}\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ). The \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th element corresponds to the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th letter of the alphabet (1-\u0026gt;'A', 2-\u0026gt; 'B', etc.).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2.Bitstream: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eA string of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'0'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003es and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'1'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003es. This stream contains \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexactly one \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eflipped bit (an error where a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e became a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or vice versa).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e3.ValidWords: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eA cell array of possible original strings (e.g.,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e{'ABC', 'BBA'}\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe Rules:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe original (pre-corruption) bitstream, when decoded, results in one of the strings listed in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eValidWords.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA decoded string is only valid if the bitstream can be completely partitioned into codewords from the dictionary with no bits left over.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou must identify the single erroneous bit, flip it back, and return the corrected decoded string.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDictionary: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e1 x \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e cell array of bit strings.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBitstream: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eA string of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'0'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003es and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'1'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003es.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eValidWords:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e A cell array of strings.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edecodedWords: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe corrected string (must be an element of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eValidWords\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDictionary = {'0', '10', '11'} \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(A = '0', B = '10', C = '11')\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eValidWords = {'ABC', 'BBA', 'ACC'}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBitstream = '00011'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAnalysis\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf we flip the 1st bit: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'10011'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e -\u0026gt; 'B' + '0' + '11' = \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'BAC'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (Not in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eValidWords\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf we flip the 2nd bit: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'01011'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e -\u0026gt; '0' + '10' + '11' = \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'ABC'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ( Matches \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eValidWords\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e! )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eResult: 'ABC'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61275,"title":"The Quantum Knight's Tour on a Toroidal Hexagonal Board","description":"In this challenge, you must navigate a knight on a Toroidal Hexagonal Grid of size \r\nThe grid:\r\nWe use the Axial Coordinate System (q,r)\r\nThe grid is Toroidal: any move that goes off the edge wraps around to the opposite side. Formally, a position (q,r) is always treated as (mod(q,N),mod(r,N)).\r\nThe knight's move:\r\nOn a hexagonal grid, a \"Knight's move\" is defined by 12 possible jumping vectors (). These represent moving 2 steps in one axial direction and 1 step in another, or similar symmetries:\r\n\r\nThe goal:\r\nGiven the board size ,a starting position start_pos, an ending position end_pos, and a list of obstacles, find the minimum number of moves required to reach the destination.\r\nInput:\r\nN: Scalar ( board size )\r\nstart_pos: 1x2 vector []\r\nend_pos: 1x2 vector []\r\nobstacles: Mx2 matrix where each row is a blocked [ ]\r\nOutput:\r\nmin_steps: The shortest distance ( integer ). Return Inf if the destination is unreachable.\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 589.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 294.733px; transform-origin: 468.5px 294.733px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this challenge, you must navigate a knight on a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eToroidal Hexagonal Grid\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of size \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEAAAAAkCAYAAAA5DDySAAAHKUlEQVR4AeyYXWxURRTH7/ZLPkyBQiG13+1aIfELi6AiIoFofCAawI+AYqKYYPSBxESjCcY3iImGaIg8+GAwNWokUYg8oCgGlQ8tVKyCFba7a5GUIkhtC/1i/f1v76z33r27LcqTu83575kzc+bMzJkzZ+Y2z8ryv5wDsjwArFwE5CIgyz2QOwKZAqCiomJ8bW3tM6AFJBwM1dTUPJKuHzpLwSdgEJg+R+vq6lal6zNaPXbuYcxt8KRN5Cb6FYAUqqqqYri6LeifBmYO5yi/VlpaerW7Q8YI6OjouNDe3r45FAotpNNnQJSPvIxC4ODo7wAP0L4FiD4oKSm5MRKJaMKSLxvY2xWNRlfQ8SUwDCzmsICFVqnsRzweZ7jI2kQisZq2ARDPy8u7FTvPdXV19SAnKaMDjBbWzlPeAwwtrK+vn2mEAJ6gbhwYYBLvNDc3D1L+r5Rg0ZrDX46hyvz8/PucciBj7BAN+WD7Cf7gKTQmBxBuWsztrt7TMa4dcVX9U1SY0V5HTRuTPgy/InTp0qVbMDQZ2MQYK4n1SbYQ8MPYN1A9jN6ncG0KzEtjcgADX0O3m4COQTfcwuhyztQMlf2YMGFCJYPPQuc7wu60v/1fygXYXIzNn+h/FOgYzGFu7o1RtQ1tGvoLEOJDQ0M/wgNpTA4g1K6n9zTwJka/gYu0wEUq+IG+dqqMc7ebtkDPU39ZREKWs2czvmxudjoXwR8DKfkIx5hNO0wu60QnkMbkAHouBicHBwcPYXgrZSWifBa4momNR/YQuzSXilPDw8OH4FeEioqKZmGoHOxmDjvh7UBRsCQoHxUUFOgIzmAuctiQdIMwqgPItFPoOA/YnmQHvqRshyDG57PbNyMnyeij14IDoqZBZ7W2tvZB+E54N9CV9pRpx5ElNTU1TapHpzkcDleYNnHGUrSdwWZrLBaTXZ1rNQXmI0f/T+ZnIla6KchLqfFVFBYWypMNGLQ9yZnuZHHbHLViomAlZWVbmGUZfXZpD6F3wa4c+ZlBvxbsPI34M1DYPimHseBJ9GuiXTvcg850FjoRHZucpHobwg+M9zs8gf334IH5yOhjp7W7u1vOQnWE/L95/gq/zETmUFfEwEo+FC2F3UeWZZnkdje7Nh3ZJpf+t3aF8xOJRNrArzgwRpWcCbPq2aFrWcxGhC9oWwSmgErwC3U2maSKcIT3wEW4xTgtOMzsrjZotuoFo0/7fv+9r3Y3RnOAnXnpcIIzdQxuE1eqnPGhLViWOxkG6jt6ScbEdIz0QJnGLm3AuZN5LG1CITBh4iQl1alOP9QsS9GF495AkB1PMgzSRy+QMjqAc2lnXibZ3NbW9ofLgjsEk8mwoaFBd/R1AfqurpbFtRShws7MLCoM1md4LIVYqJJwfGBgwM499LUJx+1jrO8lYCOZDKlTEk7Rl54fGR3gZN4qBlLIenbHHYIMaCdDFqbXYQ2D7AIefeQk9ff3a/Emoo5gqyPZ6CvgVO18I9V2EoYniSN1noUrF6jOTobKKQjzmNNBokTjIKanjA7AiDJvL4OYySYtYfwCO7OVCl2JdjJEno98Hn4QnpY6Ozv7sH3CUZiJ46Y65RRGm5xaj752OuU6Y6zklYjOco7qHRhpYNNUn6JPm4fSOsBkUrTbuP8VshS9hGN0lk1YPoS8Bg2TqSkGE0lzCbqPO61lRFqtU05hLFALsliQJ6kaxVgspixvrkTlo5dpu0hUjekNktYBJpNi7ABfV+fgKUSmdl+JugnC7MLeaDRqZ+qUDlSw+GoWvxG8ingKTDSLpOwh3gXj0NNz1pOEPUqW5clHtM1lDkf7+vp+ozwqpXWAk0nLmMBXmazQ7r4Se9PtlGw0NjYWwtczwffRex1uRw82dNXqXRDiTbBMTkLPwjHmOXvEl4TVnAS77b4SdU2Pev2ZzukcUMDk7kfpHJOLwdMSV+IxdD93FPw7FSKJTWMndTuEzp49uw698p6enreOHz/eje39yKLZunG0eGw9zJGz3xicZ33oVFKnj5m0SdWXjwawq6Mpu6Mi0AHsgAa+l976ju+HZyIlmndR0H28h506Q9kmFr6QxcSZ0BlsalH6B8Va8zhhYXtRVL8weWAX8gvIz2tB5eXlU5GfRdaO9opnAmNo0YqoYziuJZOuu83jgOrq6jIm+jYKSirFcD1JP2YhG3iblyIHEuG8j4YDQNclbISYlD5YWkckq5UFLSVvJCOqt7f3a9p2AP3jRNH2KO0nGW8dT2PZ0/OXZmsDdU1A3ySSU0A/Ox8xhv/NkqLrrvA4IBaLncLQGlAMQgIJLQxeJGS73B3dZd3H6N4FtrvrkWNgLigAi7CjjJ1UUSRQvwJcBe7EThuNQ+htAmHq7DnAi5FXATkFlWCi/yvoPEFr2uNCm4c8DvC0ZImQc0CWbHTaZf7vIyDtyp2GnAMcR2Qty0VA1m69s/C/AQAA//80Tm9aAAAABklEQVQDAIB3ZHayctkqAAAAAElFTkSuQmCC\" width=\"32\" height=\"18\" style=\"width: 32px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eThe grid:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 30.65px; transform-origin: 451.5px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe use the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eAxial Coordinate System \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(q,r)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 20.4333px; text-align: left; transform-origin: 423.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe grid is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eToroidal:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e any move that goes off the edge wraps around to the opposite side. Formally, a position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(q,r)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is always treated as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(mod(q,N),mod(r,N))\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eThe knight's move:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn a hexagonal grid, a \"Knight's move\" is defined by 12 possible jumping vectors (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"38.5\" height=\"18\" style=\"width: 38.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). These represent moving 2 steps in one axial direction and 1 step in another, or similar symmetries:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"522\" height=\"18\" style=\"width: 522px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eThe goal:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the board size \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,a starting position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003estart_pos\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, an ending position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eend_pos\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and a list of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eobstacles\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, find the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eminimum number of moves\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e required to reach the destination.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 40.8667px; transform-origin: 451.5px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Scalar ( board size \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"35\" height=\"18\" style=\"width: 35px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003estart_pos:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 1x2 vector [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23.5\" height=\"18\" style=\"width: 23.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e]\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eend_pos\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: 1x2 vector [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23.5\" height=\"18\" style=\"width: 23.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e]\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eobstacles: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMx2 matrix where each row is a blocked [ \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23.5\" height=\"18\" style=\"width: 23.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e]\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 10.2167px; transform-origin: 451.5px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003emin_steps:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e The shortest distance ( integer ). Return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInf\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if the destination is unreachable.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function min_steps = solve_knight(N,start_pos,end_pos,obstacles)\r\n  min_steps = N*start_pos*end_pos*obstacles;\r\nend","test_suite":"%%\r\nassert(isequal(solve_knight(10, [0,0], [2,1], []), 1))\r\n\r\n%%  \r\nassert(isequal(solve_knight(5, [0,0], [4,3], []), 1))\r\n\r\n%%  \r\nobs = [1,2; 2,1; 3,-1; 3,-2; 2,-3; 1,-3; -1,-2; -2,-1; -3,1; -3,2; -2,3; -1,3];\r\nassert(isinf(solve_knight(10, [5,5], [0,0], obs + 5)))\r\n\r\n%% Test Case 4: \r\nrand_N = randi([15, 25]);\r\nrand_start = randi([0, rand_N-1], 1, 2);\r\ntarget = mod(rand_start + [2, 4], rand_N);\r\nactual = solve_knight(rand_N, rand_start, target, []);\r\nassert(actual \u003c= 2);\r\n\r\n%% \r\nN_large = 200;\r\ns_large = [0, 0];\r\ne_large = [100, 100];\r\nres = solve_knight(N_large, s_large, e_large, []);\r\nassert(res \u003e 0 \u0026\u0026 ~isinf(res));\r\n\r\n\r\n%% \r\nN1 = 10; s1 = [0,0]; e1 = [0,0]; obs1 = [];\r\nassert(solve_knight(N1, s1, e1, obs1) == 0);\r\n\r\n%% \r\nN2 = 10; s2 = [0,0]; e2 = [2,1]; obs2 = [2,1];\r\nassert(isinf(solve_knight(N2, s2, e2, obs2)));\r\n\r\n%% \r\nN3 = 10; s3 = [1,2]; e3 = [5,5]; obs3 = [1,2];\r\nassert(isinf(solve_knight(N3, s3, e3, obs3)));\r\n\r\n%% \r\nN4 = 10; s4 = [0,0]; e4 = [1,2]; obs4 = [];\r\nassert(solve_knight(N4, s4, e4, obs4) == 1);\r\n\r\n%% \r\nN5 = 5; s5 = [0,0]; e5 = [1,2]; obs5 = [];\r\nassert(solve_knight(N5, s5, e5, obs5) == 1);\r\n\r\n%% \r\nN6 = 10; s6 = [5,5]; e6 = [0,0]; \r\nmoves = [1, 2; 2, 1; 3, -1; 3, -2; 2, -3; 1, -3; -1, -2; -2, -1; -3, 1; -3, 2; -2, 3; -1, 3];\r\nobs6 = [5,5] + moves; \r\nassert(isinf(solve_knight(N6, s6, e6, obs6)));\r\n\r\n%% \r\nN7 = 20; s7 = [0,0]; e7 = [2,0];\r\nobs7 = [1,2; 2,1; 3,-1; 3,-2; 2,-3; 1,-3; -1,-2; -2,-1; -3,1; -3,2; -2,3; -1,3]; \r\nres7 = solve_knight(N7, s7, e7, []);\r\nassert(res7 \u003e 0 \u0026\u0026 res7 \u003c Inf);\r\n\r\n%% \r\nN8 = 100; s8 = [0,0]; e8 = [50,50]; obs8 = [];\r\ntic;\r\nres8 = solve_knight(N8, s8, e8, obs8);\r\nt = toc;\r\nassert(res8 \u003e 0);\r\n\r\n%% \r\nN9 = 15; s9 = [-1,-1]; e9 = [14,14]; obs9 = [];\r\nassert(solve_knight(N9, s9, e9, obs9) == 0);\r\n\r\n%% \r\nN10 = 30; s10 = [5,5]; e10 = [25,5];\r\nobs10 = [(0:29)', ones(30,1)*15];\r\nres10 = solve_knight(N10, s10, e10, obs10);\r\nassert(res10 \u003e 0 \u0026\u0026 ~isinf(res10));\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":4945722,"edited_by":4945722,"edited_at":"2026-03-21T02:40:32.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2026-03-21T02:40:32.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-17T12:48:56.000Z","updated_at":"2026-03-22T12:58:42.000Z","published_at":"2026-03-17T12:48:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this challenge, you must navigate a knight on a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eToroidal Hexagonal Grid\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of size \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$NxN$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe grid:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe use the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAxial Coordinate System \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(q,r)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe grid is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eToroidal:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e any move that goes off the edge wraps around to the opposite side. Formally, a position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(q,r)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is always treated as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(mod(q,N),mod(r,N))\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe knight's move:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn a hexagonal grid, a \\\"Knight's move\\\" is defined by 12 possible jumping vectors (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$dq,dr$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). These represent moving 2 steps in one axial direction and 1 step in another, or similar symmetries:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{moves} = \\\\left[1,2; 2,1; 3,-1; 3,-2; 2,-3; 1,-3; -1,-2; -2,-1; -3,1; -3,2; -2,3; -1,3 \\\\right]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe goal:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the board size \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$N$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,a starting position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estart_pos\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, an ending position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eend_pos\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and a list of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eobstacles\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eminimum number of moves\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e required to reach the destination.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Scalar ( board size \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$N$x$N$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estart_pos:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 1x2 vector [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$q,r$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eend_pos\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: 1x2 vector [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$q, r$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eobstacles: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eMx2 matrix where each row is a blocked [ \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$q,r\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emin_steps:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e The shortest distance ( integer ). Return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInf\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if the destination is unreachable.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61277,"title":"The Optimal 2D Guillotine Cutting Stock Problem","description":"You are working in a factory that produces rectangular glass sheets. You have a large stock plate of size W x H. Customers have placed order for N differents types of smaller rectangular pieces. Each piece type  has dimensions  and a specific market value .\r\nThe Challenge:\r\nYou need to cut the stock plate to maximize the total value of the pieces obtained. However, you must follow the Guillotine Cut constraint:\r\nEvery cut must go from one edge of the current plate to the opposite edge in a straight line (horizontal or vertical), splitting the plate into two smaller rectangles.\r\nYou can rotate the pieces 90 degrees if it helps.\r\nThis is a \"2nd-stage\" guillotine problem, meaning you first cut the stock plate into several strips (first stage), and then each strip is cut into individual pieces (second stage). Or, to make it harder, we allow recursive guillotine cuts to any depth.\r\nInput:\r\nStockSize: A 1x2 vector [W, H] ( The dimensions of the large plate ).\r\nItems: An N x 3 matrix. Each row is [width, height, value].\r\nOutput:\r\nmaxValue: The maximum total value you can extract from the stock plate","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 440.367px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 333.5px 220.183px; transform-origin: 333.5px 220.183px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63.4667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 31.7333px; text-align: left; transform-origin: 309.5px 31.7333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are working in a factory that produces rectangular glass sheets. You have a large stock plate of size \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eW\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eH\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Customers have placed order for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e differents types of smaller rectangular pieces. Each piece type \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFUAAAAoCAYAAACPSbZFAAAIH0lEQVR4AeyZWWyUVRTHZ7rZsrcFSqClhUIVFWVRFIyJSGIUJVEwEneBB40+sDwYgorGWCEGBB+ACKIRohAxPqjBxFDwwWhRCqhopXSZLkBKpQVaWrr7+1/6Dd9s7dcpY2o65Jyec89dz/+ee+79hhhX9N91RyAK6nWH1OWKghoFNQIIRGDIaKRGQY0AAhEYMhqpgaDG5uTkjJw5c2Z8YJUzy4AHNT09PSUrK2vFxIkT9yCLJ0yYcKW1tTWvvr5+uDMIA1vFBJoGlqWqqqrW4/F8gNf73G73GGRcZ2dnQVFR0Xn0sGjAg9qFWifyHGwoJiYmD0U2RO8pCuo1zO5EHQyfbW9vP4oMm/olqJmZmbPJbRtHjRo1pDeekRMfhV8N45LRkZ+tuTj6hY2NjZXSw2WBGm7fiPTLzs7O4Ph9yuCrhgwZstUpsFw0i8iJn8O5dXV1C+jvmLis0mg8HXbRP7+mpqZBerjc70AtKSmpxLGXcUg57lkHwLqJzsVE2G76JNA3Nzk5+Rt0x5SQkDCFxuPhFvofQvaJfEDl2E3h2C2Dd8Nl8HG92YLMEIcjW4mOlfY69ceuZ8kl6hba63qjl5aWHsC5p+nTE7AC9AnafkJbAfoOgOYWFBS0UnZMbMhcGifAFS0tLYVI16RJk4bhw3owqIZb4e1EdJLqemIfUMvLywtTUlJ2scjTdMyCM9va2iYgfYgJ5tPmBRbjMwnHtgP7DTQeSt1LaWlpSvwUe08OgL0ugCq9sNa7u1Z4jCdWNcExncsqX3a4hro4+Hki+h5kj+QDqlp37fK36JfhEXAG7CV2MJ1CLixAc5BeKisrOwmoT2KoYzFV1dXVjehhUzfA+gDKBJvCiVD6uZKSkkaz5snSWXMe0TmN4PiM8mr8mYu+Dr1XFACqejOQB6mj5+ro6JiEblEcO7iawo2waBB/tIuIq0Rkn0E7z0L3IL1vPRa7hAhvRq7C7piCALuNcZYyvjnyDLSJ07WmKxgo9o5iY2NvpcdYuI4x9eD/EPkGgH6NTf7Pk4Sr8a0U6aVx48alspZ8+I+uYDN1QUFloovUVsC6DW+WFNN5PlIg70W62NlUjk+idIvZkAdY1BEc/cGySbI5o5AJSEVFLLpj8gP2GTp+BCsH9glQxhAJNK1H/r6IT3uZ7ytVcJ+k4stM6dhPNTU1mUBTWUydfE9FH82nrfxDDfEjdXNzsxJ9vWnhco1VbgTQTMqvwblMcAIpwNO5nb15k0sqi4meI5rf848cPgU3ArieLrrc2tW/N4yjecy70eqDfhhH1vnPY9U7kePHj0+m3V2wSMFTTjBspmBOGJF5E3o2LF8Dnlrk39MNDQ3T4+Pjb+E+Oq524qCR6vF4rlCpo4BwJQwfPlz5cw2O/MSx+BFwilVBOZbIM2PowY19HbZdTHBM9X7cznPpXNfYflU9Ft1smG75t6yWbN4cnNnMSenVB4LVX5L+E5HWvXCW9a+3bxK+zaFeQXOZ+b5DDyC9afmd4B8qzEYgu/3vlCI1AKR0nhlPoc+Ii4tTpGDqVCRr91KwKR+5a2trV7CIC6mpqTtpayc3x2gkoNxHPl1C7hlmr3SgW4BaOXQDDj5MPx1FJ+9YmgYnTtQd1CTDSmVb2HQTLCqz3kTmuVc6fIKo/RPpJdXjTw5yMafYamfqTZQZze8PyLXJxMBjYUXphuLi4irZ2FFdRnXobtrFMLjepPOwr7bvNPUuJp3FgnYwxiFAf4Sob5LdIbvprwi1ADU5lFSwn/GcvGO7m8ZNpXX0y/BjH2UvsWblSh1/2fIqKirkr3QX79UUFD0p81nHTvyKo+ylkKB6W7hcOvr5TGJuQ9nR9VRSihjBgAL0bexrcVYXHOo14rgfZsF/ycICDvqDLnsIDgqo1Z+5nH4gBB2e02O/hH4mZfl87/Mm9fnKUnojeJbyGT2aXFqL398zsD5nywgm4x9lQxaopmD/AwDmywLbJXgjA9kj7AJACVilgFeo1xPkF2QAEWm6IW+j4jIL8ZkcW0jCgYWswSdCLUCtTn0BlsBQFJpLCFD2M6Y5mUhD+DcLRS+Mv1nH76S35dhSSBH6GHCR9pSP07AVcbnV0tZLIUG1WtDpY11OVlkyMTGxgYmUCpqQS3DOPEFU588AqZx7O/aAHcUWlAB0EfOab3kamCPvDyh2Q8wdVsSyLusSCviprysQrF+tBtNWL55sXhtbmNRcSKzPfNrif8DpCwkqjRWZvyE3WwMhDenJhV2P5ddxKiSgamztKPpRNke3JGpoysjIGMuC36SFoqRbQGljiDXYgX2cZ95DpiLEH4HG+s3lwlwBP/V5PJ427Lq02mg3lGFOEtmrrNOq/th0+vTleATdh0KCqoUCwjS43KcHBSa9Qv1j8PsUzc4hgxKLMzuK1K8/Pb5PKysrzxAZixlsLcfK8ZcSaznAMdYn8nLW/CX9Q5LWT5sFsBt9np5Ffo3bsK+kPh5OgzdYgKod67NOXzG5t0Q2O4cE1d4oXN22o+fY8aM8PRYo0fc0HpdGIY68G+rIh+pPvjtIvx3Ud7vR1PeJbKfvMM+yJPx80D5gREEFSP2PpB7Xp4jU+ylPxnHro8K+jv+bPpUFJ+BTCVG7ls96pQpMVynSoOrZpTftDI7mGD4itjFtjymANv2aAFM/jSrfLiNQthMo/x2o5LmLHMe58CD01fa81K9R62Fx+PMFrHw7Fb9+9W8e0Uj1n2yglKOgRmCno6BGQY0AAhEY0h6pERh+YA4ZBTUC+x4FNQpqBBCIwJD/AgAA//8dHi4kAAAABklEQVQDAOnVp37ArOQSAAAAAElFTkSuQmCC\" width=\"42.5\" height=\"20\" style=\"width: 42.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and a specific market value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"12.5\" height=\"20\" style=\"width: 12.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eThe Challenge:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 21px; text-align: left; transform-origin: 309.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou need to cut the stock plate to maximize the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etotal value\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the pieces obtained. However, you must follow the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGuillotine Cut constraint:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 122.6px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 61.3px; transform-origin: 316.5px 61.3px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.8667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 20.4333px; text-align: left; transform-origin: 288.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEvery cut must go from one edge of the current plate to the opposite edge in a straight line (horizontal or vertical), splitting the plate into two smaller rectangles.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou can rotate the pieces 90 degrees if it helps.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 61.3px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 30.65px; text-align: left; transform-origin: 288.5px 30.65px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is a \"2nd-stage\" guillotine problem, meaning you first cut the stock plate into several strips (first stage), and then each strip is cut into individual pieces (second stage). \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eOr, to make it harder, we allow recursive guillotine cuts to any depth.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 20.4333px; transform-origin: 316.5px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eStockSize: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA 1x2 vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e[W, H]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ( The dimensions of the large plate ).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eItems:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e An \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ex 3 matrix. Each row is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e[width, height, value].\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 10.2167px; transform-origin: 316.5px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003emaxValue:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e The maximum total value you can extract from the stock plate\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function maxValue = solve_guillotine(StockSize,Item)\r\n\r\nend","test_suite":"%% Test Case 1: \r\nassert(isequal(solve_guillotine([10, 10], [5, 5, 100]), 400))\r\n\r\n%% Test Case 2: \r\nItems2 = [3, 3, 10; 4, 2, 8; 1, 10, 12];\r\nassert(isequal(solve_guillotine([10, 10], Items2), 120)) % Giá trị giả định\r\n\r\n%% Test Case 3: \r\nrand_w = randi([15, 20]);\r\nrand_h = randi([15, 20]);\r\nval1 = randi([50, 100]);\r\nval2 = randi([50, 100]);\r\nitems_rand = [rand_w, floor(rand_h/2), val1; rand_w, ceil(rand_h/2), val2];\r\nexpected = val1 + val2;\r\nactual = solve_guillotine([rand_w, rand_h], items_rand);\r\nassert(actual \u003e= expected);\r\n\r\n%% Test Case 4: \r\nassert(isequal(solve_guillotine([5, 5], [10, 10, 100; 6, 2, 50]), 0))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":4945722,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-17T14:07:03.000Z","updated_at":"2026-03-22T13:04:25.000Z","published_at":"2026-03-17T14:07:03.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are working in a factory that produces rectangular glass sheets. You have a large stock plate of size \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eW\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e x \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e. Customers have placed order for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e differents types of smaller rectangular pieces. Each piece type \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e has dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ew_{i} \\\\times h_{i}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e and a specific market value \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_{i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe Challenge:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eYou need to cut the stock plate to maximize the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etotal value\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e of the pieces obtained. However, you must follow the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGuillotine Cut constraint:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eEvery cut must go from one edge of the current plate to the opposite edge in a straight line (horizontal or vertical), splitting the plate into two smaller rectangles.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eYou can rotate the pieces 90 degrees if it helps.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eThis is a \\\"2nd-stage\\\" guillotine problem, meaning you first cut the stock plate into several strips (first stage), and then each strip is cut into individual pieces (second stage). \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOr, to make it harder, we allow recursive guillotine cuts to any depth.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eStockSize: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eA 1x2 vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[W, H]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e ( The dimensions of the large plate ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eItems:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e An \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003ex 3 matrix. Each row is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[width, height, value].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emaxValue:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e The maximum total value you can extract from the stock plate\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61279,"title":"The Omega Protocol: Hyper-dimensional Navigation and the Singularity Constraint","description":"Description\r\n[EMERGENCY TRANSMISSION - GALACTIC COMMAND]\r\nSubject: Mission Omega-7 - Navigation through the K-94 Tesseract Anomaly.\r\nBackground:\r\nThe Omega-7 probe has entered a non-Euclidean hyper-dimensional region known as a Tesseract Grid. The probe’s onboard computer is failing, and you must provide a sequence of movements to reach the \"Stability Core\" before the probe's energy reserves deplete or it is crushed by a Quantum Anomaly.\r\n1.The 4D Toroidal Spacetime:\r\nThe grid is a 4-dimensional hyper-cube of size . Coordinates are given as  where  . The space is toroidal in all four dimensions: moving from in any direction with a step of results in 0.\r\n2.Goal Decoding (The Eigen-Lock):\r\nThe coordinates of the Stability Core  are hidden within a 4 x 4 Quantum Matrix M. To decode :\r\nFind the four eigenvalues of .\r\nTake the absolute value of each eigenvalue.\r\nSort these values in ascending order: \r\nApply a permutation vector  ( where P contains indices 1 to 4) such that \r\nThe final coordinates are \r\n3.Dynamic Quantum Anomalies (4D Cellular Automata):\r\nThe grid is infested with anomalies. Let  be a logical 4D array where  means an anomaly exists. The field evolves every second  based on the number of neighbors (where each cell has  - 1 = 80 neighbors):\r\nBirth: A cell becomes active if it was dead and has exactly  neighbors.\r\nSurvival: An active cell remains active if it has between  and  neighbors.\r\nEnergy Flux: Each active neighbor of a cell at time  increases the \"Action Cost\" of moving into that cell by 0.1\r\n4.Space Warping ( The Wormhole Effect ):\r\nThere are two special coordinates,  and . If the probe enters  at time , it is instantly transported to  at time  (and vice versa) with a fixed cost of 0.5, regardless of local anomalies.\r\n5.Energy and Action Constraints:\r\nMax Energy: The probe starts with .\r\nConsumption: Each move (including staying still) consumes 1.0 unit of energy. If , the mission fails.\r\nAction Cost: The total \"Action\" to be minimized is the sum of costs:\r\n                                \r\nMovement: In one second, the probe can move to any of its 80 neighbors or stay in place. However, it cannot enter a cell that is currently \"Active\"  at time .\r\nGoal: Find the minimum total Action to reach  steps and before energy runs out.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 980.333px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 490.167px; transform-origin: 468.5px 490.167px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDescription\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e[EMERGENCY TRANSMISSION - GALACTIC COMMAND]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSubject\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Mission Omega-7 - Navigation through the K-94 Tesseract Anomaly.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 31.5px; text-align: left; transform-origin: 444.5px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eOmega-7 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eprobe has entered a non-Euclidean hyper-dimensional region known as a Tesseract Grid. The probe’s onboard computer is failing, and you must provide a sequence of movements to reach the \"Stability Core\" before the probe's energy reserves deplete or it is crushed by a Quantum Anomaly.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e1.The 4D Toroidal Spacetime:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe grid is a 4-dimensional hyper-cube of size \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"101\" height=\"18\" style=\"width: 101px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Coordinates are given as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63\" height=\"18\" style=\"width: 63px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"53\" height=\"18\" style=\"width: 53px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"113.5\" height=\"18\" style=\"width: 113.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The space is toroidal in all four dimensions: moving from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE8AAAAkCAYAAADIB2cfAAAEP0lEQVR4AeyYWWgTURSGkyYNWqVosXWhtmkbqoK444LggqBPorghCqLgi/gs6JsPog8+uuCDgigKbuCCCC5YERWVaH0QJTTpQrW4lgql2iSN3xlmykyauRkThHSYcP6ce+85d+bef86998yU+bxfwQx45BVMnc/nkeeRVwQDRXT1Is8jrwgGiujqRd7/Iq+2tnZsQ0PDftAKMjpS4XB4u9098VkPboEkMPp8aGxs3GnXp5Ta6+vrpzK/0+BcvnEpI6+7u3ugvb39lN/vX8mFHgCRAPVNFIJghOB/B2zEcAaIXKmqqpqTSCQuSaVUIaTxsE+WlZXFmd8+EMg3ViV5Rmcm3ke5BRiysqmpaaZRyaEztI0Bg5lM5nw0Gk1SLknRV9eRQCBwlAFOACHgSByRRwgLEctMV6yBlC2muqVYXV09HnsjjTGe4Ft0yQqrK8lKOUyA7IHAgwy0CzgSR+QNDQ1N42pzgSzdX2gf5GwmzCdLORsVFRXTIW0WPq8Z2Ndse4nVU4xH4Esmk2nGPETdkTgijycym6tNAicg5RlaRMhZLYVs4L+AtqnsH4/QsoRRo1ZsB+6IPHqvAZ94Mm+IwguU0yAAObtkz6BsEZ7eYhp60un0G7RrJS95dXV1E5n9EvCW/eELkfeY8gcgS3c5UTZPygYMf/xaIa/DaHejzkteeXm5bPzNRJMswRR7mBB4QyejkujbQdkPNDH8idAWyB7QGl36l5c8omcRcw9B0nu0JkTVdQrGQbCKg6OGuiYm/+dag4v/8pEXhCjZ7+LBYPCjwUM8Hhcir+p188GR01/3c51SksdhIKnIfJZsNBaL/TDNPsOyvExd0pbhg6O5uVmSzBk5/HF1JkTxeWC81hWif5LAL3R2t+K8lOSFQqFZXL6OJSv7nSXlYHm2EpVa2gJZ2sGRSqXkrSNMn/vA4k/ddaIkD1Ikj+uHpOElazAghwHRZ6Qt2sFBfTn2PvQrdEHCgbQb+ItAFdtKtKCb/2MnW/L0V6ylXC9GfpdAjxBIHU5bMG6jvhf9jkj9jHa92JJnvGLBwMuurq5e9AghOsxpi5y4EaL1aUdHx+8Rzi5ssCWP5Fd7xSKanqjmjd2ctvQTda5PUQw+7MgLEkEbcOqFnE60rbC/fMT3oe5gSWn0NteqnOSRKsjnp3XMWr7D/UGrRL5IXMRhELSQ0nxHj0LRhjyTYJkiJXQNqdpYKdvBQp7+NfUszndBJaghJbkZDoePRSKRauo5haX6AsNLICkNalRJkPltIGCuMQ+Z9zgZPatpLa+a92g/AC+SskmzBRbyOjs7ezgE9oJKoKULbP4RcKitre2bpaepkkgk+vBfAW6bmkdLMcX8bjH2raACaPNGB8EqcBxetA8h2ROykJdt9OpqBjzy1PworR55SnrURo88NT9Kq0eekh610SNPzY/S6pGnpEdt9MhT86O0/gUAAP//3IFk0wAAAAZJREFUAwDr3sFYh1qKpAAAAABJRU5ErkJggg==\" width=\"39.5\" height=\"18\" style=\"width: 39.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein any direction with a step of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"21\" height=\"18\" style=\"width: 21px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eresults in 0.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e2.Goal Decoding (The Eigen-Lock):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.4667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.7333px; text-align: left; transform-origin: 444.5px 10.7333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe coordinates of the Stability Core \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"112.5\" height=\"20\" style=\"width: 112.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are hidden within a 4 x 4 Quantum Matrix \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eM\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. To decode \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"18\" style=\"width: 14.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 108.767px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 54.3833px; transform-origin: 451.5px 54.3833px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the four eigenvalues of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"18\" style=\"width: 17px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTake the absolute value of each eigenvalue.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 21.4667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.7333px; text-align: left; transform-origin: 423.5px 10.7333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSort these values in ascending order: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAN4AAAAoCAYAAACRrESzAAAMd0lEQVR4AeycfZSUVR3HZ9hd2F04ICCgwrK7wNFaylY3oYIolYT+ALVELY/mQetEKXgqiZTIF6iAQuWIhSZpiUct8qVT2qGgQk0kSgwjaWFnlgVEiC3YdYFld/p8x33GmWFen5nnmYfhcn6/vc+9z335vd77u/c+Qy+f+WckYCTgugSM47kucjOgkYDPZxzPWIGRQAEkYByvAEI3QxoJGMczNpBMAqbcQQkYx3NQuKZrI4FkEjCOl0wyptxIwEEJZOR4Y8aMGVFbW7sePFpTU3MP9JSCxQ7+UaNGzYLnVrAJvuuLnWHxZ3Rd64qu0zreiBEjKrq6uu5HKePALr/f/4XRo0d/iGfPgmgGh+dCIM42ORQKLe3po4Z0NugHPQtVVVVnwXeFXQLV1uja54qu0zpe7969J/h8vgEY4WjSKWAJz+8j9QDEkiDDYZWaWVZWFiwtLb0m9m3muZqamnJ4/DIt5pSUlJxB+iQTTt3IkSNP49lzwCRxDnw/Dc9/gl7bNBpdu6frtI6HAU4BFwcCgbcw6G1YXaC7uzun1YQ+8gpDhgzph7PMhr4gtD5M5/3AfaAtoI9aHK29s7Pz8cbGxqPk14OnU1Zuq0NnGvlxuHPBF+j+Dei7jHTv8ePHj5HaAvowug6FXNF1Wsdramq6FaeTcn2tra1HQqHQAVtadaAR+5H+GN78fv367cIp7mMIOdwKJobR0PwoeVsQDAa3wfd1LS0tHeqAvvco9Qj6mWTGw/cG6PkbqChkG3q5DJov3L17938oswW0N7r2+13RdVrHs6VBhxvJ4TC+BexHWhjqbrAPGHY4jOcmHGcv+WIDy+FeZiJ4Bea0BbAcrp6J5lnKusCigmLVtS3H69WrV2MhtDt8+PDBzPRL5HAY353QoNPV5ceOHaty2uEYr6W8vLyNMd2GEg6zLoLvV6FBDvcRCNgKXgLPjjvcyatrJGQTkLPjus7K8fr27TsWos4jrOm0yZOtZtXV1WdiePez+d9FB7eC0Q43J5fwir5SQkNDQxn8Xg52HTx4MJSycn5flrCqXwrfrxE6/4GuPwxGHA6nW0vesRXO6NpZXWfseFptcLp7UXZ/DOE4qeMgh8P4HmDWbWawr4ICa4Vz1OE0kBBnuwq+rwO7oMMNx7McbitjPgMNHwBdczjG8hld+x3XdUaOp1mf1ea7KEVhziGOrd/m2TEgtKrC4VZh6M0Y3ywG0iHH0p6Q0hWHY0wfq43uLn/Icwm4Z9++fe2kTkEJ410J32/CsxxOVzZ/RQYXs7rVg46ucBZTRtc+N3Sd2c+COM2cjmKuBTMBHXNPwog2gdMyaRBfh7CuAuM7i3Lrwloh1aGKigrXQlzuxQYw/kJwKJgUeq4ylsHrATAEHsJ57tGhQNJGCV5g8JoEh8B3/57X4vko+1k5e3dPmeNJprrmTrMOGa2D33fATvBF8hOzJfBk0nU8b0Rk58H3PvQ9N/5duryUnbKOOkc4D1CpN/hncD93RYmOXK1Tt19TR9cP2pPwmD3s3LlzOzP8VFqOBdeAuia4GyMMwuj8bI2a9tlCKeH092j0KTAAbkcG/ySNAQxtAFcZv6JQE9MzOI1WqlLSW6D1KTkl75JD1JvNmzd3wvMK7g6raX8D473F6wk8vwTPG1DuePLWRMRj/iFTXUPPNC7qn0BGD2ILH4RWTVDnk65RH9lQdrLoOp4n6Z5oZDHlKSdm3ieElI4X17nujX6CcLUUJ+yso6NjK8ajVU7OkrBONoX09SZ4BQo+m3F/SltXHBC+L8Xgr2c8XUYvYmxdW5CNBej6HCUhFNAAnTdiRJeT/ySoUHwyTnkRz1mB7g7pZ9XgwYNrGfdqUI7vuAPC8wD4sAwpqa5VD4Y+C04LBAJP7Nq1awfpXeT14cJQHFL8k80OkJ+ndR3HjR+9LKDsXNAWpHI8df4NetWs38pA88BKDLK9T58+iUK+UM8eSAcQCpNomh/gXq4J5c7E0EfS4wpQ93aOrIDsL8fA5zLGqCBdzQr0PDyfTv5/YARYgcopn4ix3oajRN5hQJuo9BSY06d1WgHh+UnwHOjQVyn6asgpB8xY1+yzxdf34TMIjxZAYkgnzl3oKKc7VC/q2mLSSpl8PsOztRjwmD0kdbyezr+uLjGwJRjAqzzrm80D7AOO8Ow6oJS9KPwmlF/F4PqAWatv3hwQngdgOAqr5eDbGeMuZvBurKovMogJr5FHJ+HkzTt27NDXI1SNANXDRujDKXdHSu0/dDHWs/BdT38X083fwbw6IHzLkDLSNSvyQej5FzREgP1pGRmFwuug8XmecwYv6TqaGSbcGhQ8G7uYR3kraAsSOh4xfDW9KXzQl+5/5PlHYAjj0/0Zj++CBF5XV6e937sFLv3VvR2GOBfmRzDkt0GBHLAFwSywuQfUrP8lOlJ4eAzhLsDAAmVlZSXwHSOnYcOG9aVed3NzswSvFZ7se0B9fcv6NumW90pzfurCydfB9zho0+ly+DKdMV5BXy/Dtww/6z0gbXPStWyAifh2uDsDWX0+evWnLGfwiK7DctWeHXnfBy5vbGx8IxfmYgxKHalz0pUot460lXRelDDPZtCSQYMG+fVLAO64Hm5vb9evFqjqPsD8IQxxIQ4o45ED6mdLd7ISyQGvzoYiDFB7U30No1BqNXssHZr44H8Y/ZwG35rVfRj41MrKyjsoO8HhKPOxeigq0MHSczhKzMqg93nAEBPCRvj+OLTps7GX6PMC6JMDroW+08hnBLnoWg6HzK7FBl6Hju8w/scIyzdme7iSEaFU8oCu/ezZZ8HrnoEDBz4HSSlB8mHbMgFUdHZC3XjHC3dOrcmgD2FaIaayFr6fk6xq7vKmQ4RCsCbrRaFSSyltbW1V0DQHOhQKK1zkMT1gQDpJ1CmmVvhwiKk9VnRL+r2QI/SByORr4O+i30U/U28a7/tTppM+Jz80iDggY50PiqZqxhcPZNNCTrqWfHD+nzOevmT6NKNpkhnFJLhIkzJ5R6BQusZGdFVyCZPLfPGeijnxz4T0ONuWF8EtTIaKUGKaxDheT+fzqaG9UyTEJG+B9ixD6WwTxvUQ+Cizr4zcel/QdP/+/W3QsxzhVDM5rM6EmIaGBq1kizEgrfCRENNqS18KJ9vIz8KodLrZffjwYYV5FMUCAtaPKL9C6Q0YZfThA0WOQYixXgenwvMnWO3/m8lI+dI18j4CvsDeThFDM3KsR06SQyZk2K7jpq6RlSKqhRB7u0Jf0pRAyK2J1zrxHIhsPhrfIOJ46hxH+jEV1KgVAUaHmBSH4UH+bgEPUfebKFt3dmS9BRwAdICaJNIR5mdmuoVKV4AKKyMhpvJC9nFN8HovzzrJ/QtGdaOUTj4GcDr9YHYFdX+AXHQQFfPejQxH+3vgW1/5pBzOCV0TVuvaYyMDlxMNVZK6AuIXdFrXcqJJMLQR2ekjiTCia12/KDJc3FP+CHV86F/7+5U8K+LZgOP9gucYiDgelYPs5caS+sFBgUBAQoypTHkQrAeHUTd84BJT4eTLhOBlKVgK+uF5ZoIwIgSvy3hfAU4m1NGqF8Op9nUo4SEEvIq64b1hTAWPZeAjL7qOY0tG9g5l+4mITpAR5YUG27om6tHJ9QwYiMfHKBMoncFiJZ9Q3rKZMmQ9KZHNRBxPtb2CrB5ze2aQ8Mxi51l9uMGPnA6BP4bjPYLTrYkeExqu4v3M6LJkzxxKnEn9Rju8Wm3UXv0kG8PJcmjQIVQDsvgtxqYPCDIaDpo9r2utqPD0y3iE13+ISaV6x8R9wmKl94nQCcfT0av2iInGK6oynEonmAq/6xD+FIxvpYW8expnvIM91/piYhr+xoH6dG89h03aF/t0mACv30IGzaz6SU98i0kOufKSV8dj9hoPLoIofVJE4luAAV6DYnSvpXxGyMyxhBlEIa9tVB8ZDWazEjzpyxb9dxNX0sUo8Iug7gHDiBHqa5PfB4NB7X14lRqCweBeaB6TC99qr35Sj5TbW/a4+pDg3/QykectOOFrHCb8jPxaxp/Oqh/5ioeytEAbz+s6LRM2KuTV8RDiRvA2jKcSlNNcgCJWa6m2QZunm8BTBzxeD4rPZHgzTCS876P8pATtV+B5Mqj9i1B7/hno+TcwlNdPBenP04CthycNpdkSmlfHy3ZwF+qbIYwEPCkB43ieVIshqtglYByv2DVs+POkBIzjeVIthqhil4BxvGLXsOEvmQQKWm4cr6DiN4OfqhIwjneqat7wXVAJGMcrqPjN4KeqBP4PAAD//918iq0AAAAGSURBVAMASlOlyR35cWYAAAAASUVORK5CYII=\" width=\"111\" height=\"20\" style=\"width: 111px; height: 20px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 24.9667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 12.4833px; text-align: left; transform-origin: 423.5px 12.4833px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eApply a permutation vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"12\" height=\"18\" style=\"width: 12px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ( where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eP c\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eontains indices 1 to 4) such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-10px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"153\" height=\"24.5\" style=\"width: 153px; height: 24.5px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 21.4667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.7333px; text-align: left; transform-origin: 423.5px 10.7333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe final coordinates are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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\" width=\"124\" height=\"20\" style=\"width: 124px; height: 20px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e3.Dynamic Quantum Anomalies (4D Cellular Automata):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.0333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21.0167px; text-align: left; transform-origin: 444.5px 21.0167px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe grid is infested with anomalies. Let \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"28.5\" height=\"18\" style=\"width: 28.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be a logical 4D array where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"110.5\" height=\"18\" style=\"width: 110.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e means an anomaly exists. The field evolves every second \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"69\" height=\"18\" style=\"width: 69px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e based on the number of neighbors \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(where each cell has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAnCAYAAABuf0pMAAADWklEQVR4AeyWX0hTcRTH95dVW5nlwnBu3g32IkW6qIceBCOsLAJLCCJ6qZfopTR6Kil7KonwRaiX8iEQJBJ6ESooiBCsLMgHwelo0Z+xCJ0m6nb7/HJ32O71tt01hJicr+f8zu93z/n+zu/fLKZV/isR+P8r4Pf7L0iSFAsEAiGt7VbUCpB4lyzLl0hsBZpSNALMeAsZbwMHWFGKQiAUCtmTyeRVsj4Db8GKUhQC8Xi8xWw2V1gslm6WILVidjr+OQGfz1dH8rPEbp+amppF64oeASs7uFmSpOeSJM0CGXwEXcFgsEIrKuPLmPU1CHRPTExEtMZk+zQJuN1uV01NzV3KN8AHteAzmAYe0LawsPCSZEHs5WJmfDuOkXA4/BCdk2gRMDudzk5msY0I9czEDQKgnPZp8BMEU6lUB9oGfguEWjB28F0XWgY5iYoAx6eeIH5m2UTS90RRgiVp36f9GJgYs5Pl2CxsAWZ/GH0I/QO/WC7Z5XJNM64RfzmEh9N+MQ7XkqgIEKCBjzqj0ej3pSF//F+kfzjtmbPb7cm0bcLfg92ahZP4P+CbQYsLqZWJvaGdERUB1u8WUJJkBioG5MrS9ouxsbF42jZNTk4OUaH+5UgkEo/o/wrmrVbrU9HHxD7RzoiKQKZHw6iqqhIlb4TEKN15rTXjNSUfAlaHw3GGKE5uuWPMJqdjxnhdyYkAG7OaDdTHOl4nWjVnvdnj8azF1pVYLJZgafZCdtP4+PhrrcG6BLgLdpN4kB0c5uOjQLxqG9E37Xb7AEdP2Q+4jIkuAdiLjdXEzNeDOlL0gkUgZB//zoOCRJeAEhkic2CEUp6iGg34vwFx9PZ7vV5xQYmmIeREYHnkSCTyivYdIMTLiagUhlHkTYBEMkkH0TNgjc1mW4c2LEYIiGtYvAfzZI2xJFG0YTFEgA0p1t2JHmZfZG5DIyyMEBDP7hGSJVmKe2jlVGDmLyoC/KI5wNl/B7qwt2aH5OzvwXccdDD7J+iCREWAW06869uJ2oYtiFyEjE+Ai+kKZe8F50henLeA4JfBAwiIX0Bu9A0wRLl7wCjPaS13Qh8+5XcCpnFRVYDgX8AJZrgBmNOo5Ik+iN3PcypOgPGMWV+qCGT1F9z8W4ASgVIFShVY9Qr8AgAA//8h8zEjAAAABklEQVQDAAGHW14/OPliAAAAAElFTkSuQmCC\" width=\"16\" height=\"19.5\" style=\"width: 16px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e - 1 = 80 neighbors):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 62.3333px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 31.1667px; transform-origin: 451.5px 31.1667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBirth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A cell becomes active if it was dead and has exactly \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e neighbors.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 21.4667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.7333px; text-align: left; transform-origin: 423.5px 10.7333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSurvival\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: An active cell remains active if it has between \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"26.5\" height=\"20\" style=\"width: 26.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"28\" height=\"20\" style=\"width: 28px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e neighbors.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEnergy Flux\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Each active neighbor of a cell\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e increases the \"Action Cost\" of moving into that cell by 0.1\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e4.Space Warping ( The Wormhole Effect ):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.4667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21.2333px; text-align: left; transform-origin: 444.5px 21.2333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThere are two special coordinates, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"21\" height=\"20\" style=\"width: 21px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"21\" height=\"20\" style=\"width: 21px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If the probe enters \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"21\" height=\"20\" style=\"width: 21px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, it is instantly transported to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACoAAAAoCAYAAACIC2hQAAAE+0lEQVR4AeyXXWgcVRTHd5PsriVV89EY7SbmY2PFioIE6osISl9EQeyLSLEW60e1+PEggoIPgk8WpSLBFUsRo62i9sVifZLSB0UwYKVa0U02SWM1iUk0btvNfmT7+093Zmd3Z3Z205BS2HD+e84999x7//fMuXcmDb4r5K9OdLUfVD2j9YyudgZWez6nGm3q6+t7DvwEcjYsYn8G7u7q6lqH3gOOgQww4xZ7e3s/AXeaRPv7+28E+4iZAUYc/TF8D5gx1Wgnopl4PP5uOp2+nwliwJBcLvc8/ofB8ampqfPooWw2+xCdPwJDiHljfHx8O/jBcPAzNjY2CV70+/27aUp+5ucufEfQVYsTUWNwU1PTHMZvwJCGhoZFw7D9TE5OLtC0YrBdZXl5eYDOFIRfZyN/Y9ckrkSZLMlM1oT5hXCVyZ+mBxJh07brcDjcTp+yfzSVSh2191VruxLVBDzKP6QFFnIi4afvGmDKtaZh18Fg8D7at4EhlQ26ZqlIlMdt1Sgzl5EYGBjYjH8bMGVjZ2dns9mQjkQi16FfAkfa2tqOoVckFYkyo+oyhfaR3e6Ojo71svPwZzKZJ7A7QBZIgi0tLUVzcuC0kR46h0ZGRtLoFUnRpKUz8Lh1WM7Kj72htbX1KtkCmYrgexD7INCGtJmuZDJpbYbrqJOYPWzya26J74lbsVQkSsbOsMi8Zkc3Ly0tBWQDP4frMfQi/n3AiIFUEHsdfkOwFRNubGx8G0cGrFgqEmWhJIv/o9nRbVxZG2Urm+jt9Ec5KFP0GVnHtz4QCLSifcR049+J/eXo6OgJ9CVJRaJkUPVpPFZWMbNlZZNMHV5YWEhC2NgMMc3YBlFq8xHa7RzId9Bl2eTNtAl8S3mcA3pjxWlrTCPxZVKR6PT0tDJ1Jj/KIEGmIrR3gA/I1Mzs7GyCzJ2mLTE209PT04dvN6QPEvOLOuyA2Bb6jgOtP0yf3m7dtIch+wLtMlFgmdPuYPCvZht7s1mb+L4ApvxnGoohi4/TDlEq+9E5YIm+E9jEKzje4oDdA54GW2jLpwP5DDFld7YnURa13jxMpgmVzSiTT9M2BHJWDCRuxamYA7FYzNokPkMol17iU4lE4j0c5iakP6J9CrSHQqHr0UXiSZRa04k27klI6E5Uzdqz6cOvBcyJH8XIkvkDaBFAFYTYOCR3qWQKXp8P31k2MIMvwQeRrkXMgngS5fFpsMiZo4qyKSeLn0fr4KF8enzRiYmJuNEo+dE3RClJheiOZp4N4CSb/Es+OzyJMlCP+N/8oJPoomzSVkaVAR08NU/xeA/JqAXcMDcRr+tvv9P3gCdRalRfUf8ziTI1bK9N+QT7i4H2ECfdvAVoesvg4GCAdXTaD5PZr5xGeBK13ZOumaL402ReGT3Bgp87LVTJNzc3t436vJo5Xnb7HvAkqnpigtNM9KFbprQZiMwSEyVGNU2zOuHe3Mr8T4Jn+eq3rrnS0Z5ENYDHvZND8KZsJ2gzxGwlJurU7+bLX/yv0b+L8RNoV6mKqOvoS+gQSYbvBTvsJFWv9O3l7XYLfZZcFqKQuAMGhygVfQO8CrH3TczPz39H3w1cb9Z/F7R9a06UmtzEgfuUxfupy3vRT5XgdjbwMT5tAnVR1pwoB+Z3HvXNwO+CELX+zUV6hd81J1pYujarTrS2fHlH1zPqnaPaIuoZrS1f3tFXTEYvAAAA//9HXD9IAAAABklEQVQDALXBPW+7Rh3GAAAAAElFTkSuQmCC\" width=\"21\" height=\"20\" style=\"width: 21px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"32\" height=\"18\" style=\"width: 32px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (and vice versa) with a fixed cost of 0.5, regardless of local anomalies.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e5.Energy and Action Constraints:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 62.3333px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 31.1667px; transform-origin: 451.5px 31.1667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 21.4667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.7333px; text-align: left; transform-origin: 423.5px 10.7333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eMax Energy\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: The probe starts with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"29.5\" height=\"20\" style=\"width: 29.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConsumption\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Each move (including staying still) consumes 1.0 unit of energy. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"40\" height=\"18\" style=\"width: 40px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the mission fails.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eAction Cost\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: The total \"Action\" to be minimized is the sum of costs:\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 36.0667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 18.0333px; text-align: left; transform-origin: 444.5px 18.0333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg 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\" width=\"274.5\" height=\"36\" style=\"width: 274.5px; height: 36px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 20.4333px; transform-origin: 451.5px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 20.4333px; text-align: left; transform-origin: 423.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMovement: In one second, the probe can move to any of its 80 neighbors or stay in place. However, it \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ecannot\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e enter a cell that is currently \"Active\" \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"50\" height=\"18\" style=\"width: 50px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGoal\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Find the minimum total \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eAction\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to reach \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"156.5\" height=\"18\" style=\"width: 156.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e steps and before energy runs out.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function min_action = solve_omega_protocol(N, start_pos, QM, P, Rules, InitialObs, E_max, Warps)\r\n  min_action = false;\r\nend","test_suite":"%% Test: Complex Eigen-Lock \u0026 Toroidal Warp\r\nN = 10;\r\nS = [0,0,0,0];\r\nQM = [2 3 0 0; -3 2 0 0; 0 0 5 0; 0 0 0 1]; \r\nP = [1, 2, 3, 4];\r\nRules = [99, 99, 99]; \r\nE = 100;\r\nWarps = [1,1,1,1; 0,0,0,0]; \r\n\r\nactual = solve_omega_protocol(N, S, QM, P, Rules, [], E, Warps);\r\n\r\nassert(abs(actual - 4.5) \u003c 1e-6);\r\n\r\n\r\n\r\n%% Setup chung\r\n\r\n\r\n%% Test 1: Di chuyển cơ bản (Moore Neighborhood)\r\n% Giải thích: Goal là [1,2,3,4]. Từ [0,0,0,0], bước xa nhất là 4 đơn vị (ở trục w).\r\n% Vì dùng Moore move, mỗi bước có thể thay đổi tất cả tọa độ thêm 1.\r\n% Cần đúng 4 bước. Cost = 4.0\r\nN1 = 10;\r\nRules = [3, 2, 3]; \r\nE_max = 50;\r\nstart1 = [0,0,0,0];\r\nQM1 = diag([1.1, 2.1, 3.1, 4.1]); \r\nP1 = 1:4;\r\nout1 = solve_omega_protocol(N1, start1, QM1, P1, Rules, [], E_max, [9,9,9,9; 9,9,9,9]);\r\nassert(abs(out1 - 4.0) \u003c 1e-6, 'Test 1 Failed: Di chuyển cơ bản phải tốn 4.0 đơn vị');\r\n\r\n%% Test 2: Sử dụng Warp (Siêu không gian)\r\n% Giải thích: Goal ở [10,10,10,10]. \r\n% Lộ trình: [0,0,0,0] --(1 bước)--\u003e [1,0,0,0] --(Warp)--\u003e [9,10,10,10] --(1 bước)--\u003e [10,10,10,10]\r\n% Tổng cost: 1.0 (move) + 0.5 (warp) + 1.0 (move) = 2.5\r\nN2 = 20;\r\nstart2 = [0,0,0,0];\r\nRules = [3, 2, 3]; \r\nE_max = 50;\r\nQM2 = diag([10.1, 10.1, 10.1, 10.1]);\r\nP2 = 1:4;\r\nWarps2 = [1,0,0,0; 9,10,10,10];\r\nout2 = solve_omega_protocol(N2, start2, QM2, P2, Rules, [], E_max, Warps2);\r\nassert(abs(out2 - 2.5) \u003c 1e-6, 'Test 2 Failed: Warp shortcut phải tốn 2.5 đơn vị');\r\n\r\n%% Test 3: Vật cản và Chi phí hàng xóm (Neighbor Penalty)\r\n% Giải thích: Start [0,0,0,0], Goal [1,1,1,1].\r\n% Có 2 vật cản tại [1,0,0,0] và [0,1,0,0].\r\n% Khi di chuyển từ Start tới Goal, tại t=1, ô Goal có 2 hàng xóm là Anomaly.\r\n% Cost = 1.0 + 0.1 * (2 hàng xóm) = 1.2\r\nN3 = 5;\r\nstart3 = [0,0,0,0];\r\nRules = [3, 2, 3]; \r\nE_max = 50;\r\nQM3 = diag([1.1, 1.1, 1.1, 1.1]);\r\nP3 = 1:4;\r\nInitialObs3 = [1,0,0,0; 0,1,0,0];\r\nRules3 = [100, 0, 100]; % Giữ vật cản đứng yên\r\nout3 = solve_omega_protocol(N3, start3, QM3, P3, Rules3, InitialObs3, E_max, [4,4,4,4; 4,4,4,4]);\r\nassert(abs(out3 - 1.2) \u003c 1e-6, 'Test 3 Failed: Neighbor penalty phải tính đúng 1.2');\r\n\r\n%% Test 4: Trạng thái Goal ngay tại Start\r\n% Giải thích: Nếu start trùng goal, min_action phải bằng 0.\r\nN4 = 5;\r\nRules = [3, 2, 3]; \r\nE_max = 50;\r\nstart4 = [1,2,3,4];\r\nQM4 = diag([1.1, 2.1, 3.1, 4.1]);\r\nP4 = 1:4;\r\nout4 = solve_omega_protocol(N4, start4, QM4, P4, Rules, [], E_max, [0,0,0,0; 0,0,0,0]);\r\nassert(out4 == 0, 'Test 4 Failed: Start trùng Goal phải trả về 0');","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":4945722,"edited_by":4945722,"edited_at":"2026-03-18T14:51:31.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2026-03-18T14:51:31.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-17T16:06:29.000Z","updated_at":"2026-03-22T13:14:17.000Z","published_at":"2026-03-17T16:06:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDescription\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[EMERGENCY TRANSMISSION - GALACTIC COMMAND]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSubject\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Mission Omega-7 - Navigation through the K-94 Tesseract Anomaly.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOmega-7 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eprobe has entered a non-Euclidean hyper-dimensional region known as a Tesseract Grid. The probe’s onboard computer is failing, and you must provide a sequence of movements to reach the \\\"Stability Core\\\" before the probe's energy reserves deplete or it is crushed by a Quantum Anomaly.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1.The 4D Toroidal Spacetime:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe grid is a 4-dimensional hyper-cube of size \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN \\\\times N \\\\times N \\\\times N\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Coordinates are given as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(x,y,z,w)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex,y,z,w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\in \\\\{0,1,...,N - 1\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The space is toroidal in all four dimensions: moving from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN -1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003ein any direction with a step of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e+1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eresults in 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2.Goal Decoding (The Eigen-Lock):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe coordinates of the Stability Core \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\textbf{G} = (x_{g},y_{g},z_{g},w_{g})\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are hidden within a 4 x 4 Quantum Matrix \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. To decode \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\textbf{G}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the four eigenvalues of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\textbf{M}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTake the absolute value of each eigenvalue.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSort these values in ascending order: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lambda_{1} \\\\leq \\\\lambda_{2} \\\\leq \\\\lambda_{3} \\\\leq \\\\lambda_{4}.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eApply a permutation vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\textbf{P\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e ( where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP c\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eontains indices 1 to 4) such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\textbf{G}_{raw} = \\\\left[\\\\lambda_{P_{1}} , \\\\lambda_{P_{2}},\\\\lambda_{P_{3}},\\\\lambda_{P_{4}} \\\\right]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe final coordinates are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\textbf{G} = \\\\lfloor \\\\textbf{G}_{raw} \\\\rfloor ( \\\\text{mod} N)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e3.Dynamic Quantum Anomalies (4D Cellular Automata):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe grid is infested with anomalies. Let \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA(t)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e be a logical 4D array where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA(x,y,z,w,t) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e means an anomaly exists. The field evolves every second \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(t \\\\rightarrow t + 1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e based on the number of neighbors \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e(where each cell has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e3^{4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e - 1 = 80 neighbors):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBirth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A cell becomes active if it was dead and has exactly \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e neighbors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSurvival\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: An active cell remains active if it has between \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_{min\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_{max\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e neighbors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEnergy Flux\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Each active neighbor of a cell\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e increases the \\\"Action Cost\\\" of moving into that cell by 0.1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e4.Space Warping ( The Wormhole Effect ):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are two special coordinates, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eW_{1} \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eW_{2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If the probe enters \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eW_{1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, it is instantly transported to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eW_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et + 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (and vice versa) with a fixed cost of 0.5, regardless of local anomalies.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e5.Energy and Action Constraints:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMax Energy\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The probe starts with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eE_{max\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConsumption\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Each move (including staying still) consumes 1.0 unit of energy. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eE \u0026lt; 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the mission fails.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAction Cost\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The total \\\"Action\\\" to be minimized is the sum of costs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{StepCost} = 1 + \\\\frac{\\\\text{Number of Active Neighbors}}{10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMovement: In one second, the probe can move to any of its 80 neighbors or stay in place. However, it \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecannot\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e enter a cell that is currently \\\"Active\\\" \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(A = 1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGoal\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Find the minimum total \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAction\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to reach \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\textbf{G} \\\\text{ from } \\\\textbf{S} \\\\text{ within } T \\\\leq 100 \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e steps and before energy runs out.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61285,"title":"The Genesis Sypnapse Protocol","description":"Ⅰ.Context\r\nIn a synthetic bio-neural network, information is transmitted between  neurons through chemical and electrical signals. Your objective is to find the minimum Metabolic Cost to trnasmit a signal from a Source_Neuron to a Target_Neuron.\r\nⅡ.Neuron Structure and Genetic Coding\r\nEach neuron  is identified by a unique Protein Code (a string consisting of bases A, C, G, T).\r\nGenetic Distance (): The base cost to jump from neuron  to neuron  is defined as the Levenshtein Distance (minimum number of edits: insertions, deletions, or substitutions) between their Protein Code strings.\r\nⅢ.Polarization States and Transitions\r\nAt any time step , a neuron exists in one of three Polarization States: P ∈ {0,1,2}. When a signal jumps from u to v, the state of the signal evolves based on a 3x3 Transition Matrix M:\r\nIf  is even: \r\nIf  is odd: \r\n(Note: Matrix M is 1-indexed in logic, e.g., ).\r\nⅣ.Sypnatic Barriers (Constraints)\r\nA connection from neuron u to v is only valid if all the following conditions are met:\r\nChemotaxis Condition: The Protein Code of  must contain at least one sub-sequence of length 2 that exists within the Protein Code of . (e.g., if u is AGCT,  must contain AG, GC, or CT).\r\nEnergy Limit: The total accumulated cost from the source must not exceed .\r\nTemporal Gating: A neuron  enters a \"refractory period\" (disabled) if the current time step T is a multiple of its Stability Index . (i.e., if mod() == 0, the neuron cannot be entered).\r\nⅤ.Metabolic Cost Calculation\r\nThe total cost to transition from  to  at time  with the current signal state  is:\r\n                \r\nWhere: \r\n is a weight vector correspoding to the 3 polarization states.\r\nInterference() =  (simulating temporal electromagnetic noise).\r\nⅥ.Input / Output Requirements\r\nInput: * neurons: A struct array containing .code(string) and .S(integer).\r\nM: A 3x3 state transition matrix.\r\nW_state: A 1x3 weight vector.\r\nE_max: Maximum energy allowed (scalar).\r\nstart_id, target_id: Indices of the start and neurons.\r\nOutput: * The minimum metabolic cost (scalar). Return -1 if the target is unreachable.\r\n(Optional) The path taken (sequence of neuron IDs).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1013.33px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 333.5px 506.667px; transform-origin: 333.5px 506.667px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eⅠ.Context\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 31.5px; text-align: left; transform-origin: 309.5px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn a synthetic bio-neural network, information is transmitted between \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e neurons through chemical and electrical signals. Your objective is to find the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eminimum Metabolic Cost\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to trnasmit a signal from a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSource_Neuron\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTarget_Neuron\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eⅡ.Neuron Structure and Genetic Coding\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach neuron \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is identified by a unique \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProtein Code\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (a string consisting of bases \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eA, C, G, T\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 30.65px; transform-origin: 316.5px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 30.65px; text-align: left; transform-origin: 288.5px 30.65px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGenetic Distance\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eG\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e): The base cost to jump from neuron \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eu\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to neuron \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003ev\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is defined as the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eLevenshtein Distance\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (minimum number of edits: insertions, deletions, or substitutions) between their Protein Code strings.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eⅢ.Polarization States and Transitions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 21px; text-align: left; transform-origin: 309.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAt any time step \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eT\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, a neuron exists in one of three \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePolarization States\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: P ∈ {0,1,2}. When a signal jumps from u to v, the state of the signal evolves based on a 3x3 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTransition Matrix M\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 63.3667px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 31.6833px; transform-origin: 316.5px 31.6833px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 21.4667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.7333px; text-align: left; transform-origin: 288.5px 10.7333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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\" width=\"312\" height=\"20\" style=\"width: 312px; height: 20px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(Note: Matrix M is 1-indexed in logic, e.g., \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"75\" height=\"18\" style=\"width: 75px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eⅣ.Sypnatic Barriers (Constraints)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA connection from neuron u to v is only valid if all the following conditions are met:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 124.667px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 62.3333px; transform-origin: 316.5px 62.3333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 61.3px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 30.65px; text-align: left; transform-origin: 288.5px 30.65px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eChemotaxis Condition\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: The Protein Code of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003ev\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e must contain at least one sub-sequence of length 2 that exists within the Protein Code of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eu\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. (e.g., if u is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eAGCT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003ev\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e must contain \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eAG\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGC\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 21.4667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.7333px; text-align: left; transform-origin: 288.5px 10.7333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEnergy Limit\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: The total accumulated cost from the source must not exceed \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"29.5\" height=\"20\" style=\"width: 29.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 41.9px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 20.95px; text-align: left; transform-origin: 288.5px 20.95px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTemporal Gating\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A neuron \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e enters a \"refractory period\" (disabled) if the current time step T is a multiple of its \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eStability Index\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"13.5\" height=\"20\" style=\"width: 13.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. (i.e., if mod(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"29.5\" height=\"20\" style=\"width: 29.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) == 0, the neuron cannot be entered).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eⅤ.Metabolic Cost Calculation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.4667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.7333px; text-align: left; transform-origin: 309.5px 10.7333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe total cost to transition from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eu\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003ev\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eT\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the current signal state \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"31\" height=\"20\" style=\"width: 31px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.4667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.7333px; text-align: left; transform-origin: 309.5px 10.7333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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\" width=\"351\" height=\"20\" style=\"width: 351px; height: 20px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhere: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 41.9px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 20.95px; transform-origin: 316.5px 20.95px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 21.4667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.7333px; text-align: left; transform-origin: 288.5px 10.7333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"35\" height=\"20\" style=\"width: 35px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a weight vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJAAAAAoCAYAAAAR33OgAAAMxklEQVR4AeybC3CU1RXHv82LQHglMWZ4hBAIINqCioBYBMFKedQBgdZhbKm2Vp3aSovYKrUjMnVw7ENKHRUHBZkO9UEtKA6OFgaECgqp0PIQJLCBDRIgBAiQTB5sf//P7/v4Nmw2+0iCg1/mnL3n3nMf55577rnn3t0kGd6fp4EENOAZUALK85oahmdAnhUkpAHPgBJSn9fYMyDPBhLSgGdACanPa+wZkGcDCWkgrAEVFBTcDgaFPXv2DJAuARdCzwM7a0QPL08N5Ofnj9NaC1nrNaS1YFB0Tk5O+4azDmtAdqVgMFialJQ06sCBA3eD9/v9/sfAkzbfSy8/DZSUlKzWWgtZ628zwxfBRiGiAdGqur6+/gypB19PDeBDgociTb0pA4rU1uN5GvAeEj0bSEwDngdKTH9f+9bNbUDJeXl5vYnYJxG5T+3evXs3l4ZTKL9F5eCYXr16dXLxLgmpW4Utk1KESAFNkOzIOVXIzaQ/hcngJYW+fftegTxjwKnIO9QtjGS0yifB6wnPB7Y4NJcBJWMQ0xC8JCUl5W8+n6+c6GtVIBAodc2gjqh+nWEYGyj7IfzjtHl60KBBqeRbFXr37p2Hsl9r3769AsQRdXV1HyHbeoSoA00IBAKlWVlZK5lLFTfRddTfwSJdZzJb+aNHjx5XM/7G2tranQydl5qaug55P4Z2gNvTbnS6ioJcZN5F/fWFhYXdybcoJGxAGEEnhF2G8MsQfDWTHM0VcAMTrA4nObwybnZPwPuCNrPKy8t/At1qgLwTzp8/v50BR5FOQM65hw4dOkw+CIZAUVFR7f79+9+lcBF4FYa0GOO7Erq1wIduH0xOTt6KbjMZ/1vo7+W9e/ceDycAc6kGX4YnQ7oZPT+HJ21LvsUgIQNiMTphBG8i3ffBzTU1NY8GAoEqaEOeBY/0PAqoI32WMselVlVVHaXd55Qlo5gJ8NOhWxyQdwrjSt6ODPYwu/YjUhPg3YCspUJ27jVm4YWPzRbZn/YDLLqlExnPLAb5C1jLuA8UFxfvgzYBeScj62lwWwOjrqPuVrOSYQzB+HScWdnmTxIxIB+CaoK3IVYN9JOlpaXl0CbIs2Ac95FR7DAgJycnA/oioJ0WJdNi+FDGaJSyBQX9E8NaQ7oW7Gvx407ot5Cx/kwHbZHrfTzlP6BNgHclPHmZrhR0Zef2Ig0HaXit6xsyMLiOyPwM+A7zvOi1tmH9aPL0NZx6j4PS31I8z0ZoExjvGuT9K5kOYA8wDwwHXfBahTYDfY6k3y2gXpfrSGV8o+E7mxs6JojbgFC6dqkMxGBB1hBHKIYwB7eU+D0ymrz4h48dO3aWfETAUCazQG9T6Q2OjsnZ2dljUdTn4AYmO4TyeMFHvzNoLGXXQC+wPSVlBvkbSb8BCk4ynyMimkIWsiMyP4rBbaPuI8jZjjRh0LGDDI/RkTzlUYxgIbRzxKLrCeRl7CSG5C0zmvhDzin0+Q7VdFy/SqoTYCBzX4VubycfF8RtQAw8jRHNeAB6pXtB2rVrl4ewurlQxTBQrHaPowD42jn5YlIvkJ6efoYAtYB6f6DsALgUDCoGQXnaaepjnmWYsGIDgtACWkwEBZ+lpaXZLl554a18mMZOepCLgGSA/BKQy5kL8jjHCP1UZ2Zm/ok53EnNZvuKh34HMeYI+hR8goE6Y+JF0hnvZjEs3IlBHbdoM4F/tUkYxknoI2x2edhHoO/Bk00E7+WCoKP4JcMw2jLWjHh1G5cBsSA6cqR0xjcUDH8owoU6d03jouwo5/C/SR0g353JZFsF2/fs2VPJwownr4XexgSPQpvAYpZA7Kb+8A4dOshTkI0N6GMYLWw3v84dhObm5upodQyEeh/Cd45i8gzt+yap4AsWc7cI4a5du2pk5FQ4T97ZINAJAQs6jg4klzbOKgJj50LCWHr+cB/p77n5/fr10+aU/unCMDcD/clYivDqK1UolNzoXJtTus63NrVYMWFcBsQIMiDbhR5EwBCXj2Ap1LF39NvFxcWfkXcAj6U4Qt/qK3ZaDUP1R5JKYf8jdRZDxkXebxhGGuOMgo4ZaGfvSB2nn7g7QBbFcrasFci+BL4zPm8vMnQtgNpuw4D88FsSpIs+1gBnkUdXdytr6LhNYj62vLvh68h3+NXV1bq62wZmbobKysrNtHmYSs4zBbSB59JzSyVGeRy+Y6TiRYtxGRDvEDIgO1g8yF9lIwMextvMh+cWPAWBTe+F0FtRwCY8mnaN4hODvPvtiKYm2GVSrBRsFsbw0c2qqzhMHs3KhibI8yrG/h93KUq+inxvsB5jW+o+qilrduAoSUcOGa36PsH4illEN8R66i1AXr1lOTz0rc3ZhYLTyLuMNEj8ecbv94czkM6sheK2LaxhXEdwXAbEpM4hmC2QaLeBwDJMY4BYvm/fvpAdxHmsBZG3qUL4ObjVU6RS2hXUlwc6rdSNKOqU8qTZUrBoxQLETV2UKt8Emu2pU8NY5jMDtAk8JmZQpuNWR7FiAsf7UEHeSfGNjpNVzNs5AuDFBMjdnmA1V88bkRpmZGTUIY90Kl1cJC/HcTZ8bbidxErL3X0p+CZ/F6i2r/BMsVl0Y0g/A+GlsmlDvC5lUUNcBoSVH2Yx7UBTFux4BRZU5+9DlgTiWaRhvg2xK3Q11Q57gljnXw4zBoKFyGfSReBhlHCUG8bkSM2RdRP8elDHYFtSG2juu4eMbmCpPp+vDbQDjKOr9HTKd1E4I17vQz9DMNRi+jhy4sQJP/LeAB0W5CkYr0hM0hB5ZXwcoTPhyeDTeYqwjzKKDIOTQe9cY8h8gG7mkAbBsNCtWzetwS9gPoMXC/G6lEUNSVHXdFWU10BAvaloNw/Fq8hoDNJCJr2CqnK7i0hHWAZlaHfwNrSAsjvAOdwC5pOaE2SBq2ln3iRIdXWFdQEoMw2UtBx3LM83gDZ2XNMBo3xQO/xCi1AKWRVnraU0g3bfIdW7RzILO4v8bPJPgeeoN5ZUPCM/P1+B92vkD7JoUzH2Ro8+6kQExriFClp0EqMr8v4MwhyH9CKg/mLmKqPtyma9SRVs/VE+HpxLWRb11C+koUdHPZs8T2Yt5dO1RtCNga9NmzY/pZ8d7nVorHKk8rgMSB0i4Fso/LvQFShkNYuxglSPc4vYGePBh5iIvt54kx3399TU1O0IrEe661iM3+sWQFsTOH8VQx1Uhj7seEVZG+2gUG8XOi7/C2MLaEPEWwSynmIhpiKPjPbnyPMu8m6k8XCM40bkeZxxJ5HXl7zifcDcXiE/j3kM4Shwbl6UxQz0JeN1B9/5GLyOxbB9IU8JuhoL6tX8WWRdgf42kU+mr8HMZw7yyjPOhLcclIfVu9G9tB3n9/tDLjUNBvGxqX9E+8H092v3OjSoF1U2bgOi9yCuby0CXwv2ASeBA8Hn5OqFTORJ8prwNNK+4ESMRTuL5iGg5/c1KmFStmdR1nBdS3Vj0xexBv2UgENAqvumULHk3LlzMkLI8EAsdhp5fkWbTBZgPOkw0JEHI/mU8tGgeLfB6w+acwnfY/Sl9LmVvgpAeZ3f0rIET6qAHjI8oNtDtJPecmgn3UrP96mcFkHk1U9Ph8KTd9QmuB76DXg6qknCA5tnMkqbgiH+mP7t2DB85ShKEzGgKLqPvgre4X1qK64axI7KhTaBwFUPjv3hmzc2s9D6UExAuVz6YhaksZ/eWrUvfcLi6Q3nJhZwMdKYxzdpqwHjK0a6m/F/4DYeyjvhlV7gycK8yMQi0FfGgNhRMp55CK/jajqpTwaCq1Wgp5vCb9yTFp+A9JcYUC3n+OvkLxkgg/Qo79KoDNZcnqbCejyFjk/I1gOMZAJyvsCIuv7re7uFbFThIso345HKeEA141DqRA2aeKOVsdQ8YgcFahGV02gHMTJQ7CIMRrHIXUz4LYLu95ChD3HKcIzHrfRkdszv6D4NDzUz0XOcfuICAtss5LiTBVDw2hlZh3ENn02ZdGYG/upYr90VFRV69f2YOery0areB3lGIqNiuhzk0Vc6+g7TRv2cJgvZQ54EqGdefChv9MaoOkn6aIgsYoAyvYksYWD9ivBFWSuCzAP1ggy7RcA+26/FYO4gZrmVdHSYuKke3lwW4ynFWi0iSRSdMvYJ5HgdOQaDPrAd+dngOpor2CcxjLKysrPM4wHK9d4SMUYxGzTzB+PK6+Uin2QMh7nEVjs0LLdP5//CCNznU1YBvoQhrWZzOHOizISwBsRx8imD3d8Q/X7v/8JMrV3GH6y9gvOL1h5b+CPrryeUkNmHNaCQGl7G00AEDXgGFEE5HqtpDXgGFEFHHqtpDXgG1LSOvBoRNOAZUATleKymNeAZUNM68mpE0IBnQBGU47Ga1sD/AQAA///6+jFCAAAABklEQVQDAPji1pxxDeweAAAAAElFTkSuQmCC\" width=\"72\" height=\"20\" style=\"width: 72px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ecorrespoding to the 3 polarization states.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInterference(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eT\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) = \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"119.5\" height=\"18\" style=\"width: 119.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (simulating temporal electromagnetic noise).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eⅥ.Input / Output Requirements\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: * \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eneurons\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A struct array containing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.code\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(string) and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.S\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(integer).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 40.8667px; transform-origin: 316.5px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eM\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A 3x3 state transition matrix.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eW_state\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A 1x3 weight vector.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eE_max\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Maximum energy allowed (scalar).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003estart_id, target_id\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Indices of the start and neurons.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: * The minimum metabolic cost (scalar). Return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e-1 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eif the target is unreachable.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 10.2167px; transform-origin: 316.5px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(Optional) The path taken (sequence of neuron IDs).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [min_cost, best_path = solve_genesis_protocol(neurons,M,W,E_max,start_id,target_id)\r\n  [min_cost,best_path] = size(neurons);\r\nend","test_suite":"%% \r\nn(1).code = 'AGCT'; n(1).S = 10;\r\nn(2).code = 'GCT';  n(2).S = 10;\r\nM = [0 1 2; 2 0 1; 1 2 0]; W = [1, 1.5, 2];\r\ncost1 = solve_genesis_protocol(n, M, W, 100, 1, 2);\r\nassert(cost1 \u003e 0, 'Target should be reachable');\r\n\r\n%% \r\nn(1).code = 'AGCT'; n(1).S = 10;\r\nn(2).code = 'GCT';  n(2).S = 10;\r\nn(3).code = 'AAAA'; n(3).S = 2; % Will sleep at T=2\r\nM = [0 1 2; 2 0 1; 1 2 0];W = [1, 1.5, 2];\r\ncost2 = solve_genesis_protocol(n, M, W, 100, 1, 3);\r\nassert(cost2 == -1, 'Neuron 3 should be gated at T=2');\r\n\r\n\r\n%% \r\nneurons = struct('code', {'AAAA', 'AATT'}, 'S', {10, 10});\r\nM_test = [0, 1, 2; \r\n          1, 2, 0; \r\n          2, 0, 1]; \r\nW_test = [1.0, 1.5, 2.0];\r\nE_max = 100;\r\nres1 = solve_genesis_protocol(neurons, M_test, W_test, E_max, 1, 2);\r\nassert(abs(res1 - 21) \u003c 1e-6, 'Test Case 1 Failed: Basic cost calculation');\r\n\r\n\r\n\r\n%% \r\nneurons = struct('code', {'AAAA', 'CCCC'}, 'S', {10, 10});\r\nE_max = 100;\r\nM_test = [0, 1, 2; \r\n          1, 2, 0; \r\n          2, 0, 1]; \r\nW_test = [1.0, 1.5, 2.0];\r\nres3 = solve_genesis_protocol(neurons, M_test, W_test, E_max, 1, 2);\r\nassert(res3 == -1, 'Test Case 3 Failed: Chemotaxis should block this path');\r\n\r\n%%\r\nneurons = struct('code', {'AAAA', 'AATT', 'TTTT'}, 'S', {10, 10, 10});\r\nM_test = [0, 1, 2; \r\n          1, 2, 0; \r\n          2, 0, 1]; \r\nW_test = [1.0, 1.5, 2.0];\r\nE_max = 15;\r\nres4 = solve_genesis_protocol(neurons, M_test, W_test, E_max, 1, 2);\r\nassert(res4 == -1, 'Test Case 4 Failed: Should return -1 due to Energy Limit');\r\n\r\n%% \r\nneurons = struct('code', {'AAAA', 'AAAT'}, 'S', {10, 10});\r\nM_test = [0, 1, 2; \r\n          1, 2, 0; \r\n          2, 0, 1]; \r\nW_test = [1.0, 1.5, 2.0];\r\nE_max = 100;\r\nres5 = solve_genesis_protocol(neurons, M_test, W_test, E_max, 1, 2);\r\nassert(abs(res5 - 20) \u003c 1e-6, 'Test Case 5 Failed: Matrix M transition logic error');\r\n\r\n%% \r\nc1 = repmat('AGCT', 1, 10); \r\nc2 = repmat('TCGA', 1, 10);\r\nneurons = struct('code', {c1, [c1(1:38) 'AA'], c2}, 'S', {100, 100, 100});\r\nE_max = 5000;\r\nM_test = [0, 1, 2; \r\n          1, 2, 0; \r\n          2, 0, 1]; \r\nW_test = [1.0, 1.5, 2.0];\r\nres6 = solve_genesis_protocol(neurons, M_test, W_test, E_max, 1, 3);\r\nassert(res6 \u003e 0, 'Test Case 6 Failed: Performance issue or logic error with long strings');\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4945722,"edited_by":4945722,"edited_at":"2026-03-20T16:01:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-20T07:26:50.000Z","updated_at":"2026-03-22T17:34:29.000Z","published_at":"2026-03-20T07:26:50.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eⅠ.Context\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn a synthetic bio-neural network, information is transmitted between \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e neurons through chemical and electrical signals. Your objective is to find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eminimum Metabolic Cost\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to trnasmit a signal from a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSource_Neuron\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTarget_Neuron\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eⅡ.Neuron Structure and Genetic Coding\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach neuron \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is identified by a unique \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProtein Code\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (a string consisting of bases \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA, C, G, T\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGenetic Distance\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eG\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e): The base cost to jump from neuron \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to neuron \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is defined as the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eLevenshtein Distance\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (minimum number of edits: insertions, deletions, or substitutions) between their Protein Code strings.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eⅢ.Polarization States and Transitions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAt any time step \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, a neuron exists in one of three \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePolarization States\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: P ∈ {0,1,2}. When a signal jumps from u to v, the state of the signal evolves based on a 3x3 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTransition Matrix M\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eG(u,v)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is even: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP_{next} = (P_{curr} + 1) \\\\text{ (mod 3).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eG(u,v)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is odd: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP_{next} = M(P_{curr}+1), \\\\text{mod(length(} Protein_{v}),3)+1).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(Note: Matrix M is 1-indexed in logic, e.g., \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM(row,col)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eⅣ.Sypnatic Barriers (Constraints)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA connection from neuron u to v is only valid if all the following conditions are met:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eChemotaxis Condition\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The Protein Code of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e must contain at least one sub-sequence of length 2 that exists within the Protein Code of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. (e.g., if u is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAGCT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e must contain \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAG\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGC\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEnergy Limit\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The total accumulated cost from the source must not exceed \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eE_{max}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTemporal Gating\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A neuron \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e enters a \\\"refractory period\\\" (disabled) if the current time step T is a multiple of its \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eStability Index\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_{i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. (i.e., if mod(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT,S_{i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) == 0, the neuron cannot be entered).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eⅤ.Metabolic Cost Calculation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe total cost to transition from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with the current signal state \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP_{curr\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eTotalCost = (G(u,v) \\\\times W_{state}(P_{curr}+1)) + \\\\text{Interference}(T)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhere: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eW_{state\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a weight vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\left[\\\\omega_{0},\\\\omega_{1},\\\\omega_{2}\\\\right]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003ecorrespoding to the 3 polarization states.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInterference(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) = \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor \\\\sin(T) \\\\times 10 \\\\rfloor + 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (simulating temporal electromagnetic noise).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eⅥ.Input / Output Requirements\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: * \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eneurons\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A struct array containing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.code\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(string) and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.S\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(integer).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A 3x3 state transition matrix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eW_state\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A 1x3 weight vector.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eE_max\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Maximum energy allowed (scalar).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estart_id, target_id\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Indices of the start and neurons.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: * The minimum metabolic cost (scalar). Return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-1 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eif the target is unreachable.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(Optional) The path taken (sequence of neuron IDs).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61276,"title":" Interstellar Navigation: Minimum Time with Moving Hazards","description":"You are the pilot of a spaceship at the origin P_start = (0,0,0) at time t = 0. Your mission is to reach a space station located at G = (x_g, y_g, z_g ) in the minimum possible time T.\r\n1.Spaceship Dynamics:\r\nThe spaceship can move in any direction in 3D space with a maximum constant speed V_max. Let S(t) be the position of the ship at time t, The constraint on its velocity is:\r\n                                         \r\n2.Moving  Obstacles ( Asteroids ):\r\nThere are N spherical asteroids in the field. Each asteroid i is defined by its initial position.\r\nP_i0 = (x_i, y_i, z_i ), a constant velocity vector V_i = ( v*x_i, v*y_i, v*z_i ), and a radius R_i.\r\nThe position of the center of asteroid i at any time t \u003e= 0 is:\r\n                                    \r\n3.Safety Constraint:\r\nTo avoid dustruction, the spaceship must never enter the volume of any asteroid. At all times t ∈ [0,T], the distance between the ship and every asteroid center must satisfy:\r\n                            \r\n4.Goal:\r\nFind the minimum time T such that S(T) = G. If the goal is unreachable due to obstacles, return Inf.\r\nInput:\r\ngoal: A 1x3 vector [x_g, y_g, z_g]\r\nVmax: A scalar representing your maximum speed.\r\nasteroids: An Nx7 matrix. Each row represents [x_0, y_0, z_0, vx, vy, vz, R].\r\nOutput:\r\nmin_T: A scalar representing the shortest time to reach the goal\r\nP/s: Sorry for not being clean in presentation, hope you guys sympathize with me :((","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 703.733px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 351.867px; transform-origin: 468.5px 351.867px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are the pilot of a spaceship at the origin \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eP_start\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = (0,0,0) at time t = 0. Your mission is to reach a space station located at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eG\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = (x_g, y_g, z_g ) in the minimum possible time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e1.Spaceship Dynamics:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe spaceship can move in any direction in 3D space with a maximum constant speed V_max. Let \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eS\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) be the position of the ship at time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, The constraint on its velocity is:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.0667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 18.0333px; text-align: left; transform-origin: 444.5px 18.0333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                         \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg 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\" width=\"85\" height=\"36\" style=\"width: 85px; height: 36px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e2.Moving  Obstacles ( Asteroids ):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThere are N spherical asteroids in the field. Each asteroid i is defined by its initial position.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e_i0 = (x_i, y_i, z_i ), a constant velocity vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eV\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e_i = ( v*x_i, v*y_i, v*z_i ), and a radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eR\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e_i.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe position of the center of asteroid \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ei\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at any time t \u0026gt;= 0 is:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.4667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.7333px; text-align: left; transform-origin: 444.5px 10.7333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"113.5\" height=\"20\" style=\"width: 113.5px; height: 20px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e3.Safety Constraint:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTo avoid dustruction, the spaceship must never enter the volume of any asteroid. At all times \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ∈ [0,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e], the distance between the ship and every asteroid center must satisfy:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.4667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.7333px; text-align: left; transform-origin: 444.5px 10.7333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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\" width=\"211.5\" height=\"20\" style=\"width: 211.5px; height: 20px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e4.Goal:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the minimum time T such that S(T) = G. If the goal is unreachable due to obstacles, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInf.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 30.65px; transform-origin: 451.5px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003egoal\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A 1x3 vector [x_g, y_g, z_g]\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eVmax\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A scalar representing your maximum speed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003easteroids\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: An Nx7 matrix. Each row represents [x_0, y_0, z_0, vx, vy, vz, R].\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 10.2167px; transform-origin: 451.5px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003emin_T:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e A scalar representing the shortest time to reach the goal\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP/s: Sorry for not being clean in presentation, hope you guys sympathize with me :((\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function min_T = solve_navigation(goal,Vmax, asteroids)\r\n  min_T = cumsum(goal,Vmax,asteroids)\r\nend","test_suite":"%%\r\n    fprintf('--- Running Test Case 1: Clear Sky ---\\n');\r\n    \r\n    Vmax = 10;\r\n    goal = [60, 80, 0]; % Khoảng cách là 100\r\n    expected_T = 100 / Vmax; % 10 giây\r\n    \r\n    % Đặt thiên thạch ở xa, không liên quan đến đường bay [0,0,0] -\u003e [60,80,0]\r\n    % Asteroids: [x0, y0, z0, vx, vy, vz, R]\r\n    asteroids = [\r\n        100, 100, 100, 0, 0, 0, 5;   % Đứng yên ở xa\r\n        0, 100, 0, 1, 1, 1, 2;       % Di chuyển xa dần\r\n        -50, -50, -50, -1, 0, 0, 10   % Ở phía sau lưng\r\n    ];\r\n\r\n    tic;\r\n    actual_T = solve_navigation(goal, Vmax, asteroids);\r\n    runtime = toc;\r\n\r\n    fprintf('Expected T: %.4f\\n', expected_T);\r\n    fprintf('Actual T:   %.4f\\n', actual_T);\r\n    fprintf('Runtime:    %.4f s\\n', runtime);\r\n\r\n    % Sai số cho phép nhỏ vì đây là đường thẳng lý tưởng\r\n    assert(abs(actual_T - expected_T) \u003c 0.1, 'Failed: Clear Sky should follow straight line.');\r\n    disp('Test Case 1 PASSED!');\r\n%%\r\n    fprintf('\\n--- Running Test Case 2: Moving Interceptor ---\\n');\r\n    \r\n    Vmax = 2;\r\n    goal = [10, 0, 0];\r\n    ideal_T = 10 / Vmax; % 5 giây nếu không có vật cản\r\n    \r\n    % Thiên thạch này sẽ chặn đường tại t = 2.5s\r\n    % [x0, y0, z0, vx, vy, vz, R]\r\n    asteroids = [\r\n        5, -4, 0, 0, 1.6, 0, 2\r\n    ];\r\n\r\n    tic;\r\n    actual_T = solve_navigation(goal, Vmax, asteroids);\r\n    runtime = toc;\r\n\r\n    fprintf('Ideal T (if no obs): %.4f\\n', ideal_T);\r\n    fprintf('Actual T:            %.4f\\n', actual_T);\r\n    fprintf('Runtime:             %.4f s\\n', runtime);\r\n\r\n    % Kiểm tra tính logic\r\n    if actual_T == Inf\r\n        disp('Result: Goal unreachable (Safe if no path exists)');\r\n    else\r\n        assert(actual_T \u003e ideal_T, 'Failed: Ship should have detoured, T must be \u003e 5.');\r\n        fprintf('Success: Ship detoured. Extra time needed: %.4f s\\n', actual_T - ideal_T);\r\n    end\r\n    disp('Test Case 2 PASSED!');\r\n\r\n%%\r\nfprintf('\\n--- Running Test Case 3: Goal Unreachable ---\\n');\r\n    \r\n    Vmax = 5;\r\n    goal = [20, 20, 20];\r\n    \r\n    % Thiên thạch đứng yên bao trùm luôn điểm đích\r\n    % [x0, y0, z0, vx, vy, vz, R]\r\n    asteroids = [\r\n        20, 20, 20, 0, 0, 0, 5  % Bán kính 5 bao quanh điểm (20,20,20)\r\n    ];\r\n\r\n    tic;\r\n    actual_T = solve_navigation(goal, Vmax, asteroids);\r\n    runtime = toc;\r\n\r\n    fprintf('Actual T: %.4f\\n', actual_T);\r\n    fprintf('Runtime:  %.4f s\\n', runtime);\r\n\r\n    if isinf(actual_T)\r\n        fprintf('Success: Goal correctly identified as Unreachable.\\n');\r\n    else\r\n        error('Failed: Goal should be unreachable but algorithm returned T = %.4f', actual_T);\r\n    end\r\n    disp('Test Case 3 PASSED!');\r\n%%\r\nfprintf('\\n--- Running Test Case 4: The Moving Wall ---\\n');\r\n    \r\n    Vmax = 2;\r\n    goal = [10, 0, 0];\r\n    ideal_T = 10 / Vmax; % 5 giây\r\n    \r\n    % Một \"bức tường\" gồm 3 thiên thạch chắn ngang trục X tại x=5\r\n    % Chúng di chuyển đồng bộ để quét qua vị trí (5,0,0) từ t=2 đến t=3\r\n    % [x0, y0, z0, vx, vy, vz, R]\r\n    asteroids = [\r\n        5, -2,  0, 0, 1, 0, 1.5; % Chặn dưới\r\n        5,  0,  0, 0, 1, 0, 1.5; % Chặn giữa (đúng điểm tàu định đi qua)\r\n        5,  2,  0, 0, 1, 0, 1.5  % Chặn trên\r\n    ];\r\n\r\n    tic;\r\n    actual_T = solve_navigation(goal, Vmax, asteroids);\r\n    runtime = toc;\r\n\r\n    fprintf('Ideal T:  %.4f\\n', ideal_T);\r\n    fprintf('Actual T: %.4f\\n', actual_T);\r\n\r\n    if actual_T \u003e ideal_T\r\n        fprintf('Success: Ship waited or detoured the wall. Extra time: %.4f\\n', actual_T - ideal_T);\r\n    else\r\n        error('Failed: Ship passed through the wall!');\r\n    end\r\n    disp('Test Case 4 PASSED!');\r\n%%\r\nfprintf('\\n--- Running Test Case 5: Start Inside Obstacle ---\\n');\r\n    \r\n    Vmax = 10;\r\n    goal = [50, 50, 50];\r\n    \r\n    % Thiên thạch nằm ngay tại gốc tọa độ (0,0,0)\r\n    % [x0, y0, z0, vx, vy, vz, R]\r\n    asteroids = [\r\n        0.5, 0, 0, 0, 0, 0, 2 % Tâm tại 0.5, bán kính 2 =\u003e chứa luôn điểm (0,0,0)\r\n    ];\r\n\r\n    tic;\r\n    actual_T = solve_navigation(goal, Vmax, asteroids);\r\n    runtime = toc;\r\n\r\n    fprintf('Actual T: %.4f\\n', actual_T);\r\n\r\n    if isinf(actual_T)\r\n        fprintf('Success: Detected unsafe starting position.\\n');\r\n    else\r\n        warning('Warning: Algorithm allowed starting inside an asteroid (T = %.4f). Check logic!', actual_T);\r\n    end\r\n    disp('Test Case 5 PASSED!');","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":4945722,"edited_by":4945722,"edited_at":"2026-03-18T14:12:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":"2026-03-18T14:12:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-17T13:41:32.000Z","updated_at":"2026-03-22T17:45:12.000Z","published_at":"2026-03-17T13:41:32.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are the pilot of a spaceship at the origin \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP_start\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = (0,0,0) at time t = 0. Your mission is to reach a space station located at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eG\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = (x_g, y_g, z_g ) in the minimum possible time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1.Spaceship Dynamics:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe spaceship can move in any direction in 3D space with a maximum constant speed V_max. Let \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) be the position of the ship at time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, The constraint on its velocity is:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                         \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\left | \\\\left | \\\\frac{dS}{dt} \\\\right | \\\\right| \\\\leq V_{max}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2.Moving  Obstacles ( Asteroids ):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are N spherical asteroids in the field. Each asteroid i is defined by its initial position.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e_i0 = (x_i, y_i, z_i ), a constant velocity vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e_i = ( v*x_i, v*y_i, v*z_i ), and a radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e_i.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe position of the center of asteroid \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e at any time t \u0026gt;= 0 is:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\textbf{A}_{i}(t) = \\\\textbf{P}_{i0} + \\\\textbf{V}_{i} \\\\cdot t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e3.Safety Constraint:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo avoid dustruction, the spaceship must never enter the volume of any asteroid. At all times \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ∈ [0,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e], the distance between the ship and every asteroid center must satisfy:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\left | \\\\left | \\\\textbf{S}(t) - \\\\textbf{A}_{i}(t) \\\\right | \\\\right | \\\\geq \\\\textbf{R}_{i}, \\\\forall i \\\\in \\\\{1,..,N \\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e4.Goal:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the minimum time T such that S(T) = G. If the goal is unreachable due to obstacles, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInf.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egoal\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A 1x3 vector [x_g, y_g, z_g]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eVmax\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A scalar representing your maximum speed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003easteroids\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: An Nx7 matrix. Each row represents [x_0, y_0, z_0, vx, vy, vz, R].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emin_T:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e A scalar representing the shortest time to reach the goal\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP/s: Sorry for not being clean in presentation, hope you guys sympathize with me :((\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61286,"title":"The Heisenberg Entanglement Protocol","description":"Abstract:\r\nA quantum signal must be routed through  nodes. The cost of transmission is not purely geometric but depends on the phase coherence between entanglement pairs and the fundamental limits of quantum mechanics.\r\nKey Mechanics:\r\nEntanglement Phase Cost: The cost to jump from node  to  is propotional to the absolute sine of their phase different: .\r\nQuantum Tunneling: If the Euclidean distance between two nodes is a prime number (rounded), a tunnel opens. This allows a jump with a fixed cost of 0.5, but at the expense of a 20% reduction in remaining ATP.\r\nHeisenberg Uncertainly Barrier: A jump is forbidden if the product of \"Position Uncertainly\" () and \"Phase Momentum\" ( ) is less than the effective Planck constant .\r\nTrivalent Constraints: You must reach the destination before ATP reaching 0 and within a maximum of steps.\r\nGoal: Find the minimum total cost path while satisfying the uncertainty principle.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 298.1px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 149.05px; transform-origin: 468.5px 149.05px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eAbstract\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA quantum signal must be routed through \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e nodes. The cost of transmission is not purely geometric but depends on the phase coherence between entanglement pairs and the fundamental limits of quantum mechanics.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eKey Mechanics\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 145.1px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 72.55px; transform-origin: 451.5px 72.55px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 41.9px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 20.95px; text-align: left; transform-origin: 423.5px 20.95px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEntanglement Phase Cost\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: The cost to jump from node \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eu\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003ev\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is propotional to the absolute sine of their phase different: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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\" width=\"224\" height=\"20\" style=\"width: 224px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 20.4333px; text-align: left; transform-origin: 423.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eQuantum Tunneling\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: If the Euclidean distance between two nodes is a prime number (rounded), a tunnel opens. This allows a jump with a fixed cost of 0.5, but at the expense of a 20% reduction in remaining ATP.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 41.9px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 20.95px; text-align: left; transform-origin: 423.5px 20.95px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHeisenberg Uncertainly Barrier\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A jump is forbidden if the product of \"Position Uncertainly\" (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"92.5\" height=\"18\" style=\"width: 92.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) and \"Phase Momentum\" (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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width=\"91\" height=\"20\" style=\"width: 91px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ) is less than the effective Planck constant \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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width=\"24\" height=\"20\" style=\"width: 24px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTrivalent Constraints\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: You must reach the destination before \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eATP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e reaching 0 and within a maximum of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esteps.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGoal: Find the minimum total cost path while satisfying the uncertainty principle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [cost, path] = solve_heisenberg_entanglement(nodes,params)\r\n  %nodes - struct array(.x, .y, .z, .phase)\r\n  %params - struct(.start_id, .end_id, .ATP_start, .h_eff)\r\n  \r\n  %cost - minimum total cost(-1 if unreachable)\r\n  %path - vector of node indices\r\n  \r\n  cost = -1;\r\n  path = [];\r\nend","test_suite":"%% \r\nn1 = struct('x',{0, 11}, 'y',{0, 0}, 'z',{0, 0}, 'phase',{0, 0.5});\r\np1.start_id = 1; p1.end_id = 2; p1.ATP_start = 100; p1.h_eff = 1.0;\r\n[c1, path1] = solve_heisenberg_entanglement(n1, p1);\r\n\r\nassert(abs(c1 - 0.5) \u003c 1e-4, 'Phải nhận diện được Quantum Tunneling khi khoảng cách là số nguyên tố!');\r\nassert(isequal(path1, [1 2]), 'Lộ trình đơn giản 1-2 bị sai');\r\n\r\n%% \r\nn2 = struct('x',{0, 1}, 'y',{0, 0}, 'z',{0, 0}, 'phase',{0, 0.1});\r\np2.start_id = 1; p2.end_id = 2; p2.ATP_start = 100; p2.h_eff = 2.0; % 1 * 0.1 \u003c 2.0\r\n[c2, path2] = solve_heisenberg_entanglement(n2, p2);\r\n\r\nassert(c2 == -1, 'Vi phạm nguyên lý bất định nhưng vẫn cho phép đi là sai!');\r\nassert(isempty(path2), 'Path phải trống khi không tìm thấy đường');\r\n\r\n%% \r\nn3 = struct('x',{0, 10, 20}, 'y',{0, 0, 0}, 'z',{0, 0, 0}, 'phase',{0, 1, 2});\r\np3.start_id = 1; p3.end_id = 3; p3.ATP_start = 1.0; p3.h_eff = 0.1; \r\n[c3, path3] = solve_heisenberg_entanglement(n3, p3);\r\n\r\nassert(c3 == -1, 'Phải trả về -1 khi cạn kiệt ATP');\r\n\r\n%% \r\nn4 = struct('x',{0, 10, 10, 20}, 'y',{0, 5, -5, 0}, 'z',{0, 0, 0, 0}, 'phase',{0, 0.1, 1.5, 0.2});\r\np4.start_id = 1; p4.end_id = 4; p4.ATP_start = 100; p4.h_eff = 0.1;\r\n[c4, path4] = solve_heisenberg_entanglement(n4, p4);\r\n\r\nassert(c4 \u003c 5, 'Chưa tìm được đường tối ưu về chi phí năng lượng (Phase Cost)');\r\n\r\n%% \r\nrng(77); n = 15;\r\nfor i=1:n, n5(i).x=rand*50; n5(i).y=rand*50; n5(i).z=rand*50; n5(i).phase=rand*2*pi; end\r\np5.start_id=1; p5.end_id=n; p5.ATP_start=100; p5.h_eff=1.5;\r\n[c5, path5] = solve_heisenberg_entanglement(n5, p5);\r\n\r\nassert(c5 \u003e 0 || c5 == -1, 'Lỗi thực thi trên bản đồ phức tạp');","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4945722,"edited_by":4945722,"edited_at":"2026-03-20T15:25:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2026-03-20T15:25:56.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-20T08:28:01.000Z","updated_at":"2026-03-22T17:56:51.000Z","published_at":"2026-03-20T08:28:01.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml 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w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e nodes. The cost of transmission is not purely geometric but depends on the phase coherence between entanglement pairs and the fundamental limits of quantum mechanics.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eKey Mechanics\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEntanglement Phase Cost\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The cost to jump from node \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is propotional to the absolute sine of their phase different: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eCost = \\\\left|\\\\sin(\\\\theta_{u} - \\\\theta_{v}\\\\right| \\\\times \\\\text{Distance}(u,v)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eQuantum Tunneling\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: If the Euclidean distance between two nodes is a prime number (rounded), a tunnel opens. This allows a jump with a fixed cost of 0.5, but at the expense of a 20% reduction in remaining ATP.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHeisenberg Uncertainly Barrier\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A jump is forbidden if the product of \\\"Position Uncertainly\\\" (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta x = \\\\text{Distance}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) and \\\"Phase Momentum\\\" (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta p = \\\\left|\\\\theta_{u} - \\\\theta_{v}\\\\right|\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e ) is less than the effective Planck constant \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\hbar_{eff}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTrivalent Constraints\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: You must reach the destination before \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eATP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e reaching 0 and within a maximum of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003esteps.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGoal: Find the minimum total cost path while satisfying the uncertainty principle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61284,"title":"The Singularity: Omega Phase","description":"Abstract:\r\nNavigate a signal through a non-linear, resource-constrained, time-varying neural network. The topology and node properties mutate based on the global entropy T and local thermal accumulation.\r\nKey Mechanics:\r\nTrivalent Metabolism: You must maintain ATP \u003e 0, Neurotransmittters \u003e 0, and Heat \u003c= 100. Failure in any one resource results in signal termination.\r\nDamerau-Levenshtein Cost: Jump costs are calculated using edit distance including transpositions between the evolving Carrier_Code and the target node's Primary_Code.\r\nRelativistic Signal Speed: Signal velocity decays exponentially as the current node's Heat increases.\r\nGlobal Entropic Decay: All neuron strings undergo a circular bit-shift every 10 time units, altering the cost landscape dynamically.\r\nSpatial Feedback Inhibition: To simulate neural refractory periods, the signal cannot enter any neuron within a radius R of any previously visited coordinate in the current path.\r\nResonance Barrier: A synchronization lock prevents entry if sum(ASCII(Carrier_Code))%7== floor(T)%7.\r\nGoal: Find the minimum Time T to reach the Event Horizon node.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 336.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 168.45px; transform-origin: 468.5px 168.45px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eAbstract\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNavigate a signal through a non-linear, resource-constrained, time-varying neural network. The topology and node properties mutate based on the global entropy \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and local thermal accumulation.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eKey Mechanics\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 183.9px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 91.95px; transform-origin: 451.5px 91.95px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.8667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 20.4333px; text-align: left; transform-origin: 423.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTrivalent Metabolism\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: You must maintain \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eATP \u0026gt; 0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNeurotransmittters \u0026gt; 0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHeat \u0026lt;= 100\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Failure in any one resource results in signal termination.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 20.4333px; text-align: left; transform-origin: 423.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDamerau-Levenshtein Cost\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Jump costs are calculated using edit distance including transpositions between the evolving \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCarrier_Code\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the target node's \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePrimary_Code\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eRelativistic Signal Speed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Signal velocity decays exponentially as the current node's Heat increases.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGlobal Entropic Decay\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: All neuron strings undergo a circular bit-shift every 10 time units, altering the cost landscape dynamically.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 20.4333px; text-align: left; transform-origin: 423.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSpatial Feedback Inhibition\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: To simulate neural refractory periods, the signal cannot enter any neuron within a radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eR\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eany\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e previously visited coordinate in the current path.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eResonance Barrier\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A synchronization lock prevents entry if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003esum(ASCII(Carrier_Code))%7== floor(T)%7\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGoal\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Find the minimum Time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to reach the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEvent Horizon\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e node.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [min_T,best_path] = solve_omega_singularity(nodes,start_id,end_id,params)\r\n  [min_T,best_path] = size(params+nodes+start_id+end_id);\r\nend","test_suite":"%% \r\nnodes1 = struct('code',{'AAA','GGG','CCC'}, 'x',{0,10,20}, 'y',{0,0,0}, 'z',{0,0,0});\r\nparams1.Speed_base = 10; params1.R_limit = 5;\r\n[t1, path1] = solve_omega_singularity(nodes1, 1, 3, params1);\r\n\r\nassert(~isempty(path1), 'Path không được để trống');\r\nassert(path1(1)==1 \u0026\u0026 path1(end)==3, 'Sai điểm đầu hoặc điểm cuối');\r\nassert(t1 \u003e 0, 'Thời gian phải là số dương');\r\nfprintf('Test 1 Passed: t = %.4f\\n', t1);\r\n\r\n%% \r\nnodes2 = struct('code',{'AAAA','TTTT','CCCC'}, 'x',{0,45,90}, 'y',{0,0,0}, 'z',{0,0,0});\r\nparams2.Speed_base = 10; params2.R_limit = 5;\r\n[t2, path2] = solve_omega_singularity(nodes2, 1, 3, params2);\r\n\r\nassert(length(path2) \u003e= 2, 'Lộ trình quá ngắn');\r\nassert(t2 \u003c 15, 'Thời gian quá lớn, có thể thuật toán chưa tối ưu');\r\nfprintf('Test 2 Passed: t = %.4f\\n', t2);\r\n\r\n%%\r\nnodes3 = struct('code',{'A','A','A'}, 'x',{0,10,20}, 'y',{0,0,0}, 'z',{0,0,0});\r\nparams3.Speed_base = 10; params3.R_limit = 2;\r\n[t3, path3] = solve_omega_singularity(nodes3, 1, 3, params3);\r\n\r\nassert(~isempty(path3), 'Không tìm thấy đường đi do rào cản cộng hưởng');\r\nfprintf('Test 3 Passed: t = %.4f\\n', t3);\r\n\r\n\r\n%% \r\nrng(2026); n5 = 20; bases = 'ATGC';\r\nfor i=1:n5\r\n    nodes5(i).code = bases(randi(4,1,4));\r\n    nodes5(i).x = rand*50; nodes5(i).y = rand*50; nodes5(i).z = rand*50;\r\nend\r\nparams5.Speed_base = 7; params5.R_limit = 5;\r\n[t5, path5] = solve_omega_singularity(nodes5, 1, n5, params5);\r\n\r\nassert(length(path5) \u003e= 2, 'Không tìm thấy đường trong map phức tạp');\r\nif t5 ~= -1\r\n    fprintf('Test 5 Passed: t = %.4f | Nodes in path: %d\\n', t5, length(path5));\r\nend","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":4945722,"edited_by":4945722,"edited_at":"2026-03-20T15:49:50.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2026-03-20T15:23:12.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-20T05:56:14.000Z","updated_at":"2026-03-22T19:53:45.000Z","published_at":"2026-03-20T05:56:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAbstract\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNavigate a signal through a non-linear, resource-constrained, time-varying neural network. The topology and node properties mutate based on the global entropy \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and local thermal accumulation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eKey Mechanics\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTrivalent Metabolism\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: You must maintain \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eATP \u0026gt; 0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNeurotransmittters \u0026gt; 0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHeat \u0026lt;= 100\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Failure in any one resource results in signal termination.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDamerau-Levenshtein Cost\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Jump costs are calculated using edit distance including transpositions between the evolving \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCarrier_Code\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and the target node's \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePrimary_Code\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRelativistic Signal Speed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Signal velocity decays exponentially as the current node's Heat increases.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGlobal Entropic Decay\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: All neuron strings undergo a circular bit-shift every 10 time units, altering the cost landscape dynamically.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSpatial Feedback Inhibition\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: To simulate neural refractory periods, the signal cannot enter any neuron within a radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eany\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e previously visited coordinate in the current path.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eResonance Barrier\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A synchronization lock prevents entry if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esum(ASCII(Carrier_Code))%7== floor(T)%7\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGoal\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Find the minimum Time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to reach the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEvent Horizon\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e node.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61280,"title":"Project Aether: Non-Linear Temporal Flow Optimization","description":"Ⅰ. Description\r\nIn the year 2450, you are the Chief Architect of the Neo-Elysium defense grid. You must manage energy distribution between stations in 3D space. This is not a simple flow problem because:\r\nKinematics: Every station moves with a constant velocity . Their positions change every second.\r\nTemporal Rifts: Spherical anomalies appear and disappear, disabling any station trapped inside.\r\nDynamic Cost: The cost of sending 1 unit of energy between station  is the squared Euclidean distance at the exact moment of the query.\r\nCapacity Constraints: Each station has a maximum storage capacity, and each link has a maximum throughput.\r\nⅡ. Task\r\nWrite a function [max_flow, min_cost] = solve_aether(stations, events) that processes a sequence of events and returns the results for all optimization queries.\r\nInput:\r\nstations: An  matrix: [x, y, z, vx, vy, vz, capacity]\r\nevents: A cell array where each element is a vector representing an event:\r\n                * [1, id, vx, vy, vz]: Update velocity of station id.\r\n                * [2, u, v, k]: Create a directed link from  with capacity .\r\n                * [3, x, y, z, R, duration]: A rift appears at  with radius  for a certain duration.\r\n                * [4, num_sources, sourcess..., num_sinks, sinks...]: Optimization query.\r\nOutput:\r\nA  matrix where Q is the number of Types 4 events. Each row is [TotalMaxFlow, TotalMinCost].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 638.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 333.5px 319.25px; transform-origin: 333.5px 319.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eⅠ. Description\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 21px; text-align: left; transform-origin: 309.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the year 2450, you are the Chief Architect of the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNeo-Elysium\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e defense grid. You must manage energy distribution between \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003estations in 3D space. This is not a simple flow problem because:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 171.767px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 85.8833px; transform-origin: 316.5px 85.8833px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 49.1667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 24.5833px; text-align: left; transform-origin: 288.5px 24.5833px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eKinematics\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Every station moves with a constant velocity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"28\" style=\"width: 17px; height: 28px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Their positions change every second.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 20.4333px; text-align: left; transform-origin: 288.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTemporal Rifts\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Spherical anomalies appear and disappear, disabling any station trapped inside.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 20.4333px; text-align: left; transform-origin: 288.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDynamic Cost\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: The cost of sending 1 unit of energy between station \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46.5\" height=\"18\" style=\"width: 46.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the s\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003equared Euclidean distance\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at the exact moment of the query.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 20.4333px; text-align: left; transform-origin: 288.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCapacity Constraints\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Each station has a maximum storage capacity, and each link has a maximum throughput.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eⅡ. Task\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 21px; text-align: left; transform-origin: 309.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e[max_flow, min_cost] = solve_aether(stations, events)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that processes a sequence of events and returns the results for all optimization queries.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 20.4333px; transform-origin: 316.5px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003estations\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: An \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE4AAAAkCAYAAAAnxQwhAAAF+klEQVR4AeyYW2gcZRTHZy8JbZCgwUQaYrK5EC1IbYx4oWgVH/okii1SFBW1T1URYqOUBvFB7HORijfwblG0tMYLeI0UrVW3jYikLNndZBsNas0SoVS7m6y/M91vnZmdmZ2ZbNM8TDhnv8ucc75v/t855zuTqBb+BUIgBC4QbJoWAhcCFxCBgGqhx4XABUQgoFrocecCuI6OjtXd3d0PweNwqczFRCKx1Wk9ZG6FD8IFWOlM9PT03O2ks9zz8l7s52PD/tQ+ndo91j26etzMzMzpbDa7NxKJbETxM1goxvgOOnG4ipAfhW/nwfOw0DstLS3rMpnMWzJYCRyLxdaXSqUNHvdyBtlPrLKuwClhXnqe/hisaGNvb+/lamDTlphbBcuiryaTyQL9lUKRaDR6F5s5iQNsXlxcbHfgQWROwCnkjtGayBNwhKaAcL1Bs41T2GIYm7qtra0X8LyHSdtFmT9v1NXVlWDxAcDbhEPsn56enrVjnncg1857/EAE/UHfRJ6AkxNB60pYwvVvWg2Dm8kRl0jfyk1NTZdySmuRsV3UKm8YR7C5hYN6fHBwsMEwX6srepKL70EwArvRKva1K51OT7oIRZCRdKPxHgeQkwii+Z88AUdOuAKVi+FnMfQNrZAAc7N0rIz8Vcyt4dS+oK1alDlbImFLeLzIGs/k8/ldHsET0HZgUBL4nrINhvaEd01MTU19bf/07CyXRzt7uIFRtlAoJGmryAU4k+wtjH7FyFG873X6C3AMYO5lkdX0TcRpXcPE7MLCwlFaz5TJZJLoDqEguXHEA3gxgHoC+d2w6AyJDfpLooaGBjnAbvZyiAvyNztjNYHr7Oy8CMVr4WMY+Z2T+Ir+BCzhugHvWi99xUoeuXGAm1LzHtsS3vAaG96OvADhBp6ANozs02XZ7aJL37OHI2tHNcNUlGoCB/qS5PvZoIRdkUQp4L0vynAzXic3VCWvKHk8cwygTyPjl7yAd65A04ggFaY53uFnp83XBA6vuRrlRgD6hVYnvOk9OuqmuYmE3sZYJ4P8t/pEsB838EygYX64Tp6GKU3j4FWYHiYfSjmiz1t/otYJyzgOSJLf0vF4/Lh6lk6nBcR3y2PjJWErX5bz21SBNzc392QikRjB+/XwxOAwEfAc7VLDExM6VcKU0ShchG3JFTjcVsqNATaaTKVSfxkslHDjtxlLaVK5JPr7+y9k7jIbeaYDkQk8LIxwkE/RnoHrDZopTHmHI6zhSK7ANTY2rkWzkzCV/GY6VUJynJfQSxMW0S+JYrEoXxNSYH6KnkmecVAS8N5kjX0GA/u5lF5mXK81MKVVwpTBj25hynMtKj9OzGalTjsFQJUwVbKS+PE6VZrolwRj+f6bp/1eydWhlZy2gz3cZ7C1lTV2eqzzDGquXRWm8i1+EEnHMOWZM3Dlz6brEEpRv2Voq4iXqZQmPLyT8Tban/BQ29qHZ35JQKuUHCg/whoP0tYqVRDxR6QldZueIHIO19J29Dj12YSBI7lcLk9bRSRmY2kiN2sfXnqIW+6fKmH/E1bQJKftpcB9hTW81Hm+VlS3KUrf8b45WldyBI4con82ccKunyc8N5Ymp/C2pZQharN2oKnbU3Ke1yJZ2avV+gpTMeYEXJxTvQ2BPMBM0zoSpclxZD8vC5jKlvKc30a+PYew6VZy1BU8Q5h6/ky0BY6CVv6FtIk3lv+j/UvrRpJE30BASoQxypaT9IOSgCYf7Pq3J0YkPJWnMTRR3cAzhGkSR8maVnEYmIDjf1VrAE2u+Y+Qb4bbKDsOUHTu7uvra2V8liy/hKckU6l7pGyxPPU+ZO11SD8GyyG4gYaITlbwHqZIHtCfeP+phCle/qHX/GwCjtplloS/DW6GI8IY6oN3Tk5O/um0FxL2PLI3wh84yXiZR19uZPn2fZS+k6dZTeng4Sly296Pnt9SSPQfQC/Ce75gNe40NgHnJLSc8+TML3mJl1jTT3Fb4vD2oTeK3rLQigNuWd66DouEwAUEMQQuBC4gAgHVQo8LgQuIQEC10OMCAvcfAAAA//9TdODJAAAABklEQVQDAB+CVXYiA55RAAAAAElFTkSuQmCC\" width=\"39\" height=\"18\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix: [x, y, z, vx, vy, vz, capacity]\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eevents\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A cell array where each element is a vector representing an event:\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                * [1, id, vx, vy, vz]: Update velocity of station id.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                * [2, u, v, k]: Create a directed link from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with capacity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                * [3, x, y, z, R, duration]: A rift appears at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF0AAAAkCAYAAADrXDbKAAAItElEQVR4AeyZe2xURRTG77a0gDTlTeXVdktFETGQIgpBkIh/gBYDwZgYAxjkKeIrgEpINGhAJEQRITFBJYFoTCQgxqBGEBUCShERRaDvh7S0UgttDX36+9a7m929d7t7+yRxm3N65nHmzMw3Z2bO3I0xon+djkAU9E6H3DCioEdB7wIEuqDLqKdHQe8CBLqgy6in38igp6WljXS73ftHjBhxRxeM84btMiUlZTDYfJSamjo10kFG4ukuwJ7V3Ny8z+Vyrc/JyTkbqfH/g15BQcGlpqam58DmJYBfyZxj4RYpHOgCfDkWtsELcnNzTyKjFIRAfn5+KUVLAH4RDvo8aRcckloEnW0zh5av4+Wr8vLyfiQdpRAIgE8BVQvhp03cSAaRmQ0Jenp6+mjA3orewf79++9FRikMAgD/Eyq7wG07Z/040rZkC3pGRkZcY2PjOlokcF69nZWVVU86SuERaAav91GriYmJWSMcSVvIFvSKiorxaM6Az7FqfyCjFCECXKxFqOrum3HlypV7SFvIDnQXq/QYmonwicLCwkpkSOL86s3l8QjyC+RVuB5e5G0wbNiwftzqeyirRyeLY2uYt86JxE5PbGRi4w3sHSVdCueyjd3+dqgbS3mJGF05j391xGnaal77sJPTAh+gvz5BRhtw1G8oS0Q+gbRcqjEUBtDIkSP7UzAFNmj0u2QYTuLWPo3uMvSk3w25MDk5ua8GHhcXt4f6oZRVozOIY6sXacdUXFxchzOcwMZ27OViIAl2UzYT6U8CoS8FQ9BdgmwV0Uc6DYVDGtKOEyhfT+TyNzKAGFMOBXXYuBdnGUI6gCygNzQ0yHOSpUWjPyVbYsLIC/BFLhHd3lphqY+IjY29hfNtI5lD1E2D+8LD4fOUtYYaeSNcpn0Bk3oBA7/Acow5AwcOFADKGoBwBLBnk7lsMsI54RzaJVngMZQ+XV4GEy3q58jllNlGdNTpdKih1+T4+PhRyACygM6Ab0ZDhiuZXFjQ0fURnR0mUwcPwM4G2vfp16/fW+Sb4XYjgU9f+2QQOS4xMfFWpU1u7t69+zHSZ6jTeEg6pljGnsYcVhUVFfkw0MVoOtJ3OFrIiI5+y+hROyAeOQYOIAvoNNC2ClCKNINXaNurQ0N24HUdFfngiV8yrqtwX9LySpL/EeNIIdUN0H5FtoYaAXVNfn7+ab/GLi7GZ5UP50j19fWN9N0kXWSqpD9bQGcl4/wVnKSvX78uwL3RzhnAKHbS3okuk1E/59SGxb0fqbsEYejImUvZEba/xuMpa+s/7ic9FKewA1506Ei9g/u2gB6s4CRfVlZWCxi6RNTsNjxOl7LS7c5mVHXCNDyOC0sXq8EHueGMYRILvsusa7MgepmATX1XWcEOqGqrQQvorGR2a40yuOl42Hyz/WAuEV3KZrZDhC7uRix7+3KxUxczhmPEy3mUt5mYk46qNzGkTyEKFkg6ohLDCNS3gE61bn3dvIl46iDyEZEGx2Q3wptocAnuBQCTkB1G2L+IcY1XYSghe8pY8tMYw05km4kjRUfDNuxt5aiyjVTsOmFX9KSNLlEddYXBOhbQ6+rq5CECjagvtmdwA7u8bnXK19HZx+yULUjvWasLTmetiwnM0cKg5yGFeeSTzLaeMqf/evTooTvjgtqxAJMZ8Gr63k10o1ehin3stD+NC5sbMdBipEK9hXib6J2gMFafA34LVrCAziNEl8/PUmQCGZI27OIRNSA1NVWhpfdWH1pdXb0jOzv7Kqt83GzjOWsFOLYe5VaXVxqAPSEhIUFnfykRQT71WhyzSeTi/Pnz19CWtytaWkgffWpqanZTFkCt6M87JyNcpBLQkZkxTwi96PMYk2d8ZpVHWECnVM9YxaA6K+8E2B6UBRBlUwGwEHArmJCAnIfC0vLy8mqkttT3SMXr6ZzrX9HxGvKrWdB/kKq/D+k9uobgUfpmb3kuoxOWsK3vHNLTi/cV7xhU4GV0HPWHEyhSeZX5zccp9vK6vt1rKxLJbtcXRv2Y8S3HkvAJaGYHusE2PYSWfiHKYMCWy5DB6AhSPWrGWXQyMe67ZPC2H6g4ANdRV4n+4/71DEr286n3UgrbX+eyNx+xxLbn8YLcRFxte+466Q8nUqSynQHoaBU/BB6HVU6ZSEflMhzvKItjefgwjwTmrBBWj8sPaWB5GNqCzpmo1dlMg0FMJhMZQAIQngB3g6cxWX8ADXkb5XPh7vBkwizPues1Qv4k5W5Y3r2W8gLa6PIm6Zj0yeJrWu2ALROkzHDQXyyAjWLOk2mnl7k+b+tlqV35HuHooKSkpJvQmY2OgoTp6AUQx+Y46sajswscTwVUmhlb0FXH8fEpUt8YnqKzVr9SsRGS8BRFB5MY5Aco2QJGeUjii+VoKufhycsBNmz8HEF/jTjQLmzpW1IZTvEaXp5CH+/AozkG3wXUXgB6lHwRb4GDSB/xVtDO0HehPNptoMJ2TiFBN8/fZwCkGuMv6zbHSLuR7DEJRQd6Oeo4cmRbADIuT4iKR4V9W7S2PwUGgL+SqE6ef5Axr2eRryHv5i3gidLMgbuIWlawIOPB7EnGpNPCrAoUIUGXGp0VYOBh+K7Kysq1GrjK28ps0V7Yk/ecoI8t2LP1CMp9BMhj3G53Jt6daJ6bm5ngbrxSl75Pzy7Rmv6C7ZSUlPzFWHfCS+hzC4ArrPapMb454LSAMWVS773cffX+iRZBlyIrlo2hB+CJANUuwPO5oIaBLWUr66JRlKSuQjKvHjf970fhM8KxU2zxw+SP0v4TysIumNP+sOmEXFyqAnsp3v8gi+EJt1syEBZ0NWZypazwTIwer6qq8nzjUHlncW1tbTlepO/n9chyxrGYMWnBwgLe0WPEwxWPV3IHzmJMAQGFYRi23UcEutlSl8xBzji9As2izhFENtXsjNksfDw8MRJv6pyRGYqMqgB7v3kHRtStE9AjMhhVCo9AFPTwGLW7xr8AAAD//wyJguIAAAAGSURBVAMAwN8ehQ9pvxUAAAAASUVORK5CYII=\" width=\"46.5\" height=\"18\" style=\"width: 46.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for a certain duration.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                * [4, num_sources, sourcess..., num_sinks, sinks...]: Optimization query.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 20.4333px; transform-origin: 316.5px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 20.4333px; text-align: left; transform-origin: 288.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"37.5\" height=\"18\" style=\"width: 37.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix where Q is the number of Types 4 events. Each row is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e[TotalMaxFlow, TotalMinCost]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function result = solve_aether(stations,events)\r\n  result = 'binary_search';\r\nend","test_suite":"%% --- Test Case Setup ---\r\nstations = [ ...\r\n    0, 0, 0,  1, 0, 0, 10; ... % St 1: starts at origin, moves right\r\n   10, 0, 0, -1, 0, 0, 10; ... % St 2: moves left\r\n    0, 10, 0, 0,-1, 0, 10; ... % St 3: moves down\r\n   10, 10, 0, 0, 0, 0, 10; ... % St 4: static\r\n    5, 5, 5,  0, 0, 0, 10];    % St 5: Hub (static)\r\n\r\nevents = { ...\r\n    [2, 1, 5, 5], ...        % Event 1: Link 1-\u003e5, Cap 5\r\n    [2, 2, 5, 5], ...        % Event 2: Link 2-\u003e5, Cap 5\r\n    [2, 3, 5, 5], ...        % Event 3: Link 3-\u003e5, Cap 5\r\n    [4, 3, 1, 2, 3, 1, 5], ... % Event 4: Query Sources {1,2,3} to Sink {5} at T=4\r\n    [3, 5, 5, 5, 2, 10], ...   % Event 5: Rift at (5,5,5) Radius 2, duration 10\r\n    [4, 3, 1, 2, 3, 1, 5] ...  % Event 6: Same Query at T=6 (Station 5 should be disabled)\r\n};\r\nexpected = [15.0, 765.0; 0.0, 0.0];\r\nactual = solve_aether(stations, events);\r\n\r\nassert(max(abs(actual(:) - expected(:))) \u003c 1e-6);\r\ndisp('Test Passed!');\r\n\r\n%%\r\nstations = [...\r\n   13.8016   64.3856   75.3146    0.2430   -4.9817   -1.0341   44.0000\r\n   65.3592    7.8309   69.3887   -4.8116   -1.2985    2.6095   41.0000\r\n    2.5492   38.0750   13.6881   -2.3655   -0.6388   -3.3722   29.0000\r\n   23.3686   43.7689   90.6962    4.9859    1.3320   -0.3190   44.0000\r\n   97.8782   40.6951   37.8877    2.1054   -3.5322    0.9364   48.0000\r\n   94.3021   27.3786   52.9622   -2.8191    0.6537   -4.1467   10.0000\r\n   98.1064   23.1351   98.8615    1.4161   -0.9688   -0.0286   39.0000\r\n    6.6964   73.7898   95.8209   -3.7893   -4.4602    2.7690   29.0000\r\n   19.5257   87.9400   81.7646    0.5668   -3.6402   -3.6618   34.0000\r\n   42.3406   77.2488   42.3895    2.8797   -1.0949    2.0019   50.0000\r\n   53.7076    3.5833   81.7977   -0.8550   -0.4244    3.3073   44.0000\r\n   46.3277   55.4316   44.4496   -4.1634   -1.6809    0.1315   50.0000\r\n   62.5909   58.8174   38.0260    0.8711    3.5733   -4.9519   24.0000\r\n   50.2559   24.6189   70.7235    1.3927    1.0716   -1.4329   21.0000\r\n   79.1777   39.8386   23.8916   -3.7485   -3.0288    4.7302   22.0000\r\n   71.0352   80.6780   17.5765    3.6526   -3.5648   -3.5534   23.0000\r\n   56.9405   30.1836   23.8147   -0.1222    2.6738    2.7477   32.0000\r\n   15.7099   48.9634   28.3592   -2.2398    1.5272   -1.3902   21.0000\r\n   62.5603   78.1287    4.0649   -1.8853   -1.5772   -2.1842   47.0000\r\n   92.5833   44.9977   55.1417    1.6657   -4.4339    0.4341   37.0000\r\n   98.3197   83.3240   94.2499    0.0010   -0.7964   -0.9276   42.0000\r\n   72.3174   67.6675   78.7837   -0.5586   -0.3914    4.2030   17.0000\r\n   18.7558    8.6629   24.1432   -1.7442    0.3550   -1.4310   15.0000\r\n   86.0132   98.0718   69.5976    0.6592    3.2842   -3.8749   12.0000\r\n   12.9060   56.6428    1.5258   -4.8478    4.9837   -2.4492   35.0000\r\n   74.3472   20.7679   76.8548    0.5283   -1.1759   -3.4432   34.0000\r\n    4.7878    9.5609   33.1893    4.3582   -3.0992    3.1311   25.0000\r\n   64.9699    6.2521   32.2330   -0.1823    4.9239    1.2964   10.0000\r\n    5.9537    2.5782   76.5437   -1.7152    1.7994    1.5937   16.0000\r\n   91.9762   33.4127   38.4165    3.0308    4.3490    1.6412   30.0000\r\n   17.1725   55.6807   21.8627   -3.5653    1.3641    0.4728   42.0000\r\n    8.8046   84.5939   56.3322   -4.2138    1.4870   -2.1405   41.0000\r\n   30.4543   62.6754   22.0633   -0.5459   -1.1739   -4.0269   48.0000\r\n   67.1595   59.9864   16.2637   -0.3449   -4.7213    3.3122   42.0000\r\n   20.4443   21.0636   39.9640    2.3668    0.9307   -1.8498   28.0000\r\n   97.4810   25.3915    2.0395    1.9904    2.3131    0.9878   24.0000\r\n    3.9560   65.1974   42.3270    0.3309    1.5312   -0.3123   15.0000\r\n   49.1791   32.8917    0.3273   -2.9368   -4.3804    1.5821   33.0000\r\n   64.0933   52.3174    4.4860   -3.4303   -3.4696   -2.3900   18.0000\r\n   40.5016   12.4717   18.9124   -0.9776    2.5565   -2.1547   14.0000\r\n    5.7082   45.2696   20.1336   -0.6242   -0.0417    1.9106   41.0000\r\n   63.0337   99.2596   60.0350    4.7506   -1.1563    4.7348   28.0000\r\n   21.4581   39.9229   23.1722    4.2674   -2.1168   -2.1744   39.0000\r\n   62.9709    6.1912   56.6548   -1.9194   -3.1363    3.5399   14.0000\r\n   39.4561   29.2961   55.0750    3.6258    4.4734    4.0133   28.0000\r\n   79.6108   55.2272   33.8006    0.6023   -1.0194    3.3775   32.0000\r\n   87.9037   74.0127   98.9924    0.4416   -3.6085    2.5228   45.0000\r\n   78.0077   31.8404   14.8359    3.4228    0.4137   -2.4087   47.0000\r\n   70.2483   49.3858   85.1288    2.8797   -4.6948    4.4714   24.0000\r\n   42.0672   62.8669   78.7180    0.3637    0.4845    3.4713   25.0000];\r\nevents = {...\r\n    [1.0000   33.0000   -2.8119    3.6643   -1.0660],\r\n    [2 10 4 17],\r\n    [4 4 32 9 2 7 6 16 36 38 7 37 8],\r\n    [3.0000 7.8557 39.3866 81.5830 13.0000 10.0000],\r\n    [2 29 10 11],\r\n    [4     4    35     2    24    32     6    21     8    27    45    47    46],\r\n    [     4     5    44    38     8     4    24     6     5    22    15    18    46    40],\r\n    [     4     4    42    34    29    11     3    27     3    21],\r\n    [    1.0000   17.0000    4.3766    3.4737   -2.4302],\r\n    [2 37 40 5],\r\n    [    1.0000    4.0000    2.0565    3.7593   -2.2252],\r\n    [    3.0000   13.9014   37.4769   83.5878   16.0000    9.0000],\r\n    [     4     4    15    47    38    39     5    37    39    20     7     8],\r\n    [     4     3    42    47    23     5     4    26    10    15    45],\r\n    [    1.0000   39.0000   -1.5862   -0.2590   -3.9976],\r\n    [    1.0000   44.0000   -4.2913    3.8280   -1.0616],\r\n    [2 18 2 16],\r\n    [2 33 39 15],\r\n    [2 41 4 5],\r\n    [2 8 41 5],\r\n    [    1.0000   22.0000   -2.6489    4.5630   -1.2851],\r\n    [2 14 29 13],\r\n    [     4     5     5    21     2    29    34     6    35     3    33    15    17    48],\r\n    [    1.0000   13.0000   -0.6107    0.8718   -1.9299],\r\n    [2 16 46 15],\r\n    [    1.0000   33.0000   -4.6471    2.8261   -4.9820],\r\n    [2 34 2 11],\r\n    [    1.0000   30.0000   -3.0896   -1.1636    3.8218],\r\n    [    1.0000   35.0000   -2.1749    3.2141   -2.0589],\r\n    [2 48 42 19],\r\n    [     4     3    36    31    41     4    12    16    11     2],\r\n    [    3.0000   28.6149    3.0791   28.4451    6.0000    5.0000],\r\n    [    3.0000    1.0961   84.3501    6.6062   12.0000    5.0000],\r\n    [2 44 33 20],\r\n    [2 21 39 19],\r\n    [    3.0000   17.1376   31.9782   27.1206    8.0000    9.0000],\r\n    [2 49 44 14],\r\n    [     4     4    32    15    28     6     5    40    43    32     3    44],\r\n    [    1.0000   13.0000   -1.2488   -0.8647   -3.3482],\r\n    [     4     3    33    16     6     6    48    41     8    19    22    34]\r\n};\r\nexpected = [39.000 0; 0 0; 0 0 ;0 0; 18 0; 0 0; 0 0 ; 0 0; 41 0 ; 0 0];\r\nactual = solve_aether(stations,events)\r\nassert(all(abs(actual(:)-expected(:))\u003c1e-6))\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":4945722,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-18T06:10:31.000Z","updated_at":"2026-03-22T18:30:25.000Z","published_at":"2026-03-18T06:10:31.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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Description\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the year 2450, you are the Chief Architect of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNeo-Elysium\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e defense grid. You must manage energy distribution between \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003estations in 3D space. This is not a simple flow problem because:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eKinematics\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Every station moves with a constant velocity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\vec{v}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Their positions change every second.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTemporal Rifts\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Spherical anomalies appear and disappear, disabling any station trapped inside.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDynamic Cost\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The cost of sending 1 unit of energy between station \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu \\\\text{ and } v\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the s\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003equared Euclidean distance\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e at the exact moment of the query.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCapacity Constraints\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Each station has a maximum storage capacity, and each link has a maximum throughput.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eⅡ. Task\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[max_flow, min_cost] = solve_aether(stations, events)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that processes a sequence of events and returns the results for all optimization queries.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: An \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN \\\\times 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e matrix: [x, y, z, vx, vy, vz, capacity]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eevents\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A cell array where each element is a vector representing an event:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                * [1, id, vx, vy, vz]: Update velocity of station id.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                * [2, u, v, k]: Create a directed link from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu \\\\text{ to } v\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with capacity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                * [3, x, y, z, R, duration]: A rift appears at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(x, y, z)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for a certain duration.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                * [4, num_sources, sourcess..., num_sinks, sinks...]: Optimization query.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ \\\\times 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e matrix where Q is the number of Types 4 events. Each row is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[TotalMaxFlow, TotalMinCost]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61287,"title":"The Singularity: Omega Pulse ( Neural Dominance )","description":"Abstract\r\nIn the final phase of Omega experiment, you no longer control a single signal. You are tasked with commanding a Quantum Swarm of nanobots through a high-fidelity neural network. To suceed, you must reach the Event Horizon ( Target Node ) with maximum collective energy while maintaining swarm cohesion and evading an autonomous predatory AI.\r\nKey Mechanics\r\n1.Swarm Cohesion \u0026 Centroid Constraints\r\nThe swarm consists of individual agents. At any time , the Centroid () of the swarm is defined as the geometric mean of all active agent's position:\r\n                                                                                   \r\nCohesion Limit: If any agent  moves to a position where , that agent is instantly neutralized ( Energy = 0 ).\r\nMovement Cost: Energy consumption for a jump is scaled by the agent's distance from the Centroid.\r\n2.Dynamic Edge Saturation\r\nThe neural pathways exhibit Ion Saturation. Every time an agent traverses an edge between Node and Node , the resistance of that specific path increases:\r\n                                                               \r\nSubsequent agents ( or the same agent returning ) will consume significantly more ATP to cross the same path.\r\n3.Relativistic Time Dilation\r\nNodes with high Mass distort the local temporal flow. If a swarm occupies a node with mass , the local time  relative to the global clock  is:\r\n                            \r\nResonance Windows: Nodes only accept incoming signals if \r\n4. The Shadow Predator ( Adversarial AI )\r\nAn autonomous Predator Signal spawns at a designated node. It uses a Breath-First Search (BFS) to move toward the swarm's Centroid.\r\nDetection: If the swarm's Centroid enters the Line-of-Sight (LoS) of the Predator (a clear linear path with no obstructing nodes with a radius ), the swarm's energy is drained at a rate of 10 units/sec.\r\nInput / Output Specifications\r\nInputs:\r\nnodes: A struct array containing x, y, z (coordinates), mass (0 to 1), and initial_res (base resistance)\r\npredator_start: The index of the node where the Shadow Predator begins.\r\nparams: A struct containing: ( .M: Number of agents in the swarm ; \r\n                                               .R_max: Maximum allowed distance from Centroid\r\n                                               .ATP_total: Initial energy pool shared by the swarm.\r\n                                               .target: The destination Node ID. )\r\nOutputs:\r\nmax_energy: The remaining total ATP when the first agent reaches the target (or -1 if the swarm is neutralized ).\r\nbest_strategy: A cell array, where each cell contains the sequence of Node IDs visited by that specific agent.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1027.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 513.8px; transform-origin: 468.5px 513.8px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eAbstract\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 31.5px; text-align: left; transform-origin: 444.5px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the final phase of Omega experiment, you no longer control a single signal. You are tasked with commanding a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eQuantum Swarm\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003enanobots through a high-fidelity neural network. To suceed, you must reach the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEvent Horizon ( Target Node )\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with maximum collective energy while maintaining swarm cohesion and evading an autonomous predatory AI.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eKey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eMechanics\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e1.Swarm Cohesion \u0026amp; Centroid Constraints\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe swarm consists of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eindividual agents. At any time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eT\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the Centroid (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) of the swarm is defined as the geometric mean of all active agent's position:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 49px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 24.5px; text-align: left; transform-origin: 444.5px 24.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                                                                   \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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width=\"84.5\" height=\"49\" style=\"width: 84.5px; height: 49px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 41.9px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 20.95px; transform-origin: 451.5px 20.95px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 21.4667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.7333px; text-align: left; transform-origin: 423.5px 10.7333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCohesion Limit\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: If any agent \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e moves to a position where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANwAAAAoCAYAAACVWZSOAAAQAElEQVR4AeycCXxV1Z3Hbwg7oSRhByEJIBiYOoOMKFZcRmtrETeoBKitYm07/dRqh2Lrp+CMOtNOqRZxaUXLMONQC9Jaca3a1lalirJYREJoIC+BBAKBYEkAs5h+fyf3XO7Ley/Je1lM0svn/HP2/znnf85/Of9zH92c4F9AgYAC7UaBgOHajdTBQAEFHCdguOAUBBRoRwoEDNeOxA6GCigQMFxwBhKlQNAvAQoEDJcA0YIuAQUSpUCrMNyUKVN6ZGRkXDxu3LhPJDqRoF9Agb8HCiTEcJmZmamZmZk/ADZkZWUdOHLkSFW3bt3+raampspx/4kJqXsQ+JB2P1HerWqXaPDgwSmMuwz4WsMBEQ6Tx4wZ8wvmVg7UxYBq+uYDP6V+QkMc7ZHXGhj788CTQCFQDWi+ZcxrO2u4n3gOZT8CfjZx4sSemheCbxLlv6J+vPKdFVhDKutaCuQCWncsOED9etqfw1qTgA4bEmK4UCh0NBQK3VFXV7eIlfUCHNKvU3ZSaUFZWdkgyi4n3TMpKSnn6NGjZ5JulwDhM/v16/cSQmAvc1rRcNDCwsKte/bsmcu8LqPuKGDDkoKCgu7p6ek9mfsV1FcDYtjtbOji9hIap512Wh/GW5SSklLCxJ4EsoBvs56RzE97Non8Oub4Fea3hvS3gdIdO3YYgZefn/8+dYuB1eC5kroOfQiZX9TA3h1lvbcnJyd/mgYFgA3PUTaAum61tbWToMEOKq4k3sDer5SgIt8hgzYv4Ymx6Gq3cyWH4U9u2kTHjx8/BgHyTcZx3jt58mTITbdpJO3FuK8AT8NUyxisDogVJCx6OI6p3v/RRx/9ilTt5s2bq9lsMeznyR8EugNLysvLZxK3aYBBzuzRo8fbDLIUqGEd8zlY5wLrdu/erbnUkS5lfndRdz1tTgAO6c2KLSBUckl/A3gITXctcacN1dXVtQiPj9wF1BI/hlD5K3FdUVHRDurmkt4OJEOHGxG2XyfdIUOLGI4DeharSgX2V1VV+SWQc+jQoQoOxgwOz2A0xqXFxcWHadfiwOE5f+zYsZ+KhojDmoEQWM0GvM6Y99OmMWZzmL80RT/aSUPnIiT2Km0B6SmBocOvImm9a0i0mbZgbZeC/xXgH4A9zO8ShMYTpHXIiMJDWlraM5QIpKXD5k65A/3f5gB+C3osgzZTVdYZgT0dyzqGuXMvYV/EXG7W0TpLyfweMIG2144ePTrNZDrYn5YwXHcWdom7nq379u3Tot2sF9Xu2rWrTBrDK2lBQncTDs8qDuLAhmhkhlG2nPoUNuj7zRhTjCObn26ONMRbEhKO718oFDpJ1hMU4B6BuWIYlPJWDWII8P8cpEMAabK5aKmtpGMGrZE9eJYGB+lbRBwRXKaU9bES+p0W0aCJAiyG4cztJUy1q2iaDLR7YL/PY1BL9z9jTcnUpuhUYP3FNkd6EHTpbfMdKU6Y4TjgQ1nIZEDa4XfENUCbBTY+G8n2FAP0Ig6TcJQ5aNJZxLp3rcL0kmYiGzuMHz9+IJsyxW1Ry6a+4aZjRrQ/DFOKCWO2SaTCZYSV9BWzSZvdi3Z6h3yTgXm/T6PX0M4VxBFBTEmb5VSMhm5fJZagIWp+4ABLwzwN0+UBc9rrLqsZMl5v6D5daQFzed0VhMpa0JrO8DJJSXu4wsjktEUdJk6Y4Xr27JnNKkYD5WiUTcT+kIzZNwomuQbp+D1AzOmvjyedjKk1D6m2gU7yukVIOOoHsBH/Sr2Y4bfETQY8qtqgsW7DEvrnuWkvQpulUD7KFpDWOltbsCQxl4WMITOSyNnOWv+PRKPmMPUmcPjehTlvLi0trTQFUf4w750U6073RfbFrpmipgNadj/95bRYy8HPANYcPny4AJovQOj2aRpDy1pAG1kz2ishkjd8ixJ+gCk1L3vN0H3vqcbo4e/b8nR8GJrDcEkwzAUQ+AUWton0c8CLbMJ1DCU39C4utXtIOxMmTOhP3d1APlK1iIPzFO3+paKiIuIwsPGjwPdz2pYAawGZLSuJV1MuZ4fDmDPIl4FDppa1yaXFTlCeBxhGZqxpHIR/Zg67u3fvrsNFsvFAnybNFLyEk128QlYC7ueVaE1Au01kDNHSon0MDS2T0uZbHONYKAfJRkBaLm4HCkwHTxfkQDMJPDHeUPZkJVZFIXvUpoznE+xM3ynCVyDBobQBmD4d+v2UjOZG5PymsrJytRIdERplOA7+sKysrHVM/BkIvAZpejaUn8kC/0zZzYDCRndDnby8vGPU30nbG6g4DkS9G8FsQ9i8Z8Ezm7YL6DMH+BztdQ+cT7wTcHAYPE+5GE33B5lalfSZTlkSMAFQe41hnh/oow2JalpR5wXW1Vt4bAFziDBTmOM42jxCGz3myxP4XTxjMt8oar2ABJ8BthGAwkGE1B+VaG1gjXKdC+1npLmViBcaMh7908BrGA+afjNRvOCJGcB/MZUS7ETOTs5NuUxaGH00Z3MRQnAbFZ8FZHk8UFFRkYPZ3+QZoP3HEmIynA4cm6+72ec4eDdxuB9nhjJzBO+RVhATqI3SfpAJ0JeCKvq+ShwWIKLe5GSSHmcM65TQPepnNCyivqEDQM4ZXdgjNJi0Kn3+EVA4jFCQWal0TGDTdMBtHz1tFGL+DhewiVOB5bTZwjwmguQQ8Y2sv9Wl5tChQ/tBH3kmGcaEXA5QoUm18h/GMY4G4uy+fft6ZnIiw/gZD9qsAkcaeJdjEeyFdovR2hJSFLcsiIHBf64PyxW9evWq1IcWlItOP2Bc3de/jOYbxh7d2pGZTeuIynAQLYMFrQcmAivQNHJWqL0BDuNIk3CcCBct5dAg6XxiBWmcMBNAhT5IBb/3MHvixAl52zaBYL9t47p3rTcxD6+nXOC22uFyrHuW8b6By0pxrz5agjun7ktiOlXrresBGL9EQIHuilcTvwVcj8QcAxOvJS1BQ1QfRo4cORA6vQW8xwEz49fXNP9v//79pb3H+XqEZCX48q2WhKYHQCbayTGTSbrFQYwHbRZwHsZDezFeCkjvwTmzD413J3RpEeNJMDBvCWbQOnonlQDU84B1mum+9t8w2srWenbSQG0JEQwndc2AP4SAWlwuh/PH5P2Hze8RinBgyPtHe2kwIifqcwG4pSF3qQHwFQ7t2cTm7Y4NnAW8q7yAe8IYYmOf00/aVKYDRfWBDRkKDKjPNfuv1Zjq8Bwbpi84kogFPYgzgMuA1bEkJmPK7awL/RDusIOFKF5gPbqD6h3TdrU0sflWi5mvHo61j8mk5eyKxJ1gSRTG68MYd4nx2NulEk6JoObs6Z13uPpCK/NOyp7oGqG3RxXL1NTjvz5MUL7DQwTDldd/TaEHXk3+YS7wYQ+qaJxUiClm1HNAxN2HO4nMybHqDJEiGETlIhp1D5OWSToEfKvYmAzyEYF2widNEM0b6rApMjUFEX2jFTB/4bIaU2uIOsdoff1lvDsWo/0mIxAmceA8AeFvE2+atYYJk3j7x9E+XgHVLNTQoQBheTP7+R06yFTvT7wIx8fzsfaX+lghCc0pwWjqwbndCj/Kn6PQuP0pn8ZVoEUmMrjaLYQxHB4fuXm/zOiSHHuRUC+SDguYXTqsen+L+JzLbShtpUdK1cd0MgwcOHAlB0z3Qh16MfAK2ewuDhv5ie55Q21lIjEM4mlM+kdlYsqbFXQAMHHLaCzNQRRfgL4SOIL4OnbM1skw1XWYknns631MsQewifNyCQL2U4DuXBQ1LyAYPcFOD9FIgpGk40C3d2E0mf7KZ5G+TInOAGEMx4VUdzZ7SY0wF2Vusjh5IMWQEQ4MFtwdYk8jVohWr3IDepAFl74HtPeuS/v163eFqXT/yDyljX2c9ryhbrWJqJeJobuJyTf1h83S84G0nJomxMQcqt54ycYT60t971FWCOMBJP8+2htnBrG8rZ8klslO1HYBJvC+ymjpKDoTogOgd0w9Geh+uIFzoO8/p2Ih6ZMrMUxcQzUQjGG+AqyLE+D3nmhYz1WusohrjHgas98DECiXATOBocCn0awyeT000KA3zkbdkT2Li7JUgeP+C2M4FiGzzh7GbZgHYR4/vEMX0U9ODiJnG9LdehiVd5iE7jTG+weuzQ3rmeDlgLSjae9KvSVk9JW77hbXkvbscZ95qg3zJBxtvIB3Sm985t0K5jvdq4ie8H+OphZRmVgVsYCNTafuBtb3FuOtxLzx5kt5XMGlz2u+Tv8EDbVhvqLoSeiYTdvH2Uw5EaI38pUyX1kvEpSitYSUrzb+pGU0HsFzocMaQIz2EpjOYl+nc3b07peQ5geHtJhfMEYIfwSnrC9z3WFt50pZqJ8foM050GgFsAOGeR9mGEXZheTfA+pI6703CW06kfwbQA3wNHssWhlUSlO2mH1+gYIDjCurTXv2Mms2vgrwnAH+R8i/Q7tS8reIPupH2SH6bWK/zF00jOFo7HnMWMQHNPQCnTPofD8FZjLU61Mo/T5pNgPoHUQSWgfeeDCROoZBmMgdgCS3Q9kcQG9moKkPMJWeDew3g6m4yvUFv6lkPvZx+iDpv2gOwNIRI0boycG0KSoqOspcrJaUI8NoCFPZ4A/Ek5PCMnxMJm7QLSyLdD3CXF6msAIoYD12bLKOvrAZAj38jhCVx4I6cP0PlUZgEMsjp686SMYO0PNs7q6/ZD/Wh0IheR9jN3ZroJEEqUz9UmhuPlRwq+KKdJBY3xw/ozGPp0EyCUb7LKB3sYQZDTwKDQXjm6wzTPiz73o+el2NgTTWN5M4LNBHTK/7XjZ03gmznMdc55G+nYZH2bsJ0HIeTzH/Rf4OQM9R+qBdQlUfXgxA0/4vfeZC7y9pba4nXZbJQcr05ZHDODvx5H+NdvraSQpgOsrpq+QhdY18ELO535o9DmM4JuCZGjTWRdQcXggsKbqCRdnDpcluYbLX0m4+/d5ksgrSkNrU/ZS9S78v0Wd4WlraThhJ5SPIz6Cfd2lnAdWUaZJi2D/5PskR0SXldMfLZeHHaCeJ9GxJSYl5VNeAQB1jGeYmfTrSKuZhx4TTgbYeujAzhb7NDmyQ7oH62mJXenr6EXXUQUQY/ITNLIUmZay9WT+6ZSN0H/khOGoAmSL30fczpA3tib2AwOhD3Xegw3oKb2eT9XMikk0H5mSEKfF25ug9uzTds76F1sfYfkbTXmv8SczjGg6jTMr6xi38yzrDBCPztQLZj1nPOXqukeDUGZkF/dXP30Znyqybwg85J2fhUb6NWPfL/uCFlHVXV1VV3QRdJCSGULCNs3pQ6yWtn0jNpN1CTGO99zmc5d60HQS+QhguTNjR/i+UF1N/FXDJsWPHHtq7d+9uGFJONTPPMIZDAuircvszm5tYwHJgMZ23AC+D0HA0SPuT1uPwQuLbILjRhkzMaDfqe4NrEX1uYFJLdV9D5fek/BOUyemir0nMgeLeph8QTqZcv2vSWw7NnDDzlIIB4HsEQr3BxkqzUnQqUGfnU0X5QwAABnxJREFUPRo8Eg6nKt2UCMj85pHVPIicGhhQ5pXScQFrNl8/MNbvtTZ1dn9wa71qMo9zmvmj2zrotwycXwBPOSCvrbx6ryKYvp6VlTWbeD6wCqFTwphXAxfRx7vD0KepkAR+c98gfh4trS9nmupj6/Ut61w0WgHjynTUG61+sTGevZgNtBqjuQMmsU69g+pHtyqq5QzJ46l0Q5AGs++82azNetdtO8+nwNzHcH7uddeuM5hMPhO4gzIJTePso53ZUzSUrk96cnitsrLSO3OcNQkaKaON7pXAjuVAC12x9BXWhxQ+JKcacVgIYzikbQGHUl/dywMkKSCPpUycHDZYh0KmlFSjDuo7SPrLGcTvfVK9nAD9GaU3BMjJz8+X+nU43NJwkuK3MsYUDtIfOES/ZoHrgEdZ+DQ/Llzu+oxLGrWW+oHg+n/NAbySRESnAvMOUS+pP5y2F5yqqU8hmXMgoH6U+sX6EvM3C+K9wjzujuIdNQ2i/QGXzFbZ7uWMaQWQM2jQoDLGfpE+WiORk8Y67eO68o1BHVJwLQcrExwLaSizbCr49XSiX3bfB65e0OgKaHQ+dIjrvQ6NoXnIGZYLjmfA3+zA3UOf4d3DvGRmPcw8RjPXBdDcCuZm42qqIWNlQ99f0u5+QNqeyNHvEJ9gnx6kfrgKLEAL3UXteiTkHqTdWqwcWSAO65bG0xVCTpb/4Cwe0l5DV9GiirXc7Wouy5h2T5W3zkH/W6y85hIGMs9lzjY8i9JiMkv7gltMaafqxWEMp1IIuZWFnA/oAbgv8YWALol1bt1Q8iq/lQWYtxD1E4RCIX25rkdk9c0h76lc2u6jn/A+TPlNpC/k4MgUGU2s7xTDcEk6UK767rTNoo/Mh4YL1LCCOg6rDqcWe52IqkIL9F0DjosA4UoitpBN+k6NZds2FUNIHV45hvIRIrtte2k6cN0C9GAuIvZWDreEj23SZAyN/sqafwwOOR5EYzvPYaxhHodDglCb2iQufwM0hjSyNNMD4DCOBn99Y2mEqsZ7FLNrFPP6BmcgbnO0Mfz+OnDnss5ZjKPzY9eueAhlt1AfMTbl3wPURqB+c7jfmTsqc5fvQFcIT0v5vl7ZgnlpflniY0yzp+PGjRuGgJkGYx4glhY106Rcz1cLyOibVykDkqcCzD6TPjmU6JNGWTvGiiPvhQiG82o6WYKDlM9i9W3d9JSUFEmhNlkBmyjpKcm5EQ3ZB4lsHEb+wbgp66ci76empkpT+avaPY1nTl5P/Z8nLzAv/ewnrjlA14MwwdLi4tb5xX5cg7ewMcwiB11PzsUaK1QRhjKtZQmtZ00yJWV92bu92VP29RqGTqW/fg5kzG+sMV1r7qVce1+IADpBmaxBo4lhNjkVb6Re1yU5dLJHjhyZjlY+j3bmSynqutZ/da7HdBale+ASGCGTdFsESU1t4m603Z1soLlM24Eg/FQ2Sv+nxmJpPVv+ccTuvfUed+xbuauYw+Pmu3SEWSmz7xyYrRhLQ5aB1tudPdOvUsqJ5R03FhNtplKpu30h5d+H4fSbO93HhpDORmiNos2DtJEZqfKDCN5vUaefid3FWZP5uZT8j2gjjbiTM3AGFtCNnI+bYU59HEGV07UYTgccM+E2VvYaC14FIYaRbtUA4YtBKA+ZPFuPogE8hkOayXRbyAZ/ATPHf7elS7uHJO6tosWZbLrufh/3fNqVAJjRskSkWTampaWZ/8BKpiPnQsxlTEc7Icr0kbUcMzNI341JuoH436mX9/wFmPBx0vcS/5pY/gs9Haxnn3eTn0/bZcTrMHnfxBrQ88Vj5GU9XkmfuxB0RpNS1rUYTgticSdw1UvD/A5CrG5tpoORngR0V/gk962w/wYBgr9K3RyYMK57kubdmiDNxrqXIBwmI4BmcDc0jqvWHKOj42IPNrMX6TDALAlizZezUUzZ6cBUPIye1mEfv0tZT+Bi0nLt67eYT5CXv0J7fTHpbexvLrHuslnErwB5gNJpxHL2GI1J+hlAd/ALGN8wu8YXiAsVdykQgVnwf6Liv4kUsu8wXWqNjS3mgw8+0D3j7VAodD2HzJOujfUJ6tqHAl2S4SzpMA12ILG8NxRb3tVjaTQk629YpzyMREHoKBTo0gzXUYgczCOggKVAwHCWEkEcUKAdKBAwXDsQORgioIClQCdiODvlIA4o0HkpEDBc5927YOadkAIBw3XCTQum3Hkp8DcAAAD//7qSRFgAAAAGSURBVAMAgwuy561GJrsAAAAASUVORK5CYII=\" width=\"110\" height=\"20\" style=\"width: 110px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, that agent is instantly neutralized ( Energy = 0 ).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eMovement Cost\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Energy consumption for a jump is scaled by the agent's distance from the Centroid.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e2.Dynamic Edge Saturation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe neural pathways exhibit Ion Saturation. Every time an agent traverses an edge between Node \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eU\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand Node \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eV\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the resistance of that specific path increases:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.4667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.7333px; text-align: left; transform-origin: 444.5px 10.7333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                                               \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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\" width=\"226.5\" height=\"20\" style=\"width: 226.5px; height: 20px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSubsequent agents ( or the same agent returning ) will consume significantly more ATP to cross the same path.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e3.Relativistic Time Dilation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.9333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21.4667px; text-align: left; transform-origin: 444.5px 21.4667px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNodes with high \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eMass\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e distort the local temporal flow. If a swarm occupies a node with mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the local time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"32.5\" height=\"20\" style=\"width: 32.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e relative to the global clock \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"38\" height=\"20\" style=\"width: 38px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.75px; text-align: left; transform-origin: 444.5px 10.75px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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style=\"\"\u003eResonance Windows: Nodes only accept incoming signals if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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\" width=\"252\" height=\"20\" style=\"width: 252px; height: 20px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e4. The Shadow Predator ( Adversarial AI )\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn autonomous Predator Signal spawns at a designated node. It uses a Breath-First Search (BFS) to move toward the swarm's Centroid.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 20.4333px; transform-origin: 451.5px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 20.4333px; text-align: left; transform-origin: 423.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDetection: If the swarm's Centroid enters the Line-of-Sight (LoS) of the Predator (a clear linear path with no obstructing nodes with a radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e), the swarm's energy is drained at a rate of 10 units/sec.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput / Output Specifications\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInputs:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 122.6px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 61.3px; transform-origin: 451.5px 61.3px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003enodes\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A struct array containing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ex, y, z\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (coordinates), \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003emass\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (0 to 1), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003einitial_res\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (base resistance)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003epredator_start\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: The index of the node where the Shadow Predator begins.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eparams\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A struct containing: ( .M: Number of agents in the swarm ; \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                               .R_max: Maximum allowed distance from Centroid\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                               .ATP_total: Initial energy pool shared by the swarm.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                               .target: The destination Node ID. )\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutputs\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 20.4333px; transform-origin: 451.5px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003emax_energy\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: The remaining total ATP when the first agent reaches the target (or -1 if the swarm is neutralized ).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ebest_strategy\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFMAAAAkCAYAAAD1lQZ5AAAGXklEQVR4AeyZX2jbVRTHf0na0rq0s806xZWm/wy2/mNUFMWVTvesODZ0D/qmuBdBrYxZlblhi6Cvw5chDIT64Jwy9jKHOkE2Z92UWm3o39COZt26rnZMmqTd5/zICUmaX9K0vyUUfuWc37333HvOPfebc8/v3l/dhvNnGwIOmLZBaRgOmA6YNiJgoyknMh0wbUTARlNOZBYBTE9DQ8OLjY2N55ubm9ttnP+umqqrq6vA7wP4fRGOwsvCyM7W1tZ6VzO53+/fjk4YNnUpI6JP2ZGunysyFcTLLpfrJMoBeMPQ5OTk7fHx8U8XFhZ2Li8v/6yOs5Y6r9e7SdtWpQDudrt76d8Km4Tuh9jcNTY2ds4UJD0sweQXeRr0+1Dewfh74A1L1dXV5axjS9ICSj0eT2lSO2O1srLyDTp2wUpXsXOKxjK8gizBROkS6O+Fu9A6Bm9YikajD+F8M6x0L5F6nzYylQTTdsYcoC8Gm0R7YH5+ftxsZHhYgkko/6/jMRLV+lpL8lcNueYoTrbmY4Pd4Rc9+P589JLHLi0tPUM7xjqmKIWqADixdUWQzLq9Cahr6PyufbQHZmZmFrSdXrrTBXehLSZL+PsMZ/aTg06uFlABEp3T8H6M9MAlcF7EjyBbfEcclN/iyuxyT028vqKIb+9n0TnK3Aq6ROjZFYOTBIUCUyL7feb9CQ643e6cgHJqaGEhp1lQGzqiJ/pih+bqiah8gNGPY+s8nIgy5NuQryB+aHN7M+9xeIQB9bDQlVgsNiAVKy4UmAZpYxrn9uGIAJMVUAGSsd/BJpCU+0Qf3byJEHwEpS0A+SN8m7pJ1B80K0kP3d6IrrKTehgjL98y2kJ/EgRXpGLFBQNTHBBABBjqloDaCSTzCD3PY2pxcfEf5h6mrrSZSkra0O0NiIfIqdfofww2Cd1f8D/xHjGFaY+Cgilz45BlhKYBeYGoelXGi95auL6+vhq9p+BLnDnDgDRNfQ42AMdHJJZLXVi3N/WvOEp9Txow0wNtoVtE5a9SycYFB1OcEYBYTMqW52XzAjLd2gLknuHh4UkZv1YuLS1tQjeAXXlxRAEoQtvMuwCbOLgDqhewepFJNPb09/dH+CElPQigqBgjbPt/pZKNiwKmOJQOKDJbgcSewQvjCUoXQP1BKdEYBtibUocr6DdvQfHt3QHYhzlXT9AnJOnBIxV0+oPB4HWpZ+OigSlOCaCUcjBWR28SHV3rjUhsCpVgSwAJEVVjIigvL19AptHuJXKrdXsDWJ/P5zsh45LSgzQNfgyJ7Iy3HnNA/FFUMCVHsrgv8cUHC21mUcdYYKs01sNcEuSGI8ecRFTNzc0tYXMRFqoiMlsASu7ekkcPy/aWDmR+Sr0x3cDHnFuc8UbRwBQgAS6xtXH4SRyyfMvTlxeVlZXJD1IPMImoCofDtzCixxsPc75D+zn4CLskcU1E52FkepcPRiKRUdo5qShgpgNJst8zOjp6EXBTXkrriVBs7WT114k+M19SVwpqhVJ+wBM1NTVfU1dykTslPWj7QigUuqGNbGXBwcwEpOZIosPy2JRtEel9TU1Nki46kQfJk5ojaRoG0Zg4uBuGESIKP9DtTdsIBAI+xug325xXSNFRLiiYHH/8RExia0tEKpDq0BoBVXWzJBrbAESONuNDQ0P/mcL4g/n14C5AdY+MjGjbHMFhPfkLU84rpKkUf+QEs729Xb77ycFXVDbhaK1U8mUBkgXqXTvrOXI9gIq/zPM6/lXB8h025ZZDnx7cT5ELv2FMgnhpVQD2WwjMIxNllNyrLyya2ckSTAxvA4BPZmdn/8KB3XEzZdSPs42+IJ+9xJiKuDxXIee1LhyVu3ZWINVQBkDfbmtr03uyDksp8bcDf8/g42vxjt3IfuDL0SvxtkE+lIP7JLuim1uRueVbWlpqGdPLUUny614dS9lI8JzBxuesWT94IM5MlmAy0RQH2G64FXYl8VZeFm9OTEx8yxjTmcymU6Qx/nVwEDAPIX05fWsjy0hJgB4BoPcGBwezRgk+noM74RJYfJayEzt9OgH1y/Q9ig9/q4z6DPKDyNPXKjZE9i5rDul4q9ISTCuFtcrloyoOf4zDesNYlSl0ptH5iMXozWVVesUYVDAwi7G4Qs/pgGkj4g6YDpg2ImCjKScyHTBtRMBGU05k2gjmHQAAAP//2SjVoQAAAAZJREFUAwDy6gV2+mnAeAAAAABJRU5ErkJggg==\" width=\"41.5\" height=\"18\" style=\"width: 41.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ecell array, where each cell contains the sequence of Node IDs visited by that specific agent.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [max_energy, best_strategy] = solve_singularity_pulse(nodes, predator_start, params)\r\n    % SOLVE_SINGULARITY_PULSE: Multi-agent pathfinding with bio-feedback.\r\n    %\r\n    % Your goal is to coordinate M agents while maintaining swarm cohesion \r\n    % and avoiding the Shadow Predator's Line-of-Sight.\r\n    \r\n    % Initialize variables\r\n    max_energy = -1;\r\n    best_strategy = cell(1, params.M);\r\nend","test_suite":"%% PHASE 1: TORUS \u0026 RESONANCE\r\nclear n p;\r\np.M = 2; p.ATP_total = 1000; p.target = 2;\r\nn(1).coord = [0,0,0,0,0]; n(1).res = 1;\r\nn(2).coord = [90,0,0,0,0]; n(2).res = 1; % Khoảng cách Torus = 10\r\n\r\n[e1, s1] = solve_singularity_pulse(n, 0, p);\r\n% Giải thích: d=10. t_arrival = 10/20 = 0.5s.\r\n% Pulse = 1 + 2*sin(0.5*pi/2)^2 = 1 + 2*0.5 = 2.\r\n% Sat = 2 + 0.125*2*1 = 2.25.\r\n% Cost = 10 * 1 * 2.25 * 2 = 45. E = 1000 - 45 = 955.\r\nassert(abs(e1 - 955) \u003c 1e-4, 'Sai số Torus hoặc Pulse tại 0.5s');\r\n\r\n%% PHASE 2: PREDATOR INTERCEPT\r\nclear n p;\r\np.M = 1; p.ATP_total = 1000; p.target = 2;\r\nn(1).coord = [0,0,0,0,0]; n(1).res = 1;\r\nn(2).coord = [40,0,0,0,0]; n(2).res = 1; \r\nn(3).coord = [30,0,0,0,0]; % Predator bắt đầu rất gần đích\r\n% Swarm: t = 40/20 = 2s.\r\n% Pred: t = 10/15 = 0.66s. -\u003e Bị bắt!\r\n[e2, ~] = solve_singularity_pulse(n, 3, p);\r\nassert(e2 == -1, 'Predator phải bắt được Swarm ở đây!');\r\n\r\n%% PHASE 3: PATH OPTIMIZATION (Bắt buộc đi vòng)\r\nclear n p;\r\np.M = 1; p.target = 2; p.ATP_total = 1000;\r\nn(1).coord = [0,0,0,0,0]; n(1).res = 1;\r\nn(2).coord = [20,0,0,0,0]; n(2).res = 10; % Đích xa, res cao\r\nn(3).coord = [10,0,0,0,0]; n(3).res = 1;  % Trạm trung gian\r\n[e3, s3] = solve_singularity_pulse(n, 0, p);\r\nassert(length(s3{1}) \u003e= 3, 'Thuật toán chưa tìm được đường vòng tối ưu năng lượng');","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":4945722,"edited_by":4945722,"edited_at":"2026-03-22T18:52:04.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2026-03-22T18:52:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-20T09:03:18.000Z","updated_at":"2026-03-22T19:52:58.000Z","published_at":"2026-03-20T09:03:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAbstract\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the final phase of Omega experiment, you no longer control a single signal. You are tasked with commanding a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eQuantum Swarm\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003enanobots through a high-fidelity neural network. To suceed, you must reach the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEvent Horizon ( Target Node )\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with maximum collective energy while maintaining swarm cohesion and evading an autonomous predatory AI.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eKey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMechanics\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1.Swarm Cohesion \u0026amp; Centroid Constraints\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe swarm consists of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eindividual agents. At any time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the Centroid (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) of the swarm is defined as the geometric mean of all active agent's position:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                                                   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = \\\\frac{1}{M}\\\\sum_{i=1}^{M}P_{i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCohesion Limit\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: If any agent \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e moves to a position where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003edist(P_{i},C) \u0026gt; R_{max\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, that agent is instantly neutralized ( Energy = 0 ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMovement Cost\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Energy consumption for a jump is scaled by the agent's distance from the Centroid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2.Dynamic Edge Saturation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe neural pathways exhibit Ion Saturation. Every time an agent traverses an edge between Node \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eand Node \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the resistance of that specific path increases:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                               \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eResistance_{new} = Resistance_{odd} \\\\times 1.25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSubsequent agents ( or the same agent returning ) will consume significantly more ATP to cross the same path.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e3.Relativistic Time Dilation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNodes with high \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMass\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e distort the local temporal flow. If a swarm occupies a node with mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the local time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT_{local}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e relative to the global clock \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT_{global\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT_{local} = T_{global} \\\\times e^{-m\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eResonance Windows: Nodes only accept incoming signals if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003efloor(T_{local}) \\\\text{ (mod 7) \\\\neq \\\\text{NodeID (mod 7).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e4. The Shadow Predator ( Adversarial AI )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn autonomous Predator Signal spawns at a designated node. It uses a Breath-First Search (BFS) to move toward the swarm's Centroid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetection: If the swarm's Centroid enters the Line-of-Sight (LoS) of the Predator (a clear linear path with no obstructing nodes with a radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), the swarm's energy is drained at a rate of 10 units/sec.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput / Output Specifications\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enodes\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A struct array containing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex, y, z\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (coordinates), \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emass\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (0 to 1), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einitial_res\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (base resistance)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epredator_start\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The index of the node where the Shadow Predator begins.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eparams\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A struct containing: ( .M: Number of agents in the swarm ; \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                               .R_max: Maximum allowed distance from Centroid\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                               .ATP_total: Initial energy pool shared by the swarm.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                               .target: The destination Node ID. )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutputs\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emax_energy\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The remaining total ATP when the first agent reaches the target (or -1 if the swarm is neutralized ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ebest_strategy\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1 \\\\times M\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003ecell array, where each cell contains the sequence of Node IDs visited by that specific agent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61291,"title":"EXODUS - THE VOID SINGULARITY ( PHASE OMEGA-ZERO )","description":"Background:\r\nThe Swarm has reached the edge of the known universe, entering the 5th Dimension (The Void). Here, Euclidean geometry is replaced by Hyper-Torus Topology, and energy is taxed by Universal Entropy. To reach the final gate, you must navigate a swarm of particles through a 5D coordinate system:  where is the Phase Shift and  is the Spin Frequency.\r\nObjective:\r\nWrite a function [max_energy, best_path] = solve_exodus_singularity(nodes, pred_start, params) that calculates the maximum remaining energy and the optimal path for a swarm.\r\nThe Laws of the Void:\r\n1. 5D Hyper-Torus Distance: All dimensions have a period . The distance between two points is the L-inf (Chebyshev) distance across the 5-dimensional Torus.\r\n2. Relativistic Drag (): The swarm's velocity is not constant. It decays vased on the current energy and the node's mass : \r\n                                                    \r\n3. Exponential Entropy Tax: Each jump increases the Void's entropy. The cost of the -th jump is:  \r\n\r\n, where  is the step number ( starting from 1 ).\r\n\r\n4. Quantum Spin Exclusion: If , particles must maintain a \"Spin Buffer\". If two particles have the same Spin  at any node, an additional 50 ATP is consumed due to interference.\r\n5. Predator Intercept: The Predator moves at a constant speed . It starts at pred_start and moves directly toward the swarm's next intended node. If the Predator arrives before or at the same time as the swarm, the energy is reduced to -1 ( Swarm Annihilated )","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 572.867px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 286.433px; transform-origin: 468.5px 286.433px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 31.5px; text-align: left; transform-origin: 444.5px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Swarm has reached the edge of the known universe, entering the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e5th Dimension (The Void)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Here, Euclidean geometry is replaced by \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHyper-Torus Topology\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and energy is taxed by \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eUniversal Entropy\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. To reach the final gate, you must navigate a swarm of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eparticles through a 5D coordinate system: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"83\" height=\"18\" style=\"width: 83px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eψ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis the Phase Shift and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eω\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the Spin Frequency.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eObjective\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e[max_energy, best_path] = solve_exodus_singularity(nodes, pred_start, params)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that calculates the maximum remaining energy and the optimal path for a swarm.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Laws of the Void:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e1. 5D Hyper-Torus Distance:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e All dimensions have a period \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"54\" height=\"18\" style=\"width: 54px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The distance between two points is the L-inf (Chebyshev) distance across the 5-dimensional Torus.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.4667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.7333px; text-align: left; transform-origin: 444.5px 10.7333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e2. Relativistic Drag\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"24.5\" height=\"20\" style=\"width: 24.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e): The swarm's velocity is not constant. It decays vased on the current energy \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eE\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand the node's mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 55.9px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 27.95px; text-align: left; transform-origin: 444.5px 27.95px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-33px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ0AAABwCAYAAAAE/HKKAAAQAElEQVR4AeydCXRcVRnHZ5JJW2xMSOzCoTWZJqHBAmItiGBRZBE9igsgFoocVCiceuC0BxRQwQWPC+oRxQWOqHgEC7iDC0c2LaJsBWqRtjHN0qaFFJoWmqRZmtbf/zXv5SXzZuYNySxJvpz7zb3v3u/de+e7/3z33u8uUxSxP5NAjiVgoMuxwK24SMRAZyjIuQQMdDkXuRVooDMM5FwCBrqci9wKNNCNFgP2fsYSMNBlLLLRvRCPx5fMmzfvWWi/j/qJf5Dny8g9BvldjLQVpK2H3He6a2pqbpw5c2apn3G8hA10OW6plpaWO/ft2/cRim2GXHcz8ac2NzffRMReyO/2knZjNBo9ncgWaABa1tTUtOKll17qJDzunIEuD03W2tq6hWKfglz3KoH9UFIHUBeQeCj0p/7+/t/ij1tnoMtP00mbPesruopwFAp0c+fOPQhNdymJXUVFRde3tbXtITxunYEuf023zlf0G+vr65OOz0pKShbD+x7oh5s2bXoaf1w7A12emg+NtY2id0KR/fv3z+3p6QkEHROGcng+BzXwjsZ8Kbth+ArejQBdwdd3wlRw79692wBbh74QXWdlLBbTeE2Pw4ix3LlEHAfPV9By2wmPe2egy1MTdnd376boVkiuAnAlgK62trYOsF0Dwz0VFRX34k8IZ6DLUzNi7ugCUOpinRoQrnMCQx/RgYGBT/MYKy4uvn7NmjX9hCeEM9Dlrxk1NlvvFk9XG3fD8jEELwaIn4RuamxsfF5xE4UMdHlsSQC1wVd8DSsP0/QsEwn+FdDzvb29P8EXQPGGHLyHM8m4GXA2Qbuqq6vfPZRa2CEDXX7bR0biXYNVmMm47iCFMZGchX8qdN3WrVt34Cc4Vik20P1+GQ25j8QtzGzHjTY00NFiY+kyyQugvAC/YzbBnzVlypTpdXV1cwlfBZjurqys/DvhpI6xXi3a8hAYnmYJ7WX8ceEMdHlsJkDzCsVvhuQqMKPMQXtdwkMZaV9LN3lAM54A73QA+jC+1mTxCt8Z6PLYRhs3btSCvbpY1eJgtNb7CVwMiL6OTa6RcFLHmG4a/CfCsB2A+tdxiQp2ixYtKmEceAxjwLPxDyOPt0Cno12num/4eYg/QnwiN931xad05YVpZxHxxVAoZ6ALJaasMWmC4M1gKeVaaD3d7ir8lA4tJ7ve0TA5YzmAsQoAdEP90C951koGyY6LEndaR0fHUwD68M7Ozvt4/xpA+wypy8rLyzUujACeWfA8Cs9l4kHzHkl4LTxHQa4rJu9zxYdWPpQ8dpHXPwDvRS5DOt9Al05CWU6n0fwzWO02ua6pqUndbsqS0W5HwiDgvQwwrif8HSYg2jjwKOHzAcIn8OUEuOUE7oLva4z97sBGKA3rlEv5D7ndOCCTxnorvO3i6erq+jPhv0GONpZ2A1w3kc93yX8Fed2Pr/1/JfD0QqGcgS6UmLLKpAZ1ZrA05s9oyH+GLO0U+NSlvRn/swD1qYaGBgHwLzxHAJMAFEUrncnzt6DbmfH+Bl/aVelzCHcBGkdTEpZTPbqox5lVVVU1Ah6RX9y9e7e0cRTttoJ8l0E3tra2/hsAahIj7bwawN4DbyhnoAslpuwx0ZW6M9gGSvke5IACP6kDEBUkHgcNAJCvAzhv/AcgnG6V+HV0lzPxBYrdgOvn4oci2nFMvDRlM+V7oJsxY4bGhn8lj1o06U8BbDn/BGsFPvKSBtSS3Fby+B3dtUw6D8D7X/JY2tbW5qwjk5bWpQZd2teNYbQSoHFfoeG0I/h6NJH8tFnCfzhMb4Ke7O/v15qsA1SBBDCdRPx2/PsZc51MWOB6GEA9R9hxpaWlC8njGHjWASrP1KJuFgB9ASbNqJWPQObs8wO00pgC+zTC34CnijxO4f1lTHoy2ohgoEN6+XTMYHejqU6m8W4PWw8aW7PWMkCzCuOxp2EAw3tJO4Z87qL7W0dYs+Fi+O4ToIiP+FY7ykjX+E+mlmh9ff3rSY8CoEb4P0u4D/8cZqhzZs+ePZ3nYyG5y/jnOJP6/hRqV0SmZKDLVGJ55mcc5ZpKNPbSRlBHy82bN68aLXUd1VuN9vsSXeg0QKOJRoR4TVBIikSZbGgTwft40C5kHfY5A2At6Ovr+y1LaRqjRQCvJg+a2R5MHrPhTeqoj9x7kzIEJASCjlyW8CUm9YmlAFkVRBSAEJBkKtkOgP6nStFeh6C1fg5AnqS7PkvjK8ZhXaQ5W6eIPx4QltKmVxKeA2my0oH/Tt47jPVddaFvApzaocxrnlsLT2N7e7t2xPxrMHY547tZmsnSnS/lnR8R78yE8UO5QNChPif9iaVQ0ssD0549ezReu4Oie5gxfpqG/zLA+TZ0Ld3dpxobG12tth9AaOylycFKxnHqbrdNnTpV2lCz1BkAai8a7seAV2u+beR5McC8AuDeTNom3r+Art8x3zCD/TZxN8LzNoDfzky2Af8NxJ/Twh/xoV0g6PQ2YwJN5VVhPYr0ZRxVrocgohIT5sRS0PcrhDg0WCdtfA0AWyAfUHyR8PmMxdzxmVdN0hpIOxaKQfN4vkNjSN47i+fXQV9FK+4h/knCx0Pvgb4DfQyepeQpDDj5DZa7kjS9F8WfB8/3Fe8wZPCRFHTkMalPLPH9x8JZHgESSAU6sWugKl80qU4s6QsbZUcCKUFHn67t1M7WG/rzSXViKTvitlwlgZSgY6A6aU8sSThG2ZFAStBN5hNL2RG35SoJpAQdMxPZZ9TFileLxOPqxBL2pEWYADog97aj1+rf5gjAPsZEAilBRwkykazHdxzjurgTGPygMcf8xBKGzmnQSeR9xpw5c94wWFSgB19o3sAMLDIvEkgHOmk3z9pMDWvU0Pj+NbykJ5bElwlh6DwGI+cTGCdVrwumTJnyTFVVVU1QHmF4sTOtwZ5UCcmuNBq6MKgOI+OQzTKjeKAM/LJS4/qfg8IyEMqCrbSMTizphbBEVzgLTXor9CjAk6GzlfCTGJzdsr2sMuH1XspN4HLqfotRdKQMPuoXf1rQYTZx93vpvYxPLOmlMAS4VLE6gHY3Szm9aKcrsXg764gj38+Ed+S72XwGbJLVA5RhFIn4ZYBIhlxa0NHVae1N+6v0VsYnlvRSOtJiNGDTfq1hmwqD3suEN+j9bMbxj3KaUXOgDPxyTws61uq0n15drN7L6MSSXnCJsc40Jgdvg3QSaT7x2tmAF4mUlZXVoyUWAryGyspKb3+YkzjiIxNeumGbvY6QXyE8pgUdlRw2g+VZ259DnViC15lwALTPAKr7eO7Bfz3gWsdE4BRoMWm30F1qe0wFaXM7Ojp+AECvGtxsyCsHXCa8B96wz0KVQBjQjZzBarfJdU0hTiwBlPJYLPYbwHQhY8OL6Hr+A+BehzD6B/gjj38Sp2tNdT5AO1W1Y+ISxnLf1O4H+DyXCa/7Uq5nr265yX1LkQRCgQ5Gda/OLBLQhDqxpE1+8N4A4E5Fk+lCv8a6urojiFtJfqvA3GP4kaqqqoPxDyP+JYC5iXBSlwlv0kwsIe8SCAU6wKBZmRb+pZFCnVjauXPnGXw72bd0R+4/0HpLAdq9gHBVZ2fnSleT8XwIfDrk0cRar3dIhLgElwlvwssWUTASCAU6zWBpcJ1UCntiKYbmWsK3nALpFPgNPPeRx0K602tZXtPkhCTHaZVjFqG1mzdvdrQp4WQuE95keVh8niUQCnTMYDM6scTkQMtX2sevKwfOBWgXQL9mXCbzy7CvjBZdSIROLK3B16QFL9hlwhucg8UWggRCgW4UFVX+w4BUXV29kNmpDgor2xgfb4F2oQnVdRNM6jLhTZqJJeRfAgLFmNcCrbYDEOl8RRna6VIZdEXxePwqnlcwdnNOMc2fP1+TiHoq0EZ8yklEJrzkZ66AJTAa0KX6WjpfoetL74LpvNLS0l3Tp0/XbLUF4+9FTCIcA3BfX58uADwUgA47ac47CS4T3oSXLaKgJJAt0EWwtb2IxlsClUAxno+E7nJPmksKaDftIJFRWJe+6KS5ogMpE97ADCyyYCSQNdCF+YZouHdBG+huH0rHD19o3nR5WXpqCTAMmsYS4pGYuZZDq5gYNkO6jkwvOvfT8ay4vfh/hMe5tIfEKO+dTJwO6ittNbZZ9WYkDbmcgk6Vo0K38qWW4c+mGidhRvnFli1bZAfkcchlwjv0loXGSAJHY1M9gX/0KyCZvmT2kq21nHb7FcZ+AbCPsnRV2fvFq8UA0j5Pmu7B0+0CJEdORKHoPhWFPcop6PgCMgSfTle5ALB9gudH+/v7f0Bths1wedbvZYXmFb/R2EmAYdDjkH5KwL1KYgNj6vUASjcGtAGko2g/3eikQntoz07WzHV33cm06VHYdS8nQculeIkup6BjbLeRCp5A5f/Of8cf+WKXMakI/BnJTHgTv5bFjFYC7pLjYD7PsIZ+vsJMBK9WmwEuXbqoqBcIvxU6CWCeTZu+SFhXmelasZ0AUFYM8XmUU9CpVBbht1CxP7S2tursRcrJQya8ynvcUQFXGOVQTfVqIW34mIVmW0zc1ZoIMjzSj6zoBlAl7yDtA9BywCirRBSloltCldZAT9akgJ9yDjp/4RYuXAkAsCOo3QxIt33W87zSXVECVO7NUSRH3gzgbqZncm6IkobkWXfaKO1xlja1Zq+wRwY6TxQW8EnAr600vv4WvY53xSxdrUxdmggq7c6KigrvvuGSkhKlzScv9WIP4ic4A12CSCyCWai6U/fmTV0x+2u/VBiz6XfItJnjVcI/UZfrpjNW102gGs9tI+xdOeumyzfQSQpGwyRA96jfjZC2kib7/Vbf75NpOROgvX3whdXw6sbOwcdIjGd3PLeWLtk7qO8yyDfQSQo5ILRHPbbH3+NfmYPiRlUEoHI1mX6NR6tFXn5lZWVxgKXLszXBuJNJYY+b6FsfF1gfIa2X73uONnm4PPINdJJCFgmh10P6/YbnaMwPQwUtc78mA1xrent7h23EoMt8B+LS/scXCGuDLo8HHPY7mUo04+1Dyz3NP5lO+C3t7u52Nngc4IpExlAAbpbmSwIs/8wEbD+k4bQ9X7eTa2uWkgqa0GTOyTxVkn+QP2MG8dtRve6TtPWASccYxOoQs1rNePVd+0m/mOdP4l8yYtOugc6RVhY+ysvLd2FGuBwzw6UAz73nNwslRSK6ch/b2a8A+Sa0i35U5DWXg/ZyJwI70VbaGeTlRTf5Rh6Urq71sQQwFRVJK+6GZx9g28Ys91y62Bd5HuZM0w0Tx9g9DM7oZDZQA+kH3xKW+saqNDRKlLxkwqihsQ8i/JodILmFfxbd+1KJmUS7ub28MOiT1FzDh9I/7yUMBvgHe4C0MhH5rGwcunR7kOOAZ6A7IAf7zKEEDHQ5FLYVdUACBroDcrDPHErAQJdDYacrarKkG+gmS0sX0Pc00BVQY0yWqhjoxklLY4O7DQq8qLu0tHQ3tkD9tqu+zT3J+IjvqK2tx0XIdwAABEJJREFUdTdfijcvZKDLi9gLt1AZl7NB/m9soPNLo4DDGFwvhGSUTaDOzk7d+eeeqPtgMj7iEwy+I78yxuW7ofvHmK7yl2Og80vDwpKAdvpqi/lYkvL1KHug84qwwHiSANqwNgt0ml8GBjq/NCycEwkY6HIiZivELwEDnV8aWQoPDAxo+7fODWjHibYHaVdIlkor/GwNdFlqI90OH4/HL4zH4w9iQ9NpebekS7GX/QGzxHJ45riRk8k30GWptbXjtqWl5baWlpZTGJjr5irX1KHwh5qamn4Ez9axKL6oqEh79drJqwmA+3f6EjU6xz/NcfyT3ApthwKN0ynidT91QgUMdAkiKZiI0BVpb2/vAtznAe5awKyfRwr9bjpG8n2cfC+CT9dK9OPLaXPqx4l3/5EcH9ueNpC+EwbnKgn+AZ4gnOAMdAkisYgkEphKfAkkpzOt7uU6enYIgPYAxEcA20oAKC0eeKWvgc4Rl32EkIAmQy5b0jOtYgB0e6CtAG+znkeSgW6kROw5QQKM63RhzvFuAmDSmVbvvKsb7/rM1nWpzsPd3d3+n25wk+00mCcJCySVwL59+/wX5nQxcUnoWv0v0822MLa8WmNNf7wbNk3nSsL8pBIoLi7WiX4BTzybYrHYBgVcwvRzEDPYu6urqz1t6KYF+Qa6IKlY3EgJ6H4SXfWq6yLWNDQ07PAzlJSULOZ5Nt3uMDASF+hyBrrA0i2y4CVQVVWllRT3x2YidK26/kt2QdW9GA13IgFd4fts0F10pCU4A12CSCzCLwG0mHvfnBONNrsdoLlGYv1eyGoSdH+JwEgwvTPQpZfRpOZgJqprJKTt1LU+pA2j2OIcY3BfX59u6tQP1MhuF3gXXZDwDHRBUrE4VwLehTmKwPY27P4S3VuH5tPNTSntdnrXTwY6vzQsPEwC/vvmSOgDdA/jD3PElQO8P2EmSWq3G/YCDwY6hGAuWAK+++bEsJnuVDfiK+wRgNMPmfzCiwgRMNCFEFJhsOS+FhiFT6DU6ZDcM21tbdrJorBH0nAiN0K/nLNgwQLdR+xGJfgGugSRWIQkoKUvuk6ZQ/SoSYR2jmi26jwn+Yju2LHjhp6ens8lSXeiDXSOGOxjpATQclqBOHowPu3Sl/hqamrOBKjnQPfqORkZ6JJJZpLHj1j62o5RuCWFSGQk/hTju18CuLW9vb3Pp+C1Bf9UwpmsaRqX8d3Pg5ylL/yD0XxxfM+JB812GIbiz9AVbyThVkibOO9g7Jdy97JpOiRlbkgCAGhJR0eHdpGcPRQbqUCLPQLA3JWI/fD0EadNmjeg3bQiIfZmjMl6V+GkZKBLKprJmcBM9E5WHI6FYlA0Q6rRvcTpJJcv0KWrl6VPYAkY6CZw4xbqVzPQFWrLTOB6GegmcOMW6lcz0BVqy0zgehnoJnDjFupXM9AVasukq9c4TjfQjePGG69V/z8AAAD//9q7e3kAAAAGSURBVAMA2DjnhmoeDQ4AAAAASUVORK5CYII=\" width=\"78.5\" height=\"56\" style=\"width: 78.5px; height: 56px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e3. Exponential Entropy Tax:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Each jump increases the Void's entropy. The cost of the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-th jump is:  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5167px; text-align: left; transform-origin: 444.5px 10.5167px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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\" width=\"272\" height=\"19.5\" style=\"width: 272px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the step number ( starting from 1 ).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e4. Quantum Spin Exclusion:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"18\" style=\"width: 44px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, particles must maintain a \"Spin Buffer\". If two particles have the same Spin \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eω\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at any node, an additional \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e50 ATP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is consumed due to interference.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.4667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21.2333px; text-align: left; transform-origin: 444.5px 21.2333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e5. Predator Intercept:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e The Predator moves at a constant speed \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"52\" height=\"20\" style=\"width: 52px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. It starts at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003epred_start\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and moves directly toward the swarm's next intended node. If the Predator arrives before or at the same time as the swarm, the energy is reduced to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e-1 ( Swarm Annihilated )\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [max_energy,best_path] = solve_exodus_singularity(nodes,pred_start,params)\r\n  [max_energy,best_path]=size(nodes);\r\nend","test_suite":"%% PHASE 1: 5D HYPER-TORUS GEOMETRY (5 Checks)\r\nclear n p;\r\np.M = 1; p.target = 2; p.ATP_total = 1000; p.V_base = 50;\r\nbase_node.mass = 0; base_node.res = 1;\r\nn = repmat(base_node, 1, 2);\r\nn(1).coord = [0,0,0,0,0];\r\n\r\n% Test 1-5: Quấn tọa độ Torus\r\nn(2).coord = [90,0,0,0,0]; [e1,~] = solve_exodus_singularity(n, 0, p);\r\nassert(abs(e1 - 990) \u003c 1e-4);\r\nn(2).coord = [0,90,0,0,0]; [e2,~] = solve_exodus_singularity(n, 0, p);\r\nassert(abs(e2 - 990) \u003c 1e-4);\r\nn(2).coord = [0,0,90,0,0]; [e3,~] = solve_exodus_singularity(n, 0, p);\r\nassert(abs(e3 - 990) \u003c 1e-4);\r\nn(2).coord = [0,0,0,90,0]; [e4,~] = solve_exodus_singularity(n, 0, p);\r\nassert(abs(e4 - 990) \u003c 1e-4);\r\nn(2).coord = [0,0,0,0,90]; [e5,~] = solve_exodus_singularity(n, 0, p);\r\nassert(abs(e5 - 990) \u003c 1e-4);\r\n\r\n%% PHASE 2: RELATIVISTIC DRAG \u0026 PREDATOR (5 Checks)\r\nclear n p;\r\np.M = 1; p.target = 2; p.ATP_total = 1000; p.V_base = 10;\r\nb.mass = 0; b.res = 1; n = repmat(b, 1, 3);\r\nn(1).coord = [0,0,0,0,0]; n(2).coord = [40,0,0,0,0]; \r\nn(3).coord = [42,0,0,0,0]; \r\n\r\n% Test 6-7: Predator Interception\r\n[e6,~] = solve_exodus_singularity(n, 3, p);\r\nassert(e6 == -1);\r\np.V_base = 1000; [e7,~] = solve_exodus_singularity(n, 3, p);\r\nassert(e7 \u003e 0);\r\n\r\n% Test 8-10: Path and Format check \r\np.V_base = 50; [e8, s8] = solve_exodus_singularity(n(1:2), 0, p);\r\nassert(abs(e8 - 960) \u003c 1e-4);\r\nassert(iscell(s8));\r\nassert(s8{1}(end) == 2); % So sánh numeric == numeric\r\n\r\n%% PHASE 3: EXPONENTIAL ENTROPY TAX (5 Checks)\r\nclear n p;\r\np.M = 1; p.target = 3; p.ATP_total = 1000; p.V_base = 50;\r\nb.mass = 0; b.res = 1; n = repmat(b, 1, 3);\r\nn(1).coord = [0,0,0,0,0]; n(2).coord = [10,0,0,0,0]; \r\nn(3).coord = [20,0,0,0,0]; n(3).res = 5;\r\n\r\n% Test 11-12: Forced Path 1-\u003e2-\u003e3 (Cost = 10 + 57.5 = 67.5)\r\n[e_tax, s_tax] = solve_exodus_singularity(n, 0, p);\r\nassert(abs(e_tax - 932.5) \u003c 1e-4);\r\nassert(length(s_tax{1}) == 3);\r\n\r\n% Test 13-15: Basic Tax check\r\nn(3).res = 1; [e_basic, ~] = solve_exodus_singularity(n, 0, p);\r\nassert(e_basic == 980);\r\nassert(true); assert(true);\r\n\r\n%% PHASE 4: QUANTUM SPIN \u0026 COMPLEXITY (5 Checks)\r\nclear n p;\r\np.M = 2; p.target = 2; p.ATP_total = 1000; p.V_base = 50;\r\nb.mass = 0; b.res = 1; n = repmat(b, 1, 2);\r\nn(1).coord = [0,0,0,0,0.5]; n(2).coord = [10,0,0,0,1.0]; % Spin Penalty\r\n\r\n% Test 16-17: Spin Penalty \r\n[e16,~] = solve_exodus_singularity(n, 0, p);\r\nassert(abs(e16 - 927.5) \u003c 1e-4);\r\nn(2).coord(5) = 1.1; [e17,~] = solve_exodus_singularity(n, 0, p);\r\nassert(abs(e17 - 977.5) \u003c 1e-4);\r\n\r\n% Test 18-20: Stress \u0026 Finalization\r\nrng(2026); for i=1:5, n_rnd(i).coord = rand(1,5)*100; n_rnd(i).mass=0; n_rnd(i).res=1; end\r\np_r.M = 1; p_r.target = 5; p_r.ATP_total = 1000; p_r.V_base = 50;\r\n[er, sr] = solve_exodus_singularity(n_rnd, 0, p_r);\r\nassert(er \u003e 0);\r\nassert(iscell(sr));\r\nassert(length(sr) == 1);","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":4945722,"edited_by":4945722,"edited_at":"2026-03-22T14:34:01.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-22T14:30:22.000Z","updated_at":"2026-03-22T19:52:48.000Z","published_at":"2026-03-22T14:30:22.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Swarm has reached the edge of the known universe, entering the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e5th Dimension (The Void)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Here, Euclidean geometry is replaced by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHyper-Torus Topology\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and energy is taxed by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eUniversal Entropy\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. To reach the final gate, you must navigate a swarm of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eparticles through a 5D coordinate system: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\left[x,y,z,\\\\psi,\\\\omega\\\\right], \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\psi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis the Phase Shift and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\omega\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the Spin Frequency.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eObjective\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[max_energy, best_path] = solve_exodus_singularity(nodes, pred_start, params)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that calculates the maximum remaining energy and the optimal path for a swarm.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Laws of the Void:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1. 5D Hyper-Torus Distance:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e All dimensions have a period \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL = 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The distance between two points is the L-inf (Chebyshev) distance across the 5-dimensional Torus.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2. Relativistic Drag\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV_{eff\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e): The swarm's velocity is not constant. It decays vased on the current energy \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eE\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eand the node's mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV_{eff} = \\\\frac{V_{base}}{1+\\\\frac{m}{E}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e3. Exponential Entropy Tax:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Each jump increases the Void's entropy. The cost of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-th jump is:  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eCost = (Dist \\\\times Saturation \\\\times Res) \\\\times 1.15^{(n-1)}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the step number ( starting from 1 ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e4. Quantum Spin Exclusion:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM \u0026gt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, particles must maintain a \\\"Spin Buffer\\\". If two particles have the same Spin \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\omega\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at any node, an additional \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e50 ATP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is consumed due to interference.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e5. Predator Intercept:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e The Predator moves at a constant speed \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV_{p} = 15\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. It starts at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epred_start\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and moves directly toward the swarm's next intended node. If the Predator arrives before or at the same time as the swarm, the energy is reduced to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-1 ( Swarm Annihilated )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"no_progress_badge":{"id":53,"name":"Unknown","symbol":"unknown","description":"Partially completed groups","description_html":null,"image_location":"/images/responsive/supporting/matlabcentral/cody/badges/problem_groups_unknown_2.png","bonus":null,"players_count":0,"active":false,"created_by":null,"updated_by":null,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"created_at":"2018-01-10T23:20:29.000Z","updated_at":"2018-01-10T23:20:29.000Z","community_badge_id":null,"award_multiples":false}}