{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":44391,"title":"For a rectangle, if x is the length and 2x is width. Then find out x from the area of the rectangle?","description":"For a rectangle, if x is the length and 2x is the width. Then find out x from the area of the rectangle?\r\n\r\nif the area is equal to 200 then the length of the rectangle is 10.","description_html":"\u003cp\u003eFor a rectangle, if x is the length and 2x is the width. Then find out x from the area of the rectangle?\u003c/p\u003e\u003cp\u003eif the area is equal to 200 then the length of the rectangle is 10.\u003c/p\u003e","function_template":"function y = length_of_rect(A)\r\n  y = A;\r\nend","test_suite":"%%\r\nA = 200;\r\ny_correct = 10;\r\nassert(isequal(length_of_rect(A),y_correct))\r\n\r\n%%\r\nA = 32;\r\ny_correct = 4;\r\nassert(isequal(length_of_rect(A),y_correct))\r\n\r\n%%\r\nA = 18;\r\ny_correct = 3;\r\nassert(isequal(length_of_rect(A),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":93545,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":109,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-10-26T09:21:07.000Z","updated_at":"2026-02-06T18:21:25.000Z","published_at":"2017-10-26T09:21:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a rectangle, if x is the length and 2x is the width. Then find out x from the area of the rectangle?\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\u003eif the area is equal to 200 then the length of the rectangle is 10.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44308,"title":"Component area","description":"Find the area of the component below, all measurements are in mm\r\n\r\n\u003c\u003chttps://image.ibb.co/hocruF/Component.png\u003e\u003e","description_html":"\u003cp\u003eFind the area of the component below, all measurements are in mm\u003c/p\u003e\u003cimg src = \"https://image.ibb.co/hocruF/Component.png\"\u003e","function_template":"function A = your_fcn_name(h,w,r)\r\n A = h,w,r;\r\nend","test_suite":"%%\r\nh = 50;\r\nw = 20;\r\nr = 12;\r\nA_correct = 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lvc5QE9Z7lqO8q8hYEQSh9XHHFFSmHZdS68KFWlsRrGviuV155JeWERo762c9+lpObxGd8KxvJ2zqs8eGxnrcyrAmCIJQ2hg4dmvLYZrbNLIkYoMq6pogbAAdlhYE1adIkLF++PAqd/ndlxXWXtMMabd5WbQLJWxAEQSgP8gYxUnhjeJiVaJnrvKalb37HkCFDUjZverkjJ8msWbNS/OWlcKCmw8SKgryxivJqc6x6JHULgiCUPoYNG5aa/yHV+vmfZFjTNm8C5I3FRFZI2pw5cxK7vP0t/M1caJS85I0H5W8OHNYEQRCE0sfvfve71PwPga5QPk9MbdqtW7eowqfETds3yPyRRx5JJPTayqYm8hYEQRBE3mtAu3btIlH7cDGQOBzsrFRdKAIXeQuCIAgib0PEe+65Z44jNc271157bbTLF3qBIfIWBEEQRN7hv2rzDz/8MCmW5W3eIPJTTjkl5xyRt8hbEARB5F1AqXbu3LkJcXu1OdK47r///pnSushb5C0IgiDyLgDwvSBv5lnPStTSpUuXxNs8KyZd5C0IgiCIvGsZAwcOzCnzaVuHDh1SoWy1EdMt8hYEQRBE3nkA+3X37t1zQsTw3ralS5dGArcx3SJvkbcgCILIuwAAKbdp0ybxMKed29q9Qd5IkUoUKqGYyFsQBEEQef9/TJkyJYe0/WuGiwGFUpmLvAVBEASR9/8wderURLq2Md5UoTOErFevXglxy+Yt8hYEQRB5F9hhbdSoUSlHNRC2JXFUFmMa1UJC5C0IgiCIvA0nHXzwwZHAbdEsSt6jR49OpG38TlYWE3mLvAVBEETeBcTChQtD48aNU6WqO3fuHKZPn57UE5fkLfIWBEEQeRdJkhZud9ppp9TvOuaYY3KOKySJi7wFQRAEkbfIW+QtCIIgiLxF3oIgCILIW+Qt8hYEQRBE3iJvkbcgCIIg8hZ5C4IgCCJvkbfIWxAEQRB5i7xF3oIgCILIW+Qt8hYEQRB5i7xF3oIgCILIW+Qt8hYEQRBE3iJvkbcgCILIW+Qt8hYEQRBE3iJvkbcgCIIg8hZ5i7wFQRBE3iJvkbcgCIIg8hZ5i7wFQRAEkbfIW+QtCIIgiLxF3oIgCILIW+Qt8hYEQRBE3iJvkbcgCIIg8hZ5C4IgCCJvkbfIWxAEQRB5i7xF3oIgCILIW+QtCIIgiLxF3iJvQRAEQeQt8hZ5C4IgCCJvkbcgCIIg8hZ5i7wFQRAEkbfIW+QtCIIgiLxF3oIgCILIW+Qt8hYEQRBE3iJvkbcgCIIg8hZ5C4IgCCJvkbfIWxAc/vOf/ySDEO3f//538hm3+Az45z//mRrg2I99/jM0Xo+fZe3jd/E1P+d38nu55X78Dv4+/ka+5/n2O7n1xwhCXSVv2885Rirbr+1YtOPxX//6VzLudthhh/D9738//OAHPxB5i7yFYsU//vGPnEH497//PW4xoLOOt7AknDWoOcHwWgsWLAjvvfdemD9/fvj444/j6w8++CC2Dz/8MMydOze8++67mb+VRJ61AOFiIuv/ZE14glCXJW8sYjGmcE6+sZqPvHns3/72t8yxDMn7Rz/6UfxNIHCRt8hbKDJQ6s03GCnlcmDbCYIEz30gTRyPyQTbqVOnhr59+4aTTz45nH322eGss84KZ555ZmjRokWqz3N1bxsmjpNOOimcfvrpoXfv3qFPnz7hjDPOCIMHD47fi+9avXp1HEMEfxsXF/a/4Pd4TYIg1FXytqSL49HnMcY+//zzuC9fo3SNMYRF86BBg8KqVaviZxxLeN2kSZPU+BR5i7yFIiRvT35WlWaPsSpr+/mtt94aRo4cGbp27ZoQr+3TUL/ZrW3rrbdeSj1nj8F1fvjDH8atJfj1118/2X/iiSeGESNGhGHDhoUJEybkqPzxn7ykLbW5UAqSN/tyjx49csZbvmaP4ZjCOMLCmgtfkPeOO+4Y92H8SW0u8haKGH4l7wmd2+eeey48+uijkah33nnn0LBhw0wJesMNN8whaB6DCcFL2zjGXse+t5/bc/33oTVu3Dhss802UaJ48sknc/4ntQeSvoW6Tt5YSENq3nfffZOxQLLN1+rVq5fz2UYbbRT233//8O233ybjH+PIjkGRt8hbKFKQnGkPo3Pa0qVLw4wZM0LPnj3jAN9iiy1SkwQmjY033jglNXspOUstbiUAa1vzZM59mGC8Wp3H20mGUjm2OKZdu3ahU6dO4YknnghvvPFGWLZsWaVtg4JQrOTNPgytl9doYVzka3582e0JJ5wQTVHQVMFhjdfC9UXeIm+hyOCduDApYABfc8014bTTTgt77rlnihxB2htssEGmtI3XJE8cB0l4k002CZtttlnYfPPNY9tyyy3DeeedF+66664wceLEMH78+Nhuv/32qPbG9o477ghjx46NE8imm24a6tevHxcIWDjgWlmSt5cqshYS+E1t27aNE97KlSv18IU6S94Yr8uXLw9NmzaN53FMrknytloxHmsX4kcccUQc/3JYE3kLtUjCVhVMuzVtvjZcih6laF9++WWYNWtWGDVqVLj00kvDgQceGEmSK24MbGuzZoNNbO+99w577bVXdCb77W9/G6644oqoVkebNm1a+PTTT3PCUqoKno/Jbfr06bE988wz4cILLwwXXXRROP/886NmYPfddw+tW7dO2fSsNMLXmMDwX0855ZS4UIFz3eLFi1MhcPY+2pA6H94mCDVB3j6Mk30OzmZYgFqiBtFiYXzJJZckYzCroZ9j7GD7wAMPRK2UlbDxGuMH5jBcXzZvkbdQC/DOWn5gWXUxwrHgyQ2ixsDnajyfTRoSb/v27cOQIUPCzJkzw9dffx2vk+WNbhcR1st7XeBt1Pgev2Cx9+HNN98M55xzTlSbwzafpW73NvftttsuLghmz56d+m82ztySul9YCEJ1kndW32ZoGBzM0JdJuI0aNYqhl5UhU/Rrm0MBi3b7G6DtsgsDSd4ib6EGYW3WBEOmGNKFfZAuoa6GWsyTmLdVg8xAfDfddFN49tlnUwRtv4vfU1EClJpwEON35QtfI/kirvy+++4Lv/zlL6NEQTMAVfz+v2+99dZxYYMFyjfffJP5v0nYWUltBKE6yNtvbb+Ho5pdeF577bU5MdtZ4Fi1WiP0W6rdMQ6w4KU6nosDkbfIW6gF2CQqJE0kQIGKGWplHyri7V4///nPwy233JL0UTtIMdBBinRos7GhVgrnMdU5yH3GNU+WVlL2sd72N99///2pWHP73324Gmzko0ePrtQiRCp0oTrJ2/YruzDGdsmSJSnp+LLLLlurPuhV89C8sd//9Kc/TbRVyrAm8hZqAStWrEgROAYWPKyPP/74qGLDCt0SFF7TKQX7YANGeBWkV0/GTAThB6slUOzj6j9LCl0XL++sc20suv09Vs3tpXESOY7D+EPily5dumQuaCCN8P2xxx6b0jBwS58CSd1CTZF3Vp+HZshHWLz44oupNMNZjf2f4wnhYd26dUstBKxDqtTmIm+hlmAHKVRp8Pb2qmGGXZGwYcd+6623oveqJ16f2tQStM9alkVgJLh1HeTWSSyL0LM0BDZBC0ndLkhI6pBipkyZEqVsSuJc1HDRA2KHc97kyZNj+JyXxPFdCkETqpO8sxanxLx581JjGn0U/itPP/10pbRXNKEdd9xxOfZt9PMGDRrEz7kwEHmLvIUaBOOz4bjSvXv3uILmwPSr6ZYtW0bC8oToVdN2X1ZOczvJ+BW+LzSyrosST9T8PEs975328k2IltwxmWEyRWpI3C97z6wqHTbBSZMmxcVOPhW+IFSX5O2L+lDLhogPOJdZ0w/8NX71q1/lbYceemg4+OCD4+v99tsvc2F/+OGHh2bNmqWcPEXeIm+hkpKzD0eykq0lDDaoxxHyhMxnDPuwsc4Y1Ng3fPjweCykTdlo8wMFUhBz3qtXr7jQ8Uku8Hr77bcPhx12WAy1s5XOrDMQtQ6610JVyTsLTGP6+OOPx7Ht+2bW1i9EGQZKcxHMR3BMxXXpsCabt8hbWEsCt5IcPZ0tiXM/Yql32WWXqDbzjlfYIsnK9ddfHz2nrVpXKt7KazMwTpE/PZ+HOsLoEJYGNbyV8LM83wWhOsibQB+zuc19mKdNsGQX8zauGw3qc2t6wsLUZkAUeYu8hUoQd5YknrUPalvEXmcV7UBDNa8///nPqXOrUv+3XJ+Dz/cOe2LHjh2japEpYS2Jw38AyWmYI5qkrfssVDd528X9gAEDwq677hoJF17irVq1iolW9thjj/ga+xBdgS0+gyYJDYt+qN132223cPnllycSPa5NgUC5zUXeQhXI23p3U9qm3RnhTsiOZO2yJG4MOqhzv/vuuwq/S8U5Kjc5ei3FU089FcPpbN52bPEsIKnAZoixTclbUrdQE5I3HUZ5PMJB6UxpnUmzcj/gM2jjkKbYm3ZwrrV5i7xF3sJaEHiWYxXjO5GG1PcbEveRRx4ZXnnllURqxJb2MUtKUpuvGfYeeQLGJIuUrHQYoge/1YKA5Hm/vbOfIKwreVvyxDh/5513Eq0P+htMajYKgnMAFvVZ0Ru8DvahMh+d1aQ2F3kLazEYrZc2yRcx2D/+8Y9z6l2DMJAxDY5olmSyCNpmW5OH9JqfA7Ud9rlYD3VkYEOIma2ORt8DJL5ADmlBqG7yZoIkbBHfjQyCyG3eoUOHcM8990RHS3iUw4yTldbXk/bdd98d24MPPhief/75qIK3lfxE3iJvoZLSnk91iAEKgrCZkOh4guxKyFVOoCpQ1sCyCwLZYdcMH+9uF0N2Mvzoo4+ijdGXLMUW4TyQiHS/heomb/ZDJBCifdpqftAHYfP24GLURrNgXuGiE6GQVJuzH4u8Rd7C/+CLA9jwMCvZwYY1dOjQqMZiSAcbnNUefvhh2a4LQOokcpvRDZoRVFdD/nTr0Yst4muxH/XEbYifwshE3lUlb5AwJGWU2rWV/2wYGKTnk046KYY+WhU7BQXONdZ35mc/+1mqmI/IW+QtGOImafuEI/Y1vMWRIc2Gf+A1nKVQXKTQA6hckZV4xtq0YVPE8+Hzsl678OyFpC4buLAu5P3VV1+Fxo0bp7IBVtQQHYEMbDNmzMjULtlriLxF3kIFkpvdAswnDqDGNiS4rMQKyENMpxSsoEXchV2AUYKhJGRx4403xgQatH9zAQZV+ssvvyzzhVBl8kbJW88d8HuBk+Tbb78d/vSnP0UbOPtcvXr14nbChAk5C0/AhpiKvEXeQiWktyzbNjzGWVfb2q/GjRsXFi1alBAGFwAKRSoM8pkrbEU1VCTLqh2O54tsVvL6F3lXhbyRFMjat+vXrx8dVq1gAHOb1fqgHXTQQan5g1s714i8Rd5CBfBSGiRvJFSBvTQrWxKqCPkBk1XlS6i9hZd1/GFeeatRYXa2kSNHxsUXpG871mH+4LMXRN5rQ97whbHzBNIeczHJuQVx31wskpyfe+65HOJGv7We5SJvkbdQSXDS79u3b0LW1oEEYR+U0O1ET+c2OawVVuL20jMmYL9Ig2MhHIusDRJbZMfSAkzkvbbkjcIkdo5ACmTbN3ENkrfV+EA6Z5+1+fdtxkCRt8hbyIOsRCkvvfRSYpeyoWBnnnlmWLly5Rold6H2pW9bJtUnwrCJcbgFgW+11VYpiYkELoi814a84RRp+xDTm9osaXCM9DW6p0+fnlr487Uc1kTegiFom93I2qI42eP1Z599Fvr16xeLW5C0sQo+99xz42SPQVgd9bCF4iD8BQsWhAceeCA0b948ZbNELunzzjsvfPHFF6kKckqkI/LOAtTmtiLYVVddlZOMBeFhPnQM2RdtjDfnI2sbF3mLvIX/SWDWFmpVVfAKhSqVkzgGFzyR8TmPoVpcjk2lo3GhWh0V33zZRiziZs+enSzaBJF3FpAvwPYb2Lyt4yrmHas253FIrczjqNFDP1Oct8hbMM/Wg6FBGCxYAcND1OYmx8Q9c+bMTIlLkndpSN5W1T558uQ4qUJlSckHElKDBg2iBJ6Ve1oQeQPQzFm1OZI4vfbaa6kEQmPGjMkx0YCkoWL3/Upqc5G3YMDKPnZFjEGDGN8mTZokq2FO3IjtJqzTk5zSSovA2R/ghIjUlln1lwcNGqSbJfLOC2jnfDpU5CO3SViQo9zut4ICTDfQ8EBYmDNnTioSQuQt8i77SdoWt6DUNX/+/JgZyTqSQF2OZB5IzmIHhHV4EnnXfdhIAaZHBVC+1XqgQ0pCbXC7gBNE3hZI1AQNjSfnbbfdNrz++uuJwxoyNOIYa9PGa8w5NrbbNpG3yLvsYW2WnKjhnMakKxx4WDFjFWxjhj1pS21eGgs6q5VhxTjg6KOPTmXTQ9/o37+/HNZE3nmBYwcOHJgiYswrML9BmqbQ8NBDD6VU5zbVMvPvi7xF3oIja9vBX3311Shp29UyBgmqTtlzqFYthkEiVC+ypGk8W3zes2fPVG12bM866yzdNJF3XiBaBU6unkcOOOCAlHPsXXfdlUrE4vOhK8OayLvsCJoe4b4aGDs2PcXhDYo4bhsOBskKqnKeKymrvPsSbOCoywwvdErgaMjEhvhc9hHb54TyJG9bXx5FShBmiPkFWjxk9IM3ui35CTz++OOhc+fOUYDo1KlTTMP861//OrYePXrE99hedNFFkbxtpTKRt8i7JKVrn1vcltoDkIfYJkpo1KhRmDVrVrKfqlORd/nC+jTgNaqPUSJCv2nRokW0YaJv8VifF18oL8mbzrCcN1CsZMmSJTn9yb9H8RLvV2NzUuAzSt6cs0TeIu+Sg7Vr+8kUgwoZ0qyaCirzU089NSF9uwCQU5oIHJMhHNuQ7tLG3qI1a9YsErgkbpF3FnliDmH/sc6yPM4me8qXBIgaHUbDUJ0u8hZ5l6z0DdCbmCtiFBrxDiFt27aNkraN9826llB+sN7oSLDBXOi2/7Rs2VKlREXemQt9n9THm1bs/GLP9/USAJC3tYeLvEXeJQmfTAOv586dm6g+Wc8Z2wcffDDHaUlSt+DzpKM/TJs2LRU+RhJnLK8ysJW35A1NH+cNmu7AKcwlkEXc6DM009n6CD7XuXWCQ2iZyFvkXXKknfVMMaB86A/VTz58TLHcQr6+hf7x9NNP59R2P+SQQ0TeIu8c6ZpknEXaXlvjy4fa8sLY7rTTTknIotTmIu+ShVd3o0KYj+XecsstY8ajiryENRlL+vY2SgChOza8EEl+4GEslC95r8l2bQk6q/qdPd463DKiYbvttpPDmsi79CUkW3hk1apVoX379olzGlavsFMiJarCe4SqzhOY5On0iD61xx57xEQcNszQSlfqZ+UheVf3XGYlb8V5i7zLChdffHFim4StqEOHDmH16tV5pXRBqAywQLz11ltTWbJgD0fYj5WurOQuiLxF3iJvYQ3A5Ilk//554jOb6UgQqgpI1ieeeGLKea1Lly5h+fLlWhSKvEXeIm9hbTo7Cfnrr7+OmbAwqUK9idSWl1xySXIMPcx9QhdBWBNsCOI333yTskeiryEjFsCJX1K3yFvkLfIWKiENYVI97bTTkgkVKk3YJBcuXJg5OAShKqB0DW9zWyUKzpDz5s1L+qMWiSJvkbfIW6gAlLqRlhAJNRjLDbXmlClTEmciJWIR1nWBSFJm+Bjt3iRx5LbGfKL+JfIWeYu8hUpKQ6wGZWsxZ3VqxXEL1YHFixfHus123oCZ5t577439zibfEETeIm+Rd1mCNkQ2EDCzF0HyRjIWhoQxmcYTTzyhG1eARRS3fFZW62FtwbYKHEP9ssKtCtXPbHYs/x9opkGFKBaPQL9Da9CgQUzJK/OMyFvkLfIWKZi0gl6KRvEIK3FjAj388MM1edYyaN+1hWEwtrzGg4T9yiuvhMsuuyymHyXoFFYoW7Gt4W4z7/mFBz5fsWJF/A82/zTbwIED1SFE3iJvkbfgOzcmT6glv/vuu9CmTZsknhtbFLt/9dVXdaMKtMgiAVJtjAUXSNmWOkRr3rx5EmYFssOz5PGFXnj5RYSVvPHZww8/HLp27Zqq943+xwxs++67b2rhIoi8Rd4i77IFJlSvTr399ttTHr9ohx12WEE7dDkvqkhY1JRQCrfP4tlnnw2/+tWvktS1fH54vdlmm4XWrVsXdPK0/8FOpOPHjw99+vQJm2yySSrHuX3N/wIy/+STT5RTQOQt8hZ5C1mS0RlnnJHYGzGJIjQMMbiKsy2s9M3nY9XMU6dODZ07d44ZySitMskJ/RVIfoMHDy6IxzZ/L34/vh9hhiBtVKbLImwQOR3V7PyB/9O7d2/1QZG3yFvkLfhOCqlu1113TdVaHjt2bHKcwnVqn7TtFlInFlLdu3cPhx56aJLMxI81G2pFYsQ5hXh++E70q88//zzccMMNcTGI32N/H/4Dml14cF+9evWS/li/fv3wpz/9SR1D5C3yFnmXN6zNFHjxxRejxENC2HvvvcOSJUsSL2FJPbU/6XgCf+aZZ1JhVJYAPfF5MkTcfm0DWdKOPfbYnN9ky8nma1dffXWUtm3aVLwXRN4ib5G3EP7rCAVyaNWqVTJJIrsVPH+tnVKSd81IptZrnCFTfiLhvR8+fHhCZnxWO+ywQzjiiCPCc889F8/HouzTTz+NBT8aNWqUOpYx0z7sbF0mK6vKR0Pe+x133DH1vXYRwS33WRLffvvtwwknnBA++uij+NuWLVsWtQw8ByaCW265JXVf2LS4FHmLvEXeZSF120n7xhtvTCZUeJdfd911ybG0two1A+uJDRVzVvlLeprDJ4FEBtJDZMBnn32WLAR4Dh3bDjjggBRp9ujRI1kI8HvXNsmOJ3v+Nl6HznNUjVsVOX0p+BlU/2j4DHbwlStXJqRMzRBU7uiTrMGMc5Fz3y5ABJG3yFvkXVZSH7B06dLYqaF6xeS66aabJvt8Yg2h+hdRWZoQe7/5Hs8BErYdV+PGjUvOI3lyi/NYgx0NzxgSOYD67F5qXhvirmiig3ScZYf3an1rrwc5T5w4MXVPbH/bf//9U9c7//zzk2MZfiZPdJG3yFvkXTbABD9mzJjEfgrJG97AfvK0JC7UzCKKanOA1drsfuxjDD6J7913303FgtuF1kMPPRTJkouyIUOG5CzASHhrSuLiM/L5vmBV8HB6pGRtSdva6KkqxxYpUV977bXUooL/l9ccOnRoKmkQ6sl/++23qd+i/inyFnmLvEsenKzhvQxCsCU/UXyEJGLLNgo1h1NOOSWcffbZMRXo+++/n6SpZYgVyYze12iwDdsQMhzPYz/44IMwYMCA1Bj0ntokysqYRfKRtl8IwFYNaZ+k7R3prOSN11Cxw1HSLyC4qGAyGhxD8qat/LHHHkuOtf9dEHmLvEXeJQ10UMQKW2moRYsWedXkkmyqHyAd5IxnfDPIDl7+WUACHUt+sH/7Yh1IZNK/f//QrFmzHGcweptbkqys2jzr2duUpx9++GEYNGhQdFTL8oa3mh2+x+ICtnn/3Vb9zX3vvfdeTvKWo446KvERkMpc5C3yFnmXFXmj89JhCM/p5JNPTkljPhe1UP1A6k+bFa1jx46JytiS2ezZs0OnTp2SY+FdbqVoEOg222yTPEsSJt7jNdTmhLWjV+XZUsWP34aynfB4t8lh8oV/Yf8WW2wR68R7qd72NUvGNNn8+Mc/Tknz8EyHpM9j1T9F3iJvkXfJkLMNpfET5dtvvx223nrrJKkHJnlId0LV77W3C/uqXvY4hlbRCc1mGaOK28d54zxIoSBuXhehWbAB+7huXA+OYEiPCqnbh/3Z3+RD1Ljf9h0b0oaUrFjoQcK3sds0vxx//PHRBGA/Rzv44IOjg+SaVNxZ9xH59amhsKl7KXmrNK3IW+Qt8i4pWC9k63gGFeeGG26YUm0irlaoGrwKm5JpvgUVALst7Ng+uQrMFyiDyWtS1e0JCu9BYN4JDFLpmWeeGYme5Tj5e7LU0oQtK0rti7W7Qy3/k5/8JH4HHeGslN+4ceNw5513xuPhPY5QtbZt24af//znMfwQIV5esq7M5EuChpRv851vvvnmYe7cuSkHP0HkLfIWeddpZBEHAZL26k0kw9AkWDVkkSvuN+6nJ2Dug70W6WdZM92rnc8666ycyYfSsL0WUp8yBhqSNmzJIO2KHNG4gEBctQ1NyzeBgXSHDRsWdt9995yiIfjN+F6Eb82bNy+nipmtHrau9xfaIu+xjmRCUpmLvEXeIu+SAjuhJXJM1r/97W8T2yG3SGUpx5/qu+fXXHNNtFHfdNNNkXwsmfI+o066lbpBSFaCRly2leitupnfg0UXSXSXXXZJHWPVyVgsWF8GXBtS9P3335+XbPHdl19+ebSl2/FM4obWAMlVvvjiixyC9vW7+Xsq6xXuHdFw3urVq6MUb38D5hZfHU8QeYu8Rd51Gj5xByZXtAMPPDBH1Sqpe937PUmGzmPs/1gYIaEKpERsea+REMc+B1ugAw2OXdaZi+THyeXpp5+OUi+Pp7ROyZrk55/tb37zm0RaR0O1L5udDa/xH1AMxBI246zxHolT7rjjjiSbG7degrfhbN6Gv6YJ12eNw+tzzjknlejFOr8JIm+Rt8i7JCTALEkayS1s2A3s3pDEveQkVB4kI9hfMXFBArb9n/cbntaQVuH5DXs3Snq2a9cukbjhvEbCpF155syZCXlb0rv77rvjZEQSBqk+9dRTeROxfPXVV+G+++6LSVSsUxu2p59+euochBDutddemR7jWFxARf7dd9+lnNh837O2cu/0Vtn7aRciBHwBrPf6fvvtl3OMIPIWeYu8S4ZcKPk8//zzOWkrb775Zt2kdQCkwgsvvDA6mnkJ2mo3+Bqe2AS8rx9++OEoQSK5yi9+8YvElAFpF4QOdbF13MIiC3ZoxlXzunAWs8lUcBzG41133RU90rMSpmALpzJka4OtHDZ0LOjs77cFa5BQhslT7OKAr+3El0WoNgxuTVojT/r00N9qq62Se4R7KUdLkbfIW+RdcoTtJ9LRo0ennKPgIbx48WKV/awEbBEO3CuEbJ166qnRkcs6m5EYIVWT0G0ZTNxzqKpJeCQqvEaGO+/EBgK3oVNUn48aNSpK0rw2Qv8YFoZyrrgWyJgLBxvWxckLdbYx2cI+b8ma19xnn33CBRdcENOtLlq0qOBSLu4VFiM2CcykSZNS4XR2ElafLm/ytrnyt9tuu2TRh76NcrX5QihF3iLvggPSl7V5QkVqHdVgt/S1vYX8K3hInah0BbKzCW5YJQtkC3v3bbfdlkjlUPVedtllqbAqSLE0V3BhQO0IUp/aED5IwigH6p8RznnnnXdSYw2S6LnnnhvLgVJ6t05xaEhL+vjjj4cTTzwx0xENW0x0WOjxvzPUbE2SdW0B4XBc3HgJSgQu8rbPn2WPYc6yiz4sin0/LmSfFnkLKSnFvkZHRlpJ+2yQnpMkI2/zijUZwMsvvxxTmFpJlg1qbCQvmTNnTsrbGpMHXiP22tqzoYLOmmyQ35zJc3jtJk2aJIswXIuOYFCpQ4LA8Z6kbeUuLBaQvQ2/H+rxgw46KLPyFxq0BS+88ELK6c33q0JNxnwOsHXzXiLe++OPPxZZi7zz9hdsmzZtmvpdRx99dKY/hiRvkXdRAhIZPZSh7oUUSU9poXJqOEp9JGGQLCRepDDNIjdODIMHD06preH1TYCEOXHgO2z5T6qw33jjjUztCLKPWfK2BUxY5vUPf/hD+PLLL6Nt3dbWthI3HOrgDc+oBDsBZk1ohdLU4LfB+Y73Ec/gpZdeUucUeVdI4tAmWR8RZAK05J5lehF5i7wLInXbjskOaUOYECPM/czCJeQf/CS0e++9NzUJQAr0BM/JgOfAy9+SKjzNfVY2KylA8oW0bL+HYVHWWYzPFalH/bjDeVDvo+QmCpnwc/s7SOSQ3lm8hGFf/vfx/xSDZzfI2zoGIq4+S4shiLypjYHDmlWbw9ySlVu/UBB5C5mEA8DRh0SACRuOSFmJXIQ131OEUtmCIo8++miK+HzRj2nTpqXU2bCBAygqYut42/Pgj2CJGLnEuW/BggVxP0LA8OyuvfbaRJrG79p5551jOlHElkMrwDhtkh20L3gN6WPWrFmpdKh2wrMLCj8hFqLP2O/86U9/mtwbJJzxdedF3iJvAubBhg0bpsYgFt2YE2Gmsn28UEQu8hZypCaqcSdMmJByToLt03ZWxcpWvHq39weZyaxXOKqDMdOYvaeQuOGpzYmDVb6gwrZquiynQdRbRxiXjcmHh/nQoUOTMLHrr78+Hgvpmr8FFbjgkIYGz/YspzRKHrYqV5bjji9qQymlkJMxtUrInc6FKDK9wfSQVfJUKG/yxkJ3s802S/qKHQNoF198cU5CK5G3yLugEqKV4vC+ZcuWiXQGskGMMdWgUplXnsCxhcQMr20b0gUywaIJMdiQtBH7jVAuH1cNr/T58+enSJFqdi+xv/jii9HGbkO47NiCah32Xkj848ePj2QOp0SQu3diw6Kha9euMeUpJHKcU9cWbFbFybA6apMmT56cWohWpDkQyoO84ciIbIBZyYY4llCtDhK41ziJvEXeBZ/sAEzUcEii9IdUmj7Bhgg8P6ydmdIdyMP3dRC6LeDhG9R1qASWVXWM17dk88gjj8RYaxCvJW7arbHFs4QKnSUzWSzELhq6desWXn/99VTYYF02meA32zA5SFP9+vVLEbf6s8gbkR8wIWVJ3AzvxLhCrgsKMoVa7Im8hQSQAtHQKSGV2ZhklGikmqgYVEZ1Afb+4J4isxcXRCBlG5plG51kcP9h64Z3uCdQP2FA1de+ffvoKW7zkJOott122+jAhkpb/fv3j8fx+620jfAYfJ9dnNnvrIupRW2ufi6U8J+ReY0lUO09Vb8uX/JGH4BzKMeEH0tsNkufJG+Rd1EBxTGszWfFihXxc1vtSjbCyknflhgg7dlFEaVj3GNb89omQGnTpk245ZZboo38s88+yyEmXBshW/nithEvjvzjSHVLL3O7cKDk3bp165hv3cab2/9SV5+3NTEg5p7/G6FAfoGVtTASyoe8gUMOOSQzysL6kmA+ZKneQkHkLaSIgJPZpZdemiKXrBzTklAqJ3Vbz2xU30LsvFXJWTL3TmJ+PwgHXv8IDaNKm6RDZzP6KSAZyZgxY2I1MSZZsTnIbRgM7NqffPJJMmlaqdtK3t5Du9jhi+eAvPm/IXkDrKMuU5DIG/3F5kzggpjjBn0Hmdfgw+LHt8hb5F1QYNDACxc2TxIJ2sqVK5POLbX52hO4lcSR49zbouEkY8mUhM0UqmhezY59PXv2jKSLa8NbnB7tUA/DeQ1Su1eN83ugOkd4GCYfW0bUS6GloGHhBAv/AXsPRowYkZLQcZw0SuUteaMyHxMqZUneGKtZ2jWRt8i7ILBSNUKObMcdMGBAQuxZWyH//bT31eY7R+pRS9bw+IbKGt6uffr0idXCvKe4JXVK53iPawHLly8PvXv3Dvfcc0+cgJBUx0oM9jqIeYad3EcYeLLOel2X1Mq+ahrKq1qpChomzkPq0yJvLGIxLvKlAsZ4O/DAA3PGjchb5F3QSY5qQ3hS2phkZqPi5E71uia6qt9rEDW8WrFIwoSw8cYbx+QnVm0NFTvIHAU/oAmBLQ6qcGYKQ4P0jYQSeC6wiSOmGyFoCAlj5TI2VBE78sgjk9Sn5fD8/OQ6aNCglL/BlVdemeRkl9e5yBvfi3FUv379lLqc2i80pCm2YaByWBN5Fxx0vkB5SKpVsR05cmSM8fZQlrV1wwMPPJByUoMjDMja2pUtmfA1PF2h7obtG/HZiBGHlO1t2VZ7YuNS6b9QKFtdISXwsWPHJosf3neahNSfRd7sA6xnzzFlsw1eddVV8Rg6dMrmLfIuOChNwyOazwISoQ2L4HGlYgstBKwT1bBhw1JqOVs5jBOJzxlu7ztKttp4bbuFVI7roZiMzYzmf0M5EDe306dPTxY1ND1YO3c5LWhE3vmBXAlZ9m6MLWgiOZ4K2V9E3kLOJMe6zeioiEumOt13VJH3uoHZ1eBBThU3CsHMmDEjk1ytqQKqPai/EeJFsraSNjzPb7755tRCwKuDy4GofPpTZIrzPgSQvG0oXFYBGKF8yBuCCUIqvc8J3yPsshg0NSJvIacj9ujRI3GMQo5f26lF2tW3SCIuueSS1ETRq1ev5DiSCokX8aUg7T333DMlDdhwMti7aT/PF/5ULrHM1skOrxHrbr31sbVkXU4aCZF3/nlw4MCBqTFFUxTGGmo8ZOUHEHmLvAsupZx66qnJs4BK1g8kOq2JxKsO3D/eb+QthzMZCRylCJGa1BMQbG2o+EUpmylN2VBgBP4JFUUF8DvLzSmLfgSIj7elQWnztpnjlKSlvCVvEDiiEHx4Jh3WkGaXUJIWkXfRSCiY1I877riEICB5k6iLYbVZKsTNe877jnKDLMPps38tXLgw1s/2qnE2lLdEOluEivG6lDQ9IVntSTmQlF+kIPbdFprA/QR52/uhRWl5kzc0MUxSZUMymdgH49GOpbItCYoHRZsdPfoQvlFIF/xyBMNlcM9PPvnkRDJBaJJQ/Qslr86lLRYe54gjRUgTnNlQRAREzudB0oEaD2UtMVZstiche1FKdShC5OCEaatE3XrrrSltkuadwpA3538IdHax6Su/1WR+fV4fjo2+ohgaSu76fAf5KtLVdD8qOHlD7eBLEQ4fPlzqqwJMchgkSNDSokWLZDBBqhNq5l6jf1PthtdXXHFFlJ5RR71Vq1Y5aVM5RrC4evnll3MWAkIuWPnJ3ntIT3a+wf202iSFjNUuoGm15G0r2VGy5XjhM6rJPo9rw2nUpyvGghnzoc1pbqXufMmNSlrythMUVsVwxZdatjCABGhTAyKph1D98ASBiQkS4A477BAnC+tBzsVts2bNwtVXX51kA+N5WuSuWavECRXzCsibKnPcY2g3FPpYOCCxEPs65h5L0HQmtH2cWsKa1NQgiRL8ULyJCg6PXl1uNQMc27XhP1Fw8ka4il/hwClnjz32iPmZ1Wqn7brrrjEPNgjCOmccf/zxml2qGb7UJiYrlOnMiinFFuFjkE4WLVqUTAZa3K69BM573rBhw1SFKPh1wASBOQeFS1q2bKk5oRYb5nvrzY1FrCU+St0cN9BKYa6qid+y1157xb6ACns2QQv7C+ZHHIM+ghTDOBYN0R/oO9iWjeQN9YOPo8v3Xq3mmlUjshgGXiNsTKg5aRArfJTshFe/D/nis3j22WczJwRew0riQu59tvcNBACy9rHx1lnQ54FXq9156I9//GOOVMuwR0jitfU7PP+wf/h9Pvd5beUJKEpvcz+BqdVOsx2Sz+CYY44RA9SQFAjAs5/xxtb3A5917tw5VgrzUrtV00llvnb3GwB5Z3nuo8/7muhqtdPsnH/99den+jXI0DqEwbRaU78Dmhgb220J2+YG4G+wY5akbiN3atITvWjU5llSh1phBhAlD7w/+uijNfvXIFAeFBOBJRJoO/C5t9dmhZjVtF2t1Igb9xBJbHzsrs117uupq9WuAAHJm8/KRwtgW1tzYT6HUQo5WfvRaqv6XsHJGw/jjjvuiIUTJk2aFO6+++5ki8/Uaq/hOaCcJLZ33nln3CIuVqgZlTkTh1x33XXR3nbxxRfHtKf0trV2PjlTVR0M/2Eo5E033RSz1CGhzQ033BDGjBkT5xz0ebRCjD187+233x7Hn/0dGINonBM5NrmP5/P3Y4trYGvHs/0eO955TTvmC/HfseVv/eCDD3JMHrR7A7hPxcYP+D34H9ja312T47bg5M2VsV0hewlDreabB+02Ko9Y82YjPzll2WqFdZtfKjOZ+ljv2mx2nPE1fru1nzIXfb7a415K9RoHKzAxba4lx0LNufY3cqFlf68dF/xvthxnMc2feM3n4/9HyZE3H4it6iM1YGGlQTvxiUBqRhJcvXp1zqTL52BDTSR1V989t+Rkq6wV2/1lH6DpxC9C+PtxHO3BeD1v3rzw6quv5sQg41wkHbHEb00xJPNCmWBsgZx8GQAtCRZzQR272Cr5JC02Zi9rFaZW+5J3lhZEqH5YaTtrQrJpToXqIW+fw9wvkkhmtT3+7OIZOeybNm0aIxC23377MGLEiMysXnYOfeaZZ2JcMnwnUOMdWfnQcH6jRo1iHnxcE5n7shbpnjgLNff4xYN/Vja8sljnUCYGKnnytisWq6oVaRRGA8JnoVSRNbtgtWpKZo7yE5ec0qqvT3vy9vNLMfR1StTMq82GUEIuKGw/sOrzG2+8MXE2tR7TdL6jkxWcIZlOlwtGW72uEP3MahDsc7BSLBe6tWFLXpfFuBd4Strm7QdRvjyxQu2qfPzkJ9QMqfhBnk8i0WJ23ciBhJ1Pksu3aKpNUALu1q1bjuf7xIkTU/2G/QEE/Nhjj8UaBJbwbfQCQ+AYRYIStCTuYjPR+O/3tnmbmrQYidtmWSsLydsXaRBpFG7isCSuZ1A7K/SKVGzlUv2rJmHtvPlK2RZLzDwy6VFKJoF36tQpVj7z5IZxOmXKlFRecB/W5MPeSOpnn312zvxbaFK0Cys793jTQjGjopDOkiRvQRCEmiQFK7n5RROlz5rMmb0mICQTSXlIwjbuHFW3fJnX2bNnhxNOOCGRpnlOx44dw7333hseeOCB8OCDD8b20EMPxVSejEPmdZFf4IwzzkjMlLWVGSzr+Vi1OZ+FFq0ib0EQyhQ2uQfJwEuY3sZaCNVx/fr1c+zULFADNbfX2owaNSon01iHDh3iPuv8yMUKPNHr1auXygQGKRzZ5pYuXZryd6lt8DsVaSTyFgRBSBG4lepQ6MWSXq9evQpu6505c2aqYIptcGADbE4MLEDGjh2bckZjOBgXKDbUE/fghRdeyLn2gAEDknMKFYKFmvR24YKyxIVaRIm8BUEQigA2tIiAcxfUzZRwTz/99JRUWwgSg/T5zjvvhMaNG4cmTZqkSHnYsGGZTrwg5PHjx0cJevjw4XEf7PtZNa8pWdM+Tqn+3HPPTdXJLoTki/9n06MqQZTIWxAEIaUmB4lBVWydu0455ZQcsi+UhmDhwoXhggsuSKnPQcwM37Tqf5Lbu+++myreYUF7Ns7DIsU7sR111FEFNRcAl19+eYq8izkJi8hbEAShlqVvkhmSmFivbJA3vdALGWFBr/iLLrooRbCXXXZZTogY89/b32tThtrQOLRHH300SuisisXFC8ibZIltIQgcHvbWQ57ZB6U2F3kLgiAkquEtttgiVf6TanMv0dYmbHazIUOGpEK7QN5eQufWh9niP0L9jlCwfv36hf79+8fXu+22W07JS/x/7Cu0eppJabig4MJE5C3yFgShzKVuu91qq61STlunnnpqUZAFv3/w4MGp30dvcxs+lS+9Ka6B6lwMNUPDAsCaCXbaaacYSsbvpEd6oTy9EQpn/y/IW8Qt8hYEQeRdp8kbkjf2eVuwDa2yIV4gb6jdbZY1W38a3vY4BqU3Fy1alFm1S+Qt8hYEQRB5rwN52yQtWb+TDnmsDoZ0qUyHChMBipLgNcicBM4G+zokd6YhleQt8hYEQRB5V5PkTVi7fFaRDtqLvSSNa/B6NkyOaVIL+d9F3iJvQRCEkpS8rY3b/1Y4qFlitxXqGCq2bNmysOeee6auC+kcaVOtg1gh7oHIW+QtCIJQcuQNb2xbtINq8hUrVoQLL7ww1ux+8803M+3VtrTvhx9+mEjc9LQ///zzU6RdCKc1kbfIWxAEoeTIe+jQofFzGxqGmPCLL744OWa77baLzmck7Kz/89133yX5zak+79u3b3LtQkHkLfIWBEGoNHlT+mSGNUt6VmJlCJatRpZVqcxKsPZ1ZRzBbMUwkDJDuyApg7xtTXIAaVE33XTTeByd0Pbbb7/wxRdf5JSYxftXX301hojZeGo4sB1++OGJ13plktTwN/D/2bzxvvIZ487t/fL3CJ9Ds8CwNvw2aBZUClfkLQiCyLtCyRtJWnzNb19P2u6zzmKQEm38Nc+zIVz5aohb3HnnnWH33XcPrVu3Do0aNUqlMW3QoEH4yU9+Evf16dMnCQubMWNGzIVuvchB0LBt41otWrSI57Rt2zbmc2d2NetxzsIkNu1qZcGFhM/yVpEWA8fSfs+MbtaZDg3krRSpIm9BEETemeRNcjzttNNSNmUvaWZJz1aC9KlLCetkZutVZzWU+LSOZHyNMC/7vmvXrqnvgLMasqb5EDAmZ7GZ2vgax1911VXh/vvvj3nRLflSZV1Rsw5ulsDt/8/SOthkMpbkmR6VDfeqULXFRd6CIAh1RPI+88wzU4RMkiFJUfXrVeJPPvlkOO+888KgQYNiOU4cAxKj1Lg2qt+RI0emSNqTMdO5dunSJcem/dZbb4Wtt946HuPPI3HzcywGbrzxxhS5ViXDGo596aWXoiYATm+4B/jf+eztvDf+nuB4ZJCzCwzef1UVE3kLgiDyziRvECLU5tae7IFKX9dff30YPXp0rEiG8+D4Recv2pBff/31lJRpy5GuSW3+hz/8IbkWSRxkhtckXmx/8YtfZGoI7rvvvhyi91I8rgctg9UG2Hvjw9GywGNwbqtWraLd3d4DbHFfQOj4TzAHZBG/rYJm63mjWROGIPIWBEHknUPeIDp4m4OUPvnkk1h966mnnoqOXDvvvHPYZZddol3Z2ovzpR0FscN7mxL72kiODz74YOjevXtUix900EFRwsZrfNa5c+dw2GGHxS0kXB/DDcAhrV27dvF3HHDAAZHkcX63bt3i9fBffvnLX0YJn6CGoCqOYbBT23zpNEPw3vCewKO9adOmsUb53nvvHa655powZcqU8Pbbbyf/AVneuBDCNVauXCmpW+QtCILIu2K1ORzEQHJw9rKlOH1MtFdJg5istIz9HTt2DPPnzw/vv/9+mDdvXmzvvfdejLHm+6z20UcfxXNwLnKOf/bZZ2Hu3LnxPOzDZ1hc4P3HH38cbdXY4lwch2OmTp0aCRt2cByLfTgG349FCbYLFixIvg+vZ8+eHY/B9fEe16rod+L70U466aT4v0ng9t7gvvl7xnuJLc6Bmv/AAw8Mhx56aGjZsmXq2FWrVqnjirwFQRB5V0zeloTsltW4GMLkHcKonub5PIbEZc+16uu63KxK377n/fD3gITMUDB/jr1PbFCb+3A3QeQtCILIO5OYSDQgEytV+8/g9GWJ356b5TBWao2LFhK4rRFOf4B89wLmB7uQoTnC3s/Vq1ennpkg8hYEQeSdStKyJokYBATStklT7DZLNUxyJ8GR5KyEXpebt3NbEwL/K7f2PjGhDLZUn/Nzq2pXhjWRtyAIIu81St4gDZbOtJ7anni8utdK6nzdpk2bMGHChHDrrbfGxte33XZbGDduXJ1vEydOjA32at4fT+iUxP3ndrGDc/EcIKV7PwPkbK+M57vIWxAEoYzJu3fv3nEfnLjg+Yzc4ohfplrXepd7QvfpRhFSxqQnpZriE/8J98zHkltTgzUzcH/z5s1jHnPcX6jGGap2xRVXJCFnTNICiMBF3oIgiLwzyRtSYK9evZKwKRIGnKYgAX711VcxzhtkjuP23XffHDsvpe4xY8YkIU4+Q1ipZAzjYgThXNtuu22KoO1ip0ePHuG4444L06ZNi8d+8803YenSpfE+WGc03G+bHhX3cvny5eq4Im9BEETeFUveTFxi030SthgJJGrUxX7jjTdiXPXMmTNjMRAQ+tVXX50qvsFzKpPXvK6BmoWbb7455lxH7nRI1Lgvr7zySpgzZ05K45AlQdvFzLBhw1KLIJY8ld1b5C0IQpnC5ybH+4YNG6ZU36gqxvSgClGqfaCqmA0Xg6Qu8hZ5C4JQxvAlLkEIm2yySUrdi/SoWYQv1A4geVsnQEregshbEARJ4In0zfzkdEBDtjCWp1QpytqHtXlDAmfec6VIFXkLglCmAAlY6Rv21x133DGV4hS5zYlStFEXO4YMGZIkb4Gz25IlS6T9EHkLgiD8V/Jmda/NN988kgVDvCB58xih9gFnN5ttzS6kBJG3IAhlKnl71K9fP5W//De/+U2iNge8nVyoWcDmbRPeMD2qIPIWBKHMpW4CxPz5558nVb6QmGXx4sWSvAsIhN+hqtmnn34aq6ExtEySt8hbEARBEETegiAIgiCIvAVBEARBEHkLgiAIgshbEARBEASRtyAIgiAIIm9BEARBEHkLgiAIgiDyFgRBEARB5C0IgiAIIm9BEARBEETegiAIgiCIvAVBEARB5C0IgiAIgshbEARBEIRqxP8D4/IP1bSEBTgAAAAASUVORK5CYII=\"}]}"},{"id":45695,"title":"How many points lie within the rectangle and how many aren't?","description":"Suppose, you are given the coordinates of bottom-left and top-right corners of a rectangle as *input-1, R* i.e *R=[Bottom-left corner co-ordinate; Top-Right corner coordinate]*. And you are told to count the points of the *input-2, P* (which represents multiple points a,b,c,d, etc within a matrix i.e P=[a;b;c;d]) lie within the rectangle, R and how many are not. *Show them collectively within an output matrix, Y.*\r\n\r\nExample: *Inputs: R=[0 0;10 8], P=[1 5;-1 5]\r\n         Output: Y=[1 1];*\r\n","description_html":"\u003cp\u003eSuppose, you are given the coordinates of bottom-left and top-right corners of a rectangle as \u003cb\u003einput-1, R\u003c/b\u003e i.e \u003cb\u003eR=[Bottom-left corner co-ordinate; Top-Right corner coordinate]\u003c/b\u003e. And you are told to count the points of the \u003cb\u003einput-2, P\u003c/b\u003e (which represents multiple points a,b,c,d, etc within a matrix i.e P=[a;b;c;d]) lie within the rectangle, R and how many are not. \u003cb\u003eShow them collectively within an output matrix, Y.\u003c/b\u003e\u003c/p\u003e\u003cp\u003eExample: \u003cb\u003eInputs: R=[0 0;10 8], P=[1 5;-1 5]\r\n         Output: Y=[1 1];\u003c/b\u003e\u003c/p\u003e","function_template":"function Y=PointsWithinRectangle(P,R)\r\nY=1;\r\nend","test_suite":"%%\r\nP =[1 0;1 5;5 5;-1 2;5 -4];\r\nR=[0 0;10 8];\r\nY_correct =[2 3];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))\r\n%%\r\nP =[1 2;-1 4];\r\nR=[-1 2;3 8];\r\nY_correct =[0 2];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))\r\n%%\r\nP =[1 0;-4 -5;46 2;8 9;2 3;-2 4;2 -4;6,-6;4 5;1 2;8 9;1 1;0 0;-1 -2;4 5];\r\nR=[-1 4;2 8];\r\nY_correct =[15 0];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))\r\n%%\r\nP =[1 0;-4 -5;46 2;8 9;2 3;-2 3;2 -4;6,-6;4 5;1 2;-1 2;1 1;0 0;-1 -2;4 5;1 1; 4 2;7 8;1 -1;0 1;2 0];\r\nR=[0 0;10 8];\r\nY_correct =[9 12];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))\r\n%%\r\nP =[11 0;-4 -5;46 2;8 9;2 3;-2 3;2 -4;6,-6;4 5;1 2;-1 2;1 1;0 0;-1 -2;4 5;1 1; 4 2;7 8;1 -1;0 1;22 0];\r\nR=[0 0;10 8];\r\nY_correct =[11 10];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":430818,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":"2020-05-31T08:14:14.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-30T08:08:12.000Z","updated_at":"2026-03-31T13:03:03.000Z","published_at":"2020-05-31T07:15:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose, you are given the coordinates of bottom-left and top-right corners of a rectangle as\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\u003einput-1, R\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e i.e\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\u003eR=[Bottom-left corner co-ordinate; Top-Right corner coordinate]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. And you are told to count the points of the\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\u003einput-2, P\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (which represents multiple points a,b,c,d, etc within a matrix i.e P=[a;b;c;d]) lie within the rectangle, R and how many are not.\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\u003eShow them collectively within an output matrix, Y.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\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\u003eInputs: R=[0 0;10 8], P=[1 5;-1 5] Output: Y=[1 1];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61076,"title":"Covering rectangle area of a four-pointed star polygon","description":"Given the four-pointed star polygon formed by the rectangle, with dimensions l1xl2, and four triangles, with height, h, from their bases to the apices, find the rectangle, with dimensions y1xy2, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given x=[l1 l2 h], return y=[y1 y2].\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); 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: 520.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 260.4px; transform-origin: 408px 260.4px; vertical-align: baseline; \"\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; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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 four-pointed star polygon formed by the rectangle, with dimensions \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; \"\u003el1xl2\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 four triangles, with height, \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; \"\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 from their bases to the apices, find the rectangle, with dimensions \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; \"\u003ey1xy2\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, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given \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; \"\u003ex=[l1 l2 h]\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, 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-style: italic; \"\u003ey=[y1 y2]\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: 418.8px; 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; perspective-origin: 385px 209.4px; text-align: left; transform-origin: 385px 209.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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\" data-image-state=\"image-loaded\"\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; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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 y = covering(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [2 7 4];\r\ny_correct = [5 10];\r\nassert(isequal(covering(x),y_correct))\r\n\r\n%%\r\nx = [7 2 1];\r\ny_correct = [2.5 -2.5] + 1.5*sqrt(13);\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nx = [5 2 1];\r\ny_correct = [3 -3]/2 + sqrt(77)/2;\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nfiletext = fileread('covering.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = [7 9 5];\r\ny_correct = [11 13];\r\nassert(isequal(covering(x),y_correct))\r\n\r\n%%\r\nx = [7 9 1];\r\ny_correct = [-1 1] + 4*sqrt(5);\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-16T14:03:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-15T16:57:30.000Z","updated_at":"2026-03-27T12:50:09.000Z","published_at":"2025-11-16T14:03:25.000Z","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\u003eGiven the four-pointed star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1xl2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the apices, find the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey1xy2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex=[l1 l2 h]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey=[y1 y2]\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"413\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"508\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61088,"title":"Covering a four-pointed star polygon by circles","description":"Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\r\nGiven (A,h), return the 2x2 matrix M = [A1/π a1; A2/π a2], where\r\nin the first row (i=1), A1 stands for the area of the circle that covers the minimum distance (cf. left figure), and a1 stands for the logical 1 if A1 is smaller than or reaches the area A or a1 stands for the logical 0 if A1 surpasses A;\r\nin the second row (i=2), A2 stands for the area of the circle that covers the maximum distance (cf. right figure), and a2 has the same previous false-true meaning relative to the areas A2 and A. Obviously, that A2 \u003e A holds true, then a2 = 0.\r\ninput: (A, h)\r\noutput: M = [A1/π a1; A2/π 0]\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: 748.987px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 374.487px; transform-origin: 408px 374.494px; 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: 384px 21px; text-align: left; transform-origin: 384px 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 area, \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; \"\u003eA\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 a star polygon formed by the rectangle, with dimensions \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; \"\u003eL\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; \"\u003e2L\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 four triangles, with height \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; \"\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 from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\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: 384px 10.5px; text-align: left; transform-origin: 384px 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=\"\"\u003eGiven \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; \"\u003e(A,h)\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, return 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; \"\u003e2\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=\"\"\u003ex\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; \"\u003e2\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 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-style: italic; \"\u003eM = [A1/π a1; A2/π a2]\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, where\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.188px; 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: 391px 51.0875px; transform-origin: 391px 51.0938px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.875px; 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: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; 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=\"\"\u003ein the first row \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(i=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=\"\"\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-style: italic; \"\u003eA1\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 stands for the area of the circle that covers the minimum distance (cf. left figure), 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-style: italic; \"\u003ea1\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 stands for the logical \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; \"\u003e1\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 \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; \"\u003eA1\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 smaller than or reaches the area \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; \"\u003eA\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-style: italic; \"\u003ea1\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 stands for the logical \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; \"\u003e0\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 \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; \"\u003eA1\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 surpasses \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; \"\u003eA\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: 61.3125px; 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: 363px 30.65px; text-align: left; transform-origin: 363px 30.6562px; 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=\"\"\u003ein the second row \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(i=2)\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-style: italic; \"\u003eA2\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 stands for the area of the circle that covers the maximum distance (cf. right figure), 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-style: italic; \"\u003ea2\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 has the same previous false-true meaning relative to the areas \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; \"\u003eA2\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-style: italic; \"\u003eA\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. Obviously, that A2 \u0026gt; A holds true, then \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; \"\u003ea2 = 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\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: 384px 10.5px; text-align: left; transform-origin: 384px 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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-style: italic; \"\u003e(A, h)\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: 384px 10.5px; text-align: left; transform-origin: 384px 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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; \"\u003eM = [A1/π a1; A2/π 0]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 484.8px; 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: 384px 242.4px; text-align: left; transform-origin: 384px 242.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"601\" height=\"479\" style=\"vertical-align: baseline;width: 601px;height: 479px\" 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\" alt=\"Covering by circles\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = covering_by_circles(A,h)\r\n  M = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nh = 1;\r\nM_correct = [6.25 1; 16 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nA = 36;\r\nh = 2;\r\nM_correct = [12.25 0; 25 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nA = 56;\r\nh = 2;\r\nM_correct = [16 1; 36 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nfiletext = fileread('covering_by_circles.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 68;\r\nh = 1.2;\r\nM_correct = [13.69 1; 38.44 0];\r\nassert(all(isapprox(covering_by_circles(A,h),M_correct), 'all'))\r\n\r\n%%\r\nA = 89;\r\nh = 2.6;\r\nM_correct = [26.01 1; 57.76 0];\r\nassert(all(isapprox(covering_by_circles(A,h),M_correct), 'all'))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-30T13:14:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-29T14:26:03.000Z","updated_at":"2026-03-22T14:02:11.000Z","published_at":"2025-11-30T13:14:56.000Z","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\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\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\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\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 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A,h)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1/π a1; A2/π a2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\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\u003ein the first row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=1)\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\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of the circle that covers the minimum distance (cf. left figure), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is smaller than or reaches the area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e surpasses \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\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\u003ein the second row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=2)\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\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of the circle that covers the maximum distance (cf. right figure), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has the same previous false-true meaning relative to the areas \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Obviously, that A2 \u0026gt; A holds true, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2 = 0\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:rFonts w:cs=\\\"monospace\\\"/\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, h)\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:rFonts 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61086,"title":"Covering a four-pointed star polygon by rectangles","description":"Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, find the rectangles that have the same area, A, and cover the distance between opposite vertices (cf. figure below).\r\nGiven (A, L), return the 2x2 matrix M, where \r\nthe first row returns the dimensions, y1×y2, of the rectangle that covers the minimum distance (cf. left figure);\r\nthe second row returns the dimensions, z1×z2, of the rectangle that covers the maximum distance (cf. right figure).\r\ninput: (A, L)\r\noutput: M = [y1 y2; z1 z2]\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: 635.675px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 317.837px; transform-origin: 408px 317.837px; vertical-align: baseline; \"\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: 384px 31.5px; text-align: left; transform-origin: 384px 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=\"\"\u003eGiven the area, \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; \"\u003eA\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 a star polygon formed by the rectangle, with dimensions \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; \"\u003eL\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; \"\u003e2L\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 four triangles, with height \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; \"\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 from their bases to the vertices, find the rectangles that have the same area, \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; \"\u003eA\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 cover the distance between opposite vertices (cf. figure below).\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: 384px 10.5px; text-align: left; transform-origin: 384px 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=\"\"\u003eGiven \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; \"\u003e(A, L)\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, return 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; \"\u003e2\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=\"\"\u003ex\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; \"\u003e2\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 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-style: italic; \"\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, where \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; 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: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; 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: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; 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 first row returns the dimensions, y\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; \"\u003e1\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-style: italic; \"\u003ey2\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 the rectangle that covers the minimum distance (cf. left figure);\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; 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 second row returns the dimensions, \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; \"\u003ez1\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×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=\"font-style: italic; \"\u003e2\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 the rectangle that covers the maximum distance (cf. right figure).\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: 384px 10.5px; text-align: left; transform-origin: 384px 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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-style: italic; \"\u003e(A, L)\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: 384px 10.5px; text-align: left; transform-origin: 384px 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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; \"\u003eM = [y1 y2; z1 z2]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 411.8px; 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: 384px 205.9px; text-align: left; transform-origin: 384px 205.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"508\" height=\"406\" style=\"vertical-align: baseline;width: 508px;height: 406px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = covering_polygon(A,L)\r\n  M = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nL = 3;\r\nM_correct = [5 5.4; 3.375 8];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nA = 36;\r\nL = 3;\r\nM_correct = [7 36/7; 3.6 10];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nfiletext = fileread('covering_polygon.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 48;\r\nL = 4;\r\nM_correct = [20/3 36/5; 4.5 32/3];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nA = 56;\r\nL = 4;\r\nM_correct = [8 7; 14/3 12];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-28T15:21:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-27T15:06:59.000Z","updated_at":"2026-03-21T13:41:00.000Z","published_at":"2025-11-28T15:21:25.000Z","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\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\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\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, find the rectangles that have the same area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and cover the distance between opposite vertices (cf. figure below).\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 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, L)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the 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\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×z\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the rectangle that covers the maximum distance (cf. right figure).\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:rFonts w:cs=\\\"monospace\\\"/\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, L)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60421,"title":"Largest Rectangle Area in a Histogram","description":"Given a histogram represented by an array of integers, e.g., [2, 1, 4, 5, 1, 3, 3] :\r\n\r\nfind the maximum area of a rectangle that can be formed using the histogram bars. In the example histogram, the maximum area is 8 units.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 623.537px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 386.491px 311.761px; transform-origin: 386.499px 311.768px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0085px; 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; perspective-origin: 363.494px 10.4972px; text-align: left; transform-origin: 363.501px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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 a histogram represented by an array of integers, e.g., [2, 1, 4, 5, 1, 3, 3] :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 263.991px; 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; perspective-origin: 363.494px 131.989px; text-align: left; transform-origin: 363.501px 131.996px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"320\" height=\"264\" style=\"vertical-align: middle;width: 320px;height: 264px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.017px; 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; perspective-origin: 363.494px 21.0085px; text-align: left; transform-origin: 363.501px 21.0085px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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 maximum area of a rectangle that can be formed using the histogram bars. In the example histogram, the maximum area is 8 units.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 269.545px; 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; perspective-origin: 363.494px 134.773px; text-align: left; transform-origin: 363.501px 134.773px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"320\" height=\"264\" style=\"vertical-align: baseline;width: 320px;height: 264px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = max_rectangle_area(H)\r\n\r\nend\r\n","test_suite":"%%\r\nH = [2, 1, 4, 5, 1, 3, 3]\r\nbar(H)\r\na = max_rectangle_area(H)\r\na_correct = 8\r\nassert(isequal(a,a_correct))\r\n\r\n%% ones\r\nH = randi([1,100])\r\nbar(H)\r\na = max_rectangle_area(H)\r\na_correct = H\r\nassert(isequal(a,a_correct))\r\n\r\n%% two \r\nH = [31, 96]\r\nbar(H)\r\na = max_rectangle_area(H)\r\na_correct = 96\r\nassert(isequal(a,a_correct))\r\n\r\n%% two\r\nH = [31, 61]\r\nbar(H)\r\na = max_rectangle_area(H)\r\na_correct = 31*2\r\nassert(isequal(a,a_correct))\r\n\r\n%% two\r\nH = randi([1,100], 1,2)\r\nbar(H)\r\na = max_rectangle_area(H)\r\na_correct = max(2*min(H),max(H))\r\nassert(isequal(a,a_correct))\r\n\r\n%% \r\nv = randi([2,5]);\r\nn = randi([2,5]);\r\ni = randi([1,n]);\r\nH = ones(1,n);\r\nH(i) = v;\r\nH\r\nbar(H)\r\na = max_rectangle_area(H)\r\na_correct = max(v,n)\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nH = 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= max_rectangle_area(H)\r\na_correct = 355232\r\nassert(isequal(a,a_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":208445,"edited_by":208445,"edited_at":"2024-06-02T10:46:17.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2024-06-02T10:46:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-02T10:37:17.000Z","updated_at":"2024-06-02T10:46:17.000Z","published_at":"2024-06-02T10:37:17.000Z","restored_at":null,"restored_by":null,"spam":false,"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 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of a four-pointed star polygon","description":"Given the area A, of a rectangle with dimensions l1xl2, where the side lengths are integers and form the smallest possible perimeter, and given the total area A_t of the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, h, from their bases to the apices, find the vector [l1 l2 h] such that l1\u003cl2.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); 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: 490.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 245.4px; transform-origin: 408px 245.4px; vertical-align: baseline; \"\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; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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 area \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; \"\u003eA\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 a rectangle with dimensions \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; \"\u003el1xl2\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, where the side lengths are integers and form the smallest possible perimeter, and given the total area \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; \"\u003eA_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 of the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, \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; \"\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, from their bases to the apices, find the 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-style: italic; \"\u003e[l1 l2 h]\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 such that \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; \"\u003el1\u0026lt;l2\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: 418.8px; 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; perspective-origin: 385px 209.4px; text-align: left; transform-origin: 385px 209.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"508\" height=\"413\" style=\"vertical-align: baseline;width: 508px;height: 413px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = star_polygon(A,A_t)\r\n  y = A;\r\nend","test_suite":"%%\r\nA = 10;\r\nA_t = 24;\r\ny_correct = [2 5 2];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 11;\r\nA_t = 23;\r\ny_correct = [1 11 1];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 72;\r\nA_t = 106;\r\ny_correct = [8 9 2];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nfiletext = fileread('star_polygon.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 156;\r\nA_t = 180;\r\ny_correct = [12 13 0.96];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 168;\r\nA_t = 190;\r\ny_correct = [12 14 11/13];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-14T17:36:31.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-13T17:02:46.000Z","updated_at":"2026-01-15T09:17:29.000Z","published_at":"2025-11-14T17:36:31.000Z","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 w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a rectangle with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1xl2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where the side lengths are integers and form the smallest possible perimeter, and given the total area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_t\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, from their bases to the apices, find the vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[l1 l2 h]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1\u0026lt;l2\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"413\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"508\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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a 4-pointed star polygon by a circle sector","description":"Given the area, A, of a 4-pointed star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, consider the circle that covers the greater of the two distances between opposite vertices (cf. figure below).\r\nGiven (A,h), find\r\nthe width, L, of the rectangle;\r\nthe angle, α [in Radians], of the sector of the circle such that its area is equal to A;\r\nthe minimum slicing number n, corresponding to the number of congruent circle slices, such that the area of one slice does not exceed the above sector area.\r\ninput: (A, h)\r\noutput: y = [L alpha 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: 751.55px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 375.775px; transform-origin: 408px 375.775px; vertical-align: baseline; \"\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: 384px 31.5px; text-align: left; transform-origin: 384px 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=\"\"\u003eGiven the area, \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; \"\u003eA\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 a 4-pointed star polygon formed by the rectangle, with dimensions \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; \"\u003eL\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; \"\u003e2L\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 four triangles, with height \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; \"\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 from their bases to the vertices, consider the circle that covers the greater of the two distances between opposite vertices (cf. figure below).\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: 384px 10.5px; text-align: left; transform-origin: 384px 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=\"\"\u003eGiven \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; \"\u003e(A,h)\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\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.75px; 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: 391px 40.875px; transform-origin: 391px 40.875px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; 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: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; 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 width, \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; \"\u003eL,\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 the rectangle;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; 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 angle, \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; \"\u003eα\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 [in Radians], of the sector of the circle such that its area is equal to \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; \"\u003eA\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: 40.875px; 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: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; 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 minimum slicing number \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, corresponding to the number of congruent circle slices, such that the area of one slice does not exceed the above sector area.\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: 384px 10.5px; text-align: left; transform-origin: 384px 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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-style: italic; \"\u003e(A, h)\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: 384px 10.5px; text-align: left; transform-origin: 384px 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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; \"\u003ey = [L alpha n]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 486.8px; 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: 384px 243.4px; text-align: left; transform-origin: 384px 243.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"601\" height=\"481\" style=\"vertical-align: baseline;width: 601px;height: 481px\" 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\" alt=\"Covering by sector\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = covering_by_sector(A,h)\r\n  y = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nh = 1;\r\ny_correct = [3 3.375 2];\r\nassert(isequal(covering_by_sector(A,h),y_correct))\r\n\r\n%%\r\nA = 36;\r\nh = 2;\r\ny_correct = [3 2.88 3];\r\nassert(isequal(covering_by_sector(A,h),y_correct))\r\n\r\n%%\r\nA = 45;\r\nh = 3;\r\ny_correct = [3 2.5 3];\r\nassert(isequal(covering_by_sector(A,h),y_correct))\r\n\r\n%%\r\nfiletext = fileread('covering_by_sector.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 56;\r\nh = 2; \r\ny_correct = [4 28/9 3];\r\nassert(all(isapprox(covering_by_sector(A,h),y_correct), 'all'))\r\n\r\n%%\r\nA = 50;\r\nh = 5; \r\ny_correct = [2.5 16/9 4];\r\nassert(all(isapprox(covering_by_sector(A,h),y_correct), 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-12-03T10:39:21.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-30T14:56:09.000Z","updated_at":"2026-03-23T10:36:12.000Z","published_at":"2025-12-03T10:39:21.000Z","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\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a 4-pointed star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\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\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, consider the circle that covers the greater of the two distances between opposite vertices (cf. figure 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60431,"title":"Calculating the Union Area of Overlapping Rectangles","description":"Calculate the area covered by a union of multiple rectangles. Each rectangle is represented by 4 integers: the first two integers denote the coordinates of the bottom-left corner, and the next two integers denote the coordinates of the top-right corner. The input is provided as a matrix where each row represents one rectangle.\r\nThe rectangles can overlap, meaning that simply summing up the areas of each rectangle will not yield the correct total area. Instead, the overlapping regions should be counted only once.\r\n\r\nExample:\r\nGiven the rectangles [ 4  8 11 10;  6  3  8 10; 16  8 19 11 ] the area covered by the union of these rectangles is 33.\r\n\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 757.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 378.517px; transform-origin: 406.5px 378.517px; vertical-align: baseline; \"\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; perspective-origin: 383.5px 31.5px; text-align: left; transform-origin: 383.5px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.342px 7.81667px; transform-origin: 381.342px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the area covered by a union of multiple rectangles. Each rectangle is represented by 4 integers: the first two integers denote the coordinates of the bottom-left corner, and the next two integers denote the coordinates of the top-right corner. The input is provided as a matrix where each row represents one rectangle.\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; perspective-origin: 383.5px 21px; text-align: left; transform-origin: 383.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.5px 7.81667px; transform-origin: 383.5px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe rectangles can overlap, meaning that simply summing up the areas of each rectangle will not yield the correct total area. Instead, the overlapping regions should be counted only once.\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; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 7.81667px; transform-origin: 0px 7.81667px; 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; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.5px 7.81667px; transform-origin: 33.5px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample:\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; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 367.383px 7.81667px; transform-origin: 367.383px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the rectangles [ 4  8 11 10;  6  3  8 10; 16  8 19 11 ] the area covered by the union of these rectangles is 33.\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; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 7.81667px; transform-origin: 0px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 484.033px; 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; perspective-origin: 383.5px 242.017px; text-align: left; transform-origin: 383.5px 242.017px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"1077\" height=\"478\" style=\"vertical-align: baseline;width: 1077px;height: 478px\" 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rectangles_union(R)\r\n\r\nend","test_suite":"%% Example \r\nR =  [  4 8 11 10; 6 3 8 10; 16 8 19 11  ]\r\na = rectangles_union(R)\r\na_correct = 33\r\nassert(isequal(a,a_correct))\r\n\r\n%%  \r\nR =  [  4 8 11 10; 6 3 8 10; 16 8 19 11; 6 8 8 12  ]\r\na = rectangles_union(R)\r\na_correct = 37\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nR =  [  4 8 11 10; 4 8 6 12; 6 3 8 10; 16 8 19 11  ]\r\na = rectangles_union(R)\r\na_correct = 37\r\nassert(isequal(a,a_correct))\r\n\r\n%% Not overlapping\r\nR =  [  4 8 11 10; 16 8 19 11  ]\r\na = rectangles_union(R)\r\na_correct = 23\r\nassert(isequal(a,a_correct))\r\n\r\n%% Partial overlapping\r\nr = [ -3 -3 -1 -1 ];\r\nR =  [ r; r+1; r+2  ]\r\na = rectangles_union(R)\r\na_correct = 10\r\nassert(isequal(a,a_correct))\r\n\r\n%% Full Overlapping\r\nx1 = randi([10,20]);\r\ny1 = randi([10,20]);\r\na = randi([1,10]);\r\nb = randi([1,10]);\r\ns = a*b;\r\nR =  [  x1 y1 x1+a y1+b ; x1 y1 x1+a y1+b ]\r\na = rectangles_union(R)\r\na_correct = s\r\nassert(isequal(a,a_correct))\r\n\r\n%% Partial Overlapping\r\nx1 = randi([10,20]);\r\ny1 = randi([10,20]);\r\na = randi([1,10]);\r\nb = randi([1,10]);\r\nr1 = [x1 y1 x1+a y1+b];\r\nR =  [  r1 ; r1+1 ]\r\ns = 2*a*b-(a-1)*(b-1);\r\na = rectangles_union(R)\r\na_correct = s\r\nassert(isequal(a,a_correct))\r\n\r\n%% Partial Overlapping\r\na = randi([1,10]);\r\nb = randi([1,10]);\r\ns = a*b;\r\nR =  [  4, 8, 11, 10; 6, 3, 8, 10; 16, 8, 16+a, 8+b  ]\r\na = rectangles_union(R)\r\na_correct = 24 + s\r\nassert(isequal(a,a_correct))\r\n\r\n\r\n%% \r\nx1 = randi([10,20]);\r\ny1 = randi([10,20]);\r\nR = [x1 y1 x1 y1]\r\na = rectangles_union(R)\r\na_correct = 0\r\nassert(isequal(a,a_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":208445,"edited_by":223089,"edited_at":"2024-06-16T05:19:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-02T15:58:47.000Z","updated_at":"2024-06-16T05:19:18.000Z","published_at":"2024-06-02T15:58:47.000Z","restored_at":null,"restored_by":null,"spam":false,"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\u003eCalculate the area covered by a union of multiple rectangles. 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a rectangle, if x is the length and 2x is width. Then find out x from the area of the rectangle?","description":"For a rectangle, if x is the length and 2x is the width. Then find out x from the area of the rectangle?\r\n\r\nif the area is equal to 200 then the length of the rectangle is 10.","description_html":"\u003cp\u003eFor a rectangle, if x is the length and 2x is the width. Then find out x from the area of the rectangle?\u003c/p\u003e\u003cp\u003eif the area is equal to 200 then the length of the rectangle is 10.\u003c/p\u003e","function_template":"function y = length_of_rect(A)\r\n  y = A;\r\nend","test_suite":"%%\r\nA = 200;\r\ny_correct = 10;\r\nassert(isequal(length_of_rect(A),y_correct))\r\n\r\n%%\r\nA = 32;\r\ny_correct = 4;\r\nassert(isequal(length_of_rect(A),y_correct))\r\n\r\n%%\r\nA = 18;\r\ny_correct = 3;\r\nassert(isequal(length_of_rect(A),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":93545,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":109,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-10-26T09:21:07.000Z","updated_at":"2026-02-06T18:21:25.000Z","published_at":"2017-10-26T09:21:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a rectangle, if x is the length and 2x is the width. Then find out x from the area of the rectangle?\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\u003eif the area is equal to 200 then the length of the rectangle is 10.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44308,"title":"Component area","description":"Find the area of the component below, all measurements are in mm\r\n\r\n\u003c\u003chttps://image.ibb.co/hocruF/Component.png\u003e\u003e","description_html":"\u003cp\u003eFind the area of the component below, all measurements are in mm\u003c/p\u003e\u003cimg src = \"https://image.ibb.co/hocruF/Component.png\"\u003e","function_template":"function A = your_fcn_name(h,w,r)\r\n A = h,w,r;\r\nend","test_suite":"%%\r\nh = 50;\r\nw = 20;\r\nr = 12;\r\nA_correct = (h*w)-((pi*r^2)/2);\r\nassert(isequal(your_fcn_name(h,w,r),A_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":137065,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":87,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-09-10T12:15:22.000Z","updated_at":"2026-02-16T12:23:27.000Z","published_at":"2017-09-10T12:15:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area of the component below, all measurements are in mm\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" 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\"}]}"},{"id":45695,"title":"How many points lie within the rectangle and how many aren't?","description":"Suppose, you are given the coordinates of bottom-left and top-right corners of a rectangle as *input-1, R* i.e *R=[Bottom-left corner co-ordinate; Top-Right corner coordinate]*. And you are told to count the points of the *input-2, P* (which represents multiple points a,b,c,d, etc within a matrix i.e P=[a;b;c;d]) lie within the rectangle, R and how many are not. *Show them collectively within an output matrix, Y.*\r\n\r\nExample: *Inputs: R=[0 0;10 8], P=[1 5;-1 5]\r\n         Output: Y=[1 1];*\r\n","description_html":"\u003cp\u003eSuppose, you are given the coordinates of bottom-left and top-right corners of a rectangle as \u003cb\u003einput-1, R\u003c/b\u003e i.e \u003cb\u003eR=[Bottom-left corner co-ordinate; Top-Right corner coordinate]\u003c/b\u003e. And you are told to count the points of the \u003cb\u003einput-2, P\u003c/b\u003e (which represents multiple points a,b,c,d, etc within a matrix i.e P=[a;b;c;d]) lie within the rectangle, R and how many are not. \u003cb\u003eShow them collectively within an output matrix, Y.\u003c/b\u003e\u003c/p\u003e\u003cp\u003eExample: \u003cb\u003eInputs: R=[0 0;10 8], P=[1 5;-1 5]\r\n         Output: Y=[1 1];\u003c/b\u003e\u003c/p\u003e","function_template":"function Y=PointsWithinRectangle(P,R)\r\nY=1;\r\nend","test_suite":"%%\r\nP =[1 0;1 5;5 5;-1 2;5 -4];\r\nR=[0 0;10 8];\r\nY_correct =[2 3];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))\r\n%%\r\nP =[1 2;-1 4];\r\nR=[-1 2;3 8];\r\nY_correct =[0 2];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))\r\n%%\r\nP =[1 0;-4 -5;46 2;8 9;2 3;-2 4;2 -4;6,-6;4 5;1 2;8 9;1 1;0 0;-1 -2;4 5];\r\nR=[-1 4;2 8];\r\nY_correct =[15 0];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))\r\n%%\r\nP =[1 0;-4 -5;46 2;8 9;2 3;-2 3;2 -4;6,-6;4 5;1 2;-1 2;1 1;0 0;-1 -2;4 5;1 1; 4 2;7 8;1 -1;0 1;2 0];\r\nR=[0 0;10 8];\r\nY_correct =[9 12];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))\r\n%%\r\nP =[11 0;-4 -5;46 2;8 9;2 3;-2 3;2 -4;6,-6;4 5;1 2;-1 2;1 1;0 0;-1 -2;4 5;1 1; 4 2;7 8;1 -1;0 1;22 0];\r\nR=[0 0;10 8];\r\nY_correct =[11 10];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":430818,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":"2020-05-31T08:14:14.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-30T08:08:12.000Z","updated_at":"2026-03-31T13:03:03.000Z","published_at":"2020-05-31T07:15:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose, you are given the coordinates of bottom-left and top-right corners of a rectangle as\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\u003einput-1, R\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e i.e\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\u003eR=[Bottom-left corner co-ordinate; Top-Right corner coordinate]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. And you are told to count the points of the\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\u003einput-2, P\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (which represents multiple points a,b,c,d, etc within a matrix i.e P=[a;b;c;d]) lie within the rectangle, R and how many are not.\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\u003eShow them collectively within an output matrix, Y.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\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\u003eInputs: R=[0 0;10 8], P=[1 5;-1 5] Output: Y=[1 1];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61076,"title":"Covering rectangle area of a four-pointed star polygon","description":"Given the four-pointed star polygon formed by the rectangle, with dimensions l1xl2, and four triangles, with height, h, from their bases to the apices, find the rectangle, with dimensions y1xy2, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given x=[l1 l2 h], return y=[y1 y2].\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); 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: 520.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 260.4px; transform-origin: 408px 260.4px; vertical-align: baseline; \"\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; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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 four-pointed star polygon formed by the rectangle, with dimensions \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; \"\u003el1xl2\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 four triangles, with height, \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; \"\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 from their bases to the apices, find the rectangle, with dimensions \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; \"\u003ey1xy2\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, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given \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; \"\u003ex=[l1 l2 h]\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, 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-style: italic; \"\u003ey=[y1 y2]\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: 418.8px; 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; perspective-origin: 385px 209.4px; text-align: left; transform-origin: 385px 209.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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\" data-image-state=\"image-loaded\"\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; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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 y = covering(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [2 7 4];\r\ny_correct = [5 10];\r\nassert(isequal(covering(x),y_correct))\r\n\r\n%%\r\nx = [7 2 1];\r\ny_correct = [2.5 -2.5] + 1.5*sqrt(13);\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nx = [5 2 1];\r\ny_correct = [3 -3]/2 + sqrt(77)/2;\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nfiletext = fileread('covering.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = [7 9 5];\r\ny_correct = [11 13];\r\nassert(isequal(covering(x),y_correct))\r\n\r\n%%\r\nx = [7 9 1];\r\ny_correct = [-1 1] + 4*sqrt(5);\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-16T14:03:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-15T16:57:30.000Z","updated_at":"2026-03-27T12:50:09.000Z","published_at":"2025-11-16T14:03:25.000Z","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\u003eGiven the four-pointed star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1xl2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the apices, find the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey1xy2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex=[l1 l2 h]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey=[y1 y2]\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"413\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"508\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61088,"title":"Covering a four-pointed star polygon by circles","description":"Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\r\nGiven (A,h), return the 2x2 matrix M = [A1/π a1; A2/π a2], where\r\nin the first row (i=1), A1 stands for the area of the circle that covers the minimum distance (cf. left figure), and a1 stands for the logical 1 if A1 is smaller than or reaches the area A or a1 stands for the logical 0 if A1 surpasses A;\r\nin the second row (i=2), A2 stands for the area of the circle that covers the maximum distance (cf. right figure), and a2 has the same previous false-true meaning relative to the areas A2 and A. Obviously, that A2 \u003e A holds true, then a2 = 0.\r\ninput: (A, h)\r\noutput: M = [A1/π a1; A2/π 0]\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: 748.987px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 374.487px; transform-origin: 408px 374.494px; 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: 384px 21px; text-align: left; transform-origin: 384px 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 area, \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; \"\u003eA\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 a star polygon formed by the rectangle, with dimensions \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; \"\u003eL\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; \"\u003e2L\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 four triangles, with height \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; \"\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 from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\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: 384px 10.5px; text-align: left; transform-origin: 384px 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=\"\"\u003eGiven \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; \"\u003e(A,h)\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, return 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; \"\u003e2\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=\"\"\u003ex\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; \"\u003e2\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 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-style: italic; \"\u003eM = [A1/π a1; A2/π a2]\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, where\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.188px; 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: 391px 51.0875px; transform-origin: 391px 51.0938px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.875px; 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: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; 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=\"\"\u003ein the first row \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(i=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=\"\"\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-style: italic; \"\u003eA1\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 stands for the area of the circle that covers the minimum distance (cf. left figure), 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-style: italic; \"\u003ea1\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 stands for the logical \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; \"\u003e1\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 \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; \"\u003eA1\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 smaller than or reaches the area \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; \"\u003eA\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-style: italic; \"\u003ea1\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 stands for the logical \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; \"\u003e0\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 \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; \"\u003eA1\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 surpasses \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; \"\u003eA\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: 61.3125px; 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: 363px 30.65px; text-align: left; transform-origin: 363px 30.6562px; 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=\"\"\u003ein the second row \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(i=2)\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-style: italic; \"\u003eA2\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 stands for the area of the circle that covers the maximum distance (cf. right figure), 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-style: italic; \"\u003ea2\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 has the same previous false-true meaning relative to the areas \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; \"\u003eA2\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-style: italic; \"\u003eA\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. Obviously, that A2 \u0026gt; A holds true, then \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; \"\u003ea2 = 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\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: 384px 10.5px; text-align: left; transform-origin: 384px 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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-style: italic; \"\u003e(A, h)\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: 384px 10.5px; text-align: left; transform-origin: 384px 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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; \"\u003eM = [A1/π a1; A2/π 0]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 484.8px; 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: 384px 242.4px; text-align: left; transform-origin: 384px 242.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"601\" height=\"479\" style=\"vertical-align: baseline;width: 601px;height: 479px\" 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\" alt=\"Covering by circles\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = covering_by_circles(A,h)\r\n  M = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nh = 1;\r\nM_correct = [6.25 1; 16 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nA = 36;\r\nh = 2;\r\nM_correct = [12.25 0; 25 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nA = 56;\r\nh = 2;\r\nM_correct = [16 1; 36 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nfiletext = fileread('covering_by_circles.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 68;\r\nh = 1.2;\r\nM_correct = [13.69 1; 38.44 0];\r\nassert(all(isapprox(covering_by_circles(A,h),M_correct), 'all'))\r\n\r\n%%\r\nA = 89;\r\nh = 2.6;\r\nM_correct = [26.01 1; 57.76 0];\r\nassert(all(isapprox(covering_by_circles(A,h),M_correct), 'all'))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-30T13:14:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-29T14:26:03.000Z","updated_at":"2026-03-22T14:02:11.000Z","published_at":"2025-11-30T13:14:56.000Z","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\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\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\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\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 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A,h)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1/π a1; A2/π a2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\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\u003ein the first row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=1)\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\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of the circle that covers the minimum distance (cf. left figure), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is smaller than or reaches the area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e surpasses \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\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\u003ein the second row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=2)\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\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of the circle that covers the maximum distance (cf. right figure), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has the same previous false-true meaning relative to the areas \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Obviously, that A2 \u0026gt; A holds true, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2 = 0\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:rFonts w:cs=\\\"monospace\\\"/\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, h)\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:rFonts 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61086,"title":"Covering a four-pointed star polygon by rectangles","description":"Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, find the rectangles that have the same area, A, and cover the distance between opposite vertices (cf. figure below).\r\nGiven (A, L), return the 2x2 matrix M, where \r\nthe first row returns the dimensions, y1×y2, of the rectangle that covers the minimum distance (cf. left figure);\r\nthe second row returns the dimensions, z1×z2, of the rectangle that covers the maximum distance (cf. right figure).\r\ninput: (A, L)\r\noutput: M = [y1 y2; z1 z2]\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: 635.675px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 317.837px; transform-origin: 408px 317.837px; vertical-align: baseline; \"\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: 384px 31.5px; text-align: left; transform-origin: 384px 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=\"\"\u003eGiven the area, \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; \"\u003eA\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 a star polygon formed by the rectangle, with dimensions \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; \"\u003eL\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; \"\u003e2L\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 four triangles, with height \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; \"\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 from their bases to the vertices, find the rectangles that have the same area, \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; \"\u003eA\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 cover the distance between opposite vertices (cf. figure below).\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: 384px 10.5px; text-align: left; transform-origin: 384px 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=\"\"\u003eGiven \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; \"\u003e(A, L)\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, return 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; \"\u003e2\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=\"\"\u003ex\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; \"\u003e2\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 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-style: italic; \"\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, where \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; 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: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; 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: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; 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 first row returns the dimensions, y\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; \"\u003e1\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-style: italic; \"\u003ey2\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 the rectangle that covers the minimum distance (cf. left figure);\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; 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 second row returns the dimensions, \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; \"\u003ez1\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×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=\"font-style: italic; \"\u003e2\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 the rectangle that covers the maximum distance (cf. right figure).\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: 384px 10.5px; text-align: left; transform-origin: 384px 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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-style: italic; \"\u003e(A, L)\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: 384px 10.5px; text-align: left; transform-origin: 384px 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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; \"\u003eM = [y1 y2; z1 z2]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 411.8px; 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: 384px 205.9px; text-align: left; transform-origin: 384px 205.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"508\" height=\"406\" style=\"vertical-align: baseline;width: 508px;height: 406px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = covering_polygon(A,L)\r\n  M = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nL = 3;\r\nM_correct = [5 5.4; 3.375 8];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nA = 36;\r\nL = 3;\r\nM_correct = [7 36/7; 3.6 10];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nfiletext = fileread('covering_polygon.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 48;\r\nL = 4;\r\nM_correct = [20/3 36/5; 4.5 32/3];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nA = 56;\r\nL = 4;\r\nM_correct = [8 7; 14/3 12];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-28T15:21:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-27T15:06:59.000Z","updated_at":"2026-03-21T13:41:00.000Z","published_at":"2025-11-28T15:21:25.000Z","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\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\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\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, find the rectangles that have the same area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and cover the distance between opposite vertices (cf. figure below).\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 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, L)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the 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\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×z\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the rectangle that covers the maximum distance (cf. right figure).\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:rFonts w:cs=\\\"monospace\\\"/\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, L)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60421,"title":"Largest Rectangle Area in a Histogram","description":"Given a histogram represented by an array of integers, e.g., [2, 1, 4, 5, 1, 3, 3] :\r\n\r\nfind the maximum area of a rectangle that can be formed using the histogram bars. In the example histogram, the maximum area is 8 units.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 623.537px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 386.491px 311.761px; transform-origin: 386.499px 311.768px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0085px; 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; perspective-origin: 363.494px 10.4972px; text-align: left; transform-origin: 363.501px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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 a histogram represented by an array of integers, e.g., [2, 1, 4, 5, 1, 3, 3] :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 263.991px; 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; perspective-origin: 363.494px 131.989px; text-align: left; transform-origin: 363.501px 131.996px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"320\" height=\"264\" style=\"vertical-align: middle;width: 320px;height: 264px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUAAAAEICAIAAACh+br8AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAJ00lEQVR4nO3dbWiN/wPH8ev6d9A0NmZmbmcit1nbhOmYMrcNQ3J/88DGIykiRMgDJCKxBxQiE2WE3Ezmdkun3IxHB83Gppj77cTY9Xtwfr/9Fv2e7Nr/fK9P3q9Hu1a++3TOea9zzgbbcRwLgCaf6QH4T7Ztm57wN77LexYBe1ogYL6c9HSvfB/B7/5negCA5iNgQBgBA8IIGBBGwIAwAgaEETAgjIABYQQMCCNgQBgBA8IIGBBGwIAwAgaEETAgjIABYQQMCCNgQBgBA8IIGBBGwIAwAgaEETAgjIABYQQMCCNgQBgBA8IIGBBGwIAwAgaEETAgjIABYQQMCCNgQBgBA8IIGBBGwIAwAgaEETAgjIABYQQMCCNgQBgBA8Jsx3FMb/Ac27ZNT/AWHiSe5TM9wKMCAfMP2fR02yMzTE/Af+IpNCCMgAFhBAwII2BAGAEDwggYEEbAgDACBoQRMCCMgAFhBAwII2BAGAEDwggYEEbAgDACBoQRMCCMgAFhBAwII2BAGAEDwggYEEbAgDACBoQRMCCMgAFhBAwII2BAGAEDwggYEEbAgDACBoQRMCCMgAFhBAwII2BAGAEDwggYEEbAgDACBoQRMCCMgAFhBAwII2BAmO04jukNnmPbtukJ3uKRBwn3yy8cx/GZ3uBRgYD5h2x6uu2RGaYn/MsjN4hHZlg8hQakETAgjIABYQQMCCNgQBgBA8IIGBBGwIAwAgaEETAgjIABYQQMCCNgQBgBA8IIGBBGwIAwAgaEETAgjIABYQQMCCNgQBgBA8IIGBBGwIAwAgaEETAgjIABYQQMCCNgQBgBA8IIGBBGwIAwAgaEETAgjIABYQQMCCNgQBgBA8IIGBBGwIAwAgaEETAgjIABYbbjOLZtm57xN8dxTE+wLMvyzg3iEdwv3uQ4ji/8USBg/h5KT/fQ3eORG8QjM0xP+JdHbhCPzLB4Cg1II2BAGAEDwggYEEbAgDACBoQRMCCMgAFhBAwII2BAGAEDwggYEEbAgDACBoQRMCCMgAFhBAwII2BAGAEDwggYEEbAgDACBoQRMCCMgAFhBAwII2BAGAEDwggYEEbAgDACBoQRMCCMgAFhBAwII2BAGAEDwggYEEbAgDACBoQRMCCMgAFhBAwII2BAGAEDyhzHMT0BQHM4juMLfxQImM84Pd32wgzLM0uY8QuPLPHODIun0IA0AgaEETAgjIABYQQMCCNgQBgBA8IIGBBGwIAwAgaEETAgjIABYQQMCCNgQBgBA8IIGBBGwIAwAgaEETAgjIABYQQMCCNgQBgBA8IIGBBGwIAwAgaEETAgjIABYQQMCCNgQBgBA8IIGBBGwIAwAgaEETAgjIABYQQMCCNgQBgBA8IIGBBGwIAwAgaEETAgjIABZY7jmJ4AoDkcx7EJGNDFU2hAGAEDwggYEEbAgDACBoQRMCCMgAFhBAwII2BAGAEDwggYEEbAgDACBoQRMCDM5/LP19fXFxcXl5eXd+3aNTMzMzo6ukVmNU8wGLx79+6SJUsMbmj07t270tLS7OzsyH/pmpqaJ0+eNP1Mp06dBg0aFPklYW/fvr1y5crEiRM7depkasPr169LSko+fvw4ePDgESNGmJrR0NBw+/btYDDYoUOHzMzMFrhBHBcCgcCQIUPy8vK2b9+elpaWmJh4//59Nwc2z4cPH1avXt2/f/+oqKjY2NjID/jd9+/f/X5/UlKSka9eWFj4y72ck5NjZMnu3bszMjLatWtnWdbDhw+NbHAcZ9OmTQMHDly7du26detiY2MnT55cX18f+RnBYHDIkCHTp0/fsWPH+PHj27dvf/nyZZdnugo4JSUlKysr/PG3b9969+49dOhQl4Oa4dOnT/fu3fv8+fPq1as9EvCyZcu6detmMOCxY8d+bKK2ttbIklu3br158+bChQsGAy4rK7Msq7CwMHxZVFRkWdbRo0cjv2TmzJkpKSmNl36/v3fv3i7PdPUa2O/3p6amhj9u3br1+PHjHz9+XFdX5+bMZmjfvv3IkSPD3+a94ODBg2VlZevXrze4oVWrVjFNtG3b1sgMv9+fkJBg5Es3SkpKWr58eb9+/cKXo0ePtm07GAxGfsm8efNmzZrVeJmZmVleXl5fX+/mTFevgfft29f08v379wkJCaYeKx5x69atnTt3lpSUXLx40fQWWJZlRUdHHzx4sPHy0aNHjuNkZWVFfsmMGTOaXj548GDMmDGtWrVyc6bbN7Ea1dXVFRcXL1y4sKUOVPTy5cv58+efOXOmS5cuZpeUlZVlZ2dXVFT07Nlz9uzZCxYssG3b7CTjbt68WVZWdvz48aNHj2ZmZpqaUVVVVVpaev78eZ/PV1BQ4PK0Fgt41apVHTt23LZtW0sdKKeurm7atGlbt24dPny42SUZGRmnT5/2+XyVlZXHjh1btGjR06dPt2/fbnaVcUeOHHn9+rVlWc+ePQuFQlFRUUZmPHr06Pjx41VVVfHx8c+fP+/cubOr41y+hg47cOBAcnJyeXl5i5zWbGbfxFqyZMnQoUML/pGXlxcfH19QUHDt2jVTk8JycnJ8Pl8oFDI1wOybWL+oqqpKTExcunSp6SHO5s2bo6KigsGgm0Na4Bc59u7du2/fvuLi4l69erk/TVebNm06dOiQ/4+bN29++fIlPz//7NmzZodNmjTpx48f1dXVZmd4RGJiYnZ29u8/aYu83NzcUCh05coVN4e4egr98+fPNWvWPH36tKSkJDY21rKsq1evfvr0qelbbX+O/Pz8ppeHDx/etm3bjRs3Ir/k4cOHPXr0iIuLC19WV1fHxMQkJSVFfokXvHr16syZMytXrmz8THV1dWJiYuSXnDp1Kjk5ediwYY0zLMtyuaT5AX/+/HnOnDkVFRUbN268fv16+JMnTpwYNWqUm0FuNDQ0OH/8v1NfU1OTlpa2YsWKPXv2WJb1/Pnz/fv379y50+CbWA0NDZa5/wPk5MmTa9asGTFiRPgXsIqKii5dunT48OEIz2hoaMjNzc3IyLh8+bJlWaFQaMOGDYMGDZowYYKrc5v95Dv8wuZ3u3btcvOcvnm2bNmSkZERExNjWdbIkSNnzJgR+Q2/OHTokKlf5Fi7dm1cXNyUKVOmTJmSmppaUFBgZIbjOOfOnfP7/d27d7csa8CAAVlZWS9evIjwhq9fvy5evDguLm7q1Knjxo1LTk4+duxYhDeEXbx4sW/fvoMHD547d26fPn3mzp376tUrl2fyX6v8v9y5c+fChQum3vv9/v17dXV1fHz8H/5j+UahUKiysjIuLq7xlYURjuO8efOmtrY2KSnJ52uBnwERMCCMv04ICCNgQBgBA8IIGBBGwIAwAgaE/QXYxL95MKRERQAAAABJRU5ErkJggg==\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.017px; 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; perspective-origin: 363.494px 21.0085px; text-align: left; transform-origin: 363.501px 21.0085px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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 maximum area of a rectangle that can be formed using the histogram bars. In the example histogram, the maximum area is 8 units.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 269.545px; 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; perspective-origin: 363.494px 134.773px; text-align: left; transform-origin: 363.501px 134.773px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"320\" height=\"264\" style=\"vertical-align: baseline;width: 320px;height: 264px\" 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XkIGMrAIzoWurq7C5uGbHGCxR6+f4ipO+eDBd7F5ZBJteDtgns8//1SvnwLmcRaA25ERIETzYAGSHZERoOzlJ9yD5sAiOBe6snKDkK0BJSslZQZ+CZgQp7xmzRIcTAMH9Hitg9eX8XbwotGKFeE5OZVQ+gQBx49f046MgOzsOEkBkh1xJcBmq83NjVfsyhPdgAwsDR+4wrlc/tDDBkOZXGiIU+5inrMwcC0p+QDMwxjDAly103UBkh2REUC50NqHhtDSaOGUAmNMrXkvJct6CmRgEb6RQ3X38kgd+XbIvQQZWKRPnz6so/Tl5sZfvfpveOhjYiaBeS5caJk9exh+CZgQp4zznJOTp2P3Ll48Fuc5R0VNwItGxcUrwXW5ufG4HSyAv327KwIYY5mZkQy5d8GC+0HAhQstggDcDs2BNQ4ZWIRH6jDGrFZzv34DY2PXss7dGpPBPAsWjMnOroTSl5UVLcQp81hm/sU//ckPl76kpPU4z9li6Sx9r71WCqtWjLHm5ibcDhYQETGyKwL4x1tvHYIFpKQ8h7OB8Gav9esTcTvNzU0KXnvCbWgRSxo+4MTudWvgyk3Yw9P5jDHJdrouANrBwdRdHDlTLrRHQBXYJapnazCpXGhl5r2ULOspkIFFeC606u6VzIVW3r0UqaNx6O+rCETq2O12nW7iuHEhYJ6lSyeCeRoa9mVkLIKHfsuW7Nrad+B32tTU2cOHjwfzJCSELlvW+R6jZcsml5TsgTznwsKneBQOc4plTk6eDu0IAmy22lWr5kkKYFLB1FhAZKQ/vIGJnzSE4xZlZWsPHnwXOpKcPF3Zy0+4B1VgEW4AXrICA6dyD/DSl5HxPJhn5coIiGXmB/TwLot77/XF005sHr0+BNzL85zBvTiWmZe+UaMCXAkwmeZICmAdwdQyAsC9PBcaH5ay2Q7gjowaFaD4HSDcgAwsjRYyJZmLcExlRs64I4RmIQOLyOdCK5kIy/WQewkZyMAiMrnQnpXn/Iu4l+cKEJqFFrFEcC70rFlDsXmWL3+0qupT/tDzPCrIxIiPD4VIHX5gEL99OzZ2cmlp57y3pGQ1/yJjzGJJxwk7Ol0QnFVijAkCVqyYi13X0LAXt9Pefmn58ue6IkAIpv7ww+rNmw84C+CbvZS8+IS7UAUW4X7gpa+gYNf48SGso2SBe61W87FjB4VEGzCPwRCWnPws/yIvfdg8ZWWZ4Dqr1dzYWFdQsBPaCQwM4+3w0icI2L7dhmsmbqd37+u7KMBkmlNefgDaaWysA/cKAiIiRubnv6X4HSDcgAwsjRZGzqwjHFOVkTO+AoRmIQOLCLnQKs57uR5yLyEDGVgE50ILccpFRSacw4zfvs1jmfEZI2yeurpq7F6ZXGghz7mmZqcrAbwdhpJx5AV0MZhaiOapqdmp9A0g3IEWsUQgF5rv1tix4wSULPz2MKNx2p13/hFKn9E47Ykn4qD0JSVNKyzcBaVv06bVeJfF6dMncC70sGG+UPqWLBm/du1WKH2ZmZEvvljvLIB/bG+/BLs15AWsXBmBJ/A22wGLpdqVgLQ0C4w++DlEQrOQgaVxXrU6erQG3Ouc5xwba8YD17KyvXjkjN3rKheaD1zXr38NzMMYkxTAOkbOeNVKRoBzR8C98gL4FylSR8vQEFoaLfzeyzrCMZWf91Ioh6dABhbhc2DV3btjx3Guh9xLyEAGlqYrec46XRBeNIqJeQDMs2fPq6WlGeA6mXbOn2+eO3d4F/OczWYdQ+6VF+CqHbcE7Nr1guLXnnADmgOLQC601Wo+efJYYeHbaLo4CccpL126Ckqf0TgTLxq98ooFJ9qcPHmsuLhz10dw8MyoqDT+xaioCRkZ5VD6cnLi4agQYwwEsJ8ifgbg2osFpKQ8igXk5MTj2isIgI7IC7DZat96q0LBa0+4DRlYGj7gxA991/Ocy8oycaKNczvgXueBa2Vl56I3Y4x/ET4aDLmuBAgjZ9yOq47IC+AdKS5+nyJ1tAwNoaXRwikFhnKhmbLzXqEjhGYhA4vwSB3V3YtzoRm5l3AB3SERPgfmDz3ea8VjmQ2G9RCnrNMFbdny0/t7a2p2lpc/Db/3Zmfrv/jiMzjtkJAQ6uvb+f7ehQt9wTx1ddX47dt5ecampiPwRpXc3HgcbYsF8HYglKOmZmdmZiT83puXZzx16pgrAfPnj3YloLq6qrJyAxag+B0g3IAMLMJzoaFk4WTZ+PhsV3HK27cXlpT8FWrv2bMnCwredlX6nnlmB5S+jIxF+D1GZ8404lxoIZgaC9DrQyDAmedC4z1bZ840dkOAEEzNk7GVvfyEe9AQWhpn98bEZPr6BjM0cB04cDBDA84bbriBoTjlG264QfgrAANX3g4MXHk7MOKFdti1wdQyAng7d9zhI7TjlgDnjoAAQrOQgUWESB0VszVAj/LzXjzxJrQMGVgER+r8f0rG6Z57KRda49AcWATnQkdHT0pI6Jx2xsU9BOZpaNhXXJxWVrafP/RFRaYjR/ZDIOvixWP9/UPBPHPm3JuX9yaYR0i0qa/fA+3k5xtZx/t7GWMyAmy22rS0ufikIT4sJQiYN280dm96+gL4otARLIBfAcWuPNENqAKL4FzopKT1eNppsewG85SXZ8FDb7Wam5qO4DjlBx+cxTdd8NKH3eucaIPbufnm/mAexpiMAJNpzssvdybsNDUdwYelBAE5OX/BAl588SNXHcEC+BVQ+gYQ7kAGlkYLI2fWkSugysgZXwFCs3g5HA4vLy+1ZfyEw+FQWwKz2+29e9PmwWvQwn1hjGnnQdUIDofjpzlwfb36d8jPTxO3hy9i8QvS2tqSmPgInveWl2dBySotXXPs2EEIpklJmQGlr7W1ZeHCMXizBH6RksWS3thYh9u57rpfwSGnlJQZvPT5+Xm98855QcDKlRHQjowA/t5wVwKcOyIpgHckLOwOxW+CSzTyoGpEBqNFLGcgUqetrVWnC8K7NTZuTLNa98NDj3Ohk5KmQi50W1trRMQIvFkCvz3MajVDDjNv5+LFCyZTMWPMbrcnJj4cHp4IA1dBwKpV84WRsysBixb5ZWZWSApw7ogrAW1treHhw5W79IT70BxYmo6XgB0aNKhzkwM89DK50LBqhfOcsXuPHq0B91qt5uuu+xWYx2AIi49/JiRkDuvIhcYCXOVCuxIQFDTdWYBzR2QEUC609iEDS6OF33tZR66A8qtWlCzrKZCBRXgutOru3bSpmush9xIykIFFLl++zDpKX03NTvzQy+RCf/fdNzhO+ciRfdg8W7ZkY/cWFZkYynNOSAi9Ns95Cvz5kMmFFg5LyQtw7oiMAMqF9iBoEUsEInVsttoXXliPj+bgvVYpKTOGDsWrViNXrChGpW8uHBWyWs21te/gZNkrV36EbA2jcdr06ZE4micnpxIidczmpbgdLMBgCOuiAJutFh91tFrN33//LQhISZkxZ05noHRkpD9ux2xequC1J9yGDCwNH3DCsdiOxacaVwPXdetexQNXfEIQvsi6kOeMo3kYY5LtuCXAOZiaMbZ69WbmYuTs3A7lQmsZGkJLo4VTCkwqF1qZeS8ly3oKZGARngutunslc6HJvYQAGVikT58+rONIQ3a2/siRfWCeuLgQMM+FCy1z5tyLF42eeupxeOjLytbCFxljeXlG5jrPeenSQJznjNspLEx1JYAfcnIlwDmYGgtYvHgsFoDbOXjwXUGAspefcA+aA4vwSB3GmNVqbm7+DOdCjx49EcyzYMEYvNcqLS0CrzYdPbof50J7e9+IS59e/984z3njxvdxnjO0wxhramrg7TgLEJJxsADnYGpBQFJSZ7BWVNQEvGdr7doo3JGmpgYFrz3hNmRgadyNUxZGznjtmjEG7xB0K8+ZMcbb6cbIuYsCutIRyoXWMjSElkYL2RqsIxxT+Xmv0BFCs5CBRWRyoRVOxoEvquheitTROPT3VQTnQut0E8eNC5FMxmlo2IcP6G3Zko13a+TlGb29b4SBa0JC6LJlnfPeZcsml5Ts4V90zoU+ceIwtCMIWLp0InbdqlXzQEBdXTV+jbi8ACEXGp92wALsdnty8nSlbwDhDlSBRXAudGDgVO4B52SclSsjIFTdajV/9NEevFmib9/+eNqJzaPXh4B7eSwzuJfnOYN5GGOCgIyM53HNBAE2W+3WrbldFBARMTI7uzNhJyNjET4shQUYDGGjRgUofQMIdyADS6OFTEloR5WRM74ChGYhA4sIudAqJsJyPeReQgYysAjOhfboPOdfxL20iKVxaBFLBHKh+dvD8GaJ5csfhbeHWSzpOBnHYklvb78EpxR0uiC8WyM2dnJpaee8Nze38+3bFkv6J5/Ug3l0uqCAgEeg9M2aNRS7Dguw2WpLSlbzUI6fFYBfp+YcTC0IGDHCH+/ZUvDaE25DFViE+4GXrKef3o5fIwTm4XnOOBmnd+/r8Rmj5ORneaQOr73YvSbTHIh35u0UFOyE0hcYGBYTs4Z1ROoUFOzC0TzYvWVlmeBeeQG8IzLB1IIA3E5q6kalbwDhDmRgabQwcmYdudCqjJwpF9ojIAOL8Egd1d2bm1vF9ZB7CRnIwCL8OCHe5ICni9i9Fks6Q8E0iYkPX5uM0+lemXb4F3GeM3ad8MW6umrsXnkBMu3ICPjhhx+we8+fb1b06hNuQotYIpALzXdr7NjRebrAZjtgsVRDnPL333+blraJMcZjmcPD46H0JSVNKyzcBTVz5coIPH8+ffoElD6jcdqwYb5Qe5csGb927VYofViAzVZbWPgUfwES60jGAQFG47QnnuhMxlmyZHxubuduDUEAdEQQwHOho6LSoJ34+FDlLj3hPmRgaZxXrY4erQH38jhlMI9wQlCvDykr24tHzkI7eOA6ZkwwHjmvX/8auI4xJqxaYfcyxrAAHM0jtOOqI4IAyIXGHXn++VqK1NEyNISWRgu/9zKUC63wvFfoCKFZyMAifA6sunshUofcS8hABpYGjuZg9/KXX8Nij14/BS/2xMQ8gJNxUlNng3lwO3yzBF61mjt3OLhO+GJ1dRV2LxbgHM0j046MAKEjn3/+KQ6mrq6uUvjKE25Bc2ARyIXmb80Woi3APCkpM/BLwIzGmevWVUHtzc6OuzaY5ghPqOW1DvZa8UQbk6kzhzknJ7609K9Q+iorN7gSYDCELVy4HOc5p6VZcDsVFYddCRg50t9VR1asCIdgaputtrJyg2JXnugGZGBp+IAT50IzxvCr64UBJ85zds6FxuaRHzlDpA5fxOqiAOc8ZxzN40rAz3aEJ2NTpI6WoSG0NFo4pcA69nUqP+8VJt6EZiEDi+BIHabqGSOuh9xLyEB3SAQidRhjubnx/foNjI1dyxiz2+0xMZMMhp8CWS9caNHpgrZsOcQf+pqanWbzUhg5Z2frv/jiM3h/r043MTBwKrgXnw0SInWqq6sqKzfAyFlGQFtb6+zZw/Lz3+Ifa2p2ZmZGwu+9goCEhFBf3wfAvTIdcRag9A0g3IEMLIJzobF5DIaw+PhsME9CwiObN9dAycrKisarVmfPniwo6AyUxrlWQp5zRsYi/B6j114rhVUrxpiMgIiIkdnZldBOVlb0iy/WuxIg1F6ZjmABVqu5ublJwWtPuA0ZWBo+cMXmcWvk3O08Z2Ho7kpAF4OpezJyplxoj4DmwC5RPVuDo8q8l3KhPQUysAhfxFLdvSquWlEutAdBf19FIFLHbrdHR09KSOicLsbFPQQPfUPDvvT0+WCeoiITfvt2XFwIfo8RDpQWknEaGvYVF6eVle3He634772MMUHAokVjsXvT0ua6ErB48Vh//1Bw74IFY9LSNrnqiCDg+PHOXOjo6EkKXnvCbagCi/Dn2N7xEjAeqcNLFkTh8AN6L79sw1udcJzy2LGTXQVKC8k45eVZYB6r1Xzzzf1htwZjDAuIiBiZlfUSbkdGwIMPzjIYcqEj2L1CRwQBp09fkwsdEPCI4neAcAMysDRaGDmzjlwBVUbOlCzrEZCBRXjpU929MTGZXA+5l5CBDCzCc2bAeowAAA+1SURBVKFVd69Gai8PxyS0i8PhUFsCQRDdweFw/LQKXV+vvo39/Ly0IIMx5ufntXv3N6rX3oceunXz5gMq1l7eEZ1uonbuixaUaEcGoyG0K1R3r0wutJLupWRZjUMGFmlvv8QYU929rnKhyb0Ehgws8sMPl1lHpE5NzU5snqIiE45TTkgIhYf+u+++CQ8fAQ/9kSP7up7nnJAQipNxcDsyAvgZI5yMIx9MjQXIdMRZgNI3gHAH2oklAnE2NlttZmYkPuJz+PD7PNiVJ9EMHToKl6wVK4pR7Z0Lh5NsttpNm1bjt2+3t1+Ct28bjdOmT4/Eec6QjMMYM5uX4kNOeK+VwRAGApxzoYVgakEA7ojROO3OO/8IHYmM9McdMZuXKnnxCXchA0sjGacMD73zgFNItMEnBMvKMrF5GGP47WEyec6MMSGaB7tXGDnjdoRgakGA0BEhmNq5I5QLrWVoCC2NFn7vZR3DAeXnvUJHCM1CBhbhWxdUdy/kQpN7CRloCC0NBNOcPXsSDscvXjz2wQdnwWLPokV+cErhyJF9JtNcGPHu2fPqK69YINoiL8/Yt29/nOecnPwsrDYtWTIeRs579ryanR2Ho3mwgLi4kLFjJ7tqJylpGoycnQWcOdOIc6EDA8MkOyIIKCxMVf7iE12HDCwCZcdqNTc3f1ZY2BlMAwf0eJ5zZmYFOtkXgVetXnnF8txzu6D0eXvfiGsmfpFSVNSEjIxynOcM7TDGBAFwRNG5nZSUR/GqlSDg5MljxcXvo3nvJFcdwQKsVnNTU4OSF59wFzKwNHzAiR96t0bOQho7rDn/7MgZ5zkzxiQFdGXkjAW41REhUJoidTQOzYGl0cIpBcaYWvNeitTxFMjAIvyV1qq7l+dCk3sJeegOifCH2Hmrk5CMw995//rrp2DPVnn50/Bza16e0dv7Rhg5JySELlvWOV+VyYXOyzPCe4wYYzrdRIikdU7GWbZscknJHthrhXdr5OUZT506JpkL3dbWOn/+aBkBJ04chnbWrIlU+PoTbkEGFvH2vpF11Dr80AvJOBkZi8C9Nlvt9u2FeLMEXnM2GMKwe4XSl5GxCMxjtZrPnGmE9xgxxiAOXjIZB9xrs9Vu3ZqLBZw50wjude6IvADczpAhdyt9Awh3oCG0NFo4nS/TjgIjZ9wRQrOQgUV46VPdvfffHwR6yL2EK8jAIt98c451PLv/n5JxuudeyoXWODQHFrn11p9yoflqE36Pkdn8Z3joGxr2bdhg2rz5ABzQu3LlRzilEBU1Aec541Urm602Nzce2rFY0j/5pB7vkYLXfzPG4uJCYmPXQjuRkf7w2m6brbagYDkIsFjST58+gdsJDp4ZFZUmKQB3BAtgjOXnG2+6qV9MzBrekcWLxyp47Qm3IQOL8Of4Z2tveXkWmIfvtcI5zMuXF3Sx9jY21uGaCTsceemLi3sa117s3rKyTCzAuR1wbxcFsI5galz8U1M36nQTlb4HRJehIbQ0Whg5M9fhmAqMnHFHCM1CBhbhkTqquxfnQpN7CVeQgUX4cUK8WwPPe7F5SkvXMJSMIyTaYPMI7Vgs6TjRJjHxYZyMg83T2tqC3SsIkGmn6wKcOyIIUPbyE+5Bc2CRO+7w4f+w2WrT0sIrKzuzNTZuTLNa98NDf/HiBZOpmDFmt9uTkqbOnNmZjLNokR8+4oP3bFmtZrxqZTRO8/EZBqUvMfHh8PBEKH06XRB++zYWYLWaP/ywmk+DuQAfn85knCVLxuNDTnivldVq/uijPa46ggW0tbXqdEHKXXrCfcjA0nDXwUPPB67YPNdd9yt46IWTfc5vM8PuFUa8kGjDP8bHPwPtMMYqKg65EnD0aA2412AI8/O7Zq8VjubBHeFflOkIFqDXh1RUHKJIHS1DQ2hptPB7L+vYmK38vFeYeBOahQwsIkTqqLhbg+sh9xIykIGl4c9udXUVNg9/+zYs9uj1U1zlOe/Z82pq6mwwT16eEbtOpwvCq1a4nc8//1SvnwLmcRaA29Hrp+BVq7lzh3dFgHxHnAUofOUJt6A5sAjOha6s3CBka0DJSkmZgRd7hDjl7Ow4HEwDB/R4rRsxwt9VOytWhOfkVIIGQcDx49e0M2zYGJznDIHSzgLwEUX5jmABfNOYYlee6AZkYGn4wFV46FNSOvOchZGzq1zon81zFgauJSUfgHkYY1iAq3a6IqCLHREEUC609qEhtDRaOKXAOvZ1Kj/vpWRZT4EMLMIXsVR3L4/UkW+H3EuQgUVuuKEP6yh9ubnxV6/+Gx76mJhJ8NBfuNAye/Yw/BKwp556HB76wsLUI0f2oVWridi9ixePxatfUVET8KJRcfFKcF1ubjxuJyZmEnavjIDsbH1Dw15oJzMzkiH3Ch0RBOB2aA6sccjAIjxShzFmtZr79RsYG7uWdW5y6DwhuGDBmOzsSih9WVnRQpwyj2XmX8S5VgZDWFLSepznbLF0lr7XXiuFVSvGWHNzE27Hz28yrr0yAs6ePVlQ8DbU3ltvHXLtdpHOjiQkPII3e61fn4jbaW5uUvDaE25Di1jS8AEndq9bI2d4l0JPTuczxiTb6boAaMdVMPXPvseccqE1DlVgl6iercGkcqGVmfdSsqynQAYW4bnQqrtXMhdaefdSpI7Gob+vIhCpwxefEhNz4aFfunQimKehYV9GxiJ46Ldsya6tfQd+p01NnT18+Hgwj5ALjc8Y1dVVFxY+xV/Yy5ximZOTp0M7ggCbrXbVqnmSAphTMLVONzE5OU8ymkfoSFnZ2oMH34WOJCdPV/byE+5BFViEG4CXrOTkPF/fYNZR+jIyngfzrFwZsW1bAz6gh3dZ3HuvL552Yvfq9SF40Wjr1lxwL45l5qVv1KgA3o6zAJNpjqQA1hFMjQVg9wrRPEJHbLYDuCOjRgUofgcINyADS6OFTEnWtXDM/6ORM+4IoVnIwCK89KnuXsiFJvcSMpCBRXgutOru1Ujt5fvSCM1Ci1giEKnT1tY6a9ZQbJ7lyx+tqvqUP/SlpWuOHq2B9w/Fx4fec88oMI9OF4QzOmJjJ5eWdr7HqKRkNf8iY8xiScfJODpdEJxVYowJAlasmItd19CwF7fT3n4JgqnlBeCOCAL0+in4kNPs2cMUvPaE21AFloaXvoKCXePHh7COkgUPvdVqPnbsIH57mJ/fA2AegyEsOflZ/kVe+rB5ysoywXU8lhkn4wQGhvF2eOkTBGzfbsM1E7fTu/f1XRQgdEQQMG7cFBAQETEyP/8t5S8+0XXIwNJoYeTMOkbyqoyc8RUgtIvD4VBbAkEQ3cHhcHiRgQnCc6EhNEF4MGRggvBgyMAE4cGQgQnCgyEDE4QHQwYmCA+GDEwQHgwZmCA8GDIwQXgwZGCC8GDIwAThwZCBCcKDIQMThAdDBiYID6ankTpXrlzZu3dvc3PzHXfcERwcfNNNN/0isrrHqVOnamtrIyMjVdQAXLhw4fDhw9Onq5Cr/O233zY2NuL/MnDgwPvuu095JZzW1tb33nvvkUceGThwoFoavvrqq0OHDl28eHH48OH+/v5qybh69WpNTc2pU6f69+8fHBz8C1wQRw+or68fMWJETExMTk6Or6/v4MGDP/zww5402D3a2tqefPLJYcOGeXt79+vXT3kBzvz4449BQUE+Pj6q/N/feOMN4S4/9thjqijJz88PCAi4+eabGWM2m00VDQ6HIyMj409/+pPJZEpLS+vXr9/UqVOvXLmivIxTp06NGDFi1qxZubm5oaGhffv2fffdd3vYZo8MPHr06JCQEP7vf/3rX3fdddeoUaN6KKgbfP/99wcPHvz73//+5JNPasTAsbGxv/3tb1U08JQpUy4iLl26pIqS/fv3f/311zt37lTRwCdOnGCMvfHGG/xjdXU1Y2zr1q3KK5k9e/bo0aPhY1BQ0F133dXDNns0Bw4KChozZgz/9/XXXx8aGnr8+PHLly/3pM1u0Ldv3wkTJvA/81pg06ZNJ06cWLlypYoaevfufQuiT58+qsgICgq67bbbVPlfAz4+PsuWLbvnnnv4x0mTJnl5eZ06dUp5JfPnz3/iiSfgY3BwcHNz85UrV3rSZo/mwEVFRfjjd999d9ttt6n1rGiE/fv3r1u37tChQ7t27VJbC8EYYzfddNOmTZvg47FjxxwOR0hIiPJKHn/8cfzx6NGjDzzwQO/ePXp76y+WC3358uW9e/cuWrTol2rQE/niiy8WLFhQVVV1++23q6vkxIkT06dPP3v27H/913+Fh4cvXLjQy8tLXUmqs2/fvhMnTmzbtm3r1q3BwcFqyTh//vzhw4ffeuutXr167dixo4et/WIGXr58+W9+85usrKxfqkGP4/Lly48++qjZbB4/fry6SgICAl555ZVevXp9+eWXL7zwwuLFiz/++OOcnBx1ValORUXFV199xRg7ffp0e3u7t7e3KjKOHTu2bdu28+fPDxo06MyZM7feemuPmuvhHJpjsVjuvvvu5ubmX6S1bqPuIlZkZOSoUaN2dBATEzNo0KAdO3bs3r1bLUmcxx57rFevXu3t7WoJUHcRS+D8+fODBw/W6XRqC3FkZmZ6e3ufOnWqJ438Ahs5CgsLi4qK9u7de+edd/a8Nc/l17/+df/+/Us62Ldv3z/+8Y+SkpLXX39dXWFhYWF2u72lpUVdGRph8ODB06dPd/6lTXmio6Pb29vfe++9njTSoyH0v//979TU1I8//vjQoUP9+vVjjL3//vvff/89Xmr7z6GkpAR/LC8vz8rK+utf/6q8EpvN9rvf/W7AgAH8Y0tLyy233OLj46O8Ei1w7ty5qqqq5ORk+C8tLS2DBw9WXkllZeXdd989duxYkMEY66GS7hv473//e0RExNmzZ1evXv3BBx/w//jSSy8FBqr2Mo6rV686/uNz6r/99ltfX1+DwfDcc88xxs6cObNx48Z169apuIh19epVpt47QLZv356amurv7883YFVXV7/99tvl5eUKy7h69Wp0dHRAQMC7777LGGtvb1+1atV999338MMP96jdbg+++cTGmWeffbYnY/rusXbt2oCAgFtuuYUxNmHChMcff1x5DQKbN29WayOHyWQaMGDAjBkzZsyYMWbMmB07dqgiw+FwvPnmm0FBQUOGDGGM3XvvvSEhIX/7298U1vDPf/5zyZIlAwYMmDlz5kMPPXT33Xe/8MILCmvg7Nq1a+jQocOHD583b97vf//7efPmnTt3rodt0qtV/q84cODAzp071Vr7/fHHH1taWgYNGvQf/rM80N7e/uWXXw4YMABmFqrgcDi+/vrrS5cu+fj48HfT9RAyMEF4MHSckCA8GDIwQXgwZGCC8GDIwAThwZCBCcKDIQMThAfzv3eyux7Qfx6+AAAAAElFTkSuQmCC\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = max_rectangle_area(H)\r\n\r\nend\r\n","test_suite":"%%\r\nH = [2, 1, 4, 5, 1, 3, 3]\r\nbar(H)\r\na = max_rectangle_area(H)\r\na_correct = 8\r\nassert(isequal(a,a_correct))\r\n\r\n%% ones\r\nH = randi([1,100])\r\nbar(H)\r\na = max_rectangle_area(H)\r\na_correct = H\r\nassert(isequal(a,a_correct))\r\n\r\n%% two \r\nH = [31, 96]\r\nbar(H)\r\na = max_rectangle_area(H)\r\na_correct = 96\r\nassert(isequal(a,a_correct))\r\n\r\n%% two\r\nH = [31, 61]\r\nbar(H)\r\na = max_rectangle_area(H)\r\na_correct = 31*2\r\nassert(isequal(a,a_correct))\r\n\r\n%% two\r\nH = randi([1,100], 1,2)\r\nbar(H)\r\na = max_rectangle_area(H)\r\na_correct = max(2*min(H),max(H))\r\nassert(isequal(a,a_correct))\r\n\r\n%% \r\nv = randi([2,5]);\r\nn = randi([2,5]);\r\ni = randi([1,n]);\r\nH = ones(1,n);\r\nH(i) = v;\r\nH\r\nbar(H)\r\na = max_rectangle_area(H)\r\na_correct = max(v,n)\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nH = 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= max_rectangle_area(H)\r\na_correct = 355232\r\nassert(isequal(a,a_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":208445,"edited_by":208445,"edited_at":"2024-06-02T10:46:17.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2024-06-02T10:46:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-02T10:37:17.000Z","updated_at":"2024-06-02T10:46:17.000Z","published_at":"2024-06-02T10:37:17.000Z","restored_at":null,"restored_by":null,"spam":false,"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 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of a four-pointed star polygon","description":"Given the area A, of a rectangle with dimensions l1xl2, where the side lengths are integers and form the smallest possible perimeter, and given the total area A_t of the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, h, from their bases to the apices, find the vector [l1 l2 h] such that l1\u003cl2.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); 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: 490.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 245.4px; transform-origin: 408px 245.4px; vertical-align: baseline; \"\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; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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 area \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; \"\u003eA\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 a rectangle with dimensions \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; \"\u003el1xl2\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, where the side lengths are integers and form the smallest possible perimeter, and given the total area \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; \"\u003eA_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 of the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, \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; \"\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, from their bases to the apices, find the 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-style: italic; \"\u003e[l1 l2 h]\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 such that \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; \"\u003el1\u0026lt;l2\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: 418.8px; 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; perspective-origin: 385px 209.4px; text-align: left; transform-origin: 385px 209.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"508\" height=\"413\" style=\"vertical-align: baseline;width: 508px;height: 413px\" 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n2EHAAKKfOQRIvoMOwAQpAhHHuujz7ADACGJZOSxPvoMOwAQkkhGHoujz7ADAGEIe+SxMvoMOwAQtvBGHiujX1FRUVdXx7ADAGFoa2s7dOhQWVlZSM+yMvolJSWXXHKJw+Gw8AwAICmHwzFs2LCSkpKQnmXxpr906dKUlBRrzwAA0omLi0tJSVm6dGmoT7Q4+i6X65prrqH7ABCS5OTkwsJCl8sV6hOtv2Vz/fr1o0aNYuQBgCA5HI5Ro0YtW7YsjOdaH32NkQcAghb2sKMTIvqMPAAQpLCHHZ0Q0dcYeQAgCJEMOzpRoq8x8gBAryIcdnQCRZ+RBwB6EeGwoxMo+hojDwCcQ+TDjk6s6GuMPADQjSHDjk646DPyAEAXhgw7OuGirzHyAIAfo4YdnYjR1xh5AEDTNEOHHZ2g0WfkAQDN0GFHJ2j0NUYeALZn7LCjEzf6GiMPABszfNjRCR19Rh4AtmX4sKMTOvoaIw8AWzJj2NGJHn2NkQeAzZg07OgkiD4jDwBbMWnY0UkQfY2RB4BtmDfs6OSIvsbIA8AGTB12dNJEn5EHgPJMHXZ00kRfY+QBoDSzhx2dTNHXGHkAKCoKw45Osugz8gBQUhSGHZ1k0dcYeQAoJzrDjk6+6GuMPAAUErVhRxda9Pfu3Zudnb1161aTThMkRh4AyojasKMLIfpNTU1LlixpbGw07zTBY+QBoIBoDju6YKPv8Xjuueeejz/+2NTThISRB4DUojzs6AJH/8yZM++//35eXl5dXd3o0aOjcKYgMfIAkFqUhx1d4Ojv27fviSeeiI2NXbVq1Y033hiFMwWPkQeApKI/7OgCRz82NvbOO+/csmXLxIkTo3CgUDHyAJCOJcPOTx864FuMHj1aqFWnC33k+ec//9nQ0GD1WQAgKJYMO7rA0Q+Px+MpKyvr/KHT6TTv01u/fn1ubm5zc3NbW5tJHwIAjGLVsKMz68VZXq/X/4dpaWkmfSAdIw8AKVg47Px0AJPer9PpLCkpMemdd8fIA0AKFg47Oin/GoYecScPAMFZO+zo1Im+xsgDQGCWDzs6paLPy7UACMvyYUenVPQ1Rh4AQhJh2NGpFn2NkQeAYAQZdnShRX/u3Ln19fVTp0416TSGYOQBIBRBhh2dglf6GiMPAGGIM+zo1Iy+xsgDQABCDTs6ZaPPyAPAckINOzplo68x8gCwlGjDjk7l6GuMPAAsIuCwo1M8+ow8ACwh4LCjUzz6GiMPgKgTc9jRqR99jZEHQBQJO+zobBF9Rh4AUSPssKOzRfQ1Rh4AUSHysKOzS/Q1Rh4AJhN82NHZKPqMPABMJfiwo7NR9DVGHgCmEX/Y0dkr+hojDwATSDHs6GwXfUYeAIaTYtjR2S76GiMPAEPJMuzo7Bh9jZEHgEEkGnZ0No0+Iw8AQ0g07OhsGn2NkQdAxOQadnT2jb7GyAMgAtINOzpbR5+RB0DYpBt2dLaOvsbIAyAsMg47OrtHX2PkARAiSYcdHdFn5AEQGkmHHR3R1zRGHgBBk3fY0RH9nzDyAAhI6mFHR/R/wsgDICCphx0d0f8fRh4AvZB92NER/Z9h5AHQIwWGHR3R/xlGHgA9UmDY0RH9rhh5AHShxrCjI/o9YOQB0EmZYUdH9HvAyAOgkzLDjo7o94yRB4Cm1rCjI/rnxMgD2Jxiw46O6J8TIw9gc4oNOzqi3xtGHsC21Bt2dEQ/AEYewIaUHHZ0RD8ARh7AhpQcdnREPzBGHsBWVB12dEQ/KIw8gE0oPOzoiH5QGHkAm1B42NER/WAx8gDKU3vY0RH9EDDyAApTftjREf0QMPIAClN+2NER/dAw8gBKssOwoyP6IWPkARRjk2FHR/RDxsgDKMYmw46O6IeDkQdQhn2GHR3RDxMjD6AAWw07OqIfJkYeQAG2GnZ0RD98jDyA1Ow27OiIfkQYeQBJ2XDY0RH9iDDyAJKy4bCjI/qRYuQBpGPPYUdH9A3AyANIxLbDjo7oG4CRB5CIbYcdHdE3BiMPIAU7Dzs6om8YRh5AcDYfdnRBRd/r9RYXF48aNSozMzMnJ+fPf/5ze3u72SeTDiMPIDibDzu6wNHft29ffn7+hx9+eOWVV+bn53d0dDz11FOLFy+m+90x8gDCYtjRBYh+e3v7q6++euLEiZdeemndunXLly/fsmVLTk7Oxo0b3W53dI4oF0YeQEAMO50CRL++vt7tdrtcruuuu05/JCkpqaSkpE+fPu+//77P5zP9gLJh5AEExLDTKUD0P//888bGxquvvjohIaHzwYyMjLS0tM8++6ypqcnk40mJkQcQCsOOvwDRP3r0qKZpo0aN8n+wT58+F1xwwYkTJ1paWkw8mswYeQBBxMfHM+z4CxD9r776qvuD/fr1Gzx4cEtLy4kTJ8w5lfT0kSc5OdnqgwB2l5iYyLDjL673n+7xFp2YmJjzzgvwp4XH4ykrK+v8odPptNsv+vr163Nzc91tbVYfBLAvd0KCpml2i0/vAkQ/Pj6++4M+n+/s2bO9P9Hr9fr/MC0tLdSTKWDp0qULFy4s83g6Ojqam5utPg5gI0lJSXFxcWlpaSUFBQUFBVYfRyABov9///d/3R88derU0aNHExMTBwwYcK4nOp3OkpKSSE8nOZfLVVlZ6Xa7Fy5ceOjQoaamJr4LApgtMTExKSlp2LBhJSUl5L67ACuNHv26ujr/B0+fPv39998PGDAgMTHRxKOpQk//O++8k5WVlZ6ezi8aYJLExMQhQ4ZkZWWVl5dXVlZS/B4FiP4ll1wyaNAgt9vd2tra+eDBgwcPHTp0+eWX843K4JF+wDzkPngBop+WljZ+/Hi3271161b9pVjNzc3l5eVnz569+eabY2JionJIdZB+wFjkPlQBNv2EhIT7779/9+7dv/3tb9evXz906NCqqqpjx44VFRXxDfGwsfUDkdO3+0suuYTtPjS+INTX1997770jR47MyMi45ppr3njjjdOnT/fy9hs2bJg/f34w7xmffPLJpEmTuOoHgqdf3U+aNGnDhg1W/xcsnwBX+rqMjIzXXnvN7N9Ie+KqHwgeV/eRCyr6MBvpB3pH7o1C9AVC+oHuyL2xiL5wSD+gI/dmIPqCIv2wM3JvHqIvNNIPuyH3ZiP6EiD9sANyHx1EXxqkH6oi99FE9CVD+qESch99RF9KpB+yI/dWIfoSI/2QEbm3FtGXHumHLMi9CIi+Ikg/REbuxUH0lUL6IRpyLxqiryDSDxGQezERfWWRfliF3IuM6CuO9COayL34iL4tkH6YjdzLgujbCOmHGci9XIi+7ZB+GIXcy4jo2xTpRyTIvbyIvq2RfoSK3MuO6IP0IyjkXg1EHz8h/TgXcq8Soo+fIf3wR+7VQ/TRA9IPcq8qoo9zIv32RO7VRvQRAOm3D3JvB0QfQSH9aiP39kH0EQLSrx5ybzdEHyEj/Wog9/ZE9BEm0i8vcm9nRB8RIf1yIfcg+jAA6RcfuYeO6MMwpF9M5B7+iD4MRvrFQe7RHdGHKUi/tcg9zoXow0SkP/rIPXpH9GE60h8d5B7BIPqIEtJvHnKP4BF9RBXpNxa5R6iIPixA+iNH7hEeog/LkP7wkHtEgujDYqQ/eOQekSP6EALp7x25h1GIPgRC+rsj9zAW0YdwSL+O3MMMRB+CsnP6yT3MQ/QhNLuln9zDbEQfErBD+sk9ooPoQxqqpp/cI5qIPiSjUvrJPaKP6ENKsqef3MMqRB8SkzH95B7WIvqQnizpJ/cQAdGHIkROP7mHOIg+lCJa+sk9REP0oSAR0k/uISaiD2VZlX5yD5ERfSgumukn9xDfeSG99d69e7Ozs7du3WrSaQCT6Ol/5513srKy0tPTExMTjX3/iYmJQ4YMycrKKi8vr6yspPgQVghX+k1NTUuWLGlsbDTvNICpzLjq5+oecgk2+h6Pp7i4+L///a+BH9vj8WialpaWZuD7FAqfoJiMSr8CuZf0dzB4fILdBZ53zpw58/777+fl5dXV1Y0ePTr803VTUVFRUVFh4DsUDZ+gyCIZfJQZc6T+HQwGn2B3ga/09+3b98QTTzgcjlWrVn366af79u0L93iAcEK96lfg6h42F/hKPzY29s4779yyZcvEiROjcCAg+oK56lfm6h42F/hKf/To0cauOoCYznXVz9U9VGLWffoej6esrKz3t3G73SZ9dEHwCUqqoKDA7Xbv2LEjOTm5o6PD4XCkpaUVFBQE81UtF1V/BzvxCXZyOp0ul0szKfqpqan6e+9dMG8jNT5BeblcLoU/u07Kf458gp067/D5KfotLS1z5szx/0PD5XKtXr06vNew2OQ/GACQTmivyAUASO2nK/3ExMR169ZZexQAgNm40gcAGyH6AGAjRB8AbCTG5/NZfQYAQJRwpQ8ANkL0AcBGiD4A2Igo0W9pabnrrrvmz59v9UGMsX///qKiohEjRgwfPnzatGmbN29W9XsnW7dudTqde/bssfogRvL5fNXV1TNnzhwxYkRmZubEiROXLFly8uRJq89lmDNnzmzatGnatGnDhw8fMWLEzJkzq6urVf0SbW5uLioquvbaa48dO2b1WQxz4MCBCRMmZHazcuXKgM8VIvpnzpx58803q6qqrD6IMbZu3VpQUFBTUzN58uQZM2YcPXp03rx5a9asUe8/qi+//HLJkiVtbW1WH8RIPp9vzZo1s2bN2rNnz+TJk/Pz88+ePbtq1ap58+Y1NzdbfToDdHR0PPPMMw8++ODRo0dnzJgxffr02traWbNmKfkl6vP5Vq9eXV1dbfVBDObxeBobGwcMGJD2c0lJSYGf7LPaDz/88Oyzz2ZmZmZkZDz88MNWHydSx48fz8vLu/rqq3fv3q0/4vF4pk6dOmHChNraWmvPZqyamppJkyZlZGRcccUVn376qdXHMUxtbe2ECROmTp1aX1+vP/LDDz8sWrQoIyPjD3/4g7VnM8SuXbvGjh1bWFh4/Phx/RH9SzQnJ+frr7+29myGq6ysHDlyZEZGRm5u7rfffmv1cQzz2muvZWZmbtu2LYznWnylv3///ttuu+3111+/7LLLHA6HtYcxhP6Pi91www3jxo3TH0lNTX3wwQe/++67bdu2WXs2o7S2tq5evfr222//8ccfMzIyrD6Owf71r381NDTccccdnZ9aQkLCPffcM2jQoOrq6sj/IXXLffHFFw6Ho6ioKDk5WX8kNTX1+uuv93q9tbW11p7NWA0NDc8///xll112+eWXW30Wg33++ecXXHDBxRdfHMZzrYx+S0vLU089tXfv3tLS0qeffjo+Pt7Cwxhl586d7e3tTqczJiam88FRo0ZdeOGFu3bt+vHHHy08m1E+/vjjF154ITU1de3atVlZWVYfx2BHjx4dNGjQZZdd5v9gv379+vbta9WRjDV79uzq6uq8vLzORzo6Og4dOuRwOAYMGGDhwYzV0dFRVlbW0NDw6KOPBjV6yKOlpcXj8Vx88cWDBw8O4+kWX+mPGTNm06ZN8+bN69Onj7UnMcrRo0eTkpK6/OP0AwYMSEhIaGxsVGP+djgcixYt+stf/jJixAirz2K83/3ud9XV1dnZ2f4P/uc//zl8+HBqamq/fv2sOphJGhoannnmmb///e+TJ08eM2aM1ccxzJYtWzZu3Dhnzhz1/uG/kydPer3epKSk8vLy7OzszMzM7Ozs4O81MOtfzgpGYmLiY489ZuEBDHfq1Kke7xA4//zzhwwZcuTIETWu9HNycnJycqw+RfR4vd6XXnqpX79+t9xyi///wMnu2LFjM2fO/OabbzRNy8/Pf+qppxISEqw+lDG8Xu+LL76Yk5Nz++23nzlzxurjGMzr9TY2Nnq93vr6epfL1bdv36qqqlWrVm3fvn3NmjWpqam9P12Iu3eU4fP5Ojo6evyp887jl1pKDQ0NDz/8cH19/bx58yZMmGD1cYz0/fffZ2dn5+fnX3TRRRs3brz33nsPHz5s9aEM0N7evmLFipMnT86fP1+ZP8b8nThxom/fvoWFhZWVleXl5cuXL//oo48KCwu/+OKLl19++VwJ6mTllb56YmJi4uJ6/iU9e/ZslA+DyH355ZcPPPBAbW1tcXHx3XffrdJlvqZpl1566fLlyzVNa29vX7x48VtvvVVeXv7MM8+c62tYFh9++OHGjRufeOKJSy+91OqzmGLq1Km7d+/2fyQhIeH+2/fxkwAAAzpJREFU+++vqqqqqqo6duzY0KFDe3l6NC4/V65c6f/ygXHjxin2Wp5O/fr1u+iii7o//sMPPxw5cmTgwIHKfDPQDv79738XFRXV19cvXry4pKREjRsNehQfHz937twhQ4ZUV1c3NTVZfZyI6K8d+eUvf3nrrbdafZaoSk5OTk9PP3nyZGNjY+9vKfcf6QIaNmxYc3Pzt99+O3bs2M4HT5w40draeuGFF6pxW6ryfD5fRUXF448/3rdv35dffvkXv/iFYtf43Q0cODA9Pf3IkSM+yV+fdfDgwcOHDx8+fHjTpk1dfsrlcqWnp7/77rs9XpnJpbm52eFwdL8QiYuLi42N7f250Yj+3Llz586dG4UPJILx48fHx8dXVVX5l+Kzzz777rvvrr76aq70pfDhhx8+/vjjF1100SuvvKLSDS2app0+ffrJJ5/ctm3bihUr/O9Q8nq9Bw8eTEtLk/1LdPDgwUVFRf6PtLe3V1ZWtra2Tp069eKLL5b9wqujo+Ohhx7avHnzqlWrpk6d2vm41+s9cOBAMPdxcqVvsJEjRw4fPnzTpk033XTTVVddpWma1+tdsWJFSkrKlClTrD4dAqupqXnyySfT09NXr16t3kvP+vTpM3bs2Hfffbe8vHzFihX6DezNzc0vvvhiY2PjvffeK/ut+mPGjHnuuef8H2lpaZkzZ47X6120aJEC1/hxcXHXX3/95s2b33jjjauuukp/hV1TU9Ozzz57/PjxOXPmDBw4MMB7iMo5bSQlJaW4uLi0tHT27Nm5ubl9+/bdvn37qVOnHnnkESXvaldMR0fHn/70J/0VFXfddVeXnx0/fvzzzz8v+636N9988yeffPLBBx9MmTLF5XJpmrZ9+/aWlpYZM2bMnj3b6tMhsOnTpxcWFr711lvXXnvttddeq/3/38G8vLxZs2YFfDrRN96vfvWrQYMGLV269KOPPjp79uzw4cNLS0unT5+u/C6sgOPHj9fU1GiadurUqVOnTnX52bS0NNknb03TkpKSli1bNmnSpJUrV37wwQeapg0fPvw3v/nNjTfeqPA3q1USHx//9NNPZ2dnv/rqq2H8DvLPJQKAjfCKIQCwkf8Hdwfp4F3vy5sAAAAASUVORK5CYII=\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = star_polygon(A,A_t)\r\n  y = A;\r\nend","test_suite":"%%\r\nA = 10;\r\nA_t = 24;\r\ny_correct = [2 5 2];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 11;\r\nA_t = 23;\r\ny_correct = [1 11 1];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 72;\r\nA_t = 106;\r\ny_correct = [8 9 2];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nfiletext = fileread('star_polygon.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 156;\r\nA_t = 180;\r\ny_correct = [12 13 0.96];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 168;\r\nA_t = 190;\r\ny_correct = [12 14 11/13];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-14T17:36:31.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-13T17:02:46.000Z","updated_at":"2026-01-15T09:17:29.000Z","published_at":"2025-11-14T17:36:31.000Z","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 w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a rectangle with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1xl2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where the side lengths are integers and form the smallest possible perimeter, and given the total area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_t\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, from their bases to the apices, find the vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[l1 l2 h]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1\u0026lt;l2\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"413\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"508\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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a 4-pointed star polygon by a circle sector","description":"Given the area, A, of a 4-pointed star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, consider the circle that covers the greater of the two distances between opposite vertices (cf. figure below).\r\nGiven (A,h), find\r\nthe width, L, of the rectangle;\r\nthe angle, α [in Radians], of the sector of the circle such that its area is equal to A;\r\nthe minimum slicing number n, corresponding to the number of congruent circle slices, such that the area of one slice does not exceed the above sector area.\r\ninput: (A, h)\r\noutput: y = [L alpha 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: 751.55px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 375.775px; transform-origin: 408px 375.775px; vertical-align: baseline; \"\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: 384px 31.5px; text-align: left; transform-origin: 384px 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=\"\"\u003eGiven the area, \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; \"\u003eA\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 a 4-pointed star polygon formed by the rectangle, with dimensions \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; \"\u003eL\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; \"\u003e2L\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 four triangles, with height \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; \"\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 from their bases to the vertices, consider the circle that covers the greater of the two distances between opposite vertices (cf. figure below).\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: 384px 10.5px; text-align: left; transform-origin: 384px 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=\"\"\u003eGiven \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; \"\u003e(A,h)\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\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.75px; 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: 391px 40.875px; transform-origin: 391px 40.875px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; 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: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; 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 width, \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; \"\u003eL,\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 the rectangle;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; 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 angle, \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; \"\u003eα\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 [in Radians], of the sector of the circle such that its area is equal to \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; \"\u003eA\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: 40.875px; 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: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; 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 minimum slicing number \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, corresponding to the number of congruent circle slices, such that the area of one slice does not exceed the above sector area.\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: 384px 10.5px; text-align: left; transform-origin: 384px 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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-style: italic; \"\u003e(A, h)\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: 384px 10.5px; text-align: left; transform-origin: 384px 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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; \"\u003ey = [L alpha n]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 486.8px; 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: 384px 243.4px; text-align: left; transform-origin: 384px 243.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"601\" height=\"481\" style=\"vertical-align: baseline;width: 601px;height: 481px\" 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\" alt=\"Covering by sector\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = covering_by_sector(A,h)\r\n  y = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nh = 1;\r\ny_correct = [3 3.375 2];\r\nassert(isequal(covering_by_sector(A,h),y_correct))\r\n\r\n%%\r\nA = 36;\r\nh = 2;\r\ny_correct = [3 2.88 3];\r\nassert(isequal(covering_by_sector(A,h),y_correct))\r\n\r\n%%\r\nA = 45;\r\nh = 3;\r\ny_correct = [3 2.5 3];\r\nassert(isequal(covering_by_sector(A,h),y_correct))\r\n\r\n%%\r\nfiletext = fileread('covering_by_sector.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 56;\r\nh = 2; \r\ny_correct = [4 28/9 3];\r\nassert(all(isapprox(covering_by_sector(A,h),y_correct), 'all'))\r\n\r\n%%\r\nA = 50;\r\nh = 5; \r\ny_correct = [2.5 16/9 4];\r\nassert(all(isapprox(covering_by_sector(A,h),y_correct), 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-12-03T10:39:21.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-30T14:56:09.000Z","updated_at":"2026-03-23T10:36:12.000Z","published_at":"2025-12-03T10:39:21.000Z","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\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a 4-pointed star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\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\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, consider the circle that covers the greater of the two distances between opposite vertices (cf. figure 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60431,"title":"Calculating the Union Area of Overlapping Rectangles","description":"Calculate the area covered by a union of multiple rectangles. Each rectangle is represented by 4 integers: the first two integers denote the coordinates of the bottom-left corner, and the next two integers denote the coordinates of the top-right corner. The input is provided as a matrix where each row represents one rectangle.\r\nThe rectangles can overlap, meaning that simply summing up the areas of each rectangle will not yield the correct total area. Instead, the overlapping regions should be counted only once.\r\n\r\nExample:\r\nGiven the rectangles [ 4  8 11 10;  6  3  8 10; 16  8 19 11 ] the area covered by the union of these rectangles is 33.\r\n\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 757.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 378.517px; transform-origin: 406.5px 378.517px; vertical-align: baseline; \"\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; perspective-origin: 383.5px 31.5px; text-align: left; transform-origin: 383.5px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.342px 7.81667px; transform-origin: 381.342px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the area covered by a union of multiple rectangles. Each rectangle is represented by 4 integers: the first two integers denote the coordinates of the bottom-left corner, and the next two integers denote the coordinates of the top-right corner. The input is provided as a matrix where each row represents one rectangle.\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; perspective-origin: 383.5px 21px; text-align: left; transform-origin: 383.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.5px 7.81667px; transform-origin: 383.5px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe rectangles can overlap, meaning that simply summing up the areas of each rectangle will not yield the correct total area. Instead, the overlapping regions should be counted only once.\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; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 7.81667px; transform-origin: 0px 7.81667px; 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; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.5px 7.81667px; transform-origin: 33.5px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample:\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; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 367.383px 7.81667px; transform-origin: 367.383px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the rectangles [ 4  8 11 10;  6  3  8 10; 16  8 19 11 ] the area covered by the union of these rectangles is 33.\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; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 7.81667px; transform-origin: 0px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 484.033px; 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; perspective-origin: 383.5px 242.017px; text-align: left; transform-origin: 383.5px 242.017px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"1077\" height=\"478\" style=\"vertical-align: baseline;width: 1077px;height: 478px\" 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rectangles_union(R)\r\n\r\nend","test_suite":"%% Example \r\nR =  [  4 8 11 10; 6 3 8 10; 16 8 19 11  ]\r\na = rectangles_union(R)\r\na_correct = 33\r\nassert(isequal(a,a_correct))\r\n\r\n%%  \r\nR =  [  4 8 11 10; 6 3 8 10; 16 8 19 11; 6 8 8 12  ]\r\na = rectangles_union(R)\r\na_correct = 37\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nR =  [  4 8 11 10; 4 8 6 12; 6 3 8 10; 16 8 19 11  ]\r\na = rectangles_union(R)\r\na_correct = 37\r\nassert(isequal(a,a_correct))\r\n\r\n%% Not overlapping\r\nR =  [  4 8 11 10; 16 8 19 11  ]\r\na = rectangles_union(R)\r\na_correct = 23\r\nassert(isequal(a,a_correct))\r\n\r\n%% Partial overlapping\r\nr = [ -3 -3 -1 -1 ];\r\nR =  [ r; r+1; r+2  ]\r\na = rectangles_union(R)\r\na_correct = 10\r\nassert(isequal(a,a_correct))\r\n\r\n%% Full Overlapping\r\nx1 = randi([10,20]);\r\ny1 = randi([10,20]);\r\na = randi([1,10]);\r\nb = randi([1,10]);\r\ns = a*b;\r\nR =  [  x1 y1 x1+a y1+b ; x1 y1 x1+a y1+b ]\r\na = rectangles_union(R)\r\na_correct = s\r\nassert(isequal(a,a_correct))\r\n\r\n%% Partial Overlapping\r\nx1 = randi([10,20]);\r\ny1 = randi([10,20]);\r\na = randi([1,10]);\r\nb = randi([1,10]);\r\nr1 = [x1 y1 x1+a y1+b];\r\nR =  [  r1 ; r1+1 ]\r\ns = 2*a*b-(a-1)*(b-1);\r\na = rectangles_union(R)\r\na_correct = s\r\nassert(isequal(a,a_correct))\r\n\r\n%% Partial Overlapping\r\na = randi([1,10]);\r\nb = randi([1,10]);\r\ns = a*b;\r\nR =  [  4, 8, 11, 10; 6, 3, 8, 10; 16, 8, 16+a, 8+b  ]\r\na = rectangles_union(R)\r\na_correct = 24 + s\r\nassert(isequal(a,a_correct))\r\n\r\n\r\n%% \r\nx1 = randi([10,20]);\r\ny1 = randi([10,20]);\r\nR = [x1 y1 x1 y1]\r\na = rectangles_union(R)\r\na_correct = 0\r\nassert(isequal(a,a_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":208445,"edited_by":223089,"edited_at":"2024-06-16T05:19:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-02T15:58:47.000Z","updated_at":"2024-06-16T05:19:18.000Z","published_at":"2024-06-02T15:58:47.000Z","restored_at":null,"restored_by":null,"spam":false,"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\u003eCalculate the area covered by a union of multiple rectangles. 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