Problem 42498. Pancake sorting - minimum flips.

Created by Jan Orwat

Solve Later

{"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":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Sort a stack of pancakes by flipping them using spatula.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>There are</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>N</w:t></w:r><w:r><w:t> pancakes with diameters</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>1:N</w:t></w:r><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Spatula can be inserted anywhere in the stack and used to flip all the pancakes above.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Sort pancakes in increasing order.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Return a vector of places where spatula was inserted.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Minimize number of flips, your score will depend on the number of flips in the last few tests.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>References:</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.math.illinois.edu/~dwest/openp/pancake.html\"><w:r><w:t>math.illinois.edu</w:t></w:r></w:hyperlink><w:r><w:t>,</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Pancake_sorting\"><w:r><w:t>wikipedia</w:t></w:r></w:hyperlink><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example (horizontal view):</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[Initial stack: 6 4 2 5 3 1, (\",\" indicates position of spatula)\nfirst flip: 1 3 5,2 4 6\nsecond: 5 3 1 2 4,6\n... 4 2 1 3,5 6\n 3 1 2,4 5 6\n 2 1,3 4 5 6\nsorted! 1 2 3 4 5 6\n\npositions of spatula from the begining: 6 3 5 4 3 2]]></w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Sort a stack of pancakes by flipping them using spatula.<ul><li>There are N pancakes with diameters 1:N.</li><li>Spatula can be inserted anywhere in the stack and used to flip all the pancakes above.</li><li>Sort pancakes in increasing order.</li><li>Return a vector of places where spatula was inserted.</li><li>Minimize number of flips, your score will depend on the number of flips in the last few tests.</li><li>References: <a href = "http://www.math.illinois.edu/~dwest/openp/pancake.html">math.illinois.edu</a>, <a href = "https://en.wikipedia.org/wiki/Pancake_sorting">wikipedia</a>.</li></ul>Example (horizontal view):<pre class="language-matlab">Initial stack: 6 4 2 5 3 1, ("," indicates position of spatula)
first flip: 1 3 5,2 4 6
second: 5 3 1 2 4,6
... 4 2 1 3,5 6
 3 1 2,4 5 6
 2 1,3 4 5 6
sorted! 1 2 3 4 5 6
</pre><pre class="language-matlab">positions of spatula from the begining: 6 3 5 4 3 2
</pre>

Solve

Solution Stats

56 Solutions
23 Solvers

Last Solution submitted on Mar 08, 2021

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

Muthu Annamalai on 7 Aug 2015

William Gates and Christos Papadimitrou solved this problem, before the former left to co-found Microsoft. Very interesting problem indeed.

Problem Recent Solvers23

Problem Tags

pancakes sorting

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 42498. Pancake sorting - minimum flips.

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers23

Suggested Problems

More from this Author41

Problem Tags

Community Treasure Hunt

Problem 42498. Pancake sorting - minimum flips.

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers23

Suggested Problems

More from this Author41

Problem Tags

Community Treasure Hunt

Players