Problem 42498. Pancake sorting - minimum flips.

Created by Jan Orwat

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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>

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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.

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Problem 42498. Pancake sorting - minimum flips.

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