Greedy flipping of pancakes and burnt pancakes
نویسندگان
چکیده
منابع مشابه
Greedy flipping of pancakes and burnt pancakes
We prove that a stack of n pancakes is rearranged in all n! ways by repeatedly applying the following rule: Flip the maximum number of pancakes that gives a new stack. This complements the previously known pancake flipping Gray code (S. Zaks, A New Algorithm for Generation of Permutations BIT 24 (1984), 196–204) which we also describe as a greedy algorithm: Flip the minimum number of pancakes t...
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A stack of n pancakes can be rearranged in all n! ways by a sequence of n!−1 flips, and a stack of n ‘burnt’ pancakes can be rearranged in all 2nn! ways by a sequence of 2nn!−1 flips. In both cases, a computer program can efficiently generate suitable solutions. We approach these tasks instead from a human perspective. How can we determine the next flip directly from the current stack? How can ...
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The “pancake problem” is a well-known open combinatorial problem that recently has been shown to have applications to parallel processing. Given a stack of n pancakes in arbitrary order, all of different sizes, the goal is to sort them into the size-ordered configuration having the largest pancake on the bottom and the smallest on top. The allowed sorting operation is a “spatula flip”, in which...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2016
ISSN: 0166-218X
DOI: 10.1016/j.dam.2016.02.005