Polynomial-time sortable stacks of burnt pancakes
نویسندگان
چکیده
منابع مشابه
Polynomial-time sortable stacks of burnt pancakes
Pancake flipping, a famous open problem in computer science, can be formalised as the problem of sorting a permutation of positive integers using as few prefix reversals as possible. In that context, a prefix reversal of length k reverses the order of the first k elements of the permutation. The burnt variant of pancake flipping involves permutations of signed integers, and reversals in that ca...
متن کاملGreedy 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 ...
متن کاملon the Problem of Sorting Burnt Pancakes
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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We address the problem of the number of permutations that can be sorted by two stacks in series. We do this by first counting all such permutations of length less than 20 exactly, then using a numerical technique to obtain nineteen further coefficients approximately. Analysing these coefficients by a variety of methods we conclude that the OGF behaves as S(z) ∼ A(1− μ · z) , where μ = 12.45± 0....
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2011
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2010.11.004