Greedy Pancake Flipping
نویسندگان
چکیده
We prove that a stack of pancakes can be rearranged in all possible ways by a greedy process: Flip the maximum number of topmost pancakes that gives a new stack. We also show that the previous Gray code for rearranging pancakes (S. Zaks, A New Algorithm for Generation of Permutations BIT 24 (1984), 196-204) is a greedy process: Flip the minimum number of topmost pancakes that gives a new stack.
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...
متن کاملPancake Flipping Is Hard
Pancake Flipping is the problem of sorting a stack of pancakes of different sizes (that is, a permutation), when the only allowed operation is to insert a spatula anywhere in the stack and to flip the pancakes above it (that is, to perform a prefix reversal). In the burnt variant, one side of each pancake is marked as burnt, and it is required to finish with all pancakes having the burnt side d...
متن کاملComputing with living hardware
Our multi-institutional team of eleven undergraduates, one high school student, one postdoctoral fellow, and four faculty members explored the emerging field of synthetic biology and presented our results at the 2006 international Genetically Engineered Machine (iGEM) competition. Having had little or no previous research experience, biology, chemistry and mathematics students from four differe...
متن کاملThe Intrepid Waitress Problem
An intrepid waitress leaves a restaurant kitchen with a stack of n different sized pancakes. Before she reaches her patrons, she wishes to iterate through all possible stack orderings using only a spatula and performing flips of various sizes. But is this possible? This problem corresponds to constructing a Hamilton path in the “pancake network”, or equivalently, to find a Gray code for permuta...
متن کاملIndependent Even Cycles in the Pancake Graph and Greedy Prefix-Reversal Gray Codes
Any `–cycle, 6 6 `6 n!, can be embedded in the Pancake graph Pn, n > 3. In this paper we prove the existence of a family of maximal sets of even independent cycles with length bounded by O(n2). We introduce the new concept of Prefix– reversal Gray codes based on the independent cycles which extends the known greedy Prefix–reversal Gray code constructions considered by Zaks and Williams. We deri...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 44 شماره
صفحات -
تاریخ انتشار 2013