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Efficient Algorithms for a Generalized Shuffling Problem

机译:广义混洗问题的高效算法

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摘要

In this paper we study a set of generalized shuffling problems. The goal of each problem is to make a smallest number of moves to reach the final state of the problem from its initial state. We are interested in algorithms which, given integers n, generate the corresponding move sequences to reach the final state of the game with smallest number of steps. In this paper we present the optimal algorithms to generate the optimal move sequences of the problems consisting of n black coins and n white coins, and finally, we present the explicit solutions for all of the generalized shuffling problems of size n.
机译:在本文中,我们研究了一组广义改组问题。每个问题的目标是进行最少的移动,以从其初始状态达到问题的最终状态。我们对给定整数n的算法感兴趣,这些算法会生成相应的移动序列,以最少的步数达到游戏的最终状态。在本文中,我们提出了用于生成由n个黑硬币和n个白硬币组成的问题的最优移动序列的最优算法,最后,我们给出了所有大小为n的广义混洗问题的显式解。

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