Alternative Approach to Achieve a Solution of Derangement Problems by Dynamic Programming

Thitivatr Patanasakpinyo, Adel Sulaiman
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Abstract

Derangement is one well-known problem in the filed of probability theory. An in- stance of a derangement problem contains a finite collection C of n paired objects, C = {(x1 , y1 ), ..., (xn , yn )}. The derangement problem asks how many ways to gener- ate a new collection C′ ̸= C such that for each (xi,yj) ∈ C′,i ̸= j. We propose an efficient dynamic programming algorithm that divides an instance of the derangement problem into several subproblems. During a recursive process of unrolling a subproblem, there exists a repeated procedure that allows us to make a use of a subsolution that has already been computed. We present the methodology to formulate a concept of this subproblem as well as parts of designing and analyzing an efficiency of the proposed algorithm.
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用动态规划实现无序问题求解的可选方法
错乱是概率论领域中一个众所周知的问题。无序问题的一个实例包含n个配对对象的有限集合C, C = {(x1, y1),…, (xn, yn)}。无序问题要求有多少种方法生成一个新的集合C′′′,使得对于每个(xi,yj)∈C′,i′′= j。我们提出了一种有效的动态规划算法,该算法将无序问题的一个实例划分为几个子问题。在展开子问题的递归过程中,存在一个重复的过程,允许我们使用已经计算过的子解。我们给出了该子问题概念的形成方法,以及算法设计和效率分析的部分内容。
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1.60
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ARCH-COMP23 Category Report: Hybrid Systems Theorem Proving ARCH-COMP23 Category Report: Continuous and Hybrid Systems with Linear Continuous Dynamics ARCH-COMP23 Category Report: Continuous and Hybrid Systems with Nonlinear Dynamics ARCH-COMP23 Repeatability Evaluation Report ARCH-COMP23 Category Report: Artificial Intelligence and Neural Network Control Systems (AINNCS) for Continuous and Hybrid Systems Plants
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