Daxin Zhu
Quanzhou Normal University

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A Complete Combinatorial Solution for a Coins Change Puzzle and Its Computer Implementation Daxin Zhu; Xiaodong Wang
Indonesian Journal of Electrical Engineering and Computer Science Vol 12, No 8: August 2014
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijeecs.v12.i8.pp6338-6345

Abstract

In this paper, we study a combinatorial problem encountered in monetary systems. The problem concerned is to find an optimal solution R(k; n) of a combinatorial problem for some positive integers k and n. To the authors' knowledge, there is no eficient solutions for this problem in the literatures so far. We first show how to find an eficient recursive construction algorithm based on the backtracking search strategy. Furthermore, we can give an explicit formula for finding the maximal elements of the solution. Our new techniques have improved the time complexities of the search algorithm dramatically.