A Complete Combinatorial Solution for a Coins Change Puzzle and Its Computer Implementation
نویسندگان
چکیده
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 efficient solutions for this problem in the literatures so far. We first show how to find an efficient 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.
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