Canonical Coin Changing and Greedy Solutions

Authors:
Lena Chang;James F. Korsh
Affiliations:
Department of Computer and Information Science, Temple University, Philadelphia, PA;Department of Computer and Information Science, Temple University, Philadelphia, PA
Venue:
Journal of the ACM (JACM)
Year:
1976

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Abstract

A natural, and readily computable, first guess at a solution to the coin changing problem is the canonical solution. This solution is a special case of the greedy solution which is a reasonable heuristic guess for the knapsack problem. In this paper, efficient tests are given to determine whether all greedy solutions are optimal with respect to a given set of knapsack objects or coin types. These results improve or extend previous tests given in the literature. Both the incomplete and complete cases are considered.