A greedy approach to the coin exchange problem

Abstract

We consider a variation of the well known coin changing problem: Suppose that we buy some merchandise priced at x dollars in a cur- rency with n kinds of coins valued at c1; c2; ¢ ¢ ¢ ; cn dollars. What is the fewest possible number of coins required to be exchanged? In this paper, we propose a greedy algorithm, which ¯nds optimal so- lutions for the case when ci = ci¡1; i = 1; :::; n. Also if we apply our greedy algorithm to general input, then we can determine the solution to be optimal or not in O(ncn) time.