2008/09/02 by Xuan Cai, Cai, Xuan
Computer Science · Engineering · #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #G.2.1 #Optimization and Packing Problems #cs.DM #cs.DS
paper · pdf · doi:10.48550/arxiv.0809.0400
7 pages
openalex publication_date 2008/09/02 · arxiv created 2009/03/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Change-Making Problem is to represent a given value with the fewest coins under a given coin system. As a variation of the knapsack problem, it is known to be NP-hard. Nevertheless, in most real money systems, the greedy algorithm yields optimal solutions. In this paper, we study what type of coin systems that guarantee the optimality of the greedy algorithm. We provide new proofs for a sufficient and necessary condition for the so-called canonical coin systems with four or five types of coins, and a sufficient condition for non-canonical coin systems, respectively. Moreover, we present an O(m2) algorithm that decides whether a tight coin system is canonical.