The Designs and Analyses of Improved Algorithms for the Counterfeit Coins Problem

Abstract

The counterfeit coin problem is a well-known problem. Many researchers have tried to make the problem more challenging by considering some constraints for the problem. There were also a lot of researchers presenting different algorithms for variants of the problem. In this paper, we propose some improved algorithms and strategies to solve some kinds of the counterfeit coin problems, including the 2-counterfeit coins problem with unknown weights, the 3-counterfeit coins problem with known weights, the 3-counterfeit coins problem with unknown weights, the 4-counterfeit coins problem with known weights, the 4-counterfeit coins problem with unknown weights. We also tackle the k-counterfeit coins problem with unknown weights by improving the algorithm proposed by Li-Jhong Li, in which he only dealt with the k-counterfeit coins problem with known weights. In addition, we provide the analyses of the algorithms for these counterfeit coins problems. According to the analyses, we know the theoretical lower bound of the numbers of weightings to identify the counterfeit coins in a mass of coins. Thus, we can know which strategy of the problem might be further improved.