Solving Yin-Yang Puzzles Using Exhaustive Search and Prune-and-Search Algorithms

Abstract

—We investigate some algorithmic and mathematical aspects of Yin-Yang/Shiromaru-Kuromaru puzzles. Specifically, we discuss two algorithms for solving arbitrary Yin-Yang puzzles, namely the exhaustive search approach and the prune-and-search technique. We show that both algorithms have an identical asymptotic running time of O (max { mn, 2 mn − h } ) for finding all solutions of a Yin-Yang instance with h hints of size m × n . Nevertheless, our experiments show that the practical running time of the prune-and-search technique outperforms the conventional exhaustive search approach.