A Comparison of Warnsdorff’s Rule and Backtracking for Knight’s Tour on Square Boards

Abstract

Knight’s tour has been an intriguing chess puzzle for many computer scientists and mathematicians. In this paper, we describe and analyze two of the most commonly used algorithms to solve the Knight’s tour puzzle in computer science—Warnsdorff’s rule and backtracking. Various case studies are performed to showcase the differences in time complexity of each algorithm. We also point out that the starting position and dimensions of a board play a key role in determining whether a tour is possible. By doing this, we prove that a tour does not exist when the knight starts from odd squares on boards of odd dimensions.