A New Algorithm for the Subtraction Games
Guanglei He, Zhihui Qin
TL;DR
This paper introduces a simplified algorithm for solving subtraction games, enabling efficient identification of winning and losing positions, and offering an alternative to the traditional Sprague-Grundy Theory.
Contribution
The paper presents a new, simpler algorithm for subtraction games that improves ease of use over the Sprague-Grundy Theory.
Findings
The algorithm effectively identifies winning and losing positions.
It is simpler to implement than Sprague-Grundy Theory.
The method applies to one-pile subtraction games.
Abstract
Subtraction games is a class of combinatorial games. It was solved since the Sprague-Grundy Theory was put forward. This paper described a new algorithm for subtraction games. The new algorithm can find win or lost positions in subtraction games. In addition, it is much simpler than Sprague-Grundy Theory in one pile of the games.
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Taxonomy
TopicsArtificial Intelligence in Games · Software Engineering and Design Patterns · Logic, programming, and type systems