Algorithms (Apr 2012)

Finding All Solutions and Instances of Numberlink and Slitherlink by ZDDs

  • Shin-ichi Minato,
  • Koji Tsuruma,
  • Hiroaki Iwashita,
  • Ryo Yoshinaka,
  • Toshiki Saitoh,
  • Jun Kawahara

DOI
https://doi.org/10.3390/a5020176
Journal volume & issue
Vol. 5, no. 2
pp. 176 – 213

Abstract

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Link puzzles involve finding paths or a cycle in a grid that satisfy given local and global properties. This paper proposes algorithms that enumerate solutions and instances of two link puzzles, Slitherlink and Numberlink, by zero-suppressed binary decision diagrams (ZDDs). A ZDD is a compact data structure for a family of sets provided with a rich family of set operations, by which, for example, one can easily extract a subfamily satisfying a desired property. Thanks to the nature of ZDDs, our algorithms offer a tool to assist users to design instances of those link puzzles.

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