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Algorithms 2012, 5(2), 176-213; doi:10.3390/a5020176
Article

Finding All Solutions and Instances of Numberlink and Slitherlink by ZDDs

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Received: 16 November 2011; in revised form: 29 February 2012 / Accepted: 19 March 2012 / Published: 5 April 2012
(This article belongs to the Special Issue Puzzle/Game Algorithms)
Download PDF [298 KB, uploaded 5 April 2012]
Abstract: 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.
Keywords: link puzzles; Slitherlink; Numberlink; solvers; instance generations link puzzles; Slitherlink; Numberlink; solvers; instance generations
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Yoshinaka, R.; Saitoh, T.; Kawahara, J.; Tsuruma, K.; Iwashita, H.; Minato, S.-I. Finding All Solutions and Instances of Numberlink and Slitherlink by ZDDs. Algorithms 2012, 5, 176-213.

AMA Style

Yoshinaka R, Saitoh T, Kawahara J, Tsuruma K, Iwashita H, Minato S-I. Finding All Solutions and Instances of Numberlink and Slitherlink by ZDDs. Algorithms. 2012; 5(2):176-213.

Chicago/Turabian Style

Yoshinaka, Ryo; Saitoh, Toshiki; Kawahara, Jun; Tsuruma, Koji; Iwashita, Hiroaki; Minato, Shin-ichi. 2012. "Finding All Solutions and Instances of Numberlink and Slitherlink by ZDDs." Algorithms 5, no. 2: 176-213.


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