Finding All Solutions and Instances of Numberlink and Slitherlink by ZDDs
1
Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan
2
ERATO MINATO Project, Japan Science and Technology Agency, Kitaku North 14, West 9, Sapporo, 060-0814, Hokkaido, Japan
3
Graduate School of Information Science and Technology, Hokkaido University, Kitaku North 14, West 9, Sapporo, 060-0814, Hokkaido, Japan
*
Author to whom correspondence should be addressed.
Algorithms 2012, 5(2), 176-213; https://doi.org/10.3390/a5020176
Received: 16 November 2011
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Revised: 29 February 2012
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Accepted: 19 March 2012
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Published: 5 April 2012
(This article belongs to the Special Issue Puzzle/Game Algorithms)
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
Share and Cite
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. https://doi.org/10.3390/a5020176
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. https://doi.org/10.3390/a5020176
Chicago/Turabian StyleYoshinaka, Ryo, Toshiki Saitoh, Jun Kawahara, Koji Tsuruma, Hiroaki Iwashita, and Shin-ichi Minato. 2012. "Finding All Solutions and Instances of Numberlink and Slitherlink by ZDDs" Algorithms 5, no. 2: 176-213. https://doi.org/10.3390/a5020176
