Solving and Generating Nagareru Puzzles

Authors Masakazu Ishihata, Fumiya Tokumasu

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Author Details

Masakazu Ishihata
  • NTT Communication Science Laboratories, Kyoto, Japan
Fumiya Tokumasu
  • National Institute of Technology, Nara College, Nara, Japan

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Masakazu Ishihata and Fumiya Tokumasu. Solving and Generating Nagareru Puzzles. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 2:1-2:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Solving paper-and-pencil puzzles is fun for people, and their analysis is also an essential issue in computational complexity theory. There are some practically efficient solvers for some NP-complete puzzles; however, the automatic generation of interesting puzzle instances still stands out as a complex problem because it requires checking whether the generated instance has a unique solution. In this paper, we focus on a puzzle called Nagareru and propose two methods: one is for implicitly enumerating all the solutions of its instance, and the other is for efficiently generating an instance with a unique solution. The former constructs a ZDD that implicitly represents all the solutions. The latter employs the ZDD-based solver as a building block to check the uniqueness of the solution of generated instances. We experimentally showed that the ZDD-based solver was drastically faster than a CSP-based solver, and our generation method created an interesting instance in a reasonable time.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Combinatorial algorithms
  • Theory of computation → Generating random combinatorial structures
  • Mathematics of computing → Graph algorithms
  • Paper-and-pencil puzzle
  • SAT
  • CSP
  • ZDD


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