An efficient algorithm for solving nonograms

Hui-Lung Lee, Chiung-Hsueh Yu, Ling-Hwei Chen

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Nonogram is one of logical games popular in Japan and Netherlands. Solving nonogram is a NP-complete problem. There are some related papers proposed. Some use genetic algorithm (GA), but the solution may get stuck in local optima. Some use depth first search (DFS) algorithm, the execution speed is very slow. In this paper, we propose a puzzle solving algorithm to treat these problems. Based on the fact that most of nonograms are compact and contiguous, some logical rules are deduced to paint some cells. Then, we use the chronological backtracking algorithm to solve those undetermined cells and logical rules to improve the search efficiently. Experimental results show that our algorithm can solve nonograms successfully, and the processing speed is significantly faster than that of DFS. Moreover, our method can determine that a nonogram has no solution.
Original languageEnglish
Pages (from-to)18-31
Number of pages13
JournalApplied Intelligence
Issue number1
StatePublished - Aug 2011


  • Japanese puzzle; Nonogram; Depth first search; Chronological backtracking

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