An efficient algorithm for solving nonograms

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

doi:10.1007/s10489-009-0200-0

Cited by 14 publications

(9 citation statements)

References 2 publications

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“…Jing and Yu [2][5] proposed a method based on logical rules (LR) and chronological backtracking with an LR filter to solve Japanese puzzles. Their rules exploited with a new concept of "the range of a black run."…”

Section: Previous Workmentioning

confidence: 99%

“…Some put focus on the generation of questions, trying to use the least implied numbers to generate a question with only one answer. Some try to demonstrate some puzzle games are NP-Complete problems [2] [8]; besides, studying how to use programs to rapidly solve these puzzle games is an important direction. Previous researchers tried to use pattern match and DFS to solve Nonograms puzzle games [2] [5], and had breakthrough in the speed of solving them.…”

Section: Introductionmentioning

confidence: 99%

“…Some try to demonstrate some puzzle games are NP-Complete problems [2] [8]; besides, studying how to use programs to rapidly solve these puzzle games is an important direction. Previous researchers tried to use pattern match and DFS to solve Nonograms puzzle games [2] [5], and had breakthrough in the speed of solving them. However, DFS may step into a wrong track, stuck in it, and cause great deal of resource waste.…”

Section: Introductionmentioning

confidence: 99%

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An efficient algorithm for solving Fillomino

Yen

Hsu

2011

2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011)

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Fillomino is a logical puzzle game invented by Nikoli Company in Japan. Fillomino is played on a rectangular cell with no standard size; the internal cell lines are often dotted. Some cells of the cell start containing numbers, referred to as "givens". In this paper, we propose a puzzle solving algorithm to treat these problems. Based on the fact the Fillomino are compact and contiguous, some logical rules are deduced to paint some cells. Experimental results show that our algorithm can solve Fillominos successfully and efficient, and the processing speed is significantly faster than that of depth first search algorithm.

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Section: Previous Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An efficient algorithm for solving Fillomino

Yen

Hsu

2011

2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011)

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“…In [24], Yu et al proposed an algorithm to solve nonogram puzzles based on specific logical rules, using backtracking to solve undetermined cells and logical rules to improve the search efficiently. These logical rules are mainly used to help line painting (either for rows or columns), with the goal of painting as many pixels in each line as possible.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Approach to Solving Nonograms

Sun

Chen

et al. 2013

IEEE Trans. Comput. Intell. AI Games

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A nonogram puzzle is played on a rectangular grid of pixels with clues given in the form of row and column constraints. The aim of solving a nonogram puzzle, an NP-complete problem, is to paint all the pixels of the grid in black and white while satisfying these constraints. This paper proposes an efficient approach to solving nonogram puzzles. We propose a fast dynamic programming (DP) method for line solving, whose time complexity in the worst case is only, where the grid size is and is the average number of integers in one constraint, always smaller than . In contrast, the time complexity for the best line-solving method in the past is . We also propose some fully probing (FP) methods to solve more pixels before running backtracking. Our FP methods can solve more pixels than the method proposed by Batenburg and Kosters (before backtracking), while having a time complexity that is smaller than theirs by a factor of . Most importantly, these FP methods provide useful guidance in choosing the next promising pixel to guess during backtracking. The proposed methods are incorporated into a fast nonogram solver, named LalaFrogKK. The program outperformed all the programs collected in webpbn.com, and also won both nonogram tournaments that were held at the 2011 Conference on Technologies and Applications of Artificial Intelligence (TAAI 2011, Taiwan). We expect that the proposed FP methods can also be applied to solving other puzzles efficiently.

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“…Some put focus on the generation of questions, trying to use the least implied numbers to generate a question with only one answer [1]; some try to demonstrate some puzzle games are NP-Complete problems [2] [3]; besides, studying how to use programs to rapidly solve these puzzle games is an important direction. Previous researchers tried to use pattern matching and DFS to solve Nonogram puzzle games [4] [5], and had breakthrough in the speed of solving them. However, DFS may step into a wrong track, stuck in it, and cause great deal of resource waste.…”

Section: Introductionmentioning

confidence: 99%