An Efficient Approach to Solving Nonograms

Abstract

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.

Perbandingan Keefektifan Algoritma Backtracking Dan Soft Computing Dalam Memecahkan Permainan Papan Nonogram

“…Namun, terdapat algoritma-algoritma lain yang dapat digunakan untuk menyelesaikan nonogram, seperti algoritma A-star atau Depth-First Search (DFS) [14,32,36]. Meskipun solusi-solusi ini cenderung kurang efisien, namun masih populer karena implementasinya yang sederhana dan kemampuannya dalam memberikan hasil [6,24,26].…”

Design and Automated Generation of Japanese Picture Puzzles

“…Our focus is on nonograms, also known as Picross, Pic‐a‐Pix, Hanjie, and Griddlers. The scientific study of nonograms usually concentrates on the algorithmic complexity of solving them [BK09, BPRR14, MA09, Tsa12, WSC*13]. Nonograms need a coarse pixel image which can be derived from smooth vector art by rasterization.…”

Texture, Nonogram, and Convexity Priors in Binary Tomography

“…Thus, NONOGRAM is much harder to solve than BT, from both the viewpoints of existence and uniqueness. Further works on solvability and uniqueness of nonograms is published in [3,10,11,14,69,97,101].…”