Elementary Algorithmic Methods for Solving Suguru Puzzles - Butrahandisya Butrahandisya; Muhammad Atzaki; Gia Septiana Wulandari ((IJCSAM) International Journal of Computing Science and Applied Mathematics, 2024)
We discuss elementary algorithmic aspects of the Suguru puzzle---a single-player paper-and-pencil puzzle introduced in 2001 and confirmed NP-complete in 2022. We propose a backtracking algorithm with pruning optimizations for solving an $m × n$ Suguru puzzles containing $R$ regions and $H$ hint cells in $O(R · (mn-H+2)!)$ time. Despite this factorial asymptotic upper bound, a C++ implementation of our proposed algorithm successfully solved all Suguru instances with no more than $100$ cells using a personal computer in less than $0.5$ second. We also prove that any Suguru instance of size $m × n$ with either $m = 1$ or $n = 1$ can be solved in linear time in terms of the puzzle size. Finally, we provide an upper bound for the number of solutions to such tractable instances.