Solving Mahjong Solitaire boards with peeking

TL;DR

This paper proves Mahjong Solitaire with peeking is NP-complete in general, but identifies solvable cases and presents a practical, efficient algorithm for solving such boards, with potential applications to similar puzzles.

Contribution

It establishes the computational complexity of Mahjong Solitaire with peeking and introduces a practical algorithm for solving specific layout types efficiently.

Findings

NP-completeness of Mahjong Solitaire with peeking

Polynomial-time solvability for layouts with stacks of height one and two

A practical, fast algorithm with effective pruning and heuristics

Abstract

We first prove that solving Mahjong Solitaire boards with peeking is NP-complete, even if one only allows isolated stacks of the forms /aab/ and /abb/. We subsequently show that layouts of isolated stacks of heights one and two can always be solved with peeking, and that doing so is in P, as well as finding an optimal algorithm for such layouts without peeking. Next, we describe a practical algorithm for solving Mahjong Solitaire boards with peeking, which is simple and fast. The algorithm uses an effective pruning criterion and a heuristic to find and prioritize critical groups. The ideas of the algorithm can also be applied to solving Shisen-Sho with peeking.