摘要： 将魔力方块问题与八数码问题进行对比分析，通过讨论魔力方块问题是否有解、解的最少步数、状态表示、状态判重、状态转换关系等相关问题，提出一种基于双向广度优先搜索和状态转换表的求解算法。实验结果表明，与有界深度优先搜索、简单广度优先搜索及A*搜索算法相比，该算法效率较高，稳定性较好，可以实现魔力方块问题的实时求解及演示。

关键词: 魔力方块问题, 状态判重, 状态转换表, 双向广度优先搜索, 八数码问题

Abstract: This paper introduces magic square problem, and analyzes 8-puzzle problem comparatively. It comprehensively discusses some issues relevant to solving magic square problem, such as whether there is a solution, minimum steps, state representation, state repetition judging, transition relation between states of magic square problem. It proposes a solution based on bidirectional Breadth-first Search(BFS) and state transition table. Experimental results prove that compared with other algorithms, the algorithm proposed is efficient and stable, which meets the requirements of real-time solving and presentation of magic square problem.

Key words: magic square problem, state repetition judging, state transition table, bidirectional Breadth-first Search(BFS), 8-puzzle problem

中图分类号: 

• TP301.6