【HDU 1043】Eight（A*启发式搜索算法）

最新推荐文章于 2024-07-28 11:47:02 发布

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最新推荐文章于 2024-07-28 11:47:02 发布 · 1.6k 阅读

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#启发式搜索算法 #A #hdu1043

本文介绍了一个使用A*启发式搜索算法解决八数码谜题的问题。输入是8数码初始配置，输出是解决方案的移动序列。当无法解决时，输出'unsolvable'。文章还探讨了康托展开在压缩空间和判重中的应用。

Description

The 15-puzzle has been around for over 100 years; even if you don’t know it by that name, you’ve seen it. It is constructed with 15 sliding tiles, each with a number from 1 to 15 on it, and all packed into a 4 by 4 frame with one tile missing. Let’s call the missing tile ‘x’; the object of the puzzle is to arrange the tiles so that they are ordered as:

 1  2  3  4
 5  6  7  8
 9 10 11 12
13 14 15  x

where the only legal operation is to exchange ‘x’ with one of the tiles with which it shares an edge. As an example, the following sequence of moves solves a slightly scrambled puzzle:

 1  2  3  4     1  2  3  4     1  2  3  4     1  2  3  4
 5  6  7  8     5  6  7  8     5  6  7  8     5  6  7  8
 9  x 10 12     9 10  x 12     9 10 11 12     9 10 11 12
13 14 11 15    13 14 11 15    13 14  x 15    13 14 15  x
            r->            d->            r->

The letters in the previous row indicate which neighbor of the ‘x’ tile is swapped with the ‘x’ tile at each step; legal values are ‘r’,’l’,’u’ and ‘d’, for right, left, up, and down, respectively.

Not all puzzles can be solved; in