八数码难题

• 转载自https://blog.csdn.net/qq_36523667/article/details/78807436

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Time Limit: 10000/5000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 27216 Accepted Submission(s): 7257
Special Judge

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Problem 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 1870, a man named Sam Loyd was famous for distributing an unsolvable version of the puzzle, and
frustrating many people. In fact, all you have to do to make a regular puzzle into an unsolvable one is to swap two tiles (not counting the missing 'x' tile, of course).

In this problem, you will write a program for solving the less well-known 8-puzzle, composed of tiles on a three by three
arrangement.

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Input

You will receive, several descriptions of configuration of the 8 puzzle. One description is just a list of the tiles in their initial positions, with the rows listed from top to bottom, and the tiles listed from left to right within a row, where the tiles are represented by numbers 1 to 8, plus 'x'. For example, this puzzle

 1 2 3 
 x 4 6 
 7 5 8 

is described by this list:

1 2 3 x 4 6 7 5 8

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Output

You will print to standard output either the word ``unsolvable'', if the puzzle has no solution, or a string consisting entirely of the letters 'r', 'l', 'u' and 'd' that describes a series of moves that produce a solution. The string should include no spaces and start at the beginning of the line. Do not print a blank line between cases.

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Sample Input

2 3 4 1 5 x 7 6 8

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Sample Output

ullddrurdllurdruldr

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翻译：

2 3 4

1 5 x

7 6 8

是我们的目标状态

1 2 3

4 5 6

7 8 9

是我们的起始状态

u=up

l=left

d=down

r=right

输出就是输出找到后的方向，否则就是没找到，输出unsolved

思路：

可以用反向bfs，从结果出发，找到这个状态。也可以双向bfs。也可以A，也可以IDA。

1. 暴力反向BFS+存状态           http://blog.csdn.net/qq_36523667/article/details/78787668

2. 暴力反向BFS+康托展开判重           http://blog.csdn.net/qq_36523667/article/details/78790957

3. 暴力反向BFS+康托展开判重+打表          http://blog.csdn.net/qq_36523667/article/details/78793695

4. 暴力反向BFS+康托展开判重+打表+回溯记录路径          http://blog.csdn.net/qq_36523667/article/details/78797657

5. 双向BFS+康托展开判重+回溯记录路径          http://blog.csdn.net/qq_36523667/article/details/78797920

6. 双向BFS+康托展开判重+回溯记录路径+逆序数判无解          http://blog.csdn.net/qq_36523667/article/details/78798188

7. A*之曼哈顿+康托展开判重+回溯记录路径+逆序数判无解          http://blog.csdn.net/qq_36523667/article/details/78805842