Time Limit: 10000/5000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 27216 Accepted Submission(s): 7257
Special Judge
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.
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
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.
Sample Input
2 3 4 1 5 x 7 6 8
Sample Output
ullddrurdllurdruldr
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。
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暴力反向BFS+存状态 http://blog.csdn.net/qq_36523667/article/details/78787668
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暴力反向BFS+康托展开判重 http://blog.csdn.net/qq_36523667/article/details/78790957
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暴力反向BFS+康托展开判重+打表 http://blog.csdn.net/qq_36523667/article/details/78793695
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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
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双向BFS+康托展开判重+回溯记录路径 http://blog.csdn.net/qq_36523667/article/details/78797920
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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
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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