Egiht（八种方法）

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.

SampleInput

2  3  4  1  5  x  7  6  8

SampleOutput

ullddrurdllurdruldr

就是给你一个序列，然后要你通过四种移动方式，回到最初的序列，输出答案，题目有SPJ，无需输出最优方法。
这道题可谓是搜索中的精髓了，最开始我就是一个简单的双向搜索，结果TLE了，看了网上的博客加了剪枝之后过了。
但是后来和队友聊这题，发现这道题的解题思路不止一种，队友说有八种

然后找到一篇博客，里面一共讲了八种解法，应该是很全面的。
博客链接：https://www.cnblogs.com/zufezzt/p/5659276.html至于我的代码就没什么好讲的了，确实用双向BFS加剪枝可以AC这道题，但这道题的精髓远远不在于此，也见识到了自己的学识浅薄。我也道不出个所以然，所以这道题我就不详细讲了。
还是那句话以梦为马，不负韶华。