Eight

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 a description of a configuration of the 8 puzzle. The 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.
Sample Input

2 3 4 1 5 x 7 6 8
Sample Output

ullddrurdllurdruldr

      （1）编程思路1。

       1）定义结点

      用数组来表示棋盘的布局，如果将棋盘上的格子从左上角到右下角按0到8编号，就可用一维数组board[9]来顺序表示棋盘上棋子的数字，空格用“9”表示，数组元素的下标是格子编号。为方便处理，状态结点还包括该布局的空格位置space，否则需要查找“9”在数组中的位置才能确定空格的位置。另外，为节约存储空间，将数组类型定义为char（每个元素只占一个字节存储空间，还是可以存储整数1~9）。因此在程序中，定义状态结点为结构数据类型：

struct node{   

       char board[9];