POJ1077 Eight —— 经典的搜索问题

题目链接：http://poj.org/problem?id=1077

Eight

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 33267		Accepted: 14404		Special Judge

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

Source

South Central USA 1998

题解：

1.对于棋盘，所有的情况为：9! <4e5<1e6，所以使用枚举的方法是不会超时的，前提是数据较弱（如POJ1077），或者一次性枚举预处理掉所有情况（HDU1043）。

2.对于判重：使用STL的set肯定会超时的。一开始想利用十进制数，每一位保存一个格子，结果9个格子就是9位数，数组根本开不了那么大，所以此种尝试失败。后来看到康拓，不太理解为什么能用（不会有冲突吗？），但还是先用着，有时间再研究一下。如果下次遇到类似123456789这九个数需要进行哈希的，就使用康拓试试。

3.推荐阅读：八数码的八境界   ——  来自liugoodness，特此鸣谢。

写法：

1.正向BFS：http://www.cnblogs.com/DOLFAMINGO/p/7538587.html

2.反向BFS：http://www.cnblogs.com/DOLFAMINGO/p/7538586.html

3.双向BFS：http://www.cnblogs.com/DOLFAMINGO/p/7538585.html

4.  A*算法  ：http://www.cnblogs.com/DOLFAMINGO/p/7538584.html

5.IDA*算法：http://www.cnblogs.com/DOLFAMINGO/p/7538583.html