HDU1043 Eight(八数码，BFS，康托展开，hash)
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 puzzle1 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
思路
这是一个八数码问题，关于这道题的题意，可以参考Virtual Judge上面的翻译，我们的思路是从初始状态开始搜索，然后搜索完所有的状态，每次搜索的时候记录路径，并且采用康托展开进行判重，因为我们已经预处理好了所有的状态。所以最后应对 O(1) O ( 1 ) 的查询就好了
代码
#include else
puts("unsolvable");
}
return 0;
}