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:
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.
1 2 3 4where 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:
5 6 7 8
9 10 11 12
13 14 15 x
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4The 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.
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->
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
1 2 3
x 4 6
7 5 8
is described by this list:
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
解析：八数码问题，这题如果每次从起点搜到终点可能会超时，由于终点都是一样的，所以可以逆向搜索打表，每种状态可以根据数的相对位置对应一个编号（康拓展开）。
代码如下：
#include<cstdio>
#include<cstring>
#include<string>
#include<algorithm>
#include<set>
#include<map>
#include<queue>
#include<vector>
#include<iterator>
#include<utility>
#include<sstream>
#include<iostream>
#include<cmath>
#include<stack>
using namespace std;
const int INF=1000000007;
const double eps=0.00000001;
int dx[]={-1,0,1,0},dy[]={0,-1,0,1}; //方向数组
char dir[]={'d','r','u','l'}; //方向数组对应的相反方向的字符，由于是逆向打表
int fa[363000],fact[10]; //fa[]保存父亲状态的编号，fact[i]=i！
string ans[363000]; /对应的打印路径
int Cul(int n)
{
int ret=1;
for(int st=1;st<=n;st++) ret*=st;
return ret;
}
int id(int B[]) //得到编号
{
int ret=0;
for(int i=0;i<9;i++)
{
int less=0;
for(int j=i+1;j<9;j++) if(B[j]<B[i]) less++;
ret+=fact[9-1-i]*less;
}
return ret;
}
bool in(int x,int y){return x>=0&&x<3&&y>=0&&y<3;} //判断是否在界内
struct node
{
int x,y,ID; //坐标，id值，此时的状态数组
int A[9];
};
int main()
{
for(int i=0;i<10;i++) fact[i]=Cul(i);
for(int i=0;i<363000;i++) ans[i].clear();
node st;
st.x=2