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

Source

South Central USA 1998       用各种方法都写一下。 又写了一个新的代码：

/*
POJ 1077 Eight
单向搜索，
从正向开始找目标点
康托展开作为hash值

AC  G++  8876K  96MS
*/
#include<stdio.h>
#include<string.h>
#include<iostream>
#include<string>
using namespace std;
const int MAXN=362881;//9!=362880
struct Node
{
    int s[9];
    int pre;//记录前一个结点
    int dir;//记录前一个结点到该结点的方向
}que[MAXN];
bool hash[MAXN];
int path[MAXN];

int fac[]={1,1,2,6,24,120,720,5040,40320,362880};//康拖展开判重
//         0!1!2!3! 4! 5!  6!  7!   8!    9!
int cantor(int *s)
{
    int sum=0;
    for(int i=0;i<9;i++)
    {
        int num=0;
        for(int j=i+1;j<9;j++)
          if(s[j]<s[i])
            num++;
        sum+=(num*fac[9-i-1]);
    }
    return sum;
}
int move[4][2]={{-1,0},{1,0},{0,-1},{0,1}};//u,d,l,r
void output(int len)
{
    for(int i=len-1;i>=0;i--)
    {
        if(path[i]==0) printf("u");
        else if(path[i]==1) printf("d");
        else if(path[i]==2) printf("l");
        else if(path[i]==3) printf("r");
    }
    printf("\n");
}
void bfs()
{
    int front=-1,rear=0;
    que[0].pre=-1;
    que[0].dir=-1;
    memset(hash,false,sizeof(hash));
    hash[cantor(que[0].s)]=true;
    if(cantor(que[0].s)==0){output(0);return;}
    while(front<rear)
    {
        front++;
        int tmp;
        for(tmp=0;tmp<9;tmp++)
          if(que[front].s[tmp]==9)
            break;
        int x=tmp/3;
        int y=tmp%3;
        for(int i=0;i<4;i++)
        {
            int tx=x+move[i][0];
            int ty=y+move[i][1];
            if(tx<0||tx>2||ty<0||ty>2)continue;
            que[rear+1]=que[front];
            que[rear+1].pre=front;
            que[rear+1].dir=i;
            que[rear+1].s[tmp]=que[rear+1].s[tx*3+ty];
            que[rear+1].s[tx*3+ty]=9;
            int now=cantor(que[rear+1].s);
            if(now==0)//到达目标
            {
                int len=0;
                int t=rear+1;
                while(que[t].pre!=-1)
                {
                    path[len++]=que[t].dir;
                    t=que[t].pre;
                }
                output(len);
                return;
            }
            if(!hash[now])
            {
                rear++;
                hash[now]=true;
            }

        }
    }
}
int main()
{
   // freopen("in.txt","r",stdin);
   // freopen("out.txt","w",stdout);
    char str[10];
    while(scanf("%s",&str)!=EOF)
    {
        if(str[0]=='x') que[0].s[0]=9;
        else que[0].s[0]=str[0]-'0';
        for(int i=1;i<9;i++)
        {
            scanf("%s",&str);
            if(str[0]=='x') que[0].s[i]=9;
            else que[0].s[i]=str[0]-'0';
        }
        bfs();
    }
    return 0;
}