UESTC 485 Game（康托，BFS）

Today I want to introduce an interesting game to you. Like eight puzzle, it is a square board with 9 positions, but it filled by 9 numbered tiles. There is only one type of valid move, which is to rotate one row or column. That is, three tiles in a row or column are moved towards the head by one tile and the head tile is moved to the end of the row or column. So it has 12 different moves just as the picture left. The objective in the game is to begin with an arbitrary configuration of tiles, and move them so as to get the numbered tiles arranged as the target configuration.

Now the question is to calculate the minimum steps required from the initial configuration to the final configuration. Note that the initial configuration is filled with a permutation of 1 to 9, but the final configuration is filled with numbers and * (which can be any number).

The first line of input contains an integer T (T≤1000), which is the number of data sets that follow.

There are 6 lines in each data set. The first three lines give the initial configuration and the next three lines give the final configuration.

For every test case, you should output Case #k: first, where k indicates the case number and starts at 1. Then the fewest steps needed. If he can’t move to the end, just output No Solution! (without quotes).

2 
1 2 3 
4 5 6 
7 8 9 
1 2 3 
4 5 6 
7 9 8 
1 2 3 
4 5 6 
7 8 9 
8 * 9 
5 3 7 
2 * *

Case #1: No Solution! 

Case #2: 7

康托展开总结：

http://blog.csdn.net/dacc123/article/details/50952079

利用康托展开

把所有状态bfs一次，

然后再去做

利用康托展开进行bfs预处理。题目给的一个起始的九宫格，和一个目标的九宫格。 不能直接用目标的九宫格去找起始的九宫格，会超时，应该根据把起始九宫格当作 
1 2 3 
4 5 6 
7 8 9 
然后确定目标九宫格是怎么样的，这样就可以直接用之前打的表了。预处理就是处理1 2 3 4 5 6 7 8 9到每种九宫格的步数

#include <iostream>
#include <string.h>
#include <stdlib.h>
#include <algorithm>
#include <math.h>
#include <stdio.h>
#include <queue>

using namespace std;
struct Node
{
    int a[5][5];
    int sta;
};
queue<Node> q;
int b[10];
int fac[10];
int vis[400000];
int pre[400000];
int ans;
int f1[10];
int f2[10];
int tran[10];
char ch[10];
bool used[10];
Node cyk;
void facfun()
{
    fac[0]=1;
    for(int i=1;i<=9;i++)
    {
        fac[i]=i*fac[i-1];
    }
}
int kt(Node q)
{
    int cnt=0;
    for(int i=1;i<=3;i++)
        for(int j=1;j<=3;j++)
           b[++cnt]=q.a[i][j];
    int sum=0,num=0;
    for(int i=1;i<=9;i++)
    {
        num=0;
        for(int j=i+1;j<=9;j++)
        {
            if(b[i]>b[j])
                num++;
        }
        sum+=num*fac[9-i];
    }
    return sum;
}
void bfs(Node t)
{
    q.push(t);
    vis[t.sta]=1;
	pre[t.sta]=0;
    while(!q.empty())
    {
        Node term=q.front();
        q.pop();
        for(int i=1;i<=12;i++)
        {
		
            Node temp=term;
            if(i<=3)
			{
				temp.a[i][1]=term.a[i][3];
				temp.a[i][2]=term.a[i][1];
				temp.a[i][3]=term.a[i][2];
			}
            else if(i>3&&i<=6)
			{
                temp.a[i-3][1]=term.a[i-3][2];
				temp.a[i-3][2]=term.a[i-3][3];
				temp.a[i-3][3]=term.a[i-3][1];
			}
            else if(i>6&&i<=9)
			{
                temp.a[1][i-6]=term.a[3][i-6];
				temp.a[2][i-6]=term.a[1][i-6];
				temp.a[3][i-6]=term.a[2][i-6];
			}
            else if(i>9&&i<=12)
			{
                temp.a[1][i-9]=term.a[2][i-9];
				temp.a[2][i-9]=term.a[3][i-9];
				temp.a[3][i-9]=term.a[1][i-9];
			}
            int state=kt(temp);
            if(vis[state])
                continue;
		
            temp.sta=state;
            vis[state]=1;
            pre[state]=pre[term.sta]+1;
		
            q.push(temp);
        }

    }
}
void init()
{
    memset(vis,0,sizeof(vis));
    memset(pre,-1,sizeof(pre));
	facfun();
    Node st;int cnt=0;
    for(int i=1;i<=3;i++)
        for(int j=1;j<=3;j++)
           st.a[i][j]=++cnt;
    st.sta=0;
    bfs(st);
}
int anspos;
void dfs(int i)
{
	if(i==10)
	{
		/*for(int p=1;p<=3;p++)
		{
			for(int k=1;k<=3;k++)
			{
				cout<<cyk.a[p][k]<<" ";
			}
			cout<<endl;
		}*/
		int c=pre[kt(cyk)];
		if(c==-1) return;
		ans=min(ans,c);return;
	}
	if(f2[i]==0)
	{
		for(int j=1;j<=9;j++)
		{
			if(!used[j])
			{
				used[j]=true;
				int y=i%3,x;
				if(y==0){x=i/3;y=3;}
				else {x=i/3+1;}
				cyk.a[x][y]=j;
				dfs(i+1);
				used[j]=false;
			}
		}
	}
	else
	{
         int y=i%3,x;
		 if(y==0){x=i/3;y=3;}
		 else {x=i/3+1;}
		 cyk.a[x][y]=f2[i];
		 dfs(i+1);
	}
    
}

int main()
{
    int t;
    scanf("%d",&t);
    init();
    int cas=0;
    while(t--)
    {
		memset(used,0,sizeof(used));
		for(int i=1;i<=9;i++)
		{
			scanf("%d",&f1[i]);
			tran[f1[i]]=i;
		}
        for(int i=1;i<=9;i++)
		{
			scanf("%s",ch);
			f2[i]=ch[0]-'0';
			if(f2[i]>=1&&f2[i]<=9)
				f2[i]=tran[f2[i]],used[f2[i]]=true;
			else
				f2[i]=0;
		}
        ans=1000000;
        dfs(1);
		if(ans>=1000000)
			printf("Case #%d: No Solution!\n",++cas);
		else
			printf("Case #%d: %d\n",++cas,ans);
    }
    return 0;
}