POJ 2965

The Pilots Brothers' refrigerator

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 17621		Accepted: 6677		Special Judge

Description

The game “The Pilots Brothers: following the stripy elephant” has a quest where a player needs to open a refrigerator.

There are 16 handles on the refrigerator door. Every handle can be in one of two states: open or closed. The refrigerator is open only when all handles are open. The handles are represented as a matrix 4х4. You can change the state of a handle in any location [i, j] (1 ≤ i, j ≤ 4). However, this also changes states of all handles in row i and all handles in column j.

The task is to determine the minimum number of handle switching necessary to open the refrigerator.

Input

The input contains four lines. Each of the four lines contains four characters describing the initial state of appropriate handles. A symbol “+” means that the handle is in closed state, whereas the symbol “−” means “open”. At least one of the handles is initially closed.

Output

The first line of the input contains N – the minimum number of switching. The rest N lines describe switching sequence. Each of the lines contains a row number and a column number of the matrix separated by one or more spaces. If there are several solutions, you may give any one of them.

Sample Input

-+--
----
----
-+--

Sample Output

6
1 1
1 3
1 4
4 1
4 3
4 4

Source

Northeastern Europe 2004, Western Subregion

翻冰箱门 翻到全部为-为止

和1753一样BFS&DFS&数学方法

数学方法不会

BFS

#include <stdio.h>
#include <string.h>
#include <math.h>
#include <stdlib.h>
#include <ctype.h>
#include <iostream>
#include <algorithm>
#include <map>
#include <string>
#include <vector>

using namespace std;

int Map[4][4];

struct node
{
    int New[17];//新的地图
    int x;//当前位置
    int ans;//步数
    int vis[17];
} status[1000001];

int Final(node a)//判断是否为结束
{
    int sum=0;
    for(int i=0; i<16; i++)
        sum+=a.New[i];
    return sum;
}


void bfs()
{
    for(int i=0; i<4; i++)
        for(int j=0; j<4; j++)
            status[0].New[i*4+j]=Map[i][j];
    memset(status[0].vis,0,17);
    status[0].x=0;
    status[0].ans=0;
    int s=1,e=0;
    while(s>e)
    {
        node f1,f2;
        f1=status[e++];
        int flag=Final(f1);
        if(flag==0)
        {
            cout<<f1.ans<<endl;
            for(int i=0; i<16; i++)
                if(f1.vis[i]==1)
                    cout<<i/4+1<<" "<<i%4+1<<endl;;
            return ;
        }
        for(int i=0; i<16; i++)
        {
            if(f1.x<=i)
            {
                f2=f1;

                for(int j=i-i%4; j<i+4-i%4; j++)
                    f2.New[j]=1-f1.New[j];
                for(int j=i%4; j<16; j+=4)
                    f2.New[j]=1-f1.New[j];
                f2.New[i]=1-f1.New[i];//反转当前棋子
                f2.vis[i]=1;
                f2.ans=f1.ans+1;
                f2.x=i+1;
                status[s++]=f2;
            }
        }
    }
    return ;
}

int main()
{
    char a[4];
    for(int i=0; i<4; i++)
    {
        cin>>a;
        for(int j=0; j<4; j++)
        {
            if(a[j]=='-')
                Map[i][j]=0;
            else
                Map[i][j]=1;
        }
    }
    bfs();
    return 0;
}

DFS

#include <iostream>
#include <stdio.h>

using namespace std;

int Map[5][5],ans=33,ansx[33],ansy[33],x[33],y[33];

int flag()
{
    int flag=0,i,j;
    for(i=0; i<4; i++)
        for(j=0; j<4; j++)
            if(!Map[i][j])
                return 0;
    return 1;
}

void fan(int a)
{
    int i=a/4;
    int j=a%4;
    int k;
    Map[i][j]=!Map[i][j];
    for(k=0; k<4; k++)
    {
        Map[i][k]=!Map[i][k];
        Map[k][j]=!Map[k][j];
    }
}

void dfs(int a,int b)
{
    if(flag())
    {
        if(ans>b)
        {
            ans=b;
            for(int i=1; i<=ans; i++)
            {
                ansx[i]=x[i];
                ansy[i]=y[i];
            }
        }
        return;
    }
    if(a>=16)
        return;
    dfs(a+1,b);
    fan(a);
    x[b+1]=a/4+1;
    y[b+1]=a%4+1;
    dfs(a+1,b+1);
    fan(a);
}

int main()
{
    int i,j;
    char c;
    for(i=0; i<4; i++)
    {
        for(j=0; j<4; j++)
        {
            scanf("%c",&c);
            if(c=='+')
                Map[i][j]=0;
            else
                Map[i][j]=1;
        }
        getchar();
    }
    dfs(0,0);
    printf("%d\n",ans);
    for(i=1; i<=ans; i++)
        printf("%d %d\n",ansx[i],ansy[i]);
    return 0;
}