枚举 POJ 2965 The Pilots Brothers' refrigerator

题目地址：http://poj.org/problem?id=2965

 /*
     题意：4*4的矩形，改变任意点，把所有'+'变成'-',，每一次同行同列的都会反转，求最小步数，并打印方案

     DFS：把'+'记为1， '-'记为0
     1. 从(1, 1)走到(4, 4)，每一点DFS两次(改点反转或不反转)；used记录反转的位置
         详细解释：http://poj.org/showmessage?message_id=346723
     2. 比较巧妙的解法：抓住'+'位置反转，'-'位置相对不反转的特点，从状态上考虑
         详细解释：http://poj.org/showmessage?message_id=156561
     3. 枚举步骤数(1~16)，暴力解法，耗时大
         详细解释：http://poj.org/showmessage?message_id=343281
     4. 网上还有其他解法：高斯消元，BFS，+位运算等等

     注意：反转时十字形中心位置多反转了两次，要再反转一次

     我还是DFS写不出来。。。
 */
 #include <cstdio>
 #include <iostream>
 #include <algorithm>
 #include <cstring>
 #include <cmath>
 #include <string>
 #include <map>
 #include <queue>
 #include <vector>
 using namespace std;

 const int MAXN = 1e6 + ;
 const int INF = 0x3f3f3f3f;
 int a[][];
 int used[][];

 bool ok(void)
 {
     for (int i=; i<=; ++i)
     {
         for (int j=; j<=; ++j)
             if (a[i][j] == )    return false;
     }

     return true;
 }

 void change(int x, int y)
 {
     for (int i=; i<=; ++i)
     {
         a[x][i] = a[x][i] ?  : ;
         a[i][y] = a[i][y] ?  : ;
     }
     a[x][y] = a[x][y] ?  : ;
     used[x][y] = used[x][y] ?  : ;
 }

 bool DFS(int x, int y)
 {
     if (x ==  && y == )
     {
         if (ok ())    return true;

         change (x, y);
         if (ok ())    return true;

         change (x, y);
         return false;
     }
     int nx, ny;
     if (y == )        nx = x + , ny = ;
     else    nx = x, ny = y + ;

     if (DFS (nx, ny))    return true;

     change (x, y);
     if (DFS (nx, ny))    return true;

     change (x, y);
     return false;
 }

 void work(void)
 {
     if (DFS (, ))
     {
         int ans = ;
         for (int i=; i<=; ++i)
         {
             for (int j=; j<=; ++j)
             {
                 if (used[i][j])        ans++;
             }
         }
         printf ("%d\n", ans);
         for (int i=; i<=; ++i)
             for (int j=; j<=; ++j)
                 if (used[i][j])    printf ("%d %d\n", i, j);
     }
     else    printf ("WA\n");
 }

 int main(void)        //POJ 2965 The Pilots Brothers' refrigerator
 {
     //freopen ("B.in", "r", stdin);

     char ch;
     for (int i=; i<=; ++i)
     {
         for (int j=; j<=; ++j)
         {
             scanf ("%c", &ch);
             a[i][j] = (ch == '-') ?  : ;
             //printf ("%d ", a[i][j]);
         }
         getchar ();    //puts ("");
     }

     work ();

     return ;
 }

 /*
 #include <cstdio>
 #include <iostream>
 #include <algorithm>
 #include <cstring>
 #include <cmath>
 #include <string>
 #include <map>
 #include <queue>
 #include <vector>
 using namespace std;

 const int MAXN = 1e6 + 10;
 const int INF = 0x3f3f3f3f;
 bool con[5][5];
 int a[5][5];
 struct NODE
 {
     int x, y;
 }node[MAXN];

 void work(void)
 {
     for (int i=1; i<=4; ++i)
     {
         for (int j=1; j<=4; ++j)
         {
             if (a[i][j] == 1)
             {
                 con[i][j] = !con[i][j];
                 for (int k=1; k<=4; ++k)
                 {
                     con[i][k] = !con[i][k];
                     con[k][j] = !con[k][j];
                 }
             }
         }
     }
     int ans = 0;
     for (int i=1; i<=4; ++i)
     {
         for (int j=1; j<=4; ++j)
         {
             if (con[i][j] == true)
             {
                 ans++;    node[ans].x = i;    node[ans].y = j;
             }
         }
     }
     printf ("%d\n", ans);
     for (int i=1; i<=ans; ++i)
         printf ("%d %d\n", node[i].x, node[i].y);
 }

 int main(void)        //POJ 2965 The Pilots Brothers' refrigerator
 {
     //freopen ("B.in", "r", stdin);

     char ch;
     for (int i=1; i<=4; ++i)
     {
         for (int j=1; j<=4; ++j)
         {
             scanf ("%c", &ch);
             a[i][j] = (ch == '-') ? 0 : 1;
         }
         getchar ();
     }

     work ();

     return 0;
 }
 */

 /*
 #include <cstdio>
 #include <iostream>
 #include <algorithm>
 #include <cstring>
 #include <cmath>
 #include <string>
 #include <map>
 #include <queue>
 #include <vector>
 using namespace std;

 const int MAXN = 1e6 + 10;
 const int INF = 0x3f3f3f3f;
 int a[5][5];
 struct NODE
 {
     int x, y;
 }node[MAXN];
 int k;
 bool flag;

 bool ok(void)
 {
     for (int i=1; i<=4; ++i)
     {
         for (int j=1; j<=4; ++j)
             if (a[i][j] == 1)    return false;
     }

     return true;
 }

 void change(int x, int y)
 {
     for (int i=1; i<=4; ++i)
     {
         a[x][i] = !a[x][i];
         a[i][y] = !a[i][y];
     }
     a[x][y] = !a[x][y];
 }

 void DFS(int x, int y, int num, int cnt, int kk)
 {
     if (num == cnt)
     {
         flag = ok ();
         k = kk;
         return ;
     }
     for (int i=x; i<=4; ++i)
     {
         int j;
         if (i == x)    j = y + 1;
         else    j = 1;
         for (; j<=4; ++j)
         {
             node[kk].x = i;
             node[kk].y = j;
             change (i, j);
             DFS (i, j, num+1, cnt, kk+1);
             if (flag)    return ;
             change (i, j);
         }
     }
 }

 void work(void)
 {
     int cnt;
     for (cnt=1; cnt<=16; ++cnt)
     {
         flag = false;    k = 0;
         DFS (1, 0, 0, cnt, 1);
         if (flag)    break;
     }

     printf ("%d\n", cnt);
     for (int i=1; i<=k - 1; ++i)
         printf ("%d %d\n", node[i].x, node[i].y);
 }

 int main(void)        //POJ 2965 The Pilots Brothers' refrigerator
 {
     //freopen ("B.in", "r", stdin);

     char ch;
     for (int i=1; i<=4; ++i)
     {
         for (int j=1; j<=4; ++j)
         {
             scanf ("%c", &ch);
             a[i][j] = (ch == '-') ? 0 : 1;
         }
         getchar ();
     }

     work ();

     return 0;
 }
 */