运动员最佳匹配问题（km算法）

洛谷传送门

带权二分图最大权完美匹配。

裸的km算法。

注意开long long。

 #include <cstdio>
 #include <cstring>
 #include <iostream>
 
 using namespace std;
 
 const long long INF = ;
 int n, match[];
 long long p[][], q[][], love[][], ex_boy[], ex_girl[], slack[];
 bool vis_boy[], vis_girl[];
 
 bool find(int i)
 {
     int j;
     long long gap;
     vis_girl[i] = ;
     for(j = ; j <= n; j++)
     {
         if(vis_boy[j]) continue;
         gap = ex_girl[i] + ex_boy[j] - love[i][j];
         if(gap == )
         {
             vis_boy[j] = ;
             if(match[j] == - || find(match[j]))
             {
                 match[j] = i;
                 return ;
             }
         }
         else slack[j] = min(slack[j], gap);
     }
     return ;
 }
 
 long long KM()
 {
     int i, j;
     long long d, ret = ;
     memset(match, -, sizeof(match));
     for(i = ; i <= n; i++)
      for(j = ; j <= n; j++)
       ex_girl[i] = max(ex_girl[i], love[i][j]);
     for(i = ; i <= n; i++)
     {
         for(j = ; j <= n; j++) slack[j] = INF;
         while()
         {
             memset(vis_boy, , sizeof(vis_boy));
             memset(vis_girl, , sizeof(vis_girl));
             if(find(i)) break;
             d = INF;
             for(j = ; j <= n; j++)
              if(!vis_boy[j])
               d = min(d, slack[j]);
             for(j = ; j <= n; j++)
             {
                 if(vis_boy[j]) ex_boy[j] += d;
                 if(vis_girl[j]) ex_girl[j] -= d;
             }
         }
     }
     for(i = ; i <= n; i++) ret += love[match[i]][i];
     return ret;
 }
 
 int main()
 {
     int i, j;
     scanf("%d", &n);
     for(i = ; i <= n; i++)
      for(j = ; j <= n; j++)
       scanf("%lld", &p[i][j]);
     for(i = ; i <= n; i++)
      for(j = ; j <= n; j++)
       scanf("%lld", &q[i][j]);
     for(i = ; i <= n; i++)
      for(j = ; j <= n; j++)
       love[i][j] = p[i][j] * q[j][i];
     printf("%lld", KM());
     return ;
 }