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 = 99999999999999999;
int n, match[21];
long long p[21][21], q[21][21], love[21][21], ex_boy[21], ex_girl[21], slack[21];
bool vis_boy[21], vis_girl[21];

bool find(int i)
{
    int j;
    long long gap;
    vis_girl[i] = 1;
    for(j = 1; j <= n; j++)
    {
        if(vis_boy[j]) continue;
        gap = ex_girl[i] + ex_boy[j] - love[i][j];
        if(gap == 0)
        {
            vis_boy[j] = 1;
            if(match[j] == -1 || find(match[j]))
            {
                match[j] = i;
                return 1;
            }
        }
        else slack[j] = min(slack[j], gap);
    }
    return 0;
}

long long KM()
{
    int i, j;
    long long d, ret = 0;
    memset(match, -1, sizeof(match));
    for(i = 1; i <= n; i++)
     for(j = 1; j <= n; j++)
      ex_girl[i] = max(ex_girl[i], love[i][j]);
    for(i = 1; i <= n; i++)
    {
        for(j = 1; j <= n; j++) slack[j] = INF;
        while(1)
        {
            memset(vis_boy, 0, sizeof(vis_boy));
            memset(vis_girl, 0, sizeof(vis_girl));
            if(find(i)) break;
            d = INF;
            for(j = 1; j <= n; j++)
             if(!vis_boy[j])
              d = min(d, slack[j]);
            for(j = 1; j <= n; j++)
            {
                if(vis_boy[j]) ex_boy[j] += d;
                if(vis_girl[j]) ex_girl[j] -= d;
            }
        }
    }
    for(i = 1; i <= n; i++) ret += love[match[i]][i];
    return ret;
}

int main()
{
    int i, j;
    scanf("%d", &n);
    for(i = 1; i <= n; i++)
     for(j = 1; j <= n; j++)
      scanf("%lld", &p[i][j]);
    for(i = 1; i <= n; i++)
     for(j = 1; j <= n; j++)
      scanf("%lld", &q[i][j]);
    for(i = 1; i <= n; i++)
     for(j = 1; j <= n; j++)
      love[i][j] = p[i][j] * q[j][i];
    printf("%lld", KM());
    return 0;
}