UVA11383 Golden Tiger Claw —— KM算法

题目链接：https://vjudge.net/problem/UVA-11383

题解：

根据KM()算法，标杆满足：l(x) + l(y) >= w(x, y) 。

当求完最大权匹配之后，所有标杆在满足：l(x) + l(y) >= w(x, y) 的条件下，和最小。

代码如下：

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const int INF = 2e9;
const LL LNF = 9e18;
const int mod = 1e9+7;
const int MAXN = 500+10;

int nx, ny;
int g[MAXN][MAXN], linker[MAXN], lx[MAXN], ly[MAXN], slack[MAXN];
bool visx[MAXN], visy[MAXN];

bool DFS(int x)
{
    visx[x] = true;
    for(int y = 1; y<=ny; y++)
    {
        if(visy[y]) continue;
        int tmp = lx[x] + ly[y] - g[x][y];
        if(tmp==0)
        {
            visy[y] = true;
            if(linker[y]==-1 || DFS(linker[y]))
            {
                linker[y] = x;
                return true;
            }
        }
        else
            slack[y] = min(slack[y], tmp);
    }
    return false;
}

void KM()
{
    memset(linker, -1, sizeof(linker));
    memset(ly, 0, sizeof(ly));
    for(int i = 1; i<=nx; i++)
    {
        lx[i] = -INF;
        for(int j = 1; j<=ny; j++)
            lx[i] = max(lx[i], g[i][j]);
    }

    for(int x = 1; x<=nx; x++)
    {
        for(int i = 1; i<=ny; i++)
            slack[i] = INF;
        while(true)
        {
            memset(visx, 0, sizeof(visx));
            memset(visy, 0, sizeof(visy));

            if(DFS(x)) break;
            int d = INF;
            for(int i = 1; i<=ny; i++)
                if(!visy[i])
                    d = min(d, slack[i]);

            for(int i = 1; i<=nx; i++)
                if(visx[i])
                    lx[i] -= d;
            for(int i = 1; i<=ny; i++)
            {
                if(visy[i]) ly[i] += d;
                else slack[i] -= d;
            }
        }
    }
}

int main()
{
    int n;
    while(scanf("%d",&n)!=EOF)
    {
        nx = ny = n;
        for(int i = 1; i<=nx; i++)
        for(int j = 1; j<=ny; j++)
            scanf("%d",&g[i][j]);

        KM();
        int sum = 0;
        for(int i = 1; i<=nx; i++) printf("%d ", lx[i]), sum += lx[i];
        printf("
");
        for(int i = 1; i<=ny; i++) printf("%d ", ly[i]), sum += ly[i];
        printf("
");
        printf("%d
", sum);
    }
}