hdu 2255 奔小康赚大钱 (km算法模板)

题目链接：

　　http://acm.hdu.edu.cn/showproblem.php?pid=2255

解题思路：

　　了解km算法以后，就可以直接套用km算法，km算法：完备匹配下的最大权匹配，

代码：

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;

#define maxn 310
#define INF 0x3f3f3f3f
int map[maxn][maxn], used[maxn], s[maxn], n, m;
int lx[maxn], ly[maxn], visx[maxn], visy[maxn];

int find (int x)
{//匈牙利算法，增广路
    visx[x] = 1;
    for (int i=1; i<=n; i++)
    {
        if (!visy[i] && lx[x] + ly[i] == map[x][i])
        {
            visy[i] = 1;
            if (!used[i] || find(used[i]))
            {
                used[i] = x;
                return 1;
            }
        }
        else
            s[i] = min (s[i], lx[x]+ly[i]-map[x][i]);
    }
    return 0;
}

int KM ()
{
    memset (lx, 0, sizeof(lx));
    memset (ly, 0, sizeof(ly));
    memset (used, 0, sizeof(used));
    for (int i=1; i<=n; i++)
        for (int j=1; j<=n; j++)
            lx[i] = max (lx[i], map[i][j]);
    for (int i=1; i<=n; i++)
    {
        for (int j=1; j<=n; j++)
            s[j] = INF;

        while (1)
        {
            memset (visx, 0, sizeof(visx));
            memset (visy, 0, sizeof(visy));

            if (find (i))
                break;
            int num = INF;
            for (int j=1; j<=n; j++)
                if (!visy[j])
                    num = min (num, s[j]);
            for (int j=1; j<=n; j++)
            {
                if (visx[j])
                    lx[j] -= num;
                if (visy[j])
                    ly[j] += num;
                else
                    s[j] -= num;
            }
        }
    }
    int res = 0;
    for (int j=1; j<=n; j++)
        res += map[used[j]][j];
    return res;
}
int main ()
{
    while (scanf ("%d", &n) != EOF)
    {
        for (int i=1; i<=n; i++)
            for (int j=1; j<=n; j++)
                scanf ("%d", &map[i][j]);
        printf ("%d
", KM());
    }
    return 0;
}