hihocoder1127 二分图三·二分图最小点覆盖和最大独立集

思路：

对于不存在孤立点的图，|最大匹配| + |最小边覆盖| = |V|，|最大独立集| + |最小顶点覆盖| = |V|。对于二分图而言，|最大匹配| = |最小顶点覆盖|。（V是图的顶点集合）

实现：

#include <iostream>
#include <cstring>
#include <vector>
using namespace std;

const int MAXN = 1005;
vector<int> G[MAXN];
int n, m;
bool used[MAXN];
int match[MAXN];

bool dfs(int v)
{
    used[v] = true;
    for (int i = 0; i < G[v].size(); i++)
    {
        int u = G[v][i];
        int w = match[u];
        if (w == -1 || !used[w] && dfs(w))
        {
            match[v] = u;
            match[u] = v;
            return true;
        }
    }
    return false;
}

int max_match()
{
    int res = 0;
    for (int i = 1; i <= n; i++)
    {
        if (match[i] == -1)
        {
            memset(used, 0, sizeof(used));
            if (dfs(i))
                res++;
        }
    }
    return res;
}

int main()
{
    cin >> n >> m;
    int a, b;
    for (int i = 0; i < m; i++)
    {
        cin >> a >> b;
        G[a].push_back(b);
        G[b].push_back(a);
    }
    memset(match, -1, sizeof(match));
    int ans = max_match();
    cout << ans << endl;
    cout << n - ans << endl;
    return 0;
}