【二分图匹配】Plug It In!

http://codeforces.com/gym/101873

F

先对原图跑一遍匈牙利得到原始最大匹配，再遍历每个出度>1的点，考虑若新加入点，能否找到增广路，若可行则答案对应增加

代码：

#include <iostream>
#include <cstdio>
#include <vector>
#include <cstring>
#include <algorithm>
#include <queue>
using namespace std;
typedef long long ll;
const int MAX_V = 2000;
const int MAX_E = 80000;
struct Hungary {
	struct Edge {
		int to, next;
	} es[MAX_E];
	int head[MAX_V];
	int V, E, match[MAX_V];
	bool vis[MAX_V];

	void init(int V) {
		this->V = V;
		this->E = 0;
		memset(head, -1, sizeof head);
	}

	void addEdge(int u, int v) {
		es[E].to = v;
		es[E].next = head[u];
		head[u] = E++;
	}

	bool dfs(int u) {
		vis[u] = true;
		for (int i = head[u]; i != -1; i = es[i].next) {
			int v = es[i].to, w = match[v];
			if (w < 0 || !vis[w] && dfs(w)) {
				match[v] = u;
				return true;
			}
		}
		return false;
	}

	int maxMatch() {
		int res = 0;
		memset(match, -1, sizeof match);
		for (int u = 0; u < V; u++) {
			memset(vis, false, sizeof vis);
			if (dfs(u)) {
				res++;
			}
		}
		return res;
	}
} hun;
int main() {
	int m, n, k, out[2000] = { 0 }, match[2000] = { 0 };
	scanf("%d%d%d", &m, &n, &k);
	hun.init(m);
	for (int i = 0; i < k; i++) {
		int u, v;
		scanf("%d%d", &u, &v);
		hun.addEdge(u - 1, v - 1);
		out[u - 1]++;
	}
	int res = hun.maxMatch();
	int ans = res;
	memcpy(match, hun.match, sizeof hun.match);
	for (int u = 0; u < m; u++) {
		if (out[u] > 1) {
			memcpy(hun.match, match, sizeof match);
			int cnt = 0;
			for (int j = 0; j < 2; j++) {
				hun.head[m + j] = -1;
				for (int i = hun.head[u]; ~i; i = hun.es[i].next) {
					int v = hun.es[i].to;
					hun.addEdge(m + j, v);
					cnt++;
				}
			}
			hun.E -= cnt;
			int extra = 0;
			for (int j = 0; j < 2; j++) {
				memset(hun.vis, 0, sizeof hun.vis);
				if (hun.dfs(m + j)) {
					extra++;
				}
			}
			ans = max(ans, res + extra);
		}
	}
	printf("%d\n", ans);
}