HDU 2444 The Accomodation of Students 二分图判定+最大匹配

Posted 2020-09-21 jzssuanfa

题目来源：HDU 2444 The Accomodation of Students

题意：n个人能否够分成2组 每组的人不能相互认识 就是二分图判定 能够分成2组 每组选一个2个人认识能够去一个双人间 最多能够有几组

思路：二分图判定+最大匹配

#include <cstdio>
#include <cstring>
#include <vector>
using namespace std;
const int maxn = 550;
int vis[maxn];
int y[maxn];
vector <int> G[maxn];
int n, m;
int color[maxn];
bool bipartite(int u)
{
	for(int i = 0; i < G[u].size(); i++)
	{
		int v = G[u][i];
		if(color[u] == color[v])
			return false;
		if(!color[v])
		{
			color[v] = 3 - color[u];
			if(!bipartite(v))
				return false;
		}
	}
	return true;
}
bool dfs(int u)
{
	for(int i = 0; i < G[u].size(); i++)
	{
		int v = G[u][i];
		if(vis[v] || color[v] == 1)
			continue;
		vis[v] = true;
		if(y[v] == -1 || dfs(y[v]))
		{
			y[v] = u;
			return true;
		}
	}
	return false;
}
int match()
{
	int ans = 0;
	memset(y, -1, sizeof(y));
	for(int i = 1; i <= n; i++)
	{
		memset(vis, 0, sizeof(vis));
		if(color[i] == 1 && dfs(i))
			ans++;
	}
	return ans;
}

int main()
{
	//int T;
	//scanf("%d", &T);
	while(scanf("%d %d", &n, &m) != EOF)
	{
		for(int i = 0; i <= n; i++)
			G[i].clear();
		while(m--)
		{
			int u, v;
			scanf("%d %d", &u, &v);
			G[u].push_back(v);
			G[v].push_back(u);
		}
		memset(color, 0, sizeof(color));
		int flag = 0;
		for(int i = 1; i <= n; i++)
			if(!color[i])
			{
				color[i] = 1;
				if(!bipartite(i))
				{
					puts("No");
					flag = 1;
					break;
				}
			}
		if(flag)
			continue;
		printf("%d\n", match());
	
	}
	return 0;
}