Vertex Cover(图的覆盖

本文介绍了一种算法,用于判断给定点集是否为图的顶点覆盖。通过遍历每条边并检查其是否至少与点集中一个点相连,可以确定点集是否覆盖了图的所有边。输入包括图的顶点数、边数、边的连接以及待查询的点集,输出则指示每个点集是否构成顶点覆盖。

摘要生成于 C知道 ,由 DeepSeek-R1 满血版支持, 前往体验 >

给出一个点集,判断是否是图的覆盖。
就是与这些点相连的边是否覆盖了整张图。
给每条边编号,Push进相连的点里,按点集标记判断就看以了。

A vertex cover of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set. Now given a graph with several vertex sets, you are supposed to tell if each of them is a vertex cover or not.

Input Specification:
Each input file contains one test case. For each case, the first line gives two positive integers N and M (both no more than 10
​4
​​ ), being the total numbers of vertices and the edges, respectively. Then M lines follow, each describes an edge by giving the indices (from 0 to N−1) of the two ends of the edge.

After the graph, a positive integer K (≤ 100) is given, which is the number of queries. Then K lines of queries follow, each in the format:

N
​v
​​ v[1] v[2]⋯v[N
​v
​​ ]

where N
​v
​​ is the number of vertices in the set, and v[i]'s are the indices of the vertices.

Output Specification:
For each query, print in a line Yes if the set is a vertex cover, or No if not.

Sample Input:
10 11
8 7
6 8
4 5
8 4
8 1
1 2
1 4
9 8
9 1
1 0
2 4
5
4 0 3 8 4
6 6 1 7 5 4 9
3 1 8 4
2 2 8
7 9 8 7 6 5 4 2
Sample Output:
No
Yes
Yes
No
No

#include<bits/stdc++.h>
#include <iostream>

#include<vector>
#include<stack>
#include<string>

using namespace std;


int main() {
	map<int ,map<int ,int > >mp1;
	map<int ,map<int ,int > >mp2;

	int n,m;
	cin>>n>>m;
	vector<int> mp[n];

	for(int i=0; i<m; i++) {
		int a,b;
		cin>>a>>b;
		mp[a].push_back(i);
		mp[b].push_back(i);

	}
	int t;
	cin>>t;
	for(int i=0; i<t; i++) {
		int k;
		cin>>k;
		vector<int> hash(m,0);
		for(int j=0; j<k; j++) {
			int tmp;
			cin>>tmp;
			for(int p=0; p<mp[tmp].size(); p++) {
				hash[mp[tmp][p]]=1;
			}

		}
		int flag=0;
		for(int j=0; j<m; j++) {

			if(hash[j]==0) {
				flag=1;
				cout<<"No"<<endl;
				break;
			}
		}
		if(flag==0)cout<<"Yes"<<endl;
	}
}

评论
添加红包

请填写红包祝福语或标题

红包个数最小为10个

红包金额最低5元

当前余额3.43前往充值 >
需支付:10.00
成就一亿技术人!
领取后你会自动成为博主和红包主的粉丝 规则
hope_wisdom
发出的红包
实付
使用余额支付
点击重新获取
扫码支付
钱包余额 0

抵扣说明:

1.余额是钱包充值的虚拟货币,按照1:1的比例进行支付金额的抵扣。
2.余额无法直接购买下载,可以购买VIP、付费专栏及课程。

余额充值