1134 Vertex Cover (25 分)--PAT甲级(图)

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 10⁴ ), 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:

Nv v[1] v[2]⋯v[Nv]

where Nv 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
结尾无空行
Sample Output:
No
Yes
Yes
No
No
结尾无空行

题目分析：给定一个图，测试一些点判断这些点是否是顶点包含点(即包含所有的边)

存储结点以及与它的连接点可以选择通过使用邻接表的方式，之后给定了一些点，只需要将这些点插入map中（插入两个点），再判断map.size() == m * 2即可.

#include<iostream>
#include<vector>
#include<set>
using namespace std;
vector<vector<int>> v;

int main(){
	int n, m, a, b;
	scanf("%d%d", &n, &m);
	v.resize(n);
	for(int i = 0; i < m; i ++){
		scanf("%d%d", &a, &b);
		v[a].push_back(b);
		v[b].push_back(a);
	}
	int k;
	scanf("%d", &k);
	while(k --){
		scanf("%d", &a);
		set<pair<int, int>> set;
		for(int i = 0; i < a; i ++){
			scanf("%d", &b);
			for(int j = 0; j < v[b].size(); j ++){
				pair<int, int> p1, p2;
				p1.first = p2.second = b;
				p1.second = p2.first = v[b][j];
				if(set.find(p1) == set.end()){
					set.insert(p1);
					set.insert(p2);
				}
			}
		}
		if(set.size() == m * 2) puts("Yes");
		else puts("No");
	}
	return 0;
}