1134. Vertex Cover (25)

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本文介绍了一种算法，用于判断给定的顶点集合是否为图的顶点覆盖。输入包括图的顶点和边的数量，以及多个顶点集合进行查询。通过遍历每个顶点集合并检查所有边是否至少被一个顶点覆盖来确定答案。

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

Sample Output:

No
Yes
Yes
No
No
#include <iostream>
#include <cstdio>
#include <vector>
#include <set>
using namespace std;

int main()
{
    int n,m;
    cin>>n>>m;
    vector< vector<int> > edg(n);
    for(int i=0;i<m;i++)
    {
        int a,b;
        cin>>a>>b;
        edg[a].push_back(i);
        edg[b].push_back(i);
    }
    int k,nv,ver;
    cin>>k;
    set<int> s;
    for(int i=0;i<k;i++)
    {
        cin>>nv;
        for(int j=0;j<nv;j++)
        {
            cin>>ver;
            for(int t=0;t<edg[ver].size();t++)
            {
                s.insert(edg[ver][t]);
            }
        }
        if(s.size()==m) cout<<"Yes"<<endl;
        else cout<<"No"<<endl;
        s.clear();
    }
    return 0;
}