1134. Vertex Cover (25)

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;
}