1134 Vertex Cover

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 1), 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 ['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

题意：

　　给出一个图和一个图中部分顶点所构成的集合，判断图中的所有边是不是都和集合中的顶点相关。

思路：

　　利用邻接矩阵来存储图，然后查询与集合中顶点相连的边的条数（注意不要重复）是不是与M（图中边数的总和）相等。

Code：

#include <bits/stdc++.h>

using namespace std;

int main() {
    int n, m, k;
    cin >> n >> m;

    vector<vector<int> > grap(n + 1);
    int v1, v2;
    for (int i = 0; i < m; ++i) {
        cin >> v1 >> v2;
        grap[v1].push_back(v2);
        grap[v2].push_back(v1);
    }

    cin >> k;
    int nv, t, edges;
    unordered_set<int> uset;
    for (int i = 0; i < k; ++i) {
        cin >> nv;
        uset.clear();
        edges = 0;
        for (int j = 0; j < nv; ++j) {
            cin >> t;
            uset.insert(t);
            for (int k : grap[t])
                if (uset.find(k) == uset.end()) edges++;
        }
        if (edges == m)
            cout << "Yes" << endl;
        else
            cout << "No" << endl;
    }
    return 0;
}