PAT A1134 Vertex Cover (25point(s))

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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:

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

解答

#include<iostream>
#include<vector>
#include<unordered_map>

using namespace std;

int main()
{
	int vNum, eNum, u, v;
	cin >> vNum >> eNum;
	vector<vector<int>> mp(vNum);
	for (int i = 0; i < eNum; i++) {
		cin >> u >> v;
		mp[u].push_back(i);
		mp[v].push_back(i);
	}
	int qNum;
	cin >> qNum;
	for (int i = 0; i < qNum; i++) {
		int n;
		cin >> n;
		unordered_map<int, bool> tmp;
		for (int j = 0; j < n; j++) {
			cin >> u;
			for (auto it = mp[u].begin(); it != mp[u].end(); it++)
				tmp[*it] = true;
		}
		if (tmp.size() == eNum) printf("Yes\n");
		else printf("No\n");
	}
	return 0;
}