1134 Vertex Cover （25 分）（cj)

最新推荐文章于 2020-04-06 11:25:21 发布

Cute_jinx

最新推荐文章于 2020-04-06 11:25:21 发布

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本文介绍了一个图论中的顶点覆盖问题，通过输入一组顶点判断其是否构成给定图的顶点覆盖。具体实现采用C++语言，并使用了集合数据结构来高效地检查每条边是否至少有一个端点属于顶点集。

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1134 Vertex Cover （25 分）

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

code

#pragma warning(disable:4996)
#include <iostream>
#include <vector>
#include <stdio.h>
#include <string>
#include <set>
using namespace std;
int vertice[10005];
int edge[10005][2];
int main() {
	int n, m;
	cin >> n >> m;
	int x, y;
	for (int i = 0; i < m; ++i) {
		cin >> edge[i][0] >> edge[i][1];
	}
	int k, num;
	cin >> k;
	set<int> ss;
	while (k--) {
		ss.clear();
		cin >> num;
		while (num--) {
			cin >> x;
			ss.insert(x);
		}
		bool f = 1;
		for (int i = 0; i < m; ++i) {
			if (ss.find(edge[i][0]) == ss.end() && ss.find(edge[i][1]) == ss.end()) {
				f = 0; break;
			}
		}
		if (f) cout << "Yes" << endl;
		else cout << "No" << endl;
	}
	system("pause");
	return 0;
}