1134 Vertex Cover (25分)-优快云博客

本文链接：https://blog.youkuaiyun.com/zbchenchanghao/article/details/104093355

本文介绍了一个关于图论的问题，即如何判断给定的一组顶点是否构成图的顶点覆盖。通过输入图的边和顶点集，算法能够确定顶点集是否覆盖了所有边，为图论研究提供了一个实用的解决方案。

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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 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

注：在能准确理解题意的情况下，本题题目还较简单，题意为：已给图每条边的两个顶点，至少有一个顶点包含在所给的测试集合中，如果符合要求，输出Yes，ohterwise，输出No。

#include<iostream>
#include<unordered_set>

#include<vector>

using namespace std;
int main(){

    int n, m;
    cin >> n >> m;
    vector<int> vec_in(m * 2);
    for(int i = 0; i < m; i++){
        int temp_a, temp_b;
        scanf("%d %d", &temp_a, &temp_b);

        vec_in[2 * i] = temp_a;
        vec_in[2 * i + 1] = temp_b;

    }

    int k;
    cin >> k;

    for(int i = 0; i < k ; i++){
        int num;
        scanf("%d", &num);
        unordered_set<int> un_set;
        bool flag = true;
        for(int j = 0; j < num; j++){
            
            int temp_set;
            scanf("%d", &temp_set);
            un_set.insert(temp_set);
                         

        }
        for(int j = 0; j < m; j++){
            if(un_set.find(vec_in[j * 2]) == un_set.end() && un_set.find(vec_in[j * 2 + 1]) == un_set.end()){
                flag = false;
                break;
            }

        }
    
        if(flag){

            printf("Yes\n");

        }else{

            printf("No\n");

        }
        

    }




    return 0;
}