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 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​​ [ [

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：
图中的每条边的两个顶点a和b,判断a和b中是否至少一个在集合中，如果在，称之为顶点覆盖
题解：
用一个vector<int> 数组存放集合中的点，点的值为下标，所对应的数组值为1；将图中的点用结构体数组存储，遍历数组，判断时候每条边都满足顶点覆盖。

AC代码：

#include<bits/stdc++.h>
using namespace std;
const int maxn=10111;
vector<int> v;
struct node{
    int a,b;
}node[maxn];

int main(){
    int n,m,k,cnt,t;
    cin>>n>>m;
    for(int i=0;i<m;i++){
        cin>>node[i].a>>node[i].b;
    }
    cin>>k;
    for(int i=0;i<k;i++){
        cin>>t;
        int flag=1;
        vector<int> v;
        v.resize(n);
        for(int j=0;j<t;j++){
            cin>>cnt;
            v[cnt]=1;
        }
        for(int i=0;i<m;i++){
            int a1=node[i].a;
            int b1=node[i].b;
            if(v[a1]==0&&v[b1]==0){
                printf("No\n");
                flag=0;
                break;
            }
        }
        if(flag==1){
            printf("Yes\n");
        }
    }
    return 0;
}