1134. Vertex Cover (25)

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:

10 118 76 84 58 48 11 21 49 89 11 02 454 0 3 8 46 6 1 7 5 4 93 1 8 42 2 87 9 8 7 6 5 4 2

Sample Output:

NoYesYesNoNo

题目的大意是：给你一张图，对于图中的每条边，如果该边（一条边有两个点）至少有一个点在集合里，如果这个图中的每个边都是满足的，那么我们把这个集合叫做vertex cover，现在给你几个集合，让你判断他们每个是不是这样的集合

思路：

1.将边作为基本元素进行保存

2.对每个边的两个顶点，判断这两个顶点是不是在集合里

3.为提高查找效率，选择使用set

4.为进一步提高效率，采用visit数组保存对于之前已经确定在集合里的顶点，以免重复查找

#include <iostream>#include <vector>#include <set>#include <algorithm>#include <functional>using namespace std;struct edge{int u,w;edge(int x,int y):u(x),w(y){}};vector<edge> v;int main(){int n,m;cin>>n>>m;for(int i=0;i<m;++i){int u,w;cin>>u>>w;v.push_back(edge(u,w));}int k;cin>>k;while(k--){int num,visit[10000]={0},ret=1,idx;set<int> s;cin>>num;for(int i=0;i<num;++i){cin>>idx;s.insert(idx);}for(auto x:v){if(visit[x.u]||visit[x.w]) continue;//以及在集合里，直接跳过if(s.find(x.u)!=s.end()) visit[x.u]=1;else if(s.find(x.w)!=s.end()) visit[x.w]=1;else {ret=0;break;}}ret==1?cout<<"Yes\n":cout<<"No\n";}return 0;}