(PAT 1134) Vertex Cover (图中边和顶点的关系)

柔光的暖阳◎ 2022-03-22 02:58 169阅读 0赞

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

解题思路:

题目的意思是,给出M条无向边,之后给出若干组集合,判断与每条边向连的顶点是否属于集合中至少某一个元素,如果所有的边满足该条件,输出yes,如果某条边两边的顶点不属于集合中任何一个元素,输出No

我们可以把两个顶点之间那条边的边号与两个顶点绑定(通过vector容器)这样就得到了每个顶点的与之相连的边,然后我们把集合中每个顶点的边集加入到一个新的set中,由于set是不允许重复的,所以如过set的size()小于边数的话,说明有若干条边与集合中的顶点都没有关系,那么输出NO,反之输出Yes

#include <iostream>
    #include <set>
    #include <algorithm>
    #include <vector>
    #include <string.h>
    using namespace std;
    const int MAXN = 10010;
    vector<int> EDGES[MAXN];
    
    bool flagSet[MAXN];
    int main() {
    	int N, M;
    	cin >> N >> M;
    	for (int i = 0; i < M; ++i) {
    		int nx, ny;
    		cin >> nx >> ny;
    		EDGES[nx].push_back(i);
    		EDGES[ny].push_back(i);
    	}
    	int K;
    	cin >> K;
    	for (int i = 0; i < K; ++i) {
    		int n;
    		scanf("%d", &n);
    		set<int> nodeSet;
    		for (int j = 0; j < n; ++j) {
    			int node;
    			scanf("%d", &node);
    			for (int i = 0; i < EDGES[node].size(); ++i) {
    				nodeSet.insert(EDGES[node][i]);
    			}
    		}
    		
    		if (nodeSet.size() < M) {
    			cout << "No" << endl;
    		}
    		else {
    			cout << "Yes" << endl;
    		}
    	}
    
    	system("PAUSE");
    	return 0;
    }