PAT 1122 Hamiltonian Cycle

博客围绕哈密顿循环问题展开,介绍要判断给定循环是否为哈密顿循环。给出输入规格,包含顶点数、边数等信息,还有查询数量及路径;也说明了输出规格,根据路径是否构成哈密顿循环输出相应结果,并给出了示例输入和输出。

摘要生成于 C知道 ,由 DeepSeek-R1 满血版支持, 前往体验 >

The "Hamilton cycle problem" is to find a simple cycle that contains every vertex in a graph. Such a cycle is called a "Hamiltonian cycle".

In this problem, you are supposed to tell if a given cycle is a Hamiltonian cycle.

Input Specification:

Each input file contains one test case. For each case, the first line contains 2 positive integers N (2<N≤200), the number of vertices, and M, the number of edges in an undirected graph. Then M lines follow, each describes an edge in the format Vertex1 Vertex2, where the vertices are numbered from 1 to N. The next line gives a positive integer K which is the number of queries, followed by K lines of queries, each in the format:

n V​1​​ V​2​​ ... V​n​​

where n is the number of vertices in the list, and V​i​​'s are the vertices on a path.

Output Specification:

For each query, print in a line YES if the path does form a Hamiltonian cycle, or NO if not.

Sample Input:

6 10
6 2
3 4
1 5
2 5
3 1
4 1
1 6
6 3
1 2
4 5
6
7 5 1 4 3 6 2 5
6 5 1 4 3 6 2
9 6 2 1 6 3 4 5 2 6
4 1 2 5 1
7 6 1 3 4 5 2 6
7 6 1 2 5 4 3 1

Sample Output:

YES
NO
NO
NO
YES
NO
#include <iostream>
#include <cstring>
#include <vector>
int graph[202][202];
int N,M;
using namespace std;
bool judge(vector<int>& vector1){
    bool contains[N+1];
    int size=vector1.size();
    if(vector1[0]!=vector1[size-1]|| size!=N+1){
        return false;
    }
    memset(contains, false, sizeof(contains));
    for (int i = 0; i < size-1; ++i) {
        if (graph[vector1[i]][vector1[i+1]]==0){
            return false;
        }
        contains[vector1[i]]= true;
        contains[vector1[i+1]]= true;
    }
    for (int i = 1; i <= N; ++i) {
        if (!contains[i]){
            return false;
        }
    }
    return true;
}
int main() {
    cin>>N>>M;
    memset(graph,0, sizeof(graph));
    for (int i = 0; i < M; ++i) {
        int a,b;
        cin>>a>>b;
        graph[a][b]=1;
        graph[b][a]=1;
    }
    int K;
    cin>>K;
    vector<bool > res;
    for (int i = 0; i < K; ++i) {
        int num;
        cin>>num;
        vector<int> vector1;
        for (int j = 0; j < num; ++j) {
            int val;
            cin>>val;
            vector1.push_back(val);
        }
        res.push_back(judge(vector1));
    }
    for(auto x:res){
        if(x){
            cout<<"YES"<<endl;
        } else{
            cout<<"NO"<<endl;
        }
    }
    return 0;
}

 

评论
添加红包

请填写红包祝福语或标题

红包个数最小为10个

红包金额最低5元

当前余额3.43前往充值 >
需支付:10.00
成就一亿技术人!
领取后你会自动成为博主和红包主的粉丝 规则
hope_wisdom
发出的红包
实付
使用余额支付
点击重新获取
扫码支付
钱包余额 0

抵扣说明:

1.余额是钱包充值的虚拟货币,按照1:1的比例进行支付金额的抵扣。
2.余额无法直接购买下载,可以购买VIP、付费专栏及课程。

余额充值