【PAT】【Advanced Level】1122. Hamiltonian Cycle (25)

1122. Hamiltonian Cycle (25)

时间限制

300 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

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 V₁ V₂ ... 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:

6 106 23 41 52 53 14 11 66 31 24 567 5 1 4 3 6 2 56 5 1 4 3 6 29 6 2 1 6 3 4 5 2 64 1 2 5 17 6 1 3 4 5 2 67 6 1 2 5 4 3 1

Sample Output:

YESNONONOYESNO

原题链接：

https://www.patest.cn/contests/pat-a-practise/1122

思路：

邻接矩阵存储图。

判断哈密顿环：

节点数不对，排除

首尾不一致，排除

走过重复节点，排除

两点之间没有通路，排除

CODE：

#include<iostream>#include<map>#include<vector>#include<cstring>#define N 210using namespace std;int dist[N][N];int main(){memset(dist,-1,sizeof(dist));int n,m;cin>>n>>m;for (int i=0;i<m;i++){int s,e;cin>>s>>e;dist[s][e]=dist[e][s]=1;}int k;cin>>k;for (int i=0;i<k;i++){int t;cin>>t;vector<int> pa;for (int j=0;j<t;j++){int temp;cin>>temp;pa.push_back(temp);}if (t!=n+1 || pa[0]!=pa[t-1]){cout<<"NO"<<endl;continue;}bool fl[n+1];memset(fl,0,sizeof(fl));fl[pa[0]]=1;bool flag=0;for (int j=1;j<t;j++){//cout<<pa[j-1]<<" "<<pa[j]<<" "<<dist[pa[j-1]][pa[j]]<<endl;if (dist[pa[j-1]][pa[j]]==-1 || (j!=t-1&&fl[pa[j]]==1)){flag=1;break;}fl[pa[j]]=1;}if (flag==0)cout<<"YES"<<endl;elsecout<<"NO"<<endl;}return 0;}