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 ... Vn
where n is the number of vertices in the list, and Vi'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;
}