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
题目大意:给出一副无向图<N,M>,有K个询问,每个询问包含n个点,判断这n个点组成的序列是否符合哈密顿回路。
哈密顿回路:包含图中所有节点的一条简单回路(首尾节点相同,且每个顶点只出现一次)。
解题思路:对于每个询问,判断是否符合。出现以下情况就是不符合:
1、首尾节点不同
2、询问中的n节点数不等于N+1
3、路径中没有包含无向图中的所有节点
4、路径序列中相邻节点之间不连通
#include <cstdio>
#include <vector>
#include <map>
#include <set>
#include <cstdlib>
#include <climits>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
#define ll long long
const int MAXN = 200 + 5;
const int INF = 0x7f7f7f7f;
template <class XSD> inline XSD f_min(XSD a, XSD b) { if (a > b) a = b; return a; }
template <class XSD> inline XSD f_max(XSD a, XSD b) { if (a < b) a = b; return a; }
bool mp[MAXN][MAXN];
bool judge(int n, int k){
int x, y;
set<int>s;
vector<int>v;
for(int i=0; i<k; i++){
scanf("%d", &x);
s.insert(x);
v.push_back(x);
}
if(s.size()!=n || v[0]!=v[k-1] || k!=(n+1)) return false;
for(int i=1; i<k; i++) if(!mp[v[i-1]][v[i]]) return false;
return true;
}
int main(){
int n, m;
int x, y;
while(~scanf("%d%d", &n, &m)){
memset(mp, false, sizeof mp);
for(int i=0; i<m; i++){
scanf("%d%d", &x, &y);
mp[x][y] = mp[y][x] = true;
}
int q, k;
scanf("%d", &q);
while(q--){
scanf("%d", &k);
if(judge(n, k)) printf("YES\n");
else printf("NO\n");
}
}
return 0;
}