# 题目

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.

# 题解

## 思路

• 题目的意思是
• 给你一张图
• 给你一条路径
• 让你判断这个路径能不能把所有的节点走完，最后形成一个环。

## 数据结构

• edges 是一个列表，存放所有的路径
• 下标是节点的id
• 值是一个集合，存放这个节点的所有邻居
• path是给出的查询路径

## 算法

• 读入道路数据
• 读入查询路径
• 进入judge()函数判断
• 如果路径的长度不等于节点数量+1 ，或者起始和结尾不是同一个节点，或者路径里面不包含所有的节点，直接返回no
• 否则，看每个节点的下一个节点是不是在上一个节点的路径当中
• 完事儿，简单嗷

## 代码

• 由于使用Python可以AC，因此只放了Python的题解。