[Python](PAT)1122 Hamiltonian Cycle（25 分）

Python写PAT甲级，答案都在这儿了

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

题目大意

“Hamiltonian cycle”包含了图中所有的顶点，而且这个集合从头到尾的点之间都有边连接

如果给出的一个查询中的子集是“Hamiltonian cycle”，输出“YES”，否则输出NO。

Python实现

def main():
    line = input().split(" ")
    n, m = int(line[0]), int(line[1])
    dic = [ [0 for x in range(n)] for x in range(n)]
    for x in range(m):
        line = input().split(" ")
        a, b = int(line[0])-1, int(line[1])-1
        dic[a][b], dic[b][a] = 1, 1
    k = int(input())
    for x in range(k):
        line = input().split(" ")
        num = int(line[0])
        if line[1] != line[-1] or num < n:
            print("NO")
            continue
        else:
            line = line[1:]
            get = [int(x)-1 for x in line]
            flag = True
            if get.count(get[0]) > 2:
                print("NO")
                continue
            for i in range(len(line)-1):
                if dic[get[i]][get[i+1]] == 0:
                    flag = False
                    break
            if flag:
                print("YES")
            else:
                print("NO")

if __name__ == "__main__":
    main()