One-stroke Path

题目描述

You are given an undirected unweighted graph with $N$ vertices and $M$ edges that contains neither self-loops nor double edges.
Here, a self-loop is an edge where $a_i = b_i (1≤i≤M)$, and double edges are two edges where $(a_i,b_i)=(a_j,b_j)$ or (a_i,b_i)=(b_j,a_j) (1≤i<j≤M).
How many different paths start from vertex $1$ and visit all the vertices exactly once?
Here, the endpoints of a path are considered visited.
For example, let us assume that the following undirected graph shown in Figure 1 is given.

The following path shown in Figure 2 satisfies the condition. However, the following path shown in Figure 3 does not satisfy the condition, because it does not visit all the vertices. Neither the following path shown in Figure 4, because it does not start from vertex $1$.

输入格式

The input is given from Standard Input in the following format: $N$ $M$
$a_1$ $b_1$
$a_2$ $b_2$ $:$
$a_M$ $b_M$

输出格式

Print the number of the different paths that start from vertex $1$ and visit all the vertices exactly once.

3 3
1 2
1 3
2 3

2

7 7
1 3
2 7
3 4
4 5
4 6
5 6
6 7

1

提示

$2≦N≦8$ $0≦M≦N(N-1)/2$ 1≦a_i<b_i≦N The given graph contains neither self-loops nor double edges.The given graph is shown in the following figure:

The following two paths satisfy the condition:
This test case is the same as the one described in the problem statement.

标签: AtCoder|abc054C

来源

AtCoder|abc054C