Problem:
Score : 300 points

Problem Statement

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.

Figure 1: an example of an undirected graph

The following path shown in Figure 2 satisfies the condition.

Figure 2: an example of a path that satisfies the condition

However, the following path shown in Figure 3 does not satisfy the condition, because it does not visit all the vertices.

Figure 3: an example of a path that does not satisfy the condition

Neither the following path shown in Figure 4, because it does not start from vertex 1.

Figure 4: another example of a path that does not satisfy the condition

Constraints

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.

Input

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

Output

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

Sample Input 1

3 3
1 2
1 3
2 3

Sample Output 1

2

The given graph is shown in the following figure:

The following two paths satisfy the condition:

Sample Input 2

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

Sample Output 2

1

This test case is the same as the one described in the problem statement.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)


import java.util.*;

public class Main {
    public static int count;
    public static void main(final String[] args) {
        final Scanner sc = new Scanner(System.in);
        final int N = sc.nextInt();
        final int M = sc.nextInt();
        final ArrayList<ArrayList<Integer>> graph = new ArrayList<>();
        for (int i = 0; i < N; i++) {
            graph.add(new ArrayList<>());
        }
        for (int i = 0; i < M; i++) {
            final int a = sc.nextInt() - 1;
            final int b = sc.nextInt() - 1;
            graph.get(a).add(b);
            graph.get(b).add(a);
        }
        count = 0;
        final ArrayList<Integer> path = new ArrayList<>();
        path.add(0);
        step(0, graph, path);
        System.out.println(count);
    }
    public static void step(
        int u, 
        ArrayList<ArrayList<Integer>> graph, 
        ArrayList<Integer> path){
        // System.out.println(u);
        // System.out.println(path.toString());
        if(path.size() >= graph.size()){
            count ++ ;
            return;
        }else {
            for (Integer next : graph.get(u)) {
                if( ! path.contains(next)){
                    path.add(next);
                    step(next,graph,path);
                    path.remove(path.size()-1);
                }
            }
        }
    }
}