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.*;

 class Main {
     static boolean[][] graph = new boolean[8][8];

     public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int M = sc.nextInt();
        
        int a,b;
        for(int i=0;i<M;i++) {
        	a=sc.nextInt();
        	b=sc.nextInt();
        	graph[a-1][b-1]=true;
        	graph[b-1][a-1]=true;
        }
        
        boolean[] visited = new boolean[N];
		for(int i=0;i<N;i++) {
			visited[i]=false;
		}

        visited[0]=true;
        int result = dfs(0,N,visited);
        
        System.out.println(result);
    }
    
    static int dfs(int first, int max, boolean[] visited) {
    	int ret = 0;
    	boolean all_visited = true;
    	for(int i=0;i<max;i++) {
    		if(visited[i]==false) {
    			all_visited=false;    			
    		}
    	}
    	if (all_visited) {
    		return 1;
    	}
    	
    	for(int i=0;i<max;i++) {
    		if(graph[first][i]==false) {
    			continue;
    		}
    		if(visited[i]==true) {
    			continue;
    		}
    		visited[i]=true;
			ret += dfs(i,max,visited);
			visited[i] = false;
    	}
    	return ret;
    }
}