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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;

int count(int **lines,int place,int depth){
    //lines: lines in the graph 
    //place: number that searching now
    int N=lines[0][0];
    int uplines[N+1][N+1];
    int *tmp[N+1];
    int sum=0;
    if(depth==N) return 1;
    for(int i=0;i<=N;i++){
        for(int j=0;j<=N;j++)
            uplines[i][j]=lines[i][j];
        uplines[i][place]=0;
        tmp[i]=uplines[i];
    }
    for(int i=1;i<=N;i++)
        if(uplines[place][i]==1) sum+=count(tmp,i,depth+1);
    return sum;
}

int main(){
    int N,M;
    //data input
    cin>>N;
    cin>>M;
    int a[M],b[M];
    int lines[N+1][N+1];
    int *tmp[N+1];
    for(int i=0;i<M;i++){
        cin>>a[i];
        cin>>b[i];
    }

    //initialize
    for(int i=0;i<=N;i++){
        for(int j=1;j<=N;j++)
            lines[i][j]=0;        
        tmp[i]=lines[i];
    }
    lines[0][0]=N;

    //classification
    for(int i=1;i<=N;i++){
        for(int j=0;j<M;j++){
            if(a[j]==i)lines[i][b[j]]=1;
            if(b[j]==i)lines[i][a[j]]=1;
        }
    }
    cout<<count(tmp,1,1)<<endl;
    return 0;
}