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 (GCC 5.4.1) (judge verdict: Wrong Answer)


#include <stdio.h>
int matrix[10][10] = {};
int flag[10] = {};
int n;
int ans = 0;

int check(int num)
{
    int i;
    int flagb = 1;
    for (i = 1; i <= n; i++)
    {
        if (flag[i] == 0)
        {
            flagb = 0;
        }
        else if (flag[i] > num)
        {
            flag[i] = 0;
        }
    }
    return flagb;
}

void route(int j, int i, int num)
{
    int k;
    if (matrix[j][i] == 1 && flag[i] == 0)
    {
        flag[i] = 1;
        for (k = 2; k <= n; k++)
        {
            route(i, k, num + 1);
            int a = check(num);
            ans+=a;
        }
    }
}

int main()
{
    int m;
    scanf("%d %d", &n, &m);
    int i, j, k;
    for (k = 0; k < m; k++)
    {
        scanf("%d %d", &i, &j);
        matrix[i][j] = 1;
        matrix[j][i] = 1;
    }
    for (i = 2; i <= n; i++)
    {
        flag[1] = 1;
        route(1, i, 1);
        for (j = 1; j <= 10; j++)
            flag[j] = 0;
    }
    printf("%d\n", ans);
}