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 Rust (1.15.1) (judge verdict: Accepted)

use std::io::BufRead;

pub struct StdinReader<R: BufRead> {
    pub buf_reader: R,
    pub buf: String,
}
impl<R: BufRead> StdinReader<R> {
    pub fn new(r: R) -> Self {
        StdinReader {
            buf_reader: r,
            buf: String::with_capacity(10000),
        }
    }
}

#[macro_export]
macro_rules! input {
    ($reader : expr, $t : ty) => { // one variable
        match &mut $reader {
            reader => {
                use std::io::BufRead;
                reader.buf_reader.read_line(&mut reader.buf).unwrap();
                let tmp_var: $t = reader.buf.trim().parse().unwrap(); 
                reader.buf.clear();
                tmp_var
            },
        }
    };
    ($reader : expr, $t0 : ty, $t1 : ty) => { // 2 tuple
        match &mut $reader {
            reader => {
                use std::io::BufRead;
                reader.buf_reader.read_line(&mut reader.buf).unwrap();
                let tmp_var: Vec<$t0> = reader.buf.trim().split_whitespace().map(|a| a.parse().unwrap()).collect();
                reader.buf.clear();
                (tmp_var[0], tmp_var[1])
            }
        }
    };
    ($reader : expr, $t0 : ty, $t1 : ty, $t2 : ty) => { // 3 tuple
        match &mut $reader {
            reader => {
                use std::io::BufRead;
                reader.buf_reader.read_line(&mut reader.buf).unwrap();
                let tmp_var: Vec<$t0> = reader.buf.trim().split_whitespace().map(|a| a.parse().unwrap()).collect();
                reader.buf.clear();
                (tmp_var[0], tmp_var[1], tmp_var[2])
            }
        }
    };
    ($reader : expr, $t : ty, $size : expr) => { // Vector
        match &mut $reader {
            reader => {
                use std::io::BufRead;
                reader.buf_reader.read_line(&mut reader.buf).unwrap();
                let tmp_var: $t = reader.buf.trim().split_whitespace().map(|a| a.parse().unwrap()).collect();
                reader.buf.clear();
                tmp_var
            }
        }
    };
}
fn creates_bit_patterns(digit: usize) -> Vec<Vec<usize>> {
    let until = usize::pow(2, digit as u32);
    let mut v = Vec::with_capacity(until);
    for num in 0..until {
        v.push(creates_bit_pattern(num, digit));
    }
    return v;
}
fn creates_bit_pattern(mut num: usize, digit: usize) -> Vec<usize> {
    let mut v = Vec::with_capacity(digit);
    for _ in 0..digit {
        v.push(num % 2);
        num /= 2;
    }
    return v;
}

#[derive(Debug, Hash)]
struct Edge {
    a: usize,
    b: usize,
}
impl Eq for Edge {}
impl PartialEq for Edge {
    fn eq(&self, other: &Self) -> bool {
        (self.a == other.a && self.b == other.b) || (self.b == other.a && self.a == other.b)
    }
}
impl Edge {
    fn new(a: usize, b: usize) -> Self {
        Edge { a: a, b: b, }
    }
    fn reverse(&self) -> Self {
        Edge {a: self.b, b: self.a, }
    }
}

fn main() {
    let handle = std::io::stdin();
    let mut r = StdinReader::new(handle.lock());
    let (n, m) = input!(r, usize, usize);
    let inf = std::usize::MAX;
    let mut dp: Vec<Vec<usize>> = vec![vec![0; n]; (2 as usize).pow(n as u32)];
    let mut edges: Vec<Vec<bool>> = vec![vec![false; n]; n];
    dp[1][0] = 1;
    for i in 0..m {
        let (a, b) = input!(r, usize, usize);
        edges[a-1][b-1] = true;
        edges[b-1][a-1] = true;
    }
    for i in 0..(2 as usize).pow(n as u32) {
        if creates_bit_pattern(i, n)[0] != 1 { continue; }
        for j in 0..n {
            if dp[i][j] == 0 { continue; }
            for k in 0..n {
                if creates_bit_pattern(i, n)[k] == 1 { continue; } // already visit (k) node.
                if edges[j][k] {
                    dp[i + (2 as usize).pow(k as u32)][k] += dp[i][j];
                }
            }
        }
    }
    println!("{:?}", dp[(2 as usize).pow(n as u32)-1].iter().skip(1).sum::<usize>());
}