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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.Serializable;
import java.util.StringTokenizer;

/**
 * for (int i = 0; i < N; i++) {}
 * System.out.println();
 * HashMap<Integer, Integer> hm = new HashMap<>();
 * int[] s = new int[M];
 * ArrayDeque<Integer> deq = new ArrayDeque<>();
 *
 */
public class Main implements Runnable { //クラス名はMain1

	public static void main(String[] args) {
		Thread.setDefaultUncaughtExceptionHandler((t, e) -> System.exit(1));
		new Thread(null, new Main(), "", 1024 * 1024 * 1024).start(); //16MBスタックを確保して実行
	}

	public void run() {
		FastScannerMain1 sc = new FastScannerMain1(System.in);

		try {
			//String S = sc.nextLine().trim();
			int N = sc.nextInt();
			int M = sc.nextInt();

			Integer[] n = new Integer[N];

			int[][] pass = new int[N + 1][N + 1];
			//int[] a = new int[N];
			//long l = sc.nextLong();
			//ArrayList<Integer> arr = new ArrayList<Integer>();
			for (int i = 0; i < M; i++) {
				int a = sc.nextInt();
				int b = sc.nextInt();

				pass[a][b] = 1;
				pass[b][a] = 1;

			}

			for (int i = 0; i < N; i++) {
				n[i] = i + 1;
				//System.out.println(Arrays.toString(pass[i]));
			}

			int ans = 0;
			Permutation<Integer> p = new Permutation<>(n);
			do {
				//System.out.println(Arrays.toString(p.getObjes()));
				boolean judge = true;
				Integer[] per = p.getObjes();

				if (per[0] == 1) {
					//System.out.println(Arrays.toString(p.getObjes()));
					for (int i = 1; i < per.length; i++) {
						//	System.out.println(per[i - 1] + " → " + per[i]);
						if (pass[per[i - 1]][per[i]] == 0 && pass[per[i]][per[i - 1]] == 0) {
							judge = false;
						}
					}
				} else {
					judge = false;
				}

				if (judge) {
					ans++;
				}

			} while (p.next());

			System.out.println(ans);

		} catch (Exception e) {
			e.printStackTrace();
		}

	}
}

/**
*
* How to call
 Permutation<String> p = new Permutation<>(new String[] { "a", "b", "c" });
 do {
 	System.out.println(Arrays.toString(p.getObjes()));
 } while (p.next());

	PermutationWarshallFloyd<Integer> p = new PermutationWarshallFloyd<>(travels);
	do {
       //System.out.println(Arrays.toString(p.getObjes()));
       Integer[] per = p.getObjes();
       long eachans = 0;
       for (int i = 0; i < per.length; i++) {
           if (i > 0) {
       eachans += wf.distance(per[i - 1] - 1, per[i] - 1);
           }
       }
	} while (p.next());
*
*
*
* @author daichi.miyajima
*
* @param <T>
*/
class Permutation<T extends Serializable> {

	private int baseIndex;
	private int index;
	private T[] objs;

	private Permutation<T> subPermutation;

	public Permutation(T[] objs) {
		this(0, 0, objs.clone());
	}

	private Permutation(int baseIndex, int index, T[] objs) {
		if (objs == null || objs.length == 0) {
			throw new IllegalArgumentException();
		}

		this.baseIndex = baseIndex;
		this.index = index;
		this.objs = objs;

		if (this.index < this.objs.length - 1) {
			this.subPermutation = new Permutation<T>(this.baseIndex + 1, this.index + 1, this.objs);
		}
	}

	public T[] getTarget() {
		return this.objs;
	}

	public boolean next() {
		if (this.subPermutation == null) {
			return false;
		}

		boolean result = this.subPermutation.next();
		if (result == true) {
			return true;
		}

		this.swap(this.baseIndex, this.index);

		++this.index;
		if (this.objs.length <= this.index) {
			this.index = this.baseIndex;
			return false;
		}

		this.swap(this.index, this.baseIndex);
		return true;
	}

	public T[] getObjes() {
		return this.objs;
	}

	private void swap(int index1, int index2) {
		T tmp = this.objs[index1];
		this.objs[index1] = this.objs[index2];
		this.objs[index2] = tmp;
	}
}

//高速なScanner
class FastScannerMain1 {
	private BufferedReader reader = null;
	private StringTokenizer tokenizer = null;

	public FastScannerMain1(InputStream in) {
		reader = new BufferedReader(new InputStreamReader(in));
		tokenizer = null;
	}

	public String next() {
		if (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				tokenizer = new StringTokenizer(reader.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken();
	}

	public String nextLine() {
		if (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken("\n");
	}

	public long nextLong() {
		return Long.parseLong(next());
	}

	public int nextInt() {
		return Integer.parseInt(next());
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}

	public int[] nextIntArray(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = nextInt();
		return a;
	}

	public long[] nextLongArray(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nextLong();
		return a;
	}
}