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.



Sample input:
3 3
1 2
1 3
2 3


Sample output:
2

Submission status: Accepted

Solution code:
from collections import defaultdict
from itertools import permutations

def main():
    N, M = map(int, input().split())
    g = defaultdict(list)
    for _ in range(M):
        a, b = map(int, input().split())
        g[a].append(b)
        g[b].append(a)

    ans = 0
    for route in permutations(range(2, N + 1), N - 1):
        ok = True
        now = 1
        for r in route:
            if r in g[now]:
                now = r
            else:
                ok = False
        if ok:
            ans += 1

    print(ans)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
N,M = map(int, raw_input().split())
E = [[] for _ in range(N)]
for _ in range(M):
  a,b = map(int, raw_input().split())
  E[a-1] += [b-1]
  E[b-1] += [a-1]

def BT(p, c, V):
  if c==N-1:
    return 1
  V[p] = True
  ans = 0
  for e in E[p]:
    if not V[e]:
      ans += BT(e, c+1, V)
  V[p] = False
  return ans

print BT(0, 0, [False]*N)

Submission status: Accepted

Solution code:
from itertools import permutations

n, m = map(int, raw_input().split())

adj = [[] for _ in xrange(n)]
for i in xrange(m):
    a, b = map(int, raw_input().split())
    adj[a-1].append(b-1)
    adj[b-1].append(a-1)

ans = 0
for p in permutations(range(1, n)):
    f = True
    pos = 0
    for i in p:
        if i in adj[pos]:
            pos = i
        else:
            f = False
            break
    if f:
        ans += 1

print ans

Submission status: Accepted

Solution code:
import sys

stdin = sys.stdin
def na(): return map(int, stdin.readline().split())
def ns(): return stdin.readline().strip()

n,m = na()
g = [[0]*n for _ in range(n)]
for i in range(m):
    x,y = na()
    g[x-1][y-1] += 1
    g[y-1][x-1] += 1

import itertools

ct = 0
for a in itertools.permutations(range(n)):
    if a[0] != 0: break
    plus = 1
    for i in range(n-1):
        plus = plus * g[a[i]][a[i+1]]
    ct += plus
print(ct)

Submission status: Runtime Error

Solution code:
import queue 
n,m = map(int, input().split())

ma = [[] for i in range(n+1)]
for i in range(n):
  a,b = map(int, input().split())
  ma[a].append(b)
  ma[b].append(a)

ans = 0
def dfs(i):
  global ans
  if all(reach[1:]):
    ans += 1
  for j in ma[i]:
    if reach[j] == 1:
      continue
    reach[j] = 1
    dfs(j)
    reach[j] = 0

reach=[0]*(n+1)
reach[1] = 1
dfs(1)
print(ans)

Submission status: Runtime Error

Solution code:
# coding=utf-8
from math import floor, ceil, sqrt, factorial, log, gcd, log10
from itertools import accumulate, permutations, combinations, product, combinations_with_replacement, chain
from bisect import bisect_left, bisect_right
from collections import Counter, defaultdict, deque
from heapq import heappop, heappush, heappushpop, heapify
from copy import copy, deepcopy
import sys
INF = float('inf')
mod = 10**9+7
sys.setrecursionlimit(10 ** 8)


def lcm(a, b): return a * b / gcd(a, b)

# 1 2 3
# a, b, c = LI()


def LI(): return list(map(int, sys.stdin.buffer.readline().split()))

# a = I()


def I(): return int(sys.stdin.buffer.readline())

# abc def
# a, b = LS()


def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()

# a = S()


def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')

# 2
# 1
# 2
# [1, 2]


def IR(n): return [I() for i in range(n)]

# 2
# 1 2 3
# 4 5 6
# [[1,2,3], [4,5,6]]


def LIR(n): return [LI() for i in range(n)]

# 2
# abc
# def
# [abc, def]


def SR(n): return [S() for i in range(n)]

# 2
# abc def
# ghi jkl
# [[abc,def], [ghi,jkl]]


def LSR(n): return [LS() for i in range(n)]

# 2
# abcd
# efgh
# [[a,b,c,d], [e,f,g,h]]


def SRL(n): return [list(S()) for i in range(n)]




n, m = LI()
graph = [[] for _ in range(m)]
v = [False] * n

for i in range(m):
    a, b = LI()
    graph[a - 1].append(b)
    graph[b - 1].append(a)


def dfs(now, depth):
    if v[now - 1]:
        return 0
    if depth == n-1:
        return 1
    ans = 0
    v[now - 1] = True
    for node in graph[now - 1]:
        ans += dfs(node, depth+1)

    v[now - 1] = False

    return ans


print(dfs(1, 0))

Submission status: Runtime Error

Solution code:
# coding=utf-8
from math import floor, ceil, sqrt, factorial, log, gcd, log10
from itertools import accumulate, permutations, combinations, product, combinations_with_replacement, chain
from bisect import bisect_left, bisect_right
from collections import Counter, defaultdict, deque
from heapq import heappop, heappush, heappushpop, heapify
from copy import copy, deepcopy
import sys
INF = float('inf')
mod = 10**9+7
sys.setrecursionlimit(10 ** 8)


def lcm(a, b): return a * b / gcd(a, b)

# 1 2 3
# a, b, c = LI()


def LI(): return list(map(int, sys.stdin.buffer.readline().split()))

# a = I()


def I(): return int(sys.stdin.buffer.readline())

# abc def
# a, b = LS()


def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()

# a = S()


def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')

# 2
# 1
# 2
# [1, 2]


def IR(n): return [I() for i in range(n)]

# 2
# 1 2 3
# 4 5 6
# [[1,2,3], [4,5,6]]


def LIR(n): return [LI() for i in range(n)]

# 2
# abc
# def
# [abc, def]


def SR(n): return [S() for i in range(n)]

# 2
# abc def
# ghi jkl
# [[abc,def], [ghi,jkl]]


def LSR(n): return [LS() for i in range(n)]

# 2
# abcd
# efgh
# [[a,b,c,d], [e,f,g,h]]


def SRL(n): return [list(S()) for i in range(n)]


# https://qiita.com/greenteabiscuit/items/31c46ab3ceac07e749d2


n, m = LI()
graph = [[] for _ in range(m)]
v = [False] * n

for i in range(m):
    a, b = LI()
    graph[a - 1].append(b)
    graph[b - 1].append(a)


def dfs(now, depth):
    if v[now - 1]:
        return 0
    if depth == n-1:
        return 1
    ans = 0
    v[now - 1] = True
    if len(graph[now - 1]) > 0:
        for node in graph[now - 1]:
            ans += dfs(node, depth+1)

    v[now - 1] = False
    # ここが大事.上で探索の一つが終わるからリセットしている.

    return ans


print(dfs(1, 0))

Submission status: Runtime Error

Solution code:
# coding=utf-8
from math import floor, ceil, sqrt, factorial, log, gcd, log10
from itertools import accumulate, permutations, combinations, product, combinations_with_replacement, chain
from bisect import bisect_left, bisect_right
from collections import Counter, defaultdict, deque
from heapq import heappop, heappush, heappushpop, heapify
from copy import copy, deepcopy
import sys
INF = float('inf')
mod = 10**9+7
sys.setrecursionlimit(10 ** 8)


def lcm(a, b): return a * b / gcd(a, b)

# 1 2 3
# a, b, c = LI()


def LI(): return list(map(int, sys.stdin.buffer.readline().split()))

# a = I()


def I(): return int(sys.stdin.buffer.readline())

# abc def
# a, b = LS()


def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()

# a = S()


def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')

# 2
# 1
# 2
# [1, 2]


def IR(n): return [I() for i in range(n)]

# 2
# 1 2 3
# 4 5 6
# [[1,2,3], [4,5,6]]


def LIR(n): return [LI() for i in range(n)]

# 2
# abc
# def
# [abc, def]


def SR(n): return [S() for i in range(n)]

# 2
# abc def
# ghi jkl
# [[abc,def], [ghi,jkl]]


def LSR(n): return [LS() for i in range(n)]

# 2
# abcd
# efgh
# [[a,b,c,d], [e,f,g,h]]


def SRL(n): return [list(S()) for i in range(n)]


# https://qiita.com/greenteabiscuit/items/31c46ab3ceac07e749d2


n, m = LI()
graph = [[] for _ in range(m)]
v = [False] * n

for i in range(m):
    a, b = LI()
    graph[a - 1].append(b)
    graph[b - 1].append(a)


def dfs(now, depth):
    if v[now - 1]:
        return 0
    if depth == n-1:
        return 1
    ans = 0
    v[now - 1] = True
    for node in graph[now - 1]:
        ans += dfs(node, depth+1)

    v[now - 1] = False
    # ここが大事.上で探索の一つが終わるからリセットしている.

    return ans


print(dfs(1, 0))

Submission status: Runtime Error

Solution code:
# coding=utf-8
from math import floor, ceil, sqrt, factorial, log, gcd, log10
from itertools import accumulate, permutations, combinations, product, combinations_with_replacement, chain
from bisect import bisect_left, bisect_right
from collections import Counter, defaultdict, deque
from heapq import heappop, heappush, heappushpop, heapify
from copy import copy, deepcopy
import sys
INF = float('inf')
mod = 10**9+7
sys.setrecursionlimit(10 ** 9)


def lcm(a, b): return a * b / gcd(a, b)

# 1 2 3
# a, b, c = LI()


def LI(): return list(map(int, sys.stdin.buffer.readline().split()))

# a = I()


def I(): return int(sys.stdin.buffer.readline())

# abc def
# a, b = LS()


def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()

# a = S()


def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')

# 2
# 1
# 2
# [1, 2]


def IR(n): return [I() for i in range(n)]

# 2
# 1 2 3
# 4 5 6
# [[1,2,3], [4,5,6]]


def LIR(n): return [LI() for i in range(n)]

# 2
# abc
# def
# [abc, def]


def SR(n): return [S() for i in range(n)]

# 2
# abc def
# ghi jkl
# [[abc,def], [ghi,jkl]]


def LSR(n): return [LS() for i in range(n)]

# 2
# abcd
# efgh
# [[a,b,c,d], [e,f,g,h]]


def SRL(n): return [list(S()) for i in range(n)]


# https://qiita.com/greenteabiscuit/items/31c46ab3ceac07e749d2


n, m = LI()
graph = [[] for _ in range(m)]
v = [False] * n

for i in range(m):
    a, b = LI()
    graph[a - 1].append(b)
    graph[b - 1].append(a)


def dfs(now, depth):
    if v[now - 1]:
        return 0
    if depth == n-1:
        return 1
    ans = 0
    v[now - 1] = True
    for node in graph[now - 1]:
        ans += dfs(node, depth+1)

    v[now - 1] = False
    # ここが大事.上で探索の一つが終わるからリセットしている.

    return ans


print(dfs(1, 0))

Submission status: Runtime Error

Solution code:
# coding=utf-8
from math import floor, ceil, sqrt, factorial, log, gcd, log10
from itertools import accumulate, permutations, combinations, product, combinations_with_replacement, chain
from bisect import bisect_left, bisect_right
from collections import Counter, defaultdict, deque
from heapq import heappop, heappush, heappushpop, heapify
from copy import copy, deepcopy
import sys
INF = float('inf')
mod = 10**9+7
sys.setrecursionlimit(10 ** 16)


def lcm(a, b): return a * b / gcd(a, b)

# 1 2 3
# a, b, c = LI()


def LI(): return list(map(int, sys.stdin.buffer.readline().split()))

# a = I()


def I(): return int(sys.stdin.buffer.readline())

# abc def
# a, b = LS()


def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()

# a = S()


def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')

# 2
# 1
# 2
# [1, 2]


def IR(n): return [I() for i in range(n)]

# 2
# 1 2 3
# 4 5 6
# [[1,2,3], [4,5,6]]


def LIR(n): return [LI() for i in range(n)]

# 2
# abc
# def
# [abc, def]


def SR(n): return [S() for i in range(n)]

# 2
# abc def
# ghi jkl
# [[abc,def], [ghi,jkl]]


def LSR(n): return [LS() for i in range(n)]

# 2
# abcd
# efgh
# [[a,b,c,d], [e,f,g,h]]


def SRL(n): return [list(S()) for i in range(n)]


# https://qiita.com/greenteabiscuit/items/31c46ab3ceac07e749d2


n, m = LI()
graph = [[] for _ in range(m)]
v = [False] * n

for i in range(m):
    a, b = LI()
    graph[a - 1].append(b)
    graph[b - 1].append(a)


def dfs(now, depth):
    if v[now - 1]:
        return 0
    if depth == n-1:
        return 1
    ans = 0
    v[now - 1] = True
    for node in graph[now - 1]:
        ans += dfs(node, depth+1)

    v[now - 1] = False
    # ここが大事.上で探索の一つが終わるからリセットしている.

    return ans


print(dfs(1, 0))

Submission status: Runtime Error

Solution code:
# coding=utf-8
from math import floor, ceil, sqrt, factorial, log, gcd, log10
from itertools import accumulate, permutations, combinations, product, combinations_with_replacement, chain
from bisect import bisect_left, bisect_right
from collections import Counter, defaultdict, deque
from heapq import heappop, heappush, heappushpop, heapify
from copy import copy, deepcopy
import sys
INF = float('inf')
mod = 10**9+7
sys.setrecursionlimit(10 ** 7)


def lcm(a, b): return a * b / gcd(a, b)

# 1 2 3
# a, b, c = LI()


def LI(): return list(map(int, sys.stdin.buffer.readline().split()))

# a = I()


def I(): return int(sys.stdin.buffer.readline())

# abc def
# a, b = LS()


def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()

# a = S()


def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')

# 2
# 1
# 2
# [1, 2]


def IR(n): return [I() for i in range(n)]

# 2
# 1 2 3
# 4 5 6
# [[1,2,3], [4,5,6]]


def LIR(n): return [LI() for i in range(n)]

# 2
# abc
# def
# [abc, def]


def SR(n): return [S() for i in range(n)]

# 2
# abc def
# ghi jkl
# [[abc,def], [ghi,jkl]]


def LSR(n): return [LS() for i in range(n)]

# 2
# abcd
# efgh
# [[a,b,c,d], [e,f,g,h]]


def SRL(n): return [list(S()) for i in range(n)]


# https://qiita.com/greenteabiscuit/items/31c46ab3ceac07e749d2


n, m = LI()
graph = [[] for _ in range(m)]
v = [False] * n

for i in range(m):
    a, b = LI()
    graph[a - 1].append(b-1)
    graph[b - 1].append(a-1)


def dfs(now, depth):
    if v[now]:
        return 0
    if depth == n-1:
        return 1
    ans = 0
    v[now] = True
    for node in graph[now]:
        ans += dfs(node, depth+1)

    v[now - 1] = False
    # ここが大事.上で探索の一つが終わるからリセットしている.

    return ans


print(dfs(0, 0))

Submission status: Runtime Error

Solution code:
# coding=utf-8
from math import floor, ceil, sqrt, factorial, log, gcd, log10
from itertools import accumulate, permutations, combinations, product, combinations_with_replacement, chain
from bisect import bisect_left, bisect_right
from collections import Counter, defaultdict, deque
from heapq import heappop, heappush, heappushpop, heapify
from copy import copy, deepcopy
import sys
INF = float('inf')
mod = 10**9+7
sys.setrecursionlimit(10 ** 7)


def lcm(a, b): return a * b / gcd(a, b)

# 1 2 3
# a, b, c = LI()


def LI(): return list(map(int, sys.stdin.buffer.readline().split()))

# a = I()


def I(): return int(sys.stdin.buffer.readline())

# abc def
# a, b = LS()


def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()

# a = S()


def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')

# 2
# 1
# 2
# [1, 2]


def IR(n): return [I() for i in range(n)]

# 2
# 1 2 3
# 4 5 6
# [[1,2,3], [4,5,6]]


def LIR(n): return [LI() for i in range(n)]

# 2
# abc
# def
# [abc, def]


def SR(n): return [S() for i in range(n)]

# 2
# abc def
# ghi jkl
# [[abc,def], [ghi,jkl]]


def LSR(n): return [LS() for i in range(n)]

# 2
# abcd
# efgh
# [[a,b,c,d], [e,f,g,h]]


def SRL(n): return [list(S()) for i in range(n)]


# https://qiita.com/greenteabiscuit/items/31c46ab3ceac07e749d2


n, m = LI()
graph = [[] for _ in range(m)]
v = [False] * n

for i in range(m):
    a, b = LI()
    graph[a - 1].append(b)
    graph[b - 1].append(a)


def dfs(now, depth):
    if v[now - 1]:
        return 0
    if depth == n-1:
        return 1
    ans = 0
    v[now - 1] = True
    for node in graph[now - 1]:
        ans += dfs(node, depth+1)

    v[now - 1] = False
    # ここが大事.上で探索の一つが終わるからリセットしている.

    return ans


print(dfs(1, 0))

Submission status: Runtime Error

Solution code:
# coding=utf-8
from math import floor, ceil, sqrt, factorial, log, gcd, log10
from itertools import accumulate, permutations, combinations, product, combinations_with_replacement, chain
from bisect import bisect_left, bisect_right
from collections import Counter, defaultdict, deque
from heapq import heappop, heappush, heappushpop, heapify
from copy import copy, deepcopy
import sys
INF = float('inf')
mod = 10**9+7
sys.setrecursionlimit(10 ** 6)


def lcm(a, b): return a * b / gcd(a, b)

# 1 2 3
# a, b, c = LI()


def LI(): return list(map(int, sys.stdin.buffer.readline().split()))

# a = I()


def I(): return int(sys.stdin.buffer.readline())

# abc def
# a, b = LS()


def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()

# a = S()


def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')

# 2
# 1
# 2
# [1, 2]


def IR(n): return [I() for i in range(n)]

# 2
# 1 2 3
# 4 5 6
# [[1,2,3], [4,5,6]]


def LIR(n): return [LI() for i in range(n)]

# 2
# abc
# def
# [abc, def]


def SR(n): return [S() for i in range(n)]

# 2
# abc def
# ghi jkl
# [[abc,def], [ghi,jkl]]


def LSR(n): return [LS() for i in range(n)]

# 2
# abcd
# efgh
# [[a,b,c,d], [e,f,g,h]]


def SRL(n): return [list(S()) for i in range(n)]


# https://qiita.com/greenteabiscuit/items/31c46ab3ceac07e749d2


n, m = LI()
graph = [[] for _ in range(m)]
v = [False] * n

for i in range(m):
    a, b = LI()
    graph[a - 1].append(b)
    graph[b - 1].append(a)


def dfs(now, depth):
    if v[now - 1]:
        return 0
    if depth == n-1:
        return 1
    ans = 0
    v[now - 1] = True
    for node in graph[now - 1]:
        ans += dfs(node, depth+1)

    v[now - 1] = False
    # ここが大事.上で探索の一つが終わるからリセットしている.

    return ans


print(dfs(1, 0))

Submission status: Runtime Error

Solution code:
# coding=utf-8
from math import floor, ceil, sqrt, factorial, log, gcd, log10
from itertools import accumulate, permutations, combinations, product, combinations_with_replacement, chain
from bisect import bisect_left, bisect_right
from collections import Counter, defaultdict, deque
from heapq import heappop, heappush, heappushpop, heapify
from copy import copy, deepcopy
import sys
INF = float('inf')
mod = 10**9+7
sys.setrecursionlimit(10 ** 6)


def lcm(a, b): return a * b / gcd(a, b)

# 1 2 3
# a, b, c = LI()


def LI(): return list(map(int, sys.stdin.buffer.readline().split()))

# a = I()


def I(): return int(sys.stdin.buffer.readline())

# abc def
# a, b = LS()


def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()

# a = S()


def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')

# 2
# 1
# 2
# [1, 2]


def IR(n): return [I() for i in range(n)]

# 2
# 1 2 3
# 4 5 6
# [[1,2,3], [4,5,6]]


def LIR(n): return [LI() for i in range(n)]

# 2
# abc
# def
# [abc, def]


def SR(n): return [S() for i in range(n)]

# 2
# abc def
# ghi jkl
# [[abc,def], [ghi,jkl]]


def LSR(n): return [LS() for i in range(n)]

# 2
# abcd
# efgh
# [[a,b,c,d], [e,f,g,h]]


def SRL(n): return [list(S()) for i in range(n)]


# https://qiita.com/greenteabiscuit/items/31c46ab3ceac07e749d2


n, m = LI()
graph = [[] for _ in range(m)]
v = [False] * n

for i in range(m):
    a, b = LI()
    graph[a - 1].append(b)
    graph[b - 1].append(a)

def dfs(now, depth):
    if v[n - 1]:
        return 0
    if depth == n-1:
        return 1
    ans = 0
    v[now - 1] = True
    for node in graph[now - 1]:
        ans += dfs(node, depth+1)

    v[now - 1] = False
    # ここが大事.上で探索の一つが終わるからリセットしている.

    return ans

print(dfs(1, 0))

Submission status: Runtime Error

Solution code:
# coding=utf-8
from math import floor, ceil, sqrt, factorial, log, gcd, log10
from itertools import accumulate, permutations, combinations, product, combinations_with_replacement, chain
from bisect import bisect_left, bisect_right
from collections import Counter, defaultdict, deque
from heapq import heappop, heappush, heappushpop, heapify
from copy import copy, deepcopy
import sys
INF = float('inf')
mod = 10**9+7
sys.setrecursionlimit(10 ** 6)


def lcm(a, b): return a * b / gcd(a, b)

# 1 2 3
# a, b, c = LI()


def LI(): return list(map(int, sys.stdin.buffer.readline().split()))

# a = I()


def I(): return int(sys.stdin.buffer.readline())

# abc def
# a, b = LS()


def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()

# a = S()


def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')

# 2
# 1
# 2
# [1, 2]


def IR(n): return [I() for i in range(n)]

# 2
# 1 2 3
# 4 5 6
# [[1,2,3], [4,5,6]]


def LIR(n): return [LI() for i in range(n)]

# 2
# abc
# def
# [abc, def]


def SR(n): return [S() for i in range(n)]

# 2
# abc def
# ghi jkl
# [[abc,def], [ghi,jkl]]


def LSR(n): return [LS() for i in range(n)]

# 2
# abcd
# efgh
# [[a,b,c,d], [e,f,g,h]]


def SRL(n): return [list(S()) for i in range(n)]


# https://qiita.com/greenteabiscuit/items/31c46ab3ceac07e749d2


n, m = LI()
graph = [[] for _ in range(m)]
v = [False for _ in range(n)]


for i in range(m):
    a, b = LI()
    graph[a - 1].append(b)
    graph[b - 1].append(a)

def dfs(now, depth):
    if v[n - 1]:
        return 0
    if depth == m-1:
        return 1
    ans = 0
    v[now - 1] = True
    for node in graph[now - 1]:
        ans += dfs(node, depth+1)

    v[now - 1] = False
    # ここが大事.上で探索の一つが終わるからリセットしている.

    return ans

print(dfs(1, 0))

Submission status: Runtime Error

Solution code:
# coding=utf-8
from math import floor, ceil, sqrt, factorial, log, gcd, log10
from itertools import accumulate, permutations, combinations, product, combinations_with_replacement, chain
from bisect import bisect_left, bisect_right
from collections import Counter, defaultdict, deque
from heapq import heappop, heappush, heappushpop, heapify
from copy import copy, deepcopy
import sys
INF = float('inf')
mod = 10**9+7
sys.setrecursionlimit(10 ** 6)


def lcm(a, b): return a * b / gcd(a, b)

# 1 2 3
# a, b, c = LI()


def LI(): return list(map(int, sys.stdin.buffer.readline().split()))

# a = I()


def I(): return int(sys.stdin.buffer.readline())

# abc def
# a, b = LS()


def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()

# a = S()


def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')

# 2
# 1
# 2
# [1, 2]


def IR(n): return [I() for i in range(n)]

# 2
# 1 2 3
# 4 5 6
# [[1,2,3], [4,5,6]]


def LIR(n): return [LI() for i in range(n)]

# 2
# abc
# def
# [abc, def]


def SR(n): return [S() for i in range(n)]

# 2
# abc def
# ghi jkl
# [[abc,def], [ghi,jkl]]


def LSR(n): return [LS() for i in range(n)]

# 2
# abcd
# efgh
# [[a,b,c,d], [e,f,g,h]]


def SRL(n): return [list(S()) for i in range(n)]

def dfs(n, depth):
    if v[n - 1]:
        return 0
    if depth == m-1:
        return 1
    ans = 0
    v[n - 1] = True
    for node in graph[n - 1]:
        ans += dfs(node, depth+1)

    v[n - 1] = False  # ここが大事.上で探索の一つが終わるからリセットしている.

    return ans


n, m = LI()
graph = [[] for _ in range(m)]
v = [False for _ in range(n)]


for i in range(m):
    a, b = LI()
    graph[a - 1].append(b)
    graph[b - 1].append(a)

print(dfs(1, 0))

# https://qiita.com/greenteabiscuit/items/31c46ab3ceac07e749d2

Submission status: Runtime Error

Solution code:
# coding=utf-8
from math import floor, ceil, sqrt, factorial, log, gcd, log10
from itertools import accumulate, permutations, combinations, product, combinations_with_replacement, chain
from bisect import bisect_left, bisect_right
from collections import Counter, defaultdict, deque
from heapq import heappop, heappush, heappushpop, heapify
from copy import copy, deepcopy
import sys
INF = float('inf')
mod = 10**9+7
sys.setrecursionlimit(10 ** 6)


def lcm(a, b): return a * b / gcd(a, b)

# 1 2 3
# a, b, c = LI()


def LI(): return list(map(int, sys.stdin.buffer.readline().split()))

# a = I()


def I(): return int(sys.stdin.buffer.readline())

# abc def
# a, b = LS()


def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()

# a = S()


def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')

# 2
# 1
# 2
# [1, 2]


def IR(n): return [I() for i in range(n)]

# 2
# 1 2 3
# 4 5 6
# [[1,2,3], [4,5,6]]


def LIR(n): return [LI() for i in range(n)]

# 2
# abc
# def
# [abc, def]


def SR(n): return [S() for i in range(n)]

# 2
# abc def
# ghi jkl
# [[abc,def], [ghi,jkl]]


def LSR(n): return [LS() for i in range(n)]

# 2
# abcd
# efgh
# [[a,b,c,d], [e,f,g,h]]


def SRL(n): return [list(S()) for i in range(n)]


n, m = LI()
graph = [[] for _ in range(m)]
v = [False for _ in range(n)]


def dfs(n, depth):
    if v[n - 1] == True:
        return 0
    if depth == m-1:
        return 1
    ans = 0
    v[n - 1] = True
    for node in graph[n - 1]:
        ans += dfs(node, depth+1)

    v[n - 1] = False  # ここが大事.上で探索の一つが終わるからリセットしている.

    return ans


for i in range(m):
    a, b = LI()
    graph[a - 1].append(b)
    graph[b - 1].append(a)

print(dfs(1, 0))

# https://qiita.com/greenteabiscuit/items/31c46ab3ceac07e749d2

Submission status: Runtime Error

Solution code:
from itertools import permutations

N, M = map(int, input().split())
G = [[] for _ in range(N)]
for _ in range(N):
    a, b = map(int, input().split())
    a, b = a - 1, b - 1
    G[a].append(b)
    G[b].append(a)

res = 0
for P in permutations(range(N), N):
    if P[0] != 0:
        continue
    for i in range(N - 1):
        if P[i + 1] not in G[P[i]]:
            break
    else:
        res += 1

print(res)

Submission status: Runtime Error

Solution code:
import itertools

N, M = map(int, input().split())
G = [[]  for _ in range(N)]
for i in range(M):
    a, b = map(lambda x: int(x) - 1, input().split())
    G[a].append(b)
    G[b].append(a)
pattern = [i for i in range(N)]

ans = 0
for i in itertools.permutations(pattern):
    flag = True
    now = i[j]
    to = i[j+1]
    if i[0] != 0:
        continue
    for j in range(len(i) - 1):
        if not to in G[now]:
            flag = False
    if flag:
        ans += 1
print(ans)

Submission status: Runtime Error

Solution code:
import itertools

N, M = map(int, input().split())
G = [[]  for _ in range(N)]
for i in range(M):
    a, b = map(lambda x: int(x) - 1, input().split())
    G[a].append(b)
    G[b].append(a)
pattern = [i for i in range(N)]

ans = 0
for i in itertools.permutations(pattern):
    flag = True
    now = i[j]
    next = i[j+1]
    if i[0] != 0:
        continue
    for j in range(len(i) - 1):
        if not next in G[now]:
            flag = False
    if flag:
        ans += 1
print(ans)

Submission status: Runtime Error

Solution code:
n,m=map(int,input().split())
road=[[] for _ in range(n+1)]
for i in range(m):
    a,b=map(int,input().split())
    road[a].append(b)
    road[b].append(a)
dp=[[0]*(n+1) for _ in range(2**n)]
dp[1][1]=1
for i in range(1,2**n):
    for j in range(1,n+1):
        for k in road[j]:
            
                dp[i+2**(k-1)][k]+=dp[i][j]
print(sum(dp[2**n-1]))

Submission status: Runtime Error

Solution code:
import itertools
N, M = map(int, input().split())
p=[[0]*N for i in range(N)]
for i in range(M):
    a,b=map(int,input().split())
    p[a-1][b-1]=1
    p[b-1][a-1]=1
cnt=0
a=[i for i in range(N)]

for i in itertools.permutations(a):
    flag=0
    if i[0]==0:
        for j in range(1,M):
            if p[i[j]][i[j-1]]!=1:
                flag=1
        if flag==0:
            cnt+=1
    
print(cnt)

Submission status: Runtime Error

Solution code:
N,M = map(int,input.split())


#iから進める場所をリストにして保管
edges = {i:[] for i in range(1,N+1)}
for i in range(M):
  a,b = [int(a) for a in input().split()]
  edges[a].append(b)
  edges[b].append(a)


#深さ優先探索
def dfs(list):
    #lst(通過点)の数がN(頂点数)と等しくなったら探索終了（成功）
  if len(list) == N:
    return 1
  else:
    a = list[-1]
    #lstの最後尾（現在地）が次に進める場所をnextとしてリスト化
    #nextに以前通った場所が入っていないか確認
    next = [n for n in edges[a] if n not in list]
    #次に進める場所がなくなったら探索終了（失敗）
    if len(next) == 0:
      return 0

    total = 0
    #再帰でさらに探索
    for n in next:
      total += dfs(list + [n])

    return total


ans = dfs([1])

print(ans)

Submission status: Runtime Error

Solution code:
N,M = map(int,input().split())
edges = {i:[] for i in range(1,M+1)}
for i in range(M):
    a,b = map(int,input().split())
    edges[a].append(b)
    edges[b].append(a)

#深さ優先探索
def dfs(list):
    #lst(通過点)の数がN(頂点数)と等しくなったら探索終了（成功）
    if len(list) == N:
        return 1
    else:
        x = list[-1]
        #lstの最後尾（現在地）が次に進める場所をnextとしてリスト化
        #nextに以前通った場所が入っていないか確認
        next = [n for n in edges[x] if n not in list]
        #次に進める場所がなくなったら探索終了（失敗）
        if len(next) == 0:
          return 0

        total = 0
        #再帰でさらに探索
        for n in next:
          total += dfs(list + [n])

        return total

Submission status: Runtime Error

Solution code:
import itertools
N, M = map(int, input().split())
A = [list(map(int, input().split())) for i in range(N)]
cnt=0
for l in range(1,N+1):
    for i in itertools.combinations(A,l):
        a=[0]*N
        for j,k in i:
            a[j-1]+=1
            a[k-1]+=1
        if a[0]==1 and a.count(1)==2 and a.count(2)==N-2:
            cnt+=1
print(cnt)

Submission status: Runtime Error

Solution code:
#一度だけ頂点を通る⇒辺の数=頂点-1
import itertools



Mlist=[]
N,M=map(int,input().split(' '))
for i in range(N):
  Mlist.append(list(map(int,input().split(" "))))

all_parterns=itertools.permutations(range(M),r=N-1)
#all_parterns=[(0,2,3,5,6,1)]
ans=0
for partern in all_parterns:
  x=1
  IsOk=True
  for i in partern:
    a,b=Mlist[i]
    if x==a:
      x=b
    elif x==b:
      x=a
    else:
      IsOk=False
  if IsOk:
    ans+=1
print(ans)

Submission status: Runtime Error

Solution code:
from itertools import permutations
N, M = map(int, input().split())
AB = [tuple(map(int, input().split())) for _ in range(M)]
m = [set() for _ in range(1, 9)]
for a, b in AB:
    m[a].add(b)
    m[b].add(a)

def main():
    ans = []
    def traverse(n, visits):
        visits = visits | set([n])
        if len(visits) == N:
            ans.append(1)
            return
        for c in m[n] - visits:
            traverse(c, visits)
    traverse(1, set())
    return len(ans)

print(main())

Submission status: Runtime Error

Solution code:
N,M = map(int,input().split())

line = [[] for _ in range(M)]
for _ in range(N):
    a,b = map(int,input().split())
    line[a-1].append(b-1)
    line[b-1].append(a-1)

check = [False] * N

def dfs(now):
    global cnt
    global ans
    if cnt == N:
        ans += 1
    else:
        for i in line[now]:
            if check[i] == False:
                check[i] = True
                cnt += 1
                dfs(i)
                check[i] = False
                cnt -= 1

check[0] = True
cnt = 1
ans = 0
dfs(0)
print(ans)