Problem: 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

Submission attempts (in order):
def dfs(g, seen, n, ans):
    all_seen = True

    for si in seen:
        if si == False:
            all_seen = False

    if all_seen:
        ans += 1
        return ans

    for m in g[n]:
        if seen[m]:
            continue

        seen[m] = True
        ans = dfs(g, seen, m, ans)
        seen[m] = False

    return ans


def main():
    n, m = map(int, stdin.readline().split())
    ab = [map(int, stdin.readline().split()) for _ in range(n)]
    g = [[] for _ in range(n)]
    for abi in ab:
        a, b = abi
        g[a - 1].append(b - 1)
        g[b - 1].append(a - 1)
    seen = [False for _ in range(n)]
    seen[0] = True

    ans = 0

    ans = dfs(g, seen, 0, ans)

    print(ans)


if __name__ == "__main__":
    main()


def dfs(g, seen, n):
    all_seen = True

    for si in seen:
        if si == False:
            all_seen = False

    if all_seen:
        return 1

    ans = 0

    for m in g[n]:
        if seen[m]:
            continue

        seen[m] = True
        ans += dfs(g, seen, m)
        seen[m] = False

    return ans


def main():
    n, m = map(int, stdin.readline().split())
    ab = [map(int, stdin.readline().split()) for _ in range(n)]
    g = [[] for _ in range(n)]
    for abi in ab:
        a, b = abi
        g[a - 1].append(b - 1)
        g[b - 1].append(a - 1)
    seen = [False for _ in range(n)]
    seen[0] = True

    ans = dfs(g, seen, 0)

    print(ans)


if __name__ == "__main__":
    main()


from sys import stdin


def dfs(g, seen, n):
    all_seen = True

    for si in seen:
        if si == False:
            all_seen = False

    if all_seen:
        return 1

    ans = 0

    for m in g[n]:
        if seen[m]:
            continue

        seen[m] = True
        ans += dfs(g, seen, m)
        seen[m] = False

    return ans


def main():
    n, m = map(int, stdin.readline().split())
    ab = [map(int, stdin.readline().split()) for _ in range(m)]
    g = [[] for _ in range(n)]
    for abi in ab:
        a, b = abi
        g[a - 1].append(b - 1)
        g[b - 1].append(a - 1)
    seen = [False for _ in range(n)]
    seen[0] = True

    ans = dfs(g, seen, 0)

    print(ans)


if __name__ == "__main__":
    main()


Verdicts: Runtime Error

Runtime Error

Accepted