Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python3
import sys

sys.setrecursionlimit(10**9)


def dfs(v, graph, memo):
    if v in memo:
        return memo[v]

    if graph[v]:
        res = max(dfs(child, graph, memo) for child in graph[v])
        memo[v] = res + 1
    else:
        res = 0
        memo[v] = 0

    return memo[v]


def solve(N: int, M: int, x: "List[int]", y: "List[int]"):
    graph = [[] for _ in range(N)]
    for i in range(M):
        graph[x[i]-1].append(y[i]-1)

    memo = {}

    print(max(dfs(i, graph, memo) for i in range(N)))


# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    M = int(next(tokens))  # type: int
    x = [int()] * (M)  # type: "List[int]"
    y = [int()] * (M)  # type: "List[int]"
    for i in range(M):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    solve(N, M, x, y)


if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys

sys.setrecursionlimit(10**9)


def dfs(v, graph, memo):
    if v in memo:
        return memo[v]

    if graph[v]:
        res = float("-inf")
        for child in graph[v]:
            res = max(res, dfs(child, graph, memo) + 1)
        memo[v] = res
    else:
        res = 0
        memo[v] = 0

    return memo[v]


def solve(N: int, M: int, x: "List[int]", y: "List[int]"):
    graph = [[] for _ in range(N)]
    for i in range(M):
        graph[x[i]-1].append(y[i]-1)

    memo = {}

    res = float("-inf")
    for i in range(N):
        res = max(res, dfs(i, graph, memo))
    print(res)


# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    M = int(next(tokens))  # type: int
    x = [int()] * (M)  # type: "List[int]"
    y = [int()] * (M)  # type: "List[int]"
    for i in range(M):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    solve(N, M, x, y)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python3
import sys

sys.setrecursionlimit(10**9)


def solve(N: int, M: int, x: "List[int]", y: "List[int]"):
    graph = [[] for _ in range(N)]
    for i in range(M):
        graph[x[i]-1].append(y[i]-1)

    memo = {}

    def dfs(v, memo):
        if v in memo:
            return memo[v]

        if graph[v]:
            res = max(dfs(child, memo) for child in graph[v])
            memo[v] = res + 1
        else:
            res = 0
            memo[v] = 0

        return memo[v]

    print(max(dfs(i, memo) for i in range(N)))


# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    M = int(next(tokens))  # type: int
    x = [int()] * (M)  # type: "List[int]"
    y = [int()] * (M)  # type: "List[int]"
    for i in range(M):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    solve(N, M, x, y)


if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys

sys.setrecursionlimit(10**9)


def dfs(v, graph, memo):
    if v in memo:
        return memo[v]

    if graph[v]:
        res = float("-inf")
        for child in graph[v]:
            res = max(res, dfs(child, graph, memo) + 1)
        memo[v] = res
    else:
        res = 0
        memo[v] = 0

    return memo[v]


def solve(N: int, M: int, x: "List[int]", y: "List[int]"):
    graph = [[] for _ in range(N)]
    for i in range(M):
        graph[x[i]-1].append(y[i]-1)

    memo = {}

    res = float("-inf")
    for i in range(N):
        res = max(res, dfs(i, graph, memo))
    print(res)


# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    M = int(next(tokens))  # type: int
    x = [int()] * (M)  # type: "List[int]"
    y = [int()] * (M)  # type: "List[int]"
    for i in range(M):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    solve(N, M, x, y)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python3
import sys

sys.setrecursionlimit(10**9)


def solve(N: int, M: int, x: "List[int]", y: "List[int]"):
    graph = [[] for _ in range(N)]
    for i in range(M):
        graph[x[i]-1].append(y[i]-1)

    memo = {}

    def dfs(v):
        if v in memo:
            return memo[v]

        if graph[v]:
            res = max(dfs(child) for child in graph[v])
            memo[v] = res + 1
        else:
            res = 0
            memo[v] = 0

        return memo[v]

    print(max(dfs(i) for i in range(N)))


# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    M = int(next(tokens))  # type: int
    x = [int()] * (M)  # type: "List[int]"
    y = [int()] * (M)  # type: "List[int]"
    for i in range(M):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    solve(N, M, x, y)


if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys

sys.setrecursionlimit(10**9)


def dfs(v, graph, memo):
    if v in memo:
        return memo[v]

    if graph[v]:
        res = float("-inf")
        for child in graph[v]:
            res = max(res, dfs(child, graph, memo) + 1)
        memo[v] = res
    else:
        res = 0
        memo[v] = 0

    return memo[v]


def solve(N: int, M: int, x: "List[int]", y: "List[int]"):
    graph = [[] for _ in range(N)]
    for i in range(M):
        graph[x[i]-1].append(y[i]-1)

    memo = {}

    res = float("-inf")
    for i in range(N):
        res = max(res, dfs(i, graph, memo))
    print(res)


# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    M = int(next(tokens))  # type: int
    x = [int()] * (M)  # type: "List[int]"
    y = [int()] * (M)  # type: "List[int]"
    for i in range(M):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    solve(N, M, x, y)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python3
import sys

sys.setrecursionlimit(10**9)


def solve(N: int, M: int, x: "List[int]", y: "List[int]"):
    graph = [[] for _ in range(N)]
    for i in range(M):
        graph[x[i]-1].append(y[i]-1)

    memo = {}

    def dfs(v):
        if v in memo:
            return memo[v]

        if graph[v]:
            res = max(dfs(child) for child in graph[v])
            memo[v] = res + 1
        else:
            res = 0
            memo[v] = 0

        return memo[v]

    print(max(dfs(i) for i in range(N)))


# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    M = int(next(tokens))  # type: int
    x = [int()] * (M)  # type: "List[int]"
    y = [int()] * (M)  # type: "List[int]"
    for i in range(M):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    solve(N, M, x, y)


if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys

sys.setrecursionlimit(10**9)


def dfs(v, graph, memo):
    if v in memo:
        return memo[v]

    if graph[v]:
        res = float("-inf")
        for child in graph[v]:
            res = max(res, dfs(child, graph, memo) + 1)
        memo[v] = res
    else:
        res = 0
        memo[v] = 0

    return memo[v]


def solve(N: int, M: int, x: "List[int]", y: "List[int]"):
    graph = [[] for _ in range(N)]
    for i in range(M):
        graph[x[i]-1].append(y[i]-1)

    memo = {}

    res = float("-inf")
    for i in range(N):
        res = max(res, dfs(i, graph, memo))
    print(res)


# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    M = int(next(tokens))  # type: int
    x = [int()] * (M)  # type: "List[int]"
    y = [int()] * (M)  # type: "List[int]"
    for i in range(M):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    solve(N, M, x, y)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys


def solve(N: int, M: int, x: "List[int]", y: "List[int]"):
    graph = [[] for _ in range(N)]
    for i in range(M):
        graph[x[i]-1].append(y[i]-1)

    memo = {}

    def dfs(v):
        if v in memo:
            return memo[v]

        if graph[v]:
            res = max(dfs(child) for child in graph[v])
            memo[v] = res + 1
        else:
            res = 0
            memo[v] = 0

        return memo[v]

    print(max(dfs(i) for i in range(N)))


# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    M = int(next(tokens))  # type: int
    x = [int()] * (M)  # type: "List[int]"
    y = [int()] * (M)  # type: "List[int]"
    for i in range(M):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    solve(N, M, x, y)


if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys

sys.setrecursionlimit(10**9)


def dfs(v, graph, memo):
    if v in memo:
        return memo[v]

    if graph[v]:
        res = float("-inf")
        for child in graph[v]:
            res = max(res, dfs(child, graph, memo) + 1)
        memo[v] = res
    else:
        res = 0
        memo[v] = 0

    return memo[v]


def solve(N: int, M: int, x: "List[int]", y: "List[int]"):
    graph = [[] for _ in range(N)]
    for i in range(M):
        graph[x[i]-1].append(y[i]-1)

    memo = {}

    res = float("-inf")
    for i in range(N):
        res = max(res, dfs(i, graph, memo))
    print(res)


# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    M = int(next(tokens))  # type: int
    x = [int()] * (M)  # type: "List[int]"
    y = [int()] * (M)  # type: "List[int]"
    for i in range(M):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    solve(N, M, x, y)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
n, m = map(int, input().split())

memo = [-1] * (10 ** 6 + 100)

g = [[] for i in range(n + 1)]

for i in range(m):
    x, y = map(int, input().split())
    g[y].append(x)


def dfs(i):
    if memo[i] != -1:
        return memo[i]
    if not g[i]:
        return 0
    else:
        memo[i] = max(dfs(v) for v in g[i]) + 1
        return memo[i]


for i in range(1, n+1):
    dfs(i)

print(max(memo))


Fixed submission:
import sys
sys.setrecursionlimit(10 ** 6 + 100)
n, m = map(int, input().split())

memo = [-1] * (10 ** 6 + 100)

g = [[] for i in range(n + 1)]

for i in range(m):
    x, y = map(int, input().split())
    g[y].append(x)


def dfs(i):
    if memo[i] != -1:
        return memo[i]
    if not g[i]:
        return 0
    else:
        memo[i] = max(dfs(v) for v in g[i]) + 1
        return memo[i]


for i in range(1, n+1):
    dfs(i)

print(max(memo))