Problem:
 Score : 100 points    Problem Statement There is a directed graph G with N vertices and M edges.
The vertices are numbered 1, 2, \ldots, N , and for each i ( 1 \leq i \leq M ), the i -th directed edge goes from Vertex x_i to y_i . G  does not contain directed cycles .  Find the length of the longest directed path in G .
Here, the length of a directed path is the number of edges in it.      Constraints  All values in input are integers.  2 \leq N \leq 10^5  1 \leq M \leq 10^5  1 \leq x_i, y_i \leq N  All pairs (x_i, y_i) are distinct.  G  does not contain directed cycles .         Input Input is given from Standard Input in the following format:  N  M  x_1  y_1  x_2  y_2  :  x_M  y_M       Output Print the length of the longest directed path in G .        Sample Input 1 4 5
1 2
1 3
3 2
2 4
3 4      Sample Output 1 3  The red directed path in the following figure is the longest:        Sample Input 2 6 3
2 3
4 5
5 6      Sample Output 2 2  The red directed path in the following figure is the longest:        Sample Input 3 5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3      Sample Output 3 3  The red directed path in the following figure is one of the longest:

Solution (Python):
def main(sample_file = ''):

    """ convenient functions
    
    
    
    
    
    """

    """convenient decorator
    
    
        
        
        
        
        
        
        
        
        
        
    """
    
    
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product 
    
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  
        b, e = 2, 0  
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict 
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest 
    from copy import deepcopy, copy 
    import operator
    from operator import itemgetter 
    
    
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd 
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    
    
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    modpow = lambda a, n, p = MOD: pow(a, n, p) 
    def modinv(a, p = MOD):
        
        
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        
        
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    
    
    
    
    

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    """ initialize variables and set inputs
    
        
        
            
            
    
        
        
        
        
        
        
        
    
        
        
        
        
    
        
        
    """

    
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    R = lambda: list(map(int, r().split()))
    Rmap = lambda: map(int, r().split())
    Rfloat = lambda: list(map(float, r().split()))
    Rtuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    
    
    
    
    
    
    
    """

    
    if sample_file:
        sys.stdin = open(sample_file)
        
    
    

    N, M = R()
    XY = [R() for _ in range(M)]
    parents = [list() for _ in range(N)]
    tasks = []
    dp = [0] * N
    num_child = [0] * N
    for x, y in XY:
        parents[y-1].append(x-1)
        num_child[x-1] += 1
    for i, num in enumerate(num_child):
        if num == 0:
            tasks.append(i)
    while tasks:
        x = tasks.pop()
        for parent in parents[x]:
            dp[parent] = max(dp[parent], dp[x]+1)
            num_child[parent] -= 1
            if num_child[parent] == 0:
                tasks.append(parent)
    print(max(dp))

    
    
    

    """memo: how to use defaultdict of list
    
    Dic = defaultdict(list)
    
    Dic[x].append(y)
    
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    
    >>> a = 5
    >>> bin_str_a = format(a, '
    >>> print(bin_str_a)
    0b0101 
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Solution (Python):
import sys
input=sys.stdin.readline
N,M=map(int,input().split())
L=[[]for i in range(N+1)]
S=[0 for i in range(N+1)]
for i in range(M):
    x,y=map(int,input().split())
    L[x].append(y)
    S[y]+=1


start=[]
for i in range(1,N+1):
    if S[i]==0:
        start.append(i)
D=[0 for i in range(N+1)]
Q=[]
for s in start:
    for a in L[s]:
        Q.append([a,1])
for i in range(100000):
    if i==len(Q):
        break
    S[Q[i][0]]-=1
    if D[Q[i][0]]<Q[i][1]:
        D[Q[i][0]]=Q[i][1]
    if S[Q[i][0]]==0:
        for j in L[Q[i][0]]:
            Q.append([j,Q[i][1]+1])
    
print(max(D))

Solution (Python):
N, M = map(int, input().split())
G = [[] for _ in range(N)]
in_G = [0] * N

for i in range(M):
    x, y = map(int, input().split())
    G[x-1].append(y-1)
    in_G[y-1] += 1

dist = [0] * N
q = [x for x in range(N) if in_G[x] == 0]

while q:
    v = q.pop()

    for g in G[v]:
        dist[g] = max(dist[g], dist[v] + 1)
        in_G[g] -= 1
        if in_G[g] == 0:
            q.append(g)

print(max(dist))

Solution (Python):


from collections import defaultdict, deque

INF = float("inf")

def getlist():
	return list(map(int, input().split()))



def main():
	N, M = getlist()
	outE = defaultdict(list)
	inE = defaultdict(int)	
	for i in range(M):
		a, b = getlist()
		outE[a - 1].append(b - 1)
		inE[b - 1] += 1

	Q = deque()
	for i in range(N):
		if inE[i] == 0:
			Q.append(i)

	cnt = 0
	while True:
		if not Q:
			break
		cnt += 1
		q = deque()
		while Q:
			u = Q.popleft()
			for v in outE[u]:
				inE[v] -= 1
				if inE[v] == 0:
					q.append(v)
		Q = q

	print(cnt - 1)


if __name__ == '__main__':
	main()

Solution (Python):
N, M = map(int, input().split())
g = [[] for _ in range(N)]
in_deg = [0] * N
for _ in range(M):
  x, y = map(int, input().split())
  g[x - 1].append(y - 1)
  in_deg[y - 1] += 1
dist = [0] * N
q = [x for x in range(N) if in_deg[x] == 0]
while q:
  v = q.pop()
  for u in g[v]:
    dist[u] = max(dist[u], dist[v] + 1)
    in_deg[u] -= 1
    if in_deg[u] == 0:
      q.append(u)
print(max(dist))

Solution (Python):
import sys
from collections import deque
input = lambda: sys.stdin.readline().rstrip()

n, m = map(int, input().split())
graph = [list() for _ in range(n)]
deg = [0] * n

for _ in range(m):
    a, b = map(int, input().split())
    a -= 1; b -= 1
    graph[a].append(b)
    deg[b] += 1

q = deque(i for i in range(n) if deg[i] == 0)
t = []

while q:
    v = q.popleft()
    t.append(v)
    for nv in graph[v]:
        deg[nv] -= 1
        if deg[nv] == 0:
            q.append(nv)

dp = [0] * n
for v in t:
    for nv in graph[v]:
        dp[nv] = max(dp[nv], dp[v]+1)

print(dp[t[-1]])

Solution (Python):
import sys
sys.setrecursionlimit(10**5)

v, e = map(int, input().split())
adj_list = {}
for _ in range(e):
    x, y = map(int, input().split())
    adj_list.setdefault(x, []).append(y)
visited = [0] * (v + 1)
dis = [0] * (v + 1)


def dfs(cur):
    global visited
    global dis
    visited[cur] = 1
    if cur in adj_list:
        for item in adj_list[cur]:
            if not visited[item]:
                dfs(item)
            dis[cur] = max(dis[cur], 1+dis[item])


for i in range(v + 1):
    if not visited[i]:
        dfs(i)
print(max(dis))

Solution (Python):
import sys
sys.setrecursionlimit(10**5+100)

N, M = list(map(int, input().split()))
G = {i:[] for i in range(N)}
for _ in range(M):
    x, y = list(map(int, input().split()))
    G[x-1].append(y-1)
    
dp = [-1]*N
 

def rec(i):
    if dp[i] != -1:
        return dp[i]
    res = 0
    for v in G[i]:
        res = max(res, rec(v)+1)
    dp[i] = res
    return res
 
ans = 0
for i in range(N):
    ans = max(ans, rec(i))
    
print(ans)

Solution (Python):
from collections import deque

N, M = map(int, input().split())

dp = [0] * N
E = [[] for _ in range(N)]
deg = [0] * N
for _ in range(M):
    x, y = map(int, input().split())
    E[x-1].append(y-1)
    deg[y-1] += 1

que = deque(v for v in range(N) if deg[v] == 0)
while que:
    v = que.pop()
    for u in E[v]:
        deg[u] -= 1
        if deg[u] == 0:
            que.appendleft(u)
            dp[u] = max(dp[u], dp[v] + 1)

print(max(dp))

Solution (Python):
from collections import deque


def p_g_dp():
    N, M = map(int, input().split())
    outs = [[] for _ in range(N)]
    ins = [0] * N
    for _ in range(M):
        f, t = map(int, input().split())
        outs[f - 1].append(t - 1)
        ins[t - 1] += 1
    q = deque(t for t in range(N) if ins[t] == 0)
    res = []
    dp = [0] * N
    while q:
        f = q.popleft()
        res.append(f)
        for t in outs[f]:
            ins[t] -= 1
            if ins[t] == 0:
                q.append(t)
                dp[t] = max(dp[t], dp[f] + 1)
    print(max(dp))


if __name__ == '__main__':
    p_g_dp()

Solution (Python):
import sys


def recursion_g(eges, length, f):
    if length[f] != -1:
        return length[f]
    memo = [0]
    for t in eges[f]:
        memo.append(recursion_g(eges, length, t) + 1)
    length[f] = max(memo)
    return length[f]


def p_g():
    sys.setrecursionlimit(10 ** 6)
    N, M = map(int, input().split())
    edges = [[] for _ in range(N)]
    length = [-1] * N
    for _ in range(M):
        x, y = map(int, input().split())
        edges[x - 1].append(y - 1)

    for i in range(N):
        recursion_g(edges, length, i)
    print(max(length))


if __name__ == '__main__':
    p_g()

Solution (Python):
import sys

sys.setrecursionlimit(10 ** 6)


def recursion_g(eges, length, f):
    if length[f] != -1:
        return length[f]
    if not eges[f]:
        length[f] = 0
        return 0
    memo = []
    for t in eges[f]:
        memo.append(recursion_g(eges, length, t) + 1)
    length[f] = max(memo)
    return length[f]


def p_g():
    N, M = map(int, input().split())
    edges = [[] for _ in range(N)]
    length = [-1] * N
    for _ in range(M):
        x, y = map(int, input().split())
        edges[x - 1].append(y - 1)

    for i in range(N):
        recursion_g(edges, length, i)
    print(max(length))


if __name__ == '__main__':
    p_g()

Solution (Python):
import sys

sys.setrecursionlimit(10 ** 7)

N, M = map(int, input().split())
G = [[] for _ in range(N)]
H = [0]*N
for _ in range(M):
    x, y = map(int, input().split())
    G[x-1].append(y-1)
    H[y-1]+=1

def topological_sort(G, H):
    res = []
    st0 = set()
    for v, n in enumerate(H):
        if n == 0:
            st0.add(v)
    while st0:
        v = st0.pop()
        res.append(v)
        for nv in G[v]:
            H[nv]-=1
            if H[nv] == 0:
                st0.add(nv)
    return res
i_to_v = topological_sort(G, H)
v_to_i = [0]*N
for i in range(N):
    v_to_i[i_to_v[i]] = i
dp = [0]*N
for i in range(N-1):
    for nv in G[i_to_v[i]]:
        dp[v_to_i[nv]] = max(dp[i]+1, dp[v_to_i[nv]])
print(max(dp))

Solution (Python):
N, M = map(int, input().split())
adj = [[] for _ in range(N+1)]
num_in = [0] * (N+1)
for _ in range(M):
    x, y = map(int, input().split())
    adj[x].append(y)
    num_in[y] += 1

st = []
for i in range(1, N+1):
    if num_in[i] == 0:
        st.append(i)

seq = []
while st:
    v = st.pop()
    seq.append(v)
    for u in adj[v]:
        num_in[u] -= 1
        if num_in[u] == 0:
            st.append(u)

v2i = {}
i2v = {}
for i, v in enumerate(seq):
    v2i[v] = i
    i2v[i] = v

dp = [0] * N
for i in range(N):
    v = i2v[i]
    for u in adj[v]:
        dp[v2i[u]] = max(dp[v2i[u]], dp[i] + 1)

print(max(dp))

Solution (Python):
import sys
sys.setrecursionlimit(10**5+100)
N, M = [int(_) for _ in input().split()]
E = [[] for _ in range(N)]

indegree = [0] * N  
for i in range(M):
    a, b = [int(_) - 1 for _ in input().split()]
    E[a].append(b)
    indegree[b] += 1

sorted_nodes = []
dp = [0] * N


def rep(v):
    """初めて呼ばれたときに, そのノードからの最長ノード数を数えるイメージ"""
    if dp[v] != 0: return dp[v]
    for n in E[v]:
        dp[v] = max(dp[v], rep(n) + 1)
    return dp[v]


ans = 0
for i in range(N):
    ans = max(ans, rep(i))
print(ans)

Solution (Python):
from collections import deque









N, M = [int(_) for _ in input().split()]
E = [[] for _ in range(N)]

indegree = [0] * N  
for i in range(M):
    a, b = [int(_) - 1 for _ in input().split()]
    E[a].append(b)
    indegree[b] += 1

que = deque([i for i in range(N) if indegree[i] == 0])

sorted_nodes = []
dp = [0] * N
while que:
    n = que.popleft()
    sorted_nodes.append(n)
    for next_node in E[n]:
        indegree[next_node] = indegree[next_node] - 1  
        if indegree[next_node] == 0:  
            que.append(next_node)

        dp[next_node] = max(dp[next_node], dp[n] + 1)

print(max(dp))

Solution (Python):
import sys
import collections
from functools import lru_cache
d = collections.defaultdict(list)
@lru_cache(maxsize=None)
def alg_memoization_recursion(f):
    mt = 0
    for v in d[f]:
        mt = max(mt, alg_memoization_recursion(v) + 1)
    return mt


def solve():
    readline = sys.stdin.buffer.readline
    mod = 10 ** 9 + 7
    sys.setrecursionlimit(10 ** 6)
    n, m = list(map(int, readline().split()))
    for i in range(m):
        x, y = list(map(int, readline().split()))
        d[x-1] += [y-1]
    mt = 0
    for i in range(n):
        mt = max(mt, alg_memoization_recursion(i))
    print(mt)


if __name__ == '__main__':
    solve()

Solution (Python):
import sys
import collections
from functools import lru_cache

sys.setrecursionlimit(10 ** 6)
xy = []
d = collections.defaultdict(list)

@lru_cache(maxsize=None)
def alg_memoization_recursion(f):
    mt = 0
    for v in d[f]:
        mt = max(mt, alg_memoization_recursion(v) + 1)
    return mt


def solve():
    readline = sys.stdin.buffer.readline
    mod = 10 ** 9 + 7
    n, m = list(map(int, readline().split()))
    for i in range(m):
        x, y = list(map(int, readline().split()))
        d[x-1] += [y-1]
    mt = 0
    for i in range(n):
        mt = max(mt, alg_memoization_recursion(i))
    print(mt)


if __name__ == '__main__':
    solve()

Solution (Python):
import sys
import collections
from functools import lru_cache

sys.setrecursionlimit(10 ** 7 + 1)
xy = []
d = collections.defaultdict(list)

@lru_cache(maxsize=None)
def alg_memoization_recursion(f):
    mt = 0
    for v in d[f]:
        mt = max(mt, alg_memoization_recursion(v) + 1)
    return mt


def solve():
    readline = sys.stdin.buffer.readline
    mod = 10 ** 9 + 7
    n, m = list(map(int, readline().split()))
    for i in range(m):
        x, y = list(map(int, readline().split()))
        d[x-1] += [y-1]
    mt = 0
    for i in range(n):
        mt = max(mt, alg_memoization_recursion(i))
    print(mt)


if __name__ == '__main__':
    solve()

Solution (Python):
import sys
import collections
from functools import lru_cache

sys.setrecursionlimit(10 ** 7 + 1)
xy = []
d = collections.defaultdict(list)

@lru_cache(maxsize=None)
def alg_memoization_recursion(f):
    mt = 0
    for v in d[f]:
        mt = max(mt, alg_memoization_recursion(v) + 1)
    return mt


def solve():
    readline = sys.stdin.buffer.readline
    mod = 10 ** 9 + 7
    n, m = list(map(int, readline().split()))
    for i in range(m):
        x, y = list(map(int, readline().split()))
        d[x-1] += [y-1]
    mt = 0
    for i in range(n):
        mt = max(mt, alg_memoization_recursion(i))
    print(mt)


if __name__ == '__main__':
    solve()

Solution (Python):
import sys
import collections
from functools import lru_cache

xy = []
d = collections.defaultdict(list)
@lru_cache(maxsize=None)
def alg_memoization_recursion(f):
    mt = 0
    for v in d[f]:
        mt = max(mt, alg_memoization_recursion(v) + 1)
    return mt


def solve():
    readline = sys.stdin.buffer.readline
    mod = 10 ** 9 + 7
    sys.setrecursionlimit(10 ** 5 + 1)
    n, m = list(map(int, readline().split()))
    for i in range(m):
        x, y = list(map(int, readline().split()))
        d[x-1] += [y-1]
    mt = 0
    for i in range(n):
        mt = max(mt, alg_memoization_recursion(i))
    print(mt)


if __name__ == '__main__':
    solve()

Solution (Python):
import numpy as np
import sys
sys.setrecursionlimit(100000)
N,M=map(int,input().split())
d=[[] for i in range(N)]
for i in range(M):
    x,y=map(int,input().split())
    d[x-1].append(y-1)
dp=[0 for i in range(N)]

def depth(now,score,d):
    global dp
    if dp[now]==0 or not(dp[now]):
        if d[now]:
            _score=[]
            for i in d[now]:
                _score.append(depth(i,score+1,d)-score)
            dp[now]=max(_score)
        else:
            return score

        return dp[now]+score

    else:
        return dp[now]+score



Max=0
for i in range(N):
    m=depth(i,0,d)
    if  m>Max:            
        Max=m
print(Max)

Solution (Python):
import sys
from collections import deque

input = sys.stdin.readline

N,M = map(int,input().split())
edge = [list(map(int,input().split())) for _ in range(M)]

graph = [[] for _ in range(N)]
indegree = [0 for _ in range(N)]

for i in range(M):
    graph[edge[i][0]-1].append(edge[i][1]-1)
    indegree[edge[i][1]-1] += 1

queue = deque()
for i in range(N):
    if indegree[i] == 0:
        queue.append(i)

dp = [0]*N

while queue:
    node = queue.popleft()
    for adj in graph[node]:
        indegree[adj] -= 1
        if indegree[adj] == 0:
            queue.append(adj)
            dp[adj] = dp[node]+1

print(max(dp))

Solution (Python):
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

N,M = map(int,readline().split())
m = map(int,read().split())
XY = zip(m,m)

in_edge = [[] for _ in range(N+1)]
out_edge = [[] for _ in range(N+1)]
for x,y in XY:
    out_edge[x].append(y)
    in_edge[y].append(x)

out_deg = [len(x) for x in out_edge]

stack = [i for i,x in enumerate(out_deg[1:],1) if x==0]

dp = [0] * (N+1)
while stack:
    c = stack.pop()
    for p in in_edge[c]:
        y = dp[c]+1
        if dp[p] < y:
            dp[p] = y
        out_deg[p] -= 1
        if not out_deg[p]:
            stack.append(p)

answer = max(dp)
print(answer)

Solution (Python):
import sys
sys.setrecursionlimit(1000000)
def main():
    N, M = map(int, input().split())
    d = {}
    for _ in range(M):
        x, y = map(int, input().split())
        if x in d:
            d[x].append(y)
        else:
            d[x] = [y]
    l = {}
    m = 0
    for i in d:
        m = max(m, dfs(i, d, l))
    print(m)
def dfs(node, d, l):
    if node in l:
        return l[node]
    if node not in d:
        return 0
    a = 1 + max(dfs(i, d, l) for i in d[node])
    l[node] = a
    return a

main()

Solution (Python):
import sys

def dp(i, xy, l):
    if l[i] >= 0:
        return l[i]
    l[i] = t = max(dp(j, xy, l) for j in xy[i]) + 1
    return t

def main():
    sys.setrecursionlimit(10 ** 6)
    N, M = map(int, input().split())
    xy = [set() for _ in range(N)]
    for _ in range(M):
        xi, yi = map(int, input().split())
        xy[xi - 1].add(yi - 1)
    l = [0 if not i else -1 for i in xy]
    m = 0
    for i in range(N):
        m = max(m, dp(i, xy, l))
    print(m)


main()

Solution (Python):
import sys
read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines

N, M = map(int, readline().split())
xy = map(int, read().split())
graph = [[] for _ in range(N + 1)]


V = [0] * (N + 1)

for x, y in zip(xy, xy):
    graph[x].append(y)
    V[y] += 1


start = [i for i, name in enumerate(V) if name == 0]


dp = [0] * (N + 1)
queue = []

while start:
    v = start.pop()
    for go in graph[v]:
        V[go] -= 1
        if V[go] == 0:
            start.append(go)
        dp[go] = max(dp[go], dp[v] + 1)

print(max(dp))

Solution (Python):
import bisect, collections, copy, heapq, itertools, math, sys
input = sys.stdin.readline
n, m = [ int(v) for v in input().split() ]
edge = []
in_list = [0] * n
out_list = [0] * n
dp_list = [0] * n
connect_list = [ [] for i in range(n) ] 

for i in range(m):
    s, t = [ int(v)-1 for v in input().split() ]
    edge.append((s,t))
    in_list[t] += 1
    out_list[s] += 1
    connect_list[t].append(s)

search_list = [ i for i, v in enumerate(out_list) if v == 0 ]
while search_list:
    new_search_list = []
    for i in search_list:
        for j in connect_list[i]:
            out_list[j] -= 1
            if dp_list[j] < dp_list[i] + 1:
                dp_list[j] = dp_list[i] + 1
            if out_list[j] == 0:
                new_search_list.append(j)
    search_list = new_search_list

print(max(dp_list))

Solution (Python):
n, m = [ int(v) for v in input().split() ]
edge = []
in_list = [0] * n
out_list = [0] * n
dp_list = [0] * n
connect_list = [ [] for i in range(n) ] 

for i in range(m):
    s, t = [ int(v)-1 for v in input().split() ]
    edge.append((s,t))
    in_list[t] += 1
    out_list[s] += 1
    connect_list[t].append(s)

search_list = [ i for i, v in enumerate(out_list) if v == 0 ]
while search_list:
    new_search_list = []
    for i in search_list:
        for j in connect_list[i]:
            out_list[j] -= 1
            if dp_list[j] < dp_list[i] + 1:
                dp_list[j] = dp_list[i] + 1
            if out_list[j] == 0:
                new_search_list.append(j)
    search_list = new_search_list

print(max(dp_list))

Solution (Python):
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)


dp = [-1]*100100
def rec(v, G):
    if dp[v]!=-1:
        return dp[v]
    
    cnt = 0
    for nv in G[v]:
        cnt = max(cnt, rec(nv, G) + 1)
    
    dp[v] = cnt
    return dp[v]


def main():
    N, M = map(int, input().split())
    
    G = [[] for _ in range(N)]
    for _ in range(M):
        x, y = map(int, input().split())
        x -= 1
        y -= 1
        G[x].append(y)
    
    ans = 0
    for v in range(N):
        ans = max(ans, rec(v, G))

    print(ans)


if __name__ == '__main__':
    main()