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:



Sample input:
4 5
1 2
1 3
3 2
2 4
3 4


Sample output:
3

Submission status: Accepted

Solution code:
from collections import deque
N,M = map(int,input().split())
G = {i:[] for i in range(1,N+1)}
F = {i:[] for i in range(1,N+1)}
for _ in range(M):
    y,x = map(int,input().split())
    G[x].append(y)
    F[y].append(x)
A = []
hist = [0 for _ in range(N+1)]
for i in range(1,N+1):
    s = i
    if hist[s]==1:continue
    if G[s]:
        while G[s]:
            s = G[s][0]
    que = deque([s])
    A.append(s)
    hist[s] = 1
    while que:
        x = que.popleft()
        for y in F[x]:
            if hist[y]==0:
                G[y].remove(x)
                if len(G[y])==0:
                    que.append(y)
                    A.append(y)
#                     print("A={}".format(A))
                    hist[y]=1
#                     print("hist={}".format(hist))
dp = [0 for _ in range(N+1)]
for i in range(N-1):
    for x in F[A[i]]:
        dp[x] = max(dp[x],dp[A[i]]+1)
print(max(dp))

Submission status: Accepted

Solution code:
def main():
    import sys
    sys.setrecursionlimit(10**7)

    N,M=list(map(int,sys.stdin.readline().split()))
    dic=[[] for _ in range(N)]
    for i in range(M):
        x,y=list(map(int,sys.stdin.readline().split()))
        dic[x-1].append(y-1)


    dp=[0]*(N)
    def dfs(frm):
        if dp[frm]:
            return dp[frm]

        mx=0
        if not dic[frm]:
            return 0

        dp[frm]=max(dfs(val)+1 for val in dic[frm])

        return dp[frm]

    mx=0
    return max(dfs(x) for x in range(N))


print(main())

Submission status: Accepted

Solution code:
def main():
    import sys
    sys.setrecursionlimit(10**7)

    N,M=list(map(int,sys.stdin.readline().split()))
    dic=[[] for _ in range(N)]
    for i in range(M):
        x,y=list(map(int,sys.stdin.readline().split()))
        dic[x-1].append(y-1)


    dp=[0]*(N)
    def dfs(frm):
        if dp[frm]:
            return dp[frm]

        mx=0
        if not dic[frm]:
            return 0

        for val in dic[frm]:
            mx=max(mx,dfs(val)+1)

        dp[frm]=mx
        return mx

    mx=0
    for key in range(N):
        mx=max(mx,dfs(key))

    return mx

print(main())

Submission status: Accepted

Solution code:
from collections import defaultdict
import sys
sys.setrecursionlimit(100005)

class Graph:
    def __init__(self, N):
        self.in_degree = [0] * (N+1)
        self.dist = [0] * (N+1)
        self.visited = [False] * (N+1)
        self.edges = defaultdict(list)
        self.N = N

    def add_edge(self, x, y):
        self.edges[x].append(y)
        self.in_degree[y] += 1

    def dfs(self, x):
        self.visited[x] = True
        for y in self.edges[x]:
            self.dist[y] = max(self.dist[y], self.dist[x] + 1)
            self.in_degree[y] -= 1
            if self.in_degree[y] == 0:
                self.dfs(y)

    def longest_path(self):
        for i in range(1, self.N+1):
            if not self.visited[i] and self.in_degree[i] == 0:
                self.dfs(i)

        ans = 0
        for i in range(1, self.N+1):
            ans = max(ans, self.dist[i])

        return ans


def main():
    N, M = map(int, input().split())
    graph = Graph(N)
    for _ in range(M):
        x, y = map(int, input().split())
        graph.add_edge(x, y)

    ans = graph.longest_path()
    print(ans)


if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(100000)

from collections import defaultdict



class Graph:

    def __init__(self, N):
        self.graph = defaultdict(list)
        self.N = N
        self.memo = [-1] * (N+1)
        self.tovisit = set(range(1, N+1))

    def add_edge(self, x, y):
        self.graph[x].append(y)

    def _longest_path(self, node):
        if self.memo[node] == -1:
            res = 0
            for y in self.graph[node]:
                res = max(res, 1 + self._longest_path(y))

            self.memo[node] = res
            self.tovisit.discard(node)

        return self.memo[node]

    def longest_path(self):
        while self.tovisit:
            self._longest_path(self.tovisit.pop())

        res = 0
        for i in range(1, self.N+1):
            res = max(res, self.memo[i])

        return res


def main():

    N, M = map(int, input().split())
    graph = Graph(N)
    for _ in range(M):
        x, y = map(int, input().split())
        graph.add_edge(x, y)

    ans = graph.longest_path()
    print(ans)


if __name__ == "__main__":
    main()

Submission status: Accepted

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

    """ convenient functions
    # for i, a in enumerate(iterable)
    # q, mod = divmod(a, b)
    # divmod(x, y) returns the tuple (x//y, x%y)
    # Higher-order function: reduce(operator.mul, xyz_count, 1)
    # manage median(s) using two heapq https://atcoder.jp/contests/abc127/tasks/abc127_f
    """

    """convenient decorator
    # @functools.lru_cache():
    # to facilitate use of recursive function
        # ex:
        # from functools import lru_cache
        # import sys
        # sys.setrecursionlimit(10**9)
        # @lru_cache(maxsize=None)
        # def fib(n):
        #     if n < 2:
        #         return n
        #     return fib(n-1) + fib(n-2)
        # print(fib(1000))
    """
    
    # import numpy as np
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product # https://docs.python.org/ja/3/library/itertools.html
    # accumulate() returns iterator! to get list: list(accumulate())
    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 = []  # prime factor
        b, e = 2, 0  # base, exponent
        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
        """
        # TODO: How should I do when n - r is negative?
        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 # https://docs.python.org/ja/3/library/collections.html#collections.deque
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest # https://docs.python.org/ja/3/library/heapq.html
    from copy import deepcopy, copy # https://docs.python.org/ja/3/library/copy.html
    import operator
    from operator import itemgetter #sort 
    # ex1: List.sort(key=itemgetter(1))
    # ex2: sorted(tuples, key=itemgetter(1,2))
    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 # Deprecated since version 3.5: Use math.gcd() instead.
    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)
    
    # first create factorial_list
    # fac_list = mod_factorial_list(n)
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    modpow = lambda a, n, p = MOD: pow(a, n, p) # Recursive function in python is slow!
    def modinv(a, p = MOD):
        # evaluate reciprocal using Fermat's little theorem:
        # a**(p-1) is identical to 1 (mod p) when a and p is coprime
        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):
        # fac_list = modfactorial_list(100)
        # print(modcomb(100, 5, modfactorial_list(100)))
        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]

    # Graph: https://en.wikipedia.org/wiki/Directed_graph
    # Bellman-Ford: O(|V||E|). Use this if there exists an edge with negative length in the graph
    # After N steps, the shortest path has converded if there doesn't exist an cycle of edges with negative
    # Watch out: d[N] == d[2*N] doesn't necessarily mean the graph doesn't have negative cycle
    # ref: https://www.youtube.com/watch?v=1Z6ofKN03_Y

    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
    # initialize variables
        # to initialize list, use [0] * n
        # to initialize two dimentional array:
            # ex) [[0] * N for _ in range(N)]
            # ex2) dp = [[0] * (N+1) for _ in range(W*2)]
    # set inputs
        # put inputs between specific values (almost as quickly)
        # ex) S = [-INF] + [int(r()) for _ in range(A)] + [INF]
        # open(0).read() is sometimes useful:
        # ex) n, m, *x = map(int, open(0).read().split())
        #     min(x[::2]) - max(x[1::2])
        # ex2) *x, = map(int, open(0).read().split())
        #     don't forget to add comma after *x if only one variable is used
    # preprocessing
        # transpose = [x for x in zip(*data)]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [(1, 4, 7), (2, 5, 8), (3, 6, 9)]
        # flat = [flatten for inner in data for flatten in inner]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [1, 2, 3, 4, 5, 6, 7, 8, 9]
    # calculate and output
        # output pattern
        # ex1) print(*l) => when l = [2, 5, 6], printed 2 5 6
    """

    # functions to read input
    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
    # single int: int(r())
    # single string: r()
    # single float: float(r())
    # line int: R()
    # line string: r().split()
    # line (str, int, int): [j if i == 0 else int(j) for i, j in enumerate(r().split())]
    # lines int: [R() for _ in range(n)]
    """

    # for test
    if sample_file:
        sys.stdin = open(sample_file)
        
    # ----------------------------------
    # main

    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))

    # to finish code, use return instead of exit()
    # end of main
    # ----------------------------------

    """memo: how to use defaultdict of list
    # initialize
    Dic = defaultdict(list)
    # append / extend
    Dic[x].append(y)
    # three methods for loop: keys(), values(), items()
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    # to make binary digits text
    >>> a = 5
    >>> bin_str_a = format(a, '#06b')
    >>> print(bin_str_a)
    0b0101 # first 2 strings (='0b') indicates it is binary
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
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
#print(L)
#print(S)
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(Q)
print(max(D))
#print(S)

Submission status: Accepted

Solution code:
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))

Submission status: Accepted

Solution code:

#ライブラリインポート
from collections import defaultdict, deque

INF = float("inf")
#入力受け取り
def getlist():
	return list(map(int, input().split()))


#処理内容
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()

Submission status: Accepted

Solution code:
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))

Submission status: Accepted

Solution code:
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]])

Submission status: Accepted

Solution code:
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))

Submission status: Accepted

Solution code:
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
 
# node iを起点とした時の有効パスの最大値
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)

Submission status: Accepted

Solution code:
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))

Submission status: Accepted

Solution code:
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()

Submission status: Accepted

Solution code:
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()

Submission status: Accepted

Solution code:
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()

Submission status: Accepted

Solution code:
import sys
#input = sys.stdin.readline
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))

Submission status: Accepted

Solution code:
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))

Submission status: Accepted

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

indegree = [0] * N  # 入次数
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)

Submission status: Accepted

Solution code:
from collections import deque

# deque
# https://docs.python.org/ja/3/library/collections.html#collections.deque
# pop(0), append が高速

# トポロジカルソート
# https://csacademy.com/lesson/topological_sorting/


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

indegree = [0] * N  # 入次数
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  # 枝刈り
        if indegree[next_node] == 0:  # 入次数0なら queue に追加
            que.append(next_node)

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

Submission status: Accepted

Solution code:
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()