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 in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define int long long int
#define S second
#define F first

using namespace std ;

const int N = 2e6 + 100 , M = 1e5 + 100;
int dp[N] , n , m , cnt[N] , k[N] ;
pair <int , int> p[N] ;
vector <int> v[N] , ans;
queue <int> q ;

int32_t main(){
	cin >> n >> m ;
	for(int i = 0 ; i < m ; i++){
		int aa , bb ;
		cin >> aa >> bb ;
		v[aa-1].push_back(bb - 1) ;
		cnt[bb - 1]++ ;
	}
	for(int i = 0 ; i < n ; i++){
		if(cnt[i] == 0){
			q.push(i) ;
		}
	}
	while(q.size()){
		int u = q.front() ;
		q.pop() ;
		ans.push_back(u) ;
		for(auto x : v[u]){
			cnt[x]-- ;
			if(!cnt[x]){
				q.push(x) ;
			}
		}
	}
	//sort(p , p + n) ; 
	reverse(ans.begin() , ans.end()) ;
	for(int i = 0 ; i < n ; i++){
		k[ans[i]] = i ;
	}
	int mx = 0 ;
	for(int i = 0 ; i < n ; i++){
		//cout << ans[i] << " " ;
		for(auto j : v[ans[i]]){
			dp[i] = max(dp[k[j]] + 1 , dp[i]) ;
		}
		mx = max(mx , dp[i]) ;
	}
	cout << mx;
	return 0 ; 
}
/*
#include <radman/roderc++.h>
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         \\\\\//\       \:::\\\\/      |||||///|[[[*   \\\\\\///      \\\\\//\~~~~~///////'            *@@\/////////////////////"
         \\\\\//\        \___\\/       \\\\\///|*       \\\\\/"       \\\\\//\~~////////'                 **"///////////"""
         \\\\\//\                     |||||///|                       \\\\\//\///////"
         \\\\\//\                     \\\\\///|                       \\\\\//\////"
         \\\\\///                    |||||////|                       \\\\\////"
         \\\\\/"                     \\\\\///*                        \\\\\/"
                                     """""*
*/