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>
using namespace std;
typedef long long ll;
typedef pair<int,int> p;
typedef pair<int,p> p1;
typedef pair<p,p> p2;
int n,m;
vector<int>edge[100005];
int dp[100005];
int rec(int x)
{
  if(dp[x]>=0)return dp[x];
  if(edge[x].size()==0)return dp[x]=0;
  for(int i=0;i<edge[x].size();i++)
  {
int to=edge[x][i];
    dp[x]=max(dp[x],rec(to)+1);
  }
  return dp[x];
}
int main()
{
  cin>>n>>m;
  for(int i=0;i<m;i++)
  {
int a,b;cin>>a>>b;edge[a].push_back(b);
} 
  for(int i=1;i<=n;i++)
    dp[i]=-1;
  for(int i=1;i<=n;i++)
  {
rec(i);
}
  int ans=0;
  for(int i=1;i<=n;i++)ans=max(ans,dp[i]);
  cout<<ans<<"\n";
  return 0;
}