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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
int dp[100001];
vector<int> adj[100001];
bool visited[100001];
void dfs(int s)
{
    if (!visited[s])
    {
        visited[s]=true;
        stack<int> stck; //changed this line
        stck.push(s);    //changed this line

        // dp[s] = 0;
        while (!stck.empty()) //changed this line
        {
            int topElement = stck.top(); //added this line
            stck.pop();                  //changed this line
            if (!adj[topElement].empty())
            {
                for (auto i = adj[topElement].begin(); i != adj[topElement].end(); i++) //changed this line
                {
                    stck.push(*i);
                    visited[*i]=true;                              //*i return the value stored at the memory location represented by i, stack -> stck
                    dp[*i] = max((1 + dp[topElement]), dp[*i]); // i -> *i, s -> topElement
                }
            }
            // s = stack.top();
        }
    }
}
int main()
{

    int v;
    int e;
    cin >> v;
    cin >> e;
    // memset(dp, 0, (v+1) * sizeof(int));
    for (int i = 0; i <= v; i++)
    {
        dp[i] = 0;
        visited[i] = false;
    }
    // vector<int> adj[v+1];
    for (int i = 1; i <= e; i++)
    {
        int a;
        int b;
        cin >> a;
        cin >> b;
        adj[a].push_back(b);
    }

    // dfs(1);

    //added these three lines
    for (int i = 1; i <= v; i++)
    {
        dfs(i);
    }

    int *ma;
    ma = max_element(dp, dp + (v + 1));
    cout << *ma << "\n";
}