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 <iostream>
#include <vector>
#include <unordered_map>
#include <unordered_set>
#include <string>
#include <algorithm>
#include <climits> 
//#include <iterator>

using namespace std;
using ll = long long;
using ull = unsigned long long;

struct Edge{
    int from;
    int to;
};

int findMax(int cur, int N, unordered_map<int, vector<int>>& edgeMap, vector<int>& maxLen) {
    if (maxLen[cur] >= 0) return maxLen[cur];
    int r = 0;
    for (auto e : edgeMap[cur]) {
        r = max(r, findMax(e, N, edgeMap, maxLen)+1);
    }
    maxLen[cur] = r;
    return maxLen[cur];
}

int longestPath(int N, int M, unordered_map<int, vector<int>>& edgeMap) {
    vector<int> maxLen(N+1,-1);
    int ans = 0;
    for (int i = 1; i <= N; ++ i) {
        ans = max(ans, findMax(i, N, edgeMap, maxLen));
    }
    return ans;
}

int main() {
    int M,N;
    cin>>N>>M;
    vector<Edge> edges(M);
    unordered_map<int, vector<int>> edgeMap; 
    for (auto& e : edges) {
        cin>>e.from>>e.to;
        edgeMap[e.from].push_back(e.to);
    }
    cout<<longestPath(N, M, edgeMap)<<endl;
    return 0;
}