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 Rust (1.15.1) (judge verdict: Accepted)

#![allow(unused, non_snake_case, dead_code, non_upper_case_globals)]
#![macro_use]

use std::cmp::*;
use std::collections::*;
use std::io::*;
use std::mem::*;
use std::num::*;
use std::slice::*;

fn main() {
    let (r, w, e) = (stdin(), stdout(), stderr());
    let mut io = IO::new(r.lock(), w.lock(), e.lock());
    // =============================================== //

    let mut g: Vec<Vec<usize>> = vec![Vec::new(); 101010];
    let mut revg: Vec<Vec<usize>> = vec![Vec::new(); 101010];

    let (n, m): (usize, usize) = (io.read(), io.read());
    for _ in 0..m {
        let (x, y): (usize, usize) = (io.read(), io.read());
        g[x - 1].push(y - 1);
        revg[y - 1].push(x - 1);
    }

    let mut ga: G = G {
        g: g,
        mem: vec![0; 100101],
    };
    ga.memc();
    let mut ans = 0;
    for i in 0..n {
        let tmp = ga.dfs(0, i);
        ans = max(ans, tmp);
    }
    io.writeln(ans);
    // let mut gb: G = G {
    //     g: revg,
    //     mem: vec![0; 100101],
    // };
    // let a = ga.dfs(0, 0);
    // let b = gb.dfs(0, 0);
    // io.writeln(a + b);
}
struct G {
    g: Vec<Vec<usize>>,
    mem: Vec<isize>,
}
impl G {
    fn memc(&mut self) {
        self.mem = vec![-1isize; 101010];
    }
    fn dfs(&mut self, depth: usize, now: usize) -> isize {
        if self.mem[now] == -1 {
            self.mem[now] = 0;
            let mut longest = 0;
            for i in 0..self.g[now].len() {
                let next = self.g[now][i];
                longest = max(longest, self.dfs(depth + 1, next) + 1);
            }
            // println!("{:?}", longest);
            self.mem[now] = longest;
            return longest;
        }
        return self.mem[now];
        // if self.mem[now] > 0 {
        //     return self.mem[now];
        // }
        // if self.g[now].len() == 0 {
        //     self.mem[now] = depth;
        //     return depth;
        // }

        // for &next in self.g[now].iter() {
        //     longest = max(longest, self.dfs(depth + 1, next));
        // }
    }
}
// IO
struct IO<R: Read, W: Write, E: Write> {
    Read: R,
    Write: BufWriter<W>,
    Error: BufWriter<E>,
}
impl<R: Read, W: Write, E: Write> IO<R, W, E> {
    fn new(r: R, w: W, e: E) -> IO<R, W, E> {
        IO {
            Read: r,
            Write: BufWriter::new(w),
            Error: BufWriter::new(e),
        }
    }
    fn read<T>(&mut self) -> T
    where
        T: std::str::FromStr,
    {
        let next: String = self
            .Read
            .by_ref()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect();
        next.parse().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
    fn readn<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read::<T>()).collect::<Vec<_>>()
    }
    fn readmat<T: std::str::FromStr>(&mut self, n: usize, m: usize) -> Vec<Vec<T>> {
        (0..n).map(|_| self.readn(m)).collect()
    }
    fn write<S: ToString>(&mut self, val: S) {
        self.Write.write(val.to_string().as_bytes());
    }
    fn writeln<S: ToString>(&mut self, val: S) {
        self.Write.write(val.to_string().as_bytes());
        self.Write.write(b"\n");
    }
    fn debug<S: std::fmt::Debug>(&mut self, val: S) {
        writeln!(self.Error, "(debug ) {:?}", &val);
    }
    fn debug2<S: std::fmt::Debug, T: std::fmt::Debug>(&mut self, val1: S, val2: T) {
        writeln!(self.Error, "(debug2) {:?} -> {:?}", val1, val2);
    }
}