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 Go (1.6) (judge verdict: Accepted)

package main

import (
  "bufio"
  "fmt"
  "os"
  "strconv"
  "strings"
)

var graph [][]int
var lngth []int

func main() {
  input := Input{bufio.NewReaderSize(os.Stdin,100)}
  n,m := input.NextInts()
  graph = make([][]int,n)
  lngth = make([]int,n)
  for i:=0;i<m;i++ {
    x,y := input.NextInts()
    graph[x-1] = append(graph[x-1],y-1)
  }
  for i:=0;i<n;i++ { lngth[i] = -1 }
  max := 0
  for i:=0;i<n;i++ {
    t := dfs(i)
    if max < t { max = t }
  }
  fmt.Println(max)
}
func dfs(v int) int {
  if lngth[v] != -1 { return lngth[v] }
  max := -1
  for _,e := range graph[v] {
    t := dfs(e)
    if max < t { max = t }
  }
  lngth[v] = max+1
  return max+1
}

type Input struct { reader *bufio.Reader }
func(i *Input) NextLine() string {
  var buffer []byte
  for {
    line,isPrefix,err := i.reader.ReadLine()
    if err != nil { panic(err) }
    buffer = append(buffer,line...)
    if !isPrefix { break }
  }
  return string(buffer)
}
func(i *Input) NextInts() (int,int) {
  s := strings.Split(i.NextLine()," ")
  a,_ := strconv.Atoi(s[0])
  b,_ := strconv.Atoi(s[1])
  return a,b
}