G - Longest Path

Problem Statement

There is a directed graph $\mathrm{GG}$ with $\mathrm{NN}$ vertices and $\mathrm{MM}$ edges. The vertices are numbered $\mathrm{1,2,\dots ,N1,2,\dots ,N}$, and for each $\mathrm{ii}$ ($\mathrm{1\le i\le M1\le i\le M}$), the $\mathrm{ii}$-th directed edge goes from Vertex ${\mathrm{xixi}}^{}$ to ${\mathrm{yiyi}}^{}$. $\mathrm{GG}$ does not contain directed cycles.

Find the length of the longest directed path in $\mathrm{GG}$. Here, the length of a directed path is the number of edges in it.

Constraints

• All values in input are integers.
• $\mathrm{2\le N\le 1052\le N\le 105}$
• $\mathrm{1\le M\le 1051\le M\le 105}$
• $\mathrm{1\le xi,yi\le N1\le xi,yi\le N}$
• All pairs $(xi,yi)(xi,yi)$ are distinct.
• $\mathrm{GG}$ does not contain directed cycles.

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Input

Input is given from Standard Input in the following format:

$\mathrm{NN}$ $\mathrm{MM}$
${\mathrm{x1x1}}^{}$ ${\mathrm{y1y1}}^{}$
${\mathrm{x2x2}}^{}$ ${\mathrm{y2y2}}^{}$
$::$
${\mathrm{xMxM}}^{}$ ${\mathrm{yMyM}}^{}$

Output

Print the length of the longest directed path in $\mathrm{GG}$.

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Sample Input 1 Copy

Copy

4 5
1 2
1 3
3 2
2 4
3 4

Sample Output 1 Copy

Copy

3

The red directed path in the following figure is the longest:

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Sample Input 2 Copy

Copy

6 3
2 3
4 5
5 6

Sample Output 2 Copy

Copy

2

The red directed path in the following figure is the longest:

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Sample Input 3 Copy

Copy

5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3

Sample Output 3 Copy

Copy

3

The red directed path in the following figure is one of the longest:

#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <set>
#include <queue>
#include <map>
#include <sstream>
#include <cstdio>
#include <cstring>
#include <numeric>
#include <cmath>
#include <iomanip>
#include <deque>
#include <bitset>
#include <unordered_set>
#include <unordered_map>
#define ll              long long
#define PII             pair<int, int>
#define rep(i,a,b)      for(int  i=a;i<=b;i++)
#define dec(i,a,b)      for(int  i=a;i>=b;i--)
using namespace std;
int dir[4][2] = { { 0,1 } ,{ 0,-1 },{ 1,0 },{ -1,0 } };
const long long INF = 0x7f7f7f7f7f7f7f7f;
const int inf = 0x3f3f3f3f;
const double pi = 3.14159265358979323846;
const double eps = 1e-6;
const int mod =1e9+7;
const int N = 1e5+5;
//if(x<0 || x>=r || y<0 || y>=c)

inline ll read()
{
    ll x = 0; bool f = true; char c = getchar();
    while (c < '0' || c > '9') { if (c == '-') f = false; c = getchar(); }
    while (c >= '0' && c <= '9') x = (x << 1) + (x << 3) + (c ^ 48), c = getchar();
    return f ? x : -x;
}
ll gcd(ll m, ll n)
{
    return n == 0 ? m : gcd(n, m % n);
}
ll lcm(ll m, ll n)
{
    return m * n / gcd(m, n);
}
bool prime(int x) {
    if (x < 2) return false;
    for (int i = 2; i * i <= x; ++i) {
        if (x % i == 0) return false;
    }
    return true;
}
ll qpow(ll m, ll k, ll mod)
{
    ll res = 1, t = m;
    while (k)
    {
        if (k & 1)
            res = res * t % mod;
        t = t * t % mod;
        k >>= 1;
    }
    return res;
}      

int main()
{
    int n, m;
    cin >> n >> m;
    vector<vector<int>> a(n+1);
    vector<int> in(n + 1),dp(n+1);
    rep(i, 1, m)
    {
        int u, v;
        cin >> u >> v;
        a[u].push_back(v);
        in[v]++;
    }
    queue<int> q;
    rep(i, 1, n)
    {
        if (!in[i])
            q.push(i);
    }
    while (!q.empty())
    {
        int f = q.front();
        q.pop();
        for (int i = 0; i < a[f].size(); i++)
        {
            int to = a[f][i];
            in[to]--;
            if (!in[to])
            {
                dp[to] = dp[f] + 1;
                q.push(to);
            }
        }
    }
    int ans = 0;
    for (int i = 1; i <= n; i++)
        ans = max(ans, dp[i]);
    cout << ans << endl;
    return 0;
}