很不错的一道思维题。
Code:

#include<cstdio>
#include<algorithm>
#include<iostream>
using namespace std;
const int maxn = 1000000 + 4;
const int inf = 100000 + 4;
int  n, m; 
int root[maxn],  maxv[maxn << 2],ch[maxn << 2][2], cnt;
inline void get_max(int &a,int b)
{
    if(b > a) a = b;
}
struct Segment_Tree
{
    #define lson ch[o][0]
    #define rson ch[o][1]
    inline void update(int l,int r,int delta,int val,int &o)
    {
        if(!o) o = ++cnt;
        if(l == r)
        {
            get_max(maxv[o], delta);
            return;
        }
        int mid = (l + r) >> 1;
        if(val <= mid) 
            update(l, mid, delta, val, ch[o][0]);
        else   
            update(mid + 1, r, delta, val, ch[o][1]);
        get_max(maxv[o], max(maxv[lson], maxv[rson]));
    }
    inline int query(int l,int r,int L,int R,int o)
    {
        if(!o) return 0;
        if(l > r || r < L || l > R  || L > R)  return 0;
        if(l >= L && r <= R) 
            return maxv[o];
        int mid = (l + r) >> 1;
        return max(query(l, mid, L, R, lson), query(mid + 1, r, L, R, rson));
    }
}T;
int main()
{
    //freopen("input.in","r",stdin);
    scanf("%d%d",&n,&m);
    int ans = 0;
    for(int i = 1;i <= m; ++i)
    {
        int from, to, val;
        scanf("%d%d%d",&from, &to,&val);
        ++ val;
        int tmp = T.query(1, inf , 1, val - 1, root[from]);
        T.update(1, inf, tmp + 1, val, root[to]);
        get_max(ans, tmp + 1);
    }
    printf("%d",ans);
    return 0;
}