一個顯然的dp是設f[i][j]為i子樹內權值<=j時的答案，則f[i][j]=Σf[son][j]，f[i][a[i]~n]++。這樣是可以線段樹合並的，將各兒子加起來然後打上加法標記即可。需要標記永久化。

　　另一種做法是考慮擴展經典的單調隊列優化LIS的做法，維護子樹內答案為k時最小的最大值，用平衡樹維護，在父親處啟發式合並，然後將父親處權值插入即可。

#include<iostream> 
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include
 
<algorithm>
using namespace std;
#define ll long long
#define N 200010
#define lson tree[k].ch[0]
#define rson tree[k].ch[1]
char getc(){char c=getchar();while ((c<‘A‘||c>‘Z‘)&&(c<‘a‘||c>‘z‘)&&(c<‘0‘||c>‘9‘)) c=getchar();return c;}
int gcd(int n,int m){return m==0?n:gcd(m,n%m);}
 
int read()
{
    int x=0,f=1;char c=getchar();
    while (c<‘0‘||c>‘9‘) {if (c==‘-‘) f=-1;c=getchar();}
    while (c>=‘0‘&&c<=‘9‘) x=(x<<1)+(x<<3)+(c^48),c=getchar();
    return x*f;
}
int n,a[N],b[N],fa[N],p[N],root[N],t,cnt;
struct data{int to,nxt;
}edge[N<<1];
struct
 
 data2{int x,p,ch[2],s;
}tree[N<<5];
void addedge(int x,int y){t++;edge[t].to=y,edge[t].nxt=p[x],p[x]=t;}
void up(int k){tree[k].s=tree[lson].s+tree[rson].s+1;}
void move(int &k,int p)
{
    int t=tree[k].ch[p];
    tree[k].ch[p]=tree[t].ch[!p],tree[t].ch[!p]=k,up(k),up(t),k=t;
}
void ins(int &k,int x)
{
    if (k==0) {k=++cnt;tree[k].x=x,tree[k].p=rand(),tree[k].s=1;return;}
    tree[k].s++;
    if (tree[k].x<x) {ins(rson,x);if (tree[rson].p>tree[k].p) move(k,1);}
    else {ins(lson,x);if (tree[lson].p>tree[k].p) move(k,0);}
}
void del(int &k,int x)
{
    if (tree[k].x==x)
    {
        if (lson==0||rson==0) {k=lson|rson;return;}
        if (tree[lson].p>tree[rson].p) move(k,0),del(rson,x);
        else move(k,1),del(lson,x);
    }
    else if (tree[k].x<x) del(rson,x);
    else del(lson,x);
    up(k);
}
int qrank(int k,int x)
{
    if (!k) return 0;
    if (tree[k].x>=x) return qrank(lson,x);
    else return qrank(rson,x)+tree[lson].s+1;
}
int find(int k,int x)
{
    if (tree[lson].s+1==x) return tree[k].x;
    if (tree[lson].s+1>x) return find(lson,x);
    else return find(rson,x-tree[lson].s-1);
}
void dfsins(int k,int &x)
{
    if (!k) return;
    ins(x,tree[k].x);
    dfsins(lson,x),dfsins(rson,x);
}
int merge(int x,int y)
{
    if (tree[x].s<tree[y].s) swap(x,y);
    dfsins(y,x);
    return x;
}
void dfs(int k)
{
    for (int i=p[k];i;i=edge[i].nxt)
    if (edge[i].to!=fa[k])
    {
        dfs(edge[i].to);
        root[k]=merge(root[k],root[edge[i].to]);
    }
    int x=qrank(root[k],a[k]);
    if (x<tree[root[k]].s) del(root[k],find(root[k],x+1));
    ins(root[k],a[k]);
}
int main()
{
#ifndef ONLINE_JUDGE
    freopen("bzoj4919.in","r",stdin);
    freopen("bzoj4919.out","w",stdout);
    const char LL[]="%I64d\n";
#else
    const char LL[]="%lld\n";
#endif
    n=read();srand(20020509);
    for (int i=1;i<=n;i++)
    {
        b[i]=a[i]=read(),fa[i]=read();
        addedge(fa[i],i);
    }
    sort(b+1,b+n+1);
    int u=unique(b+1,b+n+1)-b-1;
    for (int i=1;i<=n;i++) a[i]=lower_bound(b+1,b+u+1,a[i])-b;
    dfs(1);
    cout<<tree[root[1]].s;
    return 0;
}

BZOJ4919 大根堆（動態規劃+線段樹合並/treap+啟發式合並）