[luogu4114] Qtree1 题解

\(LCT\) 动态维护树上路径最值，典中典了。

时间复杂度 \(O(n\log n)\)。

#include<bits/stdc++.h>
#define fa(x) lct[x].fa
#define fl(x) lct[x].fl
#define mx(x) lct[x].mx
#define val(x) lct[x].val
#define sn(x,i) lct[x].sn[i]
using namespace std;
const int N=20005;
struct node{
    int sn[2],fa,fl,mx,val;
}lct[N];int n,tp,st[N];
int check(int x){
    return sn(fa(x),0)!=x&&sn(fa(x),1)!=x;
}int chksn(int x){
    return sn(fa(x),1)==x;
}void push_up(int x){
    mx(x)=max({mx(sn(x,0)),mx(sn(x,1)),val(x)});
}void push_down(int x){
    if(!x||!fl(x)) return;
    fl(sn(x,0))^=1,fl(sn(x,1))^=1;
    swap(sn(x,0),sn(x,1)),fl(x)=0;
}void rotate(int x){
    int y=fa(x),z=fa(y),k=chksn(x);
    if(!check(y)) sn(z,chksn(y))=x;
    fa(x)=z,fa(y)=x,fa(sn(x,1-k))=y;
    sn(y,k)=sn(x,1-k),sn(x,1-k)=y;
    push_up(y);
}void splay(int x){
    st[tp=1]=x;
    for(int i=x;!check(i);i=fa(i)) st[++tp]=fa(i);
    while(tp) push_down(st[tp--]);
    while(!check(x)){
        int y=fa(x),z=fa(y);
        if(!check(y))
            rotate(chksn(x)!=chksn(y)?x:y);
        rotate(x);
    }push_up(x);
}void access(int x){
    for(int i=0;x;i=x,x=fa(x))
        splay(x),sn(x,1)=i,push_up(x);
}void mk(int x){
    access(x),splay(x),fl(x)^=1;
}void split(int x,int y){
    mk(x),access(y),splay(y);
}void cut(int x,int y){
    split(x,y),fa(x)=sn(y,0)=0;
}void link(int x,int y){
    mk(x),access(y),fa(x)=y;
}int main(){
    ios::sync_with_stdio(0);
    cin.tie(0),cout.tie(0);
    cin>>n;string s;
    for(int i=1,x,y;i<n;i++){
        cin>>x>>y>>mx(n+i);
        val(n+i)=mx(n+i);
        link(x,n+i),link(n+i,y);
    }while(cin>>s){
        if(s=="DONE") return 0;
        int x,y;cin>>x>>y;
        if(s=="CHANGE") mk(x+n),val(x+n)=y;
        else split(x,y),cout<<mx(y)<<"\n";
    }return 0;
}