P3380-二逼平衡树

P3380 【模板】二逼平衡树（树套树）

模版：

#include <bits/stdc++.h>
using namespace std;
const int maxn=5e4+10;
const ll inf=1e16;
const int maxm=5e5+10;
const ld eps=1e-12;
int n,m;
//-------shuru
int yuan[maxn],lisan[maxn<<2],totshu;
struct xunwen{
    int zhong,lo,ro,kth;
}allq[maxn];
//-------
//-----zhuxishu
struct node{
    int lo;int ro;int zhi;
}all[maxn*80];
int rt[maxn],tot;
void pushup(int now,int lo,int ro){all[now].zhi=all[lo].zhi+all[ro].zhi;}
void build(int &now,int lo,int ro){
    now=++tot;
    if(lo==ro) return;
    int mid=(lo+ro)>>1;
    build(all[now].lo,lo,mid);
    build(all[now].ro,mid+1,ro);
}
void inser(int &now,int rnow,int lo,int ro,int pos,int zhi){
    now=++tot;all[now]=all[rnow];
    if(lo==ro){all[now].zhi+=zhi;return;}
    int mid=(lo+ro)>>1;
    if(pos<=mid) inser(all[now].lo,all[rnow].lo,lo,mid,pos,zhi);
    else inser(all[now].ro,all[rnow].ro,mid+1,ro,pos,zhi);
    pushup(now,all[now].lo,all[now].ro);
}
//------------
//-----------shuzhuagshuzu
int s[maxn];
inline int lowbit(int x){return x&(-x);}
//------------
//----------shutaoshu
int totx,toty;
int xbi[510],ybi[510];
ll reqkth(int wlo,int wro,int lo1,int ro1,int lo,int ro,int kth){
    if(lo==ro) return lo;
    int mid=(lo+ro)>>1;
    int sum=0;
    for(int i=1;i<=totx;i++) sum-=all[all[xbi[i]].lo].zhi;
    for(int i=1;i<=toty;i++) sum+=all[all[ybi[i]].lo].zhi;
    sum+=(all[all[ro1].lo].zhi-all[all[lo1].lo].zhi);//
    if(sum>=kth){
        for(int i=1;i<=totx;i++) xbi[i]=all[xbi[i]].lo;
        for(int i=1;i<=toty;i++) ybi[i]=all[ybi[i]].lo;
        return reqkth(wlo,wro,all[lo1].lo,all[ro1].lo,lo,mid,kth);//
    }
    else{
        for(int i=1;i<=totx;i++) xbi[i]=all[xbi[i]].ro;
        for(int i=1;i<=toty;i++) ybi[i]=all[ybi[i]].ro;
        return reqkth(wlo,wro,all[lo1].ro,all[ro1].ro,mid+1,ro,kth-sum);
    }
}
ll reqrk(int wlo,int wro,int lo1,int ro1,int lo,int ro,int pos){
    if(lo==ro) return 0;
    int mid=(lo+ro)>>1;
    debug4(lo,ro,pos,mid)
    if(pos<=mid){
        for(int i=1;i<=totx;i++) xbi[i]=all[xbi[i]].lo;
        for(int i=1;i<=toty;i++) ybi[i]=all[ybi[i]].lo;
        return reqrk(wlo,wro,all[lo1].lo,all[ro1].lo,lo,mid,pos);
    }
    else{
        int sum=0;
        for(int i=1;i<=totx;i++) sum-=all[all[xbi[i]].lo].zhi;
        for(int i=1;i<=toty;i++) sum+=all[all[ybi[i]].lo].zhi;
        sum+=(all[all[ro1].lo].zhi-all[all[lo1].lo].zhi);
        for(int i=1;i<=totx;i++) xbi[i]=all[xbi[i]].lo;
        for(int i=1;i<=toty;i++) ybi[i]=all[ybi[i]].lo;
        return reqrk(wlo,wro,all[lo1].ro,all[ro1].ro,mid+1,ro,pos)+sum;
    }
}
ll findpre(int wlo,int wro,int lo1,int ro1,int lo,int ro,int pos){
    if(lo==ro) return lo;
    int mid=(lo+ro)>>1;
    if(pos<=mid){
        int sum=0;
        for(int i=wlo;i;i-=lowbit(i)) sum-=all[all[xbi[i]].lo].zhi;
        for(int i=wro;i;i-=lowbit(i)) sum+=all[all[ybi[i]].lo].zhi;
        sum+=(all[all[ro1].lo].zhi-all[all[lo1].lo].zhi);//
        if(sum==0) return -1;////
        for(int i=wlo;i;i-=lowbit(i)) xbi[i]=all[xbi[i]].lo;
        for(int i=wro;i;i-=lowbit(i)) ybi[i]=all[ybi[i]].lo;
        return findpre(wlo,wro,all[lo1].lo,all[ro1].lo,lo,mid,pos);
    }
    else{
        int sum=0;
        for(int i=wlo;i;i-=lowbit(i)) sum-=all[all[xbi[i]].ro].zhi;
        for(int i=wro;i;i-=lowbit(i)) sum+=all[all[ybi[i]].ro].zhi;
        sum+=all[all[ro1].ro].zhi;
        sum-=all[all[lo1].ro].zhi;
        int xbii[510],ybii[510];
        for(int i=wlo;i;i-=lowbit(i)) xbii[i]=xbi[i],xbi[i]=all[xbi[i]].ro;
        for(int i=wro;i;i-=lowbit(i)) ybii[i]=ybi[i],ybi[i]=all[ybi[i]].ro;
        if(sum) sum=findpre(wlo,wro,all[lo1].ro,all[ro1].ro,mid+1,ro,pos);
        else sum=-1;
        if(sum!=-1) return sum;////
        sum=0;
        for(int i=wlo;i;i-=lowbit(i)) sum-=all[all[xbii[i]].lo].zhi;
        for(int i=wro;i;i-=lowbit(i)) sum+=all[all[ybii[i]].lo].zhi;
        sum+=all[all[ro1].lo].zhi;
        sum-=all[all[lo1].lo].zhi;
        for(int i=wlo;i;i-=lowbit(i)) xbi[i]=all[xbii[i]].lo;
        for(int i=wro;i;i-=lowbit(i)) ybi[i]=all[ybii[i]].lo;
        if(sum) return findpre(wlo,wro,all[lo1].lo,all[ro1].lo,lo,mid,pos);
        else return -1;
    }
}
ll findhou(int wlo,int wro,int lo1,int ro1,int lo,int ro,int pos){
    if(lo==ro) return lo;
    int mid=(lo+ro)>>1;
    if(pos<=mid){
        int sum=0;
        for(int i=wlo;i;i-=lowbit(i)) sum-=all[all[xbi[i]].lo].zhi;
        for(int i=wro;i;i-=lowbit(i)) sum+=all[all[ybi[i]].lo].zhi;
        sum+=(all[all[ro1].lo].zhi-all[all[lo1].lo].zhi);
        int xbii[510],ybii[510];
        for(int i=wlo;i;i-=lowbit(i)) xbii[i]=xbi[i],xbi[i]=all[xbi[i]].lo;
        for(int i=wro;i;i-=lowbit(i)) ybii[i]=ybi[i],ybi[i]=all[ybi[i]].lo;
        if(sum) sum=findhou(wlo,wro,all[lo1].lo,all[ro1].lo,lo,mid,pos);
        else sum=-1;
        if(sum!=-1) return sum;
        sum=0;
        for(int i=wlo;i;i-=lowbit(i)) sum-=all[all[xbii[i]].ro].zhi;
        for(int i=wro;i;i-=lowbit(i)) sum+=all[all[ybii[i]].ro].zhi;
        sum+=all[all[ro1].ro].zhi;
        sum-=all[all[lo1].ro].zhi;
        for(int i=wlo;i;i-=lowbit(i)) xbi[i]=all[xbii[i]].ro;
        for(int i=wro;i;i-=lowbit(i)) ybi[i]=all[ybii[i]].ro;
        if(sum) return findhou(wlo,wro,all[lo1].ro,all[ro1].ro,mid+1,ro,pos);
        else return -1;
    }
    else{
        int sum=0;
        for(int i=wlo;i;i-=lowbit(i)) sum-=all[all[xbi[i]].ro].zhi;
        for(int i=wro;i;i-=lowbit(i)) sum+=all[all[ybi[i]].ro].zhi;
        sum+=(all[all[ro1].ro].zhi-all[all[lo1].ro].zhi);
        if(sum==0) return -1;
        for(int i=wlo;i;i-=lowbit(i)) xbi[i]=all[xbi[i]].ro;
        for(int i=wro;i;i-=lowbit(i)) ybi[i]=all[ybi[i]].ro;
        return findhou(wlo,wro,all[lo1].ro,all[ro1].ro,mid+1,ro,pos);
    }
}
void add(int pos,int zhi,int val){
    for(int i=pos;i<=n;i+=lowbit(i)) inser(s[i],s[i],1,totshu,zhi,val);//totshu
}
//------------------
signed main(){
    ios;fre();
    cin>>n>>m;
    for(int i=1;i<=n;i++){
        cin>>yuan[i];lisan[i]=yuan[i];
    }
    totshu=n;////
    for(int i=1;i<=m;i++){
        cin>>allq[i].zhong;
        if(allq[i].zhong==3) cin>>allq[i].lo>>allq[i].ro,lisan[++totshu]=allq[i].ro;//pos->lo,zhi->ro,modify
        else if(allq[i].zhong==2) cin>>allq[i].lo>>allq[i].ro>>allq[i].kth;
        else{
            cin>>allq[i].lo>>allq[i].ro>>allq[i].kth;
            lisan[++totshu]=allq[i].kth;//chaxunmoushu k
        }
    }
    sort(lisan+1,lisan+1+totshu);
    totshu=unique(lisan+1,lisan+1+totshu)-lisan-1;
    build(rt[0],1,totshu);
    for(int i=1;i<=n;i++){
        int now1=lower_bound(lisan+1,lisan+1+totshu,yuan[i])-lisan;
        yuan[i]=now1;
        inser(rt[i],rt[i-1],1,totshu,now1,1);
    }
    for(int i=1;i<=n;i++) s[i]=rt[0];////

    /*------------debug
    totx=toty=0;
    for(int j=0;j;j-=lowbit(j)) xbi[++totx]=s[j];
    for(int j=4;j;j-=lowbit(j)) ybi[++toty]=s[j];
    int nowk1=lower_bound(lisan+1,lisan+1+totshu,1)-lisan;
    int nowk=reqrk(0,4,rt[0],rt[4],1,totshu,nowk1)+1;
    debug1(nowk)
    -------------*/
    for(int i=1;i<=m;i++){
        if(allq[i].zhong==1){
            int now1=lower_bound(lisan+1,lisan+1+totshu,allq[i].kth)-lisan;
            int lo=allq[i].lo-1,ro=allq[i].ro;
            totx=toty=0;
            for(int j=lo;j;j-=lowbit(j)) xbi[++totx]=s[j];
            for(int j=ro;j;j-=lowbit(j)) ybi[++toty]=s[j];
            int now2=reqrk(lo,ro,rt[lo],rt[ro],1,totshu,now1)+1;////congxiaodaoda+1
            cout<<now2<<endl;
        }
        else if(allq[i].zhong==2){
            int lo=allq[i].lo-1,ro=allq[i].ro;
            debug2(lo,ro)
            totx=toty=0;
            for(int j=lo;j;j-=lowbit(j)) xbi[++totx]=s[j];
            for(int j=ro;j;j-=lowbit(j)) ybi[++toty]=s[j];
            int now2=reqkth(lo,ro,rt[lo],rt[ro],1,totshu,allq[i].kth);//congxiaodaoda
            cout<<lisan[now2]<<endl;
        }
        else if(allq[i].zhong==3){
            add(allq[i].lo,yuan[allq[i].lo],-1);
            yuan[allq[i].lo]=lower_bound(lisan+1,lisan+1+totshu,allq[i].ro)-lisan;
            add(allq[i].lo,yuan[allq[i].lo],1);
        }
        else if(allq[i].zhong==4){
            int now1=lower_bound(lisan+1,lisan+1+totshu,allq[i].kth)-lisan-1;//kth's qianqu
            int lo=allq[i].lo-1,ro=allq[i].ro;
            for(int j=lo;j;j-=lowbit(j)) xbi[j]=s[j];
            for(int j=ro;j;j-=lowbit(j)) ybi[j]=s[j];
            now1=findpre(lo,ro,rt[lo],rt[ro],1,totshu,now1);
            if(now1==-1) cout<<-2147483647<<endl;
            else cout<<lisan[now1]<<endl;
        }
        else{
            int now1=lower_bound(lisan+1,lisan+1+totshu,allq[i].kth)-lisan+1;
            int lo=allq[i].lo-1,ro=allq[i].ro;
            for(int j=lo;j;j-=lowbit(j)) xbi[j]=s[j];
            for(int j=ro;j;j-=lowbit(j)) ybi[j]=s[j];
            now1=findhou(lo,ro,rt[lo],rt[ro],1,totshu,now1);
            if(now1==-1) cout<<2147483647<<endl;
            else cout<<lisan[now1]<<endl;
        }
    }
    return 0;
}

• 代码比较丑，为了优化\(ydii[i],xdii[i],xdi[i],ydi[i]\)数组的空间，记录进数组的时候改了一点写法，但有些部分还没改。
• 使用的是树状数组套主席树，常数不是很大。洛谷跑了\(1.28s\).
• 注意这里的排名\(kth\)是从小到大的排名，查询完\(rk\)之后要加\(1\)(\(reqrk\)函数实际上查询的是比当前数小的数有多少个)
• 树套树支持动态的区间\(rk/kth\)查询，查询某个数的区间前驱和后继。