模板：替罪羊树

替罪羊树模板

Code（指针版）：

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
bool Finish_read;
template<class T>inline void read(T &x){Finish_read=0;x=0;int f=1;char ch=getchar();while(!isdigit(ch)){if(ch=='-')f=-1;if(ch==EOF)return;ch=getchar();}while(isdigit(ch))x=x*10+ch-'0',ch=getchar();x*=f;Finish_read=1;}
template<class T>inline void print(T x){if(x/10!=0)print(x/10);putchar(x%10+'0');}
template<class T>inline void writeln(T x){if(x<0)putchar('-');x=abs(x);print(x);putchar('\n');}
template<class T>inline void write(T x){if(x<0)putchar('-');x=abs(x);print(x);}
/*================Header Template==============*/
const double alpha=0.7;
int n;
/*==================Define Area================*/
namespace ScapegoatTree {
	struct node {
		node *l,*r;
		int v,sz,valid;
		bool del;
		bool Bad() {
			return (double)l->sz>alpha*(double)sz||(double)r->sz>alpha*(double)sz;
		}
		void Update() {
			sz=!del+l->sz+r->sz;
			valid=!del+l->valid+r->valid;
		}
	};
	node *null;
	void Dfs(node *o,std::vector<node*> &v) {
		if(o==null) return ;
		Dfs(o->l,v);
		if(!o->del) v.push_back(o);
		Dfs(o->r,v);
		if(o->del) delete o; 
	}
	node *Build(std::vector<node*> &v,int l,int r) {
		if(l>=r) return null;
		int mid=(l+r)>>1;
		node *o=v[mid];
		o->l=Build(v,l,mid);
		o->r=Build(v,mid+1,r);
		o->Update();
		return o;
	}
	void ReBuild(node* &o) {
		std::vector<node*>v;
		Dfs(o,v);
		o=Build(v,0,v.size());
	}
	void Insert(int x,node* &o) {
		if(o==null) {
			o=new node;
			o->l=o->r=null;
			o->del=false;
			o->sz=o->valid=1;
			o->v=x;
			return ;
		}
		++o->sz;++o->valid;
		if(x>=o->v) Insert(x,o->r);
		else Insert(x,o->l);
		if(o->Bad()) ReBuild(o);
	}
	int GetRank(node* o,int x) {
		int ans=1;
		while(o!=null) {
			if(o->v>=x) o=o->l;
			else {
				ans+=o->l->valid+!o->del;
				o=o->r;
			}
		}
		return ans;
	}
	int FindKth(node* o,int x) {
		while(o!=null) {
			if(!o->del&&o->l->valid+1==x) return o->v;
			if(o->l->valid>=x) o=o->l;
			else {
				x-=o->l->valid+!o->del;
				o=o->r;
			}
		}
	}
	void Delete(node *o,int rnk) {
		if(!o->del&&rnk==o->l->valid+1) {
			o->del=1;
			--o->valid;
			return ;
		}
		--o->valid;
		if(rnk<=o->l->valid+!o->del) Delete(o->l,rnk);
		else Delete(o->r,rnk-o->l->valid-!o->del);
	}
	node *rt;
}
using namespace ScapegoatTree;

int main() {
	null=new node;
	rt=null;
	read(n);
	while(n--) {
		int opt,x;
		read(opt);read(x);
		if(opt==1) Insert(x,rt);
		if(opt==2) Delete(rt,GetRank(rt,x));
		if(opt==3) writeln(GetRank(rt,x));
		if(opt==4) writeln(FindKth(rt,x));
		if(opt==5) writeln(FindKth(rt,GetRank(rt,x)-1));
		if(opt==6) writeln(FindKth(rt,GetRank(rt,x+1)));
	}
	return 0;
}

Code（数组版）：

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
bool Finish_read;
template<class T>inline void read(T &x){Finish_read=0;x=0;int f=1;char ch=getchar();while(!isdigit(ch)){if(ch=='-')f=-1;if(ch==EOF)return;ch=getchar();}while(isdigit(ch))x=x*10+ch-'0',ch=getchar();x*=f;Finish_read=1;}
template<class T>inline void print(T x){if(x/10!=0)print(x/10);putchar(x%10+'0');}
template<class T>inline void writeln(T x){if(x<0)putchar('-');x=abs(x);print(x);putchar('\n');}
template<class T>inline void write(T x){if(x<0)putchar('-');x=abs(x);print(x);}
/*================Header Template==============*/
#define PAUSE printf("Press Enter key to continue..."); fgetc(stdin);
const double alpha=0.7;
const int N=1e5+500;
int n;
/*==================Define Area================*/
namespace ScapegoatTree {
    struct node {
        int l,r,v,sz,valid;
        bool del;
        void New(int x) {l=r=0;v=x;sz=valid=1;del=0;}
    }t[N<<2];
    #define ls(o) t[o].l
    #define rs(o) t[o].r
    #define pb push_back
    int tot=0,rt=0;
    bool Bad(int o) {
        return (double)t[ls(o)].sz>alpha*t[o].sz||(double)t[rs(o)].sz>alpha*t[o].sz;
    }
    void Updata(int o) {
        t[o].sz=t[ls(o)].sz+t[rs(o)].sz+!t[o].del;
        t[o].valid=t[ls(o)].valid+t[rs(o)].valid+!t[o].del;
    }
    void Dfs(int o,std::vector<int> &v) {
        if(!o) return ;
        Dfs(ls(o),v);
        if(!t[o].del) v.pb(o);
        Dfs(rs(o),v);
        return ;
    }
    int Build(std::vector<int> &v,int l,int r) {
        if(l>=r) return 0;
        int mid=(l+r)>>1;
        int o=v[mid];
        ls(o)=Build(v,l,mid);
        rs(o)=Build(v,mid+1,r);
        Updata(o);
        return o;
    }
    void ReBuild(int &o) {
        std::vector<int>v;
        Dfs(o,v);
        o=Build(v,0,(int)v.size());
    }
    void Insert(int x,int &o) {
        if(!o) {
            o=++tot;
            t[o].New(x);
            return ;
        }
        t[o].sz++;t[o].valid++;
        if(x>=t[o].v) Insert(x,rs(o));
        else Insert(x,ls(o));
        if(Bad(o)) ReBuild(o);
        return ;
    }
    int GetRank(int o,int x) {
        int ans=1;
        while(o) {
            if(t[o].v>=x) o=ls(o);
            else {
                ans+=t[ls(o)].valid+!t[o].del;
                o=rs(o);
            }
        }
        return ans;
    }
    int FindKth(int o,int x) {
        while(o) {
            if(!t[o].del&&t[ls(o)].valid+1==x) {return t[o].v;}
            if(t[ls(o)].valid>=x) o=ls(o); 
            else {
                x-=t[ls(o)].valid+!t[o].del;
                o=rs(o);
            }
        }
    }
    void Delete(int o,int Rnk) {
        if(!t[o].del&&Rnk==t[ls(o)].valid+1) {
            t[o].del=1;
            --t[o].valid;
            return ;
        }
        --t[o].valid;
        if(Rnk<=t[ls(o)].valid+!t[o].del) Delete(ls(o),Rnk);
        else Delete(rs(o),Rnk-t[ls(o)].valid-!t[o].del);
    }
}
using namespace ScapegoatTree;

int main() {
    read(n);
    rt=0;
    while(n--) {
        int opt,x;
        read(opt);read(x);
        if(opt==1) Insert(x,rt);
        if(opt==2) Delete(rt,GetRank(rt,x));
        if(opt==3) writeln(GetRank(rt,x));
        if(opt==4) writeln(FindKth(rt,x));
        if(opt==5) writeln(FindKth(rt,GetRank(rt,x)-1));
        if(opt==6) writeln(FindKth(rt,GetRank(rt,x+1)));
    }
    return 0;
}