[luogu3369/bzoj3224]普通平衡树(splay模板、平衡树初探)

解题关键：splay模板题整理。

如何不加入极大极小值？（待思考）

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cstdlib>
#include<iostream>
#include<cstdlib>
using namespace std;
typedef long long ll;
const int N = 100005;
int ch[N][2],par[N],val[N],cnt[N],size[N],ncnt,root;

bool chk(int x){
    return ch[par[x]][1]==x;
}

void pushup(int x){
    size[x]=size[ch[x][0]]+size[ch[x][1]]+cnt[x];//和线段树不同的是需要+上自身的cnt
}

void rotate(int x){
    int y=par[x],z=par[y],k=chk(x),w=ch[x][k^1];
    ch[y][k]=w;par[w]=y;
    ch[z][chk(y)]=x;par[x]=z;
    ch[x][k^1]=y;par[y]=x;
    pushup(y);pushup(x);
}

void splay(int x,int goal=0){
    while(par[x]!=goal){
        int y=par[x],z=par[y];
        if(z!=goal){
            if(chk(x)==chk(y)) rotate(y);
            else rotate(x);
        }
        rotate(x);
    }
    if(!goal) root=x;
}

void insert(int x){
    int cur=root,p=0;
    while(cur&&val[cur]!=x){
        p=cur;
        cur=ch[cur][x>val[cur]];
    }
    if(cur){
        cnt[cur]++;
    }else{
        cur=++ncnt;
        if(p) ch[p][x>val[p]]=cur;
        ch[cur][0]=ch[cur][1]=0;
        par[cur]=p;val[cur]=x;
        cnt[cur]=size[cur]=1;
    }
    splay(cur);
}

void find(int x){
    int cur=root;
    if(!cur) return;
    while(ch[cur][x>val[cur]]&&x!=val[cur]){
        cur=ch[cur][x>val[cur]];
    }
    splay(cur);
}
//从0开始
int kth(int k){
    k++;
    int cur=root;
    while(1){
        if(ch[cur][0]&&k<=size[ch[cur][0]]){
            cur=ch[cur][0];
        }else if(k>size[ch[cur][0]]+cnt[cur]){
            k-=size[ch[cur][0]]+cnt[cur];
            cur=ch[cur][1];
        }else{
            return cur;
        }
    }
}

int rnk(int x){
    find(x);
    if(val[root]>=x) return size[ch[root][0]];
    else return size[ch[root][0]]+cnt[root];
}

int pre(int x){
    find(x);
    if(val[root]<x) return root;
    int cur=ch[root][0];
    while(ch[cur][1]) cur=ch[cur][1];
    return cur;
}

int succ(int x) {
    find(x);
    if(val[root]>x) return root;
    int cur=ch[root][1];
    while(ch[cur][0]) cur=ch[cur][0];
    return cur;
}

void remove(int x) {
    int last=pre(x),nxt=succ(x);
    splay(last);splay(nxt,last);
    int del=ch[nxt][0];
    if(cnt[del]>1){
        cnt[del]--;
        splay(del);
    }
    else ch[nxt][0]=0;
}

void init(){
    insert(-2e9);
    insert(2e9);
}

int n,op,x;

int main() {
    scanf("%d",&n);
    init();
    while(n--){
        scanf("%d%d",&op,&x);
        switch(op){
            case 1: insert(x); break;
            case 2: remove(x); break;
            case 3: printf("%d
",rnk(x)); break;
            case 4: printf("%d
",val[kth(x)]); break;
            case 5: printf("%d
",val[pre(x)]); break;
            case 6: printf("%d
",val[succ(x)]); break;
        }
    }
}