splay模版

最新推荐文章于 2024-05-06 23:29:48 发布

Elemmir

最新推荐文章于 2024-05-06 23:29:48 发布

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文章标签： splay 模版

本文链接：https://blog.youkuaiyun.com/Elemmir/article/details/50956988

版权

本文介绍了一种自平衡二叉搜索树的数据结构，并提供了详细的C++代码实现。该数据结构支持插入、删除、查找等操作，并通过旋转操作保持树的平衡，确保操作效率。此外，还实现了查询节点排名、寻找第k小元素等功能。

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#include<cstdio>
#include<iostream>
#include<cstdlib>
using namespace std;
const int MIN=-19999999;
const int MAX= 19999999;
 
struct node{
    int key,siz,cnt;
    node* ch[2],*pnt;
    node(){}
    node(int x,int y,int z):key(x),siz(y),cnt(z){}
    void rs(){siz=ch[0]->siz+ch[1]->siz+cnt;}
};
node nil(0,0,0);
typedef node* pnode;
pnode null=&nil,root=null;
 
void rotate(pnode x, bool d){
    pnode y=x->pnt;
    y->ch[!d]=x->ch[d];
    if(x->ch[d]!=null)x->ch[d]->pnt=y;
    x->pnt=y->pnt;
    if(y->pnt!=null){
    if(y == y->pnt->ch[0])
        y->pnt->ch[0]=x;
    else
        y->pnt->ch[1]=x;
    }
    x->ch[d]=y;y->pnt=x;
    y->rs();x->rs();
}
void splay(pnode x,pnode tar){
    pnode y;
    while(x->pnt != tar){
    y=x->pnt;
    if(x == y->ch[0]){
        if(y->pnt!=tar && y == y->pnt->ch[0])
        rotate(y,1);
        rotate(x,1);
    }else{
        if(y->pnt!=tar && y == y->pnt->ch[1])
        rotate(y,0);
        rotate(x,0);
        }
    }
    if(tar == null)root=x;
}
void ins(int key){
    if(root == null){
    root=new struct node(key,1,1);
    root->ch[0]=root->ch[1]=root->pnt=null;
    return;
    }
    pnode x=root,y;
    while(1){
    x->siz++;
    if( key == x->key ){
        x->cnt++;
        x->rs();
        y=x;
        break;
    }else{
        bool fg=(key > x->key);
        if(x->ch[fg] != null)x=x->ch[fg];
        else{
        y=new struct node(key,1,1);
        x->ch[fg]=y;
        y->ch[1]=y->ch[0]=null;
        y->pnt=x;
        break;
        }
    }
    }
    splay(y,null);
}
pnode search(int key){
    if (root == null) return null;
    pnode x=root,y=null;
    while(1){
    if(key == x->key){
        y=x;break;
    }else{
        bool fg=key > x->key;
        if(x->ch[fg] != null)x=x->ch[fg];
        else break;
    }
    }
    splay(x,null);
    return y;
}
pnode searchmin(pnode x){
    pnode y=x->pnt;
    while(x->ch[0]!=null)x=x->ch[0];
    splay(x,y);
    return x;
}
void del(int key){
    if(root == null)return;
    pnode x=search(key),y;
    if(x == null)return;
    if(x->cnt > 1){x->cnt--;x->rs();return;}
    else if(x->ch[0]==null && x->ch[1]==null){root=null;return;}
    else if(x->ch[0]==null){root=x->ch[1];x->ch[1]->pnt=null;return;}
    else if(x->ch[1]==null){root=x->ch[0];x->ch[0]->pnt=null;return;}
    y=searchmin(x->ch[1]);
    y->pnt=null;
    y->ch[0]=x->ch[0];
    x->ch[0]->pnt=y;
    y->rs();
    root=y;
}
void order(pnode t){
    if(t == null)return;
    order(t->ch[0]);
    for(int i=1;i<=t->cnt;i++)printf("%d ",t->key);
    order(t->ch[1]);
}
int quer_no(int key){
    pnode t=search(key);
    return t==null?-1:t->ch[0]->siz+1;
}
int find_k(int k){
    pnode t=root,ret;
    while(k && t!=null){
    if(t->ch[0]->siz < k && t->ch[0]->siz+t->cnt>=k)ret=t;
    if(t->ch[0]->siz >= k)t=t->ch[0];
    else{
        k -= t->ch[0]->siz+t->cnt;
        t=t->ch[1];
    }
    }
    splay(ret,null);
    return ret->key;
}
int pred(pnode t,int x){
    if(t == null)return MIN;
    if(x <= t->key) return pred(t->ch[0],x);
    return max(t->key,pred(t->ch[1],x));
}
int succ(pnode t,int x){
    if(t == null)return MAX;
    if(x >= t->key) return succ(t->ch[1],x);
    return min(t->key,succ(t->ch[0],x));
}
int fg,x,n;
int main(){
    scanf("%d",&n);
    while(n--){
    scanf("%d%d",&fg,&x);
    switch(fg){
    case 1:
        ins(x);break;
    case 2:
        del(x);break;
    case 3:
        printf("%d\n",quer_no(x));break;
    case 4:
        printf("%d\n",find_k(x));break;
    case 5:
        printf("%d\n",pred(root,x));break;
    case 6:
        printf("%d\n",succ(root,x));break;
    }
    }
}