hdu 4006 The kth great number

最新推荐文章于 2020-11-27 18:02:08 发布

原创最新推荐文章于 2020-11-27 18:02:08 发布 · 549 阅读

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#AVL树

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本文介绍了如何在AVL树上维护节点大小信息，通过优化查找算法来快速确定数列中第k大的数，提供了一种在平衡二叉树基础上的高效解决方案。

动态询问一些数中第k大的数（没有删除操作）。为了学习AVL树，用AVL码的，居然1A了，但是效率并不比普通二叉树有所提高。做法是在AVL树的基础上，维护每个节点的大小，根据大小信息查找第k大。

#include <iostream>    
#include <stdio.h>    
#include <string>    
#include <map>    
#include <vector>    
#include <stack>    
#include <queue>    
#include <string.h>    
#include <algorithm>    
#include <math.h>    
    
using namespace std;    


struct avl{
	int data;
	int height;
	avl* pleft;
	avl* pright;
	int size;
};

int Height(avl* pNode){
	if(NULL==pNode)return -1;
	return pNode->height;
}

int Size(avl* pNode){
	if(NULL==pNode)return 0;
	return pNode->size;
}

avl* LLRotate(avl* pNode){
	avl* l=pNode->pleft;
	pNode->pleft=l->pright;
	l->pright=pNode;
	pNode->size=Size(pNode->pleft)+Size(pNode->pright)+1;
	l->size=Size(l->pleft)+Size(l->pright)+1;
	pNode->height=max(Height(pNode->pleft),Height(pNode->pright))+1;
	l->height=max(Height(l->pleft),Height(l->pright))+1;
	return l;
}

avl* RRRotate(avl* pNode){
	avl* r=pNode->pright;
	pNode->pright=r->pleft;
	r->pleft=pNode;
	pNode->size=Size(pNode->pleft)+Size(pNode->pright)+1;
	r->size=Size(r->pleft)+Size(r->pright)+1;
	pNode->height=max(Height(pNode->pleft),Height(pNode->pright))+1;
	r->height=max(Height(r->pleft),Height(r->pright))+1;
	return r;
}

avl* LRRotate(avl* pNode){
	pNode->pleft=RRRotate(pNode->pleft);
	return LLRotate(pNode);
}

avl* RLRotate(avl* pNode){
	pNode->pright=LLRotate(pNode->pright);
	return RRRotate(pNode);
}

avl* insert(avl* pNode,int data){
	if(pNode==NULL){
		
		pNode=new avl();
		pNode->data=data;
		pNode->height=0;
		pNode->size=1;
	}else if(data>pNode->data){
		pNode->pleft=insert(pNode->pleft,data);
		pNode->size++;
		if(Height(pNode->pleft)-Height(pNode->pright)==2){	//不平衡 
			if(data>pNode->pleft->data){
				pNode=LLRotate(pNode);
			}else{
				pNode=LRRotate(pNode);
			}
		}
		
		
	}else{
		pNode->pright=insert(pNode->pright,data);
		pNode->size++;
		if(Height(pNode->pright)-Height(pNode->pleft)==2){	//不平衡 
			if(data<pNode->pright->data){
				pNode=RRRotate(pNode);
			}else{
				pNode=RLRotate(pNode);
			}
		}
		
	}
	pNode->height=max(Height(pNode->pleft),Height(pNode->pright));
	return pNode;
}

int query(avl* pNode,int q){
	
	int lsiz=0;
	if(pNode->pleft)lsiz=pNode->pleft->size;
	int rsiz=0;
	if(pNode->pright)rsiz=pNode->pright->size;
	if(lsiz+1==q) return pNode->data;
	else if(lsiz>=q) return query(pNode->pleft,q);
	else return query(pNode->pright,q-1-lsiz);
}

int main(){
	int n,k;
	while(cin>>n>>k){
		avl* root=NULL;
	
		for(int i=1;i<=n;i++){
			char op[2];
			scanf("%s",op);
			if(op[0]=='I'){
				int num;
				scanf("%d",&num);
				root=insert(root,num);
			}else{
				int ans=query(root,k);
				printf("%d\n",ans);
			}
	
		}
	}
	return 0;
}