Root of AVL Tree（25 分）

04-树5 Root of AVL Tree（25 分）

An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illustrate the rotation rules.

 

Now given a sequence of insertions, you are supposed to tell the root of the resulting AVL tree.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer $N$ ($\le 20$) which is the total number of keys to be inserted. Then $N$ distinct integer keys are given in the next line. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print the root of the resulting AVL tree in one line.

Sample Input 1:

588 70 61 96 120

Sample Output 1:

70

Sample Input 2:

788 70 61 96 120 90 65

Sample Output 2:

88

作者: 陈越

单位: 浙江大学

时间限制: 400ms

内存限制: 64MB

代码长度限制: 16KB

参考了www.dongjinbao.com觉得做法很巧妙，简洁。十分佩服！

觉得自己还不能充分理解递归！！！！

#include<iostream>
using namespace std;
struct treenode{
int data,h;
treenode* left=NULL;
treenode* right=NULL;
};
using tree=treenode*;
int height(tree t){
//cout<<"height(tree t)"<<endl;
if(!t) return 0;
return max(height(t->left),height(t->right))+1;
}
tree RotateLL(tree t){
//cout<<" RotateLL(tree t)"<<endl;
tree a=t->left;
t->left=a->right;
a->right=t;
a->h=max(height(a->left),height(a->right))+1;
t->h=max(height(t->left),height(t->right))+1;
return a; 
}
tree RotateRR(tree t){
//cout<<"RotateRR(tree t)"<<endl;
tree a=t->right;
t->right=a->left;
a->left=t;
    a->h=max(height(a->left),height(a->right))+1;
t->h=max(height(t->left),height(t->right))+1;
return a; 
}
tree RotateLR(tree t){
//cout<<"RotateLR(tree t)"<<endl;
t->left=RotateRR(t->left);
return RotateLL(t);
}
tree RotateRL(tree t){
//cout<<"RotateRL(tree t)"<<endl;
t->right=RotateLL(t->right);
return RotateRR(t);
}
tree insert(tree t,int v){
//cout<<" insert(tree t,int v)"<<endl;
if(t==NULL){
t=new treenode();
t->data=v; t->h=0;
return t;
}else if(v<t->data){
t->left=insert(t->left,v);
if(height(t->left)-height(t->right)==2)
if(v<t->left->data) 
t=RotateLL(t);
else t=RotateLR(t); 
}else{
t->right=insert(t->right,v);
if(height(t->left)-height(t->right)==-2)
if(v>t->right->data)
t=RotateRR(t);
else t=RotateRL(t); 
}
t->h=height(t);
return t;
} 
int main()
{
int n;
cin>>n;
tree t=NULL;
for(int i=0;i<n;i++){
int v; cin>>v;
t=insert(t,v);
}
cout<<t->data<<endl;
return 0;
}