1066. Root of AVL Tree (25)

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 (<=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 ythe root of the resulting AVL tree in one line.
Sample Input 1:

5
88 70 61 96 120

Sample Output 1:

70

Sample Input 2:

7
88 70 61 96 120 90 65

Sample Output 2:

88

avl树的基本操作。

#include <iostream>
using namespace std;
inline int MAX(int x,int y){return x > y ? x : y;}
struct avl_node
{
int key;
avl_node * left;
avl_node * right;
int height;
avl_node(int k,avl_node * l=NULL,avl_node * r = NULL,int h = 0):key(k),left(l),right(r),height(h){}
//h in single node is defined as 1 and that in NULL node defined as -1
};
inline int height(avl_node * node){return node == NULL?-1:node->height;}
void rotate_left_chiled(avl_node * & root)
{
avl_node  * tmp=root->left;
root->left=tmp->right;
tmp->right=root;
tmp->height=MAX(height(tmp->left),height(tmp->right))+1;
root->height=MAX(height(root->left),height(root->right))+1;
root=tmp;
}
void rotate_right_chiled(avl_node * & root)
{
avl_node * tmp=root->right;
root->right = tmp->left;
tmp->left=root;
tmp->height=MAX(height(tmp->left),height(tmp->right))+1;
root->height=MAX(height(root->left),height(root->right))+1;
root=tmp;
}
void double_rotate_left(avl_node * & root)
{
rotate_right_chiled(root->left);
rotate_left_chiled(root);
}
void double_rotate_right(avl_node * & root)
{
rotate_left_chiled(root->right);
rotate_right_chiled(root);
}
void insert(avl_node * & root,int key)
{
if( root == NULL )
{
root = new avl_node(key);
}
else
{
if(key < root -> key)
{
insert(root->left,key);
if(height(root->left) - height(root->right) == 2)
{
if(key < root->left->key)
rotate_left_chiled(root);
else
double_rotate_left(root);
}
}
else
{
insert(root->right,key);
if(height(root->right)-height(root->left) == 2)
{
if(key>root->right->key)
rotate_right_chiled(root);
else
double_rotate_right(root);
}
}
}
root->height=MAX(height(root->left),height(root->right))+1;
}
int main()
{
int n;
cin>>n;
avl_node * root;
for(int i=0;i<n;i++)
{
int node;
cin>>node;
insert(root,node);
}
cout<<root->key;
return 0;
}