PAT A1066

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.
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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

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#include "stdio.h"
#include "math.h"
#include "string.h"
//#include "iostream"
//#include "stdlib.h"
#include "vector"
//#include "set"
//#include "map"
//#include "stack"
#include "queue"
#include "algorithm"
using namespace std;

//typedef long long LL;
struct node {
int v, height;//v为结点权值,height为当前子树高度
node *lchild,*rchild;
} *root, *null;

//生成一个新结点,v为结点权值
node* newNode(int v){
node* Node = new node;
Node->v = v;
Node->height = 1;
Node->lchild = Node->rchild = NULL;
return Node;
}
//获取以root为根的子树当前的高度height
int getHeight(node* root){
if (root == NULL) {
return 0;
}
return root->height;
}
//更新结点root的height
void updateHeight(node* root){
//max+1
root->height = max(getHeight(root->lchild), getHeight(root->rchild)) + 1;
}
//计算结点root的平衡因子
int getBalance(node* root){
return getHeight(root->lchild) - getHeight(root->rchild);
}
//左旋
void L(node* &root){
node* temp = root->rchild;
root->rchild = temp->lchild;
temp->lchild = root;
updateHeight(root);
updateHeight(temp);
root = temp;
}
//右旋
void R(node* &root){
node* temp = root->lchild;
root->lchild = temp->rchild;
temp->rchild = root;
updateHeight(root);
updateHeight(temp);
root = temp;
}
//插入权值为v的结点
void insert(node* &root, int v){
if (root == NULL) {
root = newNode(v);
return;
}
if (v < root->v) {
insert(root->lchild, v);//往左子树插入
updateHeight(root);
if (getBalance(root) == 2) {
if (getBalance(root->lchild) == 1) {//LL
R(root);
}else if(getBalance(root->lchild) == -1){//LR
L(root->lchild);
R(root);
}
}
}else{
insert(root->rchild, v);//往右子树插入
updateHeight(root);
if (getBalance(root) == -2) {
if (getBalance(root->rchild) == -1) {//RR
L(root);
}else if(getBalance(root->rchild) == 1){//RL
R(root->rchild);
L(root);
}
}
}
}
int main(){
int n, v;
scanf("%d", &n);
for (int i = 0 ; i < n; i++) {
scanf("%d", &v);
insert(root, v);
}
printf("%d\n", root->v);
return 0;
}