PAT甲级真题 1066 Root of AVL Tree (25分) C++实现（建立AVL树）

题目

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 the 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

思路

难题，考察平衡二叉树的建立，学了很多资料才搞明白，整理出了:

彻底搞懂平衡二叉树（AVL）建树过程（左旋、右旋）

学习了柳神的代码：1066. Root of AVL Tree (25)-PAT甲级真题

自己根据理解和记忆又写了一遍，发现几个容易出错的点：

主函数循环体中：

//每插入一个节点都要更新根的值
root = insertVal(root, val);  

插入节点函数insertVal中：

//若节点插入到左子树，则需更新root->l的值
if (val < root->val){
   
   
        root->l = insertVal(root->l, val);
        ...
}

右旋函数rotateRight中：

Node* rotateRight(Node *root){
   
   
    Node *p = root->l;  
    //下面两行代码次序不能颠倒
    root->l = p->r;
    p->r = root;
    return p;