MOOC数据结构 04-树5 Root of AVL Tree (25分)_6-5 height of binary search tree (25 分) you are su-优快云博客

本文链接：https://blog.youkuaiyun.com/thx_00928/article/details/105055661

本文介绍了AVL树的基本概念和旋转规则，包括如何通过旋转操作来保持树的平衡。通过给出的示例展示了插入一系列元素后的根节点计算，帮助读者深入理解AVL树的工作原理。

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MOOC数据结构 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.
在这里插入图片描述 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:

Sample Input 2:

7
88 70 61 96 120 90 65

Sample Output 2:

88
对AVLTree的理解：
1、定义：左右子树的高度差不超过1
2、旋转结点的选取：在每次旋转时主要抓取三个结点，①平衡被破坏的结点；②平衡破坏结点的下一个结点（根据破坏者的位置确定）；③破坏结点（即使破坏结点没有与第二个结点直接相连，可以将包含破坏结点的②结点的一整棵子树看作一个结点）；
3、LL旋转：将被破坏结点的left指向②结点的right，同时将②结点的right指向①；RR同理；
LR旋转：先从②结点开始，进行一次RR旋转（RR是将结点进行一次逆时针旋转）后，形式上就会变为LL，所以对被破坏结点使用一次LL旋转即可完成LR旋转；RL同理；

#include <stdio.h>
#include <stdlib.h>

typedef struct AVLTree {
   
	int data;
	struct AVLTree *left;
	struct AVLTree *right;
	int height;
} *AVLTree;

AVLTree Insert (AVLTree T, int data);//将数值插入树中
int Max (int a, int b);//寻找两数之间最大值
int GetHeight (AVLTree T);//寻找当前结点的高度
AVLTree SingleLeftRotation (AVLTree T);