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数据结构与算法分析-AVL树深入探讨

Table of Contents

• 1. 数据结构之-AVL树深入探讨
  • 1.1. AVL树介绍
  • 1.2. AVL树的四种不平衡情形

1 数据结构之-AVL树深入探讨

之前学习数据结构与算法分析C语言描述的时候, 学到了AVL树, 陷入了重重的陷阱, 如今把一一踩过的陷阱都描述出来, 好让自己温故知新.

1.1 AVL树介绍

• AVL(Adelson-Velskii和Landis)树是带有平衡条件的二叉查找树.这个平衡条件必须要容易保持.而且它须保证树的深度是 \(O(\log{N})\).
• 一棵AVL树是其任意节点的左子树和右子树的高度绝对值最多差1的二叉查找树.
• 下图是AVL树和非AVL树

1.2 AVL树的四种不平衡情形

• AVL树的任意节点 a 的两棵子树(左儿子和右儿子)的高度差2就会出现不平衡状态.
• 不平衡情形分为四种
  • 对 a 的左儿子(L)的左子树(L)进行一次插入. LL情形
  • 对 a 的左儿子(L)的右子树(R)进行一次插入. LR情形
  • 对 a 的右儿子(R)的左子树(L)进行一次插入. RL情形
  • 对 a 的右儿子(R)的右边子树(R)进行一次插入. RR情形

Date: 2018-11-19 22:15

Author: devinkin

Created: 2018-11-19 一 22:16

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原文地址：https://www.cnblogs.com/devinkin/p/9986167.html