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en/docs/chapter_tree/avl_tree.md
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@@ -18,11 +18,11 @@ For example, in the perfect binary tree shown in Figure 7-25, after inserting tw
<p align="center"> Figure 7-25 &nbsp; Degradation of an AVL tree after inserting nodes </p>
In 1962, G. M. Adelson-Velsky and E. M. Landis proposed the "AVL Tree" in their paper "An algorithm for the organization of information". The paper detailed a series of operations to ensure that after continuously adding and removing nodes, the AVL tree would not degrade, thus maintaining the time complexity of various operations at $O(\log n)$ level. In other words, in scenarios where frequent additions, removals, searches, and modifications are needed, the AVL tree can always maintain efficient data operation performance, which has great application value.
In 1962, G. M. Adelson-Velsky and E. M. Landis proposed the <u>AVL Tree</u> in their paper "An algorithm for the organization of information". The paper detailed a series of operations to ensure that after continuously adding and removing nodes, the AVL tree would not degrade, thus maintaining the time complexity of various operations at $O(\log n)$ level. In other words, in scenarios where frequent additions, removals, searches, and modifications are needed, the AVL tree can always maintain efficient data operation performance, which has great application value.
## 7.5.1 &nbsp; Common terminology in AVL trees
An AVL tree is both a binary search tree and a balanced binary tree, satisfying all properties of these two types of binary trees, hence it is a "balanced binary search tree".
An AVL tree is both a binary search tree and a balanced binary tree, satisfying all properties of these two types of binary trees, hence it is a <u>balanced binary search tree</u>.
### 1. &nbsp; Node height
@@ -489,7 +489,7 @@ The "node height" refers to the distance from that node to its farthest leaf nod
### 2. &nbsp; Node balance factor
The "balance factor" of a node is defined as the height of the node's left subtree minus the height of its right subtree, with the balance factor of a null node defined as $0$. We will also encapsulate the functionality of obtaining the node balance factor into a function for easy use later on:
The <u>balance factor</u> of a node is defined as the height of the node's left subtree minus the height of its right subtree, with the balance factor of a null node defined as $0$. We will also encapsulate the functionality of obtaining the node balance factor into a function for easy use later on:
=== "Python"