Red-Black Trees Basics and Visualization

Prerequisites

Before reading this article, you should first learn:

• Basics and Common Types of Binary Trees
• Recursive and Level-order Traversal of Multi-way Trees
• Applications and Visualization of Binary Search Trees

Summary in One Sentence

A red-black tree is a self-balancing binary search tree, maintaining its height at $O(\log N)$ (perfect balance) at all times. This ensures that the time complexity for insertion, deletion, search, and update operations is $O(\log N)$.

The visualization panel supports creating red-black trees:

The article Applications and Visualization of Binary Search Trees discusses the implementation of TreeMap/TreeSet using a regular binary search tree to store key-value pairs.

The efficiency of operations on a binary search tree depends on its height. A more balanced tree has a height close to $\log N$, leading to higher efficiency in insertion, deletion, search, and update operations. The main issue with a regular binary search tree is that it does not automatically balance itself, and in specific cases, it can degrade into a linked list, causing the time complexity of operations to degrade to $O(N)$.

The following visualization panel is an example: if you insert several ordered key-value pairs, you will notice that each new key is added to the far right, causing this binary search tree to degrade into a linked list:

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