AVL and Red-Black Trees: Balancing Search Trees with Rotations

Summary

This document introduces two self-balancing binary search trees and explains how their balancing rules support efficient lookup, insertion, and deletion. For AVL trees, it defines node height and balance factor, then describes single and double rotations and how insertion and deletion update heights and restore balance. It states logarithmic time complexity for the core operations.

The red-black tree section outlines node colors, black roots and leaves, restrictions on red nodes, and equal black-node counts along paths. It describes rotations and recoloring as repair tools, and contrasts the looser balance with fewer rotations against AVL trees. The examples show basic AVL operations and a partial red-black implementation, including an omitted deletion routine. The material is a conceptual and code-oriented introduction, not a complete, tested library; readers must handle missing cases and implementation details before relying on it.

Key ideas

• AVL trees keep each node's left and right subtree heights within one of each other.
• AVL insertion and deletion restore balance by updating heights and applying single or double rotations.
• Red-black trees use node colors and path constraints to maintain approximate balance.
• Red-black repairs combine rotations with recoloring and may require fewer rotations than AVL repairs.
• The red-black code is incomplete, especially its deletion logic, and should not be treated as a ready-to-use implementation.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.