Self-Balancing Trees

Overview

Self-balancing trees are data structures that automatically maintain their balance during operations to ensure efficient performance.

Key Features

• Efficient searching
• Automatic balancing
• Fast insertion and deletion

This is an example of an unbalanced tree (we want to avoid an ugly tree like this!

Red-Black Trees

Red-Black Trees are a type of self-balancing binary search tree with the following properties:

• The root is always black.
• No two red nodes can be adjacent.
• Every path from a node to its descendant NULL nodes has the same number of black nodes.

AVL Trees

AVL Trees are self-balancing binary search trees that maintain balance using rotations. They ensure:

• The height difference between the left and right subtree of any node is at most 1.
• Guarantee O(log n) complexity for operations.

B-Trees

B-Trees are balanced tree data structures commonly used in databases and file systems. Key features include:

• Nodes can have multiple children.
• Keeps data sorted and allows searches, sequential access, insertions, and deletions in logarithmic time.