Red-Black Trees

What is a Red-Black Tree?

A Red-Black Tree is a self-balancing binary search tree where each node contains an extra bit for denoting the color of the node, either red or black. This color bit ensures that the tree remains approximately balanced during insertions and deletions.

Key Properties

Red-Black Trees must satisfy the following properties:

• Every node is either red or black
• The root node is always black
• All leaf nodes (NIL nodes) are black
• Red nodes cannot have red children (no two red nodes can be adjacent)
• Every path from a node to its descendant NIL nodes contains the same number of black nodes

Common Operations

Red-Black Trees support efficient operations:

1. Insertion: Add a new node and rebalance using rotations and recoloring (O(log n) time)
2. Deletion: Remove a node and maintain tree properties through rotations (O(log n) time)
3. Search: Find a value in the tree using binary search (O(log n) time)
4. Traversal: Visit all nodes in a specific order (in-order, pre-order, post-order)

Why Use Red-Black Trees?

Red-Black Trees guarantee O(log n) time complexity for insertions, deletions, and searches, making them ideal for applications requiring predictable performance. They are used in many standard library implementations, including Java's TreeMap and C++'s map.

Learn More

For a deeper understanding of Red-Black Trees and their implementation, visit the Wikipedia page on Red-Black Trees.