What is a Red-Black Tree?
A Red-Black Tree is a self-balancing binary search tree that maintains balance by adding a color attribute (red or black) to each node. Red-Black Trees ensure that basic operations (insertion, deletion, search) have O(log n) time complexity in the worst case.
Red-Black Tree Properties
A Red-Black Tree must satisfy the following five important properties:
- Color Property: Every node is either red or black
- Root Property: The root node must be black
- Leaf Property: All leaf nodes (NIL nodes) are black
- Red Property: Both children of every red node are black (no two consecutive red nodes)
- Path Property: Every path from any node to all of its descendant leaf nodes contains the same number of black nodes
Red-Black Tree Structure
Red-Black Tree Structure Diagram - Shows node color distribution and balancing properties
Main Operations
Red-Black Trees support the following basic operations, all with O(log n) time complexity:
- Search: Find a specific value in the tree
- Insert: Add a new node to the tree and maintain balance through rotations and recoloring
- Delete: Remove a node from the tree and rebalance the structure
- Traversal: Visit all nodes in a specific order
Advantages and Applications
Main advantages of Red-Black Trees over regular binary search trees:
- Guarantees O(log n) time complexity in the worst case
- Insertion and deletion operations are relatively simple with fewer rotations
- Widely used in various data structure and algorithm libraries
Red-Black Trees are extremely important in practical applications. They are used in many programming language standard libraries, such as Java's TreeMap and TreeSet, C++'s map and set, etc.