What is a Binary Search Tree?
A Binary Search Tree is a hierarchical data structure where each node has at most two children. The left child contains values less than the parent node, and the right child contains values greater than the parent node. This property makes BSTs extremely efficient for search operations.
Key Properties
- Ordered Structure: For any node, all values in the left subtree are smaller, and all values in the right subtree are larger
- Efficient Search: Average time complexity of O(log n) for search, insert, and delete operations in a balanced tree
- In-Order Traversal: Visiting nodes in left-root-right order produces a sorted sequence of values
- Dynamic Size: Can grow and shrink dynamically as elements are added or removed
Common Operations
Basic BST Operations
- Insert a new value while maintaining BST property
- Search for a specific value in the tree
- Delete a node (handling three cases: leaf, one child, two children)
- Traverse the tree (in-order, pre-order, post-order)
Visual Representation
Example of a Binary Search Tree structure
Performance Considerations
In the worst case (when the tree becomes skewed), operations can degrade to O(n) time complexity. This is why balanced BST variants like AVL trees and Red-Black trees are often preferred in practice.
Learn More
For a comprehensive guide to Binary Search Trees and their implementations, visit the Wikipedia page on Binary Search Trees.