Binary Search Trees

Introduction

A Binary Search Tree (BST) is a node-based binary tree data structure that maintains its elements in sorted order, allowing for efficient insertion, deletion, and search operations.

BST Properties

For any node in a Binary Search Tree:

• All keys in the left subtree are less than the node's key
• All keys in the right subtree are greater than the node's key
• Both the left and right subtrees must also be binary search trees

Basic Operations

Search Operation

1. Start at the root node
2. Compare the target value with the current node's value
3. If equal, return the node
4. If less, search in the left subtree
5. If greater, search in the right subtree
6. Repeat until found or reach a null node

Insertion Operation

1. Start at the root node
2. Compare the new value with the current node's value
3. If less, go to left child; if greater, go to right child
4. When reaching a null position, insert the new node
5. Maintain the BST property throughout

BST Visualization

Example of a balanced Binary Search Tree

Time Complexity

• Search: O(h) where h is the height of the tree
• Insertion: O(h)
• Deletion: O(h)
• In-order Traversal: O(n)

Note: In balanced BSTs, h = O(log n), making operations efficient.

Pros of BSTs

1. Efficient searching compared to arrays and linked lists
2. Flexible size - grows and shrinks dynamically
3. Maintains data in sorted order without explicit sorting
4. Supports range queries and ordered operations

Learn More

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