A Binary Search Tree (BST) is a fundamental data structure in computer science, widely used for efficient searching, insertion, and deletion operations. It is a node-based binary tree where each node has at most two children, and the tree maintains a specific ordering property.

Key Properties 🔍

  • Left Subtree: All values are less than the parent node.
  • Right Subtree: All values are greater than the parent node.
  • Recursive Structure: Each subtree follows the same BST property.
  • Time Complexity:
    • Search/Insert/Delete: O(log n) on average, O(n) in worst-case (unbalanced tree).

Common Operations 🔄

  1. Search
    • Traverse the tree by comparing the target value with the current node.
    • Use 🔍 to denote the search process.
  2. Insert
    • Add a new node while maintaining the BST property.
    • Example: Inserting 15 into a tree with root 10 would go to the right subtree.
  3. Delete
    • Remove a node and adjust the tree to preserve ordering.
    • Use 🗑️ to visualize deletion.

Applications 📊

  • Database indexing for fast data retrieval.
  • Implementing dynamic sets and lookup tables.
  • Expression parsing and syntax tree construction.
  • For further reading on advanced tree structures, check out our article on AVL Trees.
binary_search_tree

Visualize BST Structure 📈

A typical BST looks like this: 

       10  
      /   \  
     5     15  
    / \    / \  
   3   7  12  18

Use 🌲 to represent the tree's hierarchical nature.

For interactive examples or code implementations, explore our Data Structures Playground. 🧩