Learn BST Data Structure with Animation - Interactive Learning
Master Binary Tree - DSA Learning Platform 🌳 Master Binary Search Tree Hierarchical Data O(log n) Operations Learn BST operations with interactive animations and traversal visualization 📖 Understanding Binary Search Tree Introduction Structure Operations Traversals Applications What is a Binary Search Tree? A Binary Search Tree (BST) is a hierarchical data structure where each node has at most two children, referred to as the left child and right child. The key property of BST is: for any node, all values in its left subtree are smaller, and all values in its right subtree are larger. This property enables efficient searching, insertion, and deletion operations. BSTs provide O(log n) average time complexity for search, insert, and delete operations, making them much faster than linear data structures for large datasets. 🔑 Key Properties Each node has at most 2 children Left subtree values < Node value Right subtree values > Node value No duplicate values (typically) Inorder traversal gives sorted order Height determines efficiency BST Node Structure Each node in a BST contains: Data/Key: The value stored in the node Left Pointer: Reference to left child Right Pointer: Reference to right child Parent Pointer: (Optional) Reference to parent Tree Terminology Root: Topmost node (no parent) Leaf: Node with no children Height: Longest path from root to leaf Depth: Distance from root to a node Level: All nodes at same depth 📍 BST Structure Example (50) ← Root / \ (30) (70) / \ / \ (20)(40)(60)(80) ← Leaves Left subtree: All values < 50 Right subtree: All values > 50 BST Operations 📥 Insert Operation Start at root If value < current node, go left If value > current node, go right Repeat until finding empty spot Insert new node at empty spot 🔍 Search Operation Start at root If value equals current, found! If value < current, search left If value > current, search right If null reached, not found 🗑️ Delete Operation Three cases: Leaf node: Simply remove One child: Replace with child Two children: Replace with inorder successor ⏱️ Time Complexity Search: O(log n) avg, O(n) worst Insert: O(log n) avg, O(n) worst Delete: O(log n) avg, O(n) worst Traversal: O(n) Note: Worst case O(n) occurs with skewed trees (like a linked list). 💡 Balanced BST AVL Tree Red-Black Tree Guarantee O(log n) operations Tree Traversal Methods 📋 Inorder (Left, Root, Right) Visits nodes in sorted order for BST Example: 20, 30, 40, 50, 60, 70, 80 📋 Preorder (Root, Left, Right) Used for copying the tree Example: 50, 30, 20, 40, 70, 60, 80 📋 Postorder (Left, Right, Root) Used for deleting the tree Example: 20, 40, 30, 60, 80, 70, 50 📋 Level Order (BFS) Visits level by level using a queue Example: 50, 30, 70, 20, 40, 60, 80 📍 Traversal Visualization (50) / \ (30) (70) / \ / \ (20)(40)(60)(80) Inorder: L → Root → R Preorder: Root → L → R Postorder: L → R → Root Level: Top → Bottom Real-World Applications 🗄️ Database Indexing B-trees and B+ trees for fast data retrieval. 📁 File...
Subject: Data Structures with Animation | Chapter: Binary Search Tree