Tree Data Structures
Master hierarchical data organization with Binary Trees, BST, AVL Trees. Learn tree traversal algorithms, self-balancing techniques, and real-world applications for efficient searching and sorting.
Binary Search Tree Implementation
class TreeNode {
constructor(value) {
this.value = value;
this.left = null;
this.right = null;
}
}
class BinarySearchTree {
constructor() {
this.root = null;
}
insert(value) {
const newNode = new TreeNode(value);
if (!this.root) {
this.root = newNode;
return this;
}
let current = this.root;
while (true) {
if (value === current.value) return undefined;
if (value < current.value) {
if (!current.left) {
current.left = newNode;
return this;
}
current = current.left;
} else {
if (!current.right) {
current.right = newNode;
return this;
}
current = current.right;
}
}
}
search(value) {
if (!this.root) return false;
let current = this.root;
while (current) {
if (value === current.value) return true;
if (value < current.value) {
current = current.left;
} else {
current = current.right;
}
}
return false;
}
// Inorder Traversal (DFS)
inorder(node = this.root, result = []) {
if (node) {
this.inorder(node.left, result);
result.push(node.value);
this.inorder(node.right, result);
}
return result;
}
}
Why Learn Tree Data Structures?
Hierarchical Data
Master organization of hierarchical data like file systems and organization charts
Efficient Searching
BST provides O(log n) search complexity for balanced trees
Balanced Structures
Learn self-balancing trees (AVL) for optimal performance
Real Applications
Used in databases, compilers, file systems, and game AI
Course Curriculum
Module 1: Introduction to Trees
- Definition of a Tree
- Tree Terminology (Node, Root, Parent, Child)
- Leaf Nodes & Height/Depth
- Applications of Trees
- Tree vs Graph Differences
Module 2: Binary Trees
- Binary Tree Definition
- Full, Complete & Perfect Binary Trees
- Linked List & Array Representation
- Basic Operations (Insertion, Deletion)
- Searching in Binary Trees
Module 3: Binary Search Trees (BST)
- BST Property & Definition
- Search, Insert, Delete Operations
- Time Complexity Analysis
- Advantages & Disadvantages
- Applications: Dictionary, Priority Queue
Module 4: AVL Trees
- Need for Self-Balancing Trees
- Balance Factor Concept
- Rotations (Left, Right, Left-Right, Right-Left)
- Insertion & Deletion Examples
- Time Complexity Analysis
Module 5: Tree Traversal
- Depth-First Traversal (DFS)
- Inorder, Preorder, Postorder
- Breadth-First Traversal (BFS)
- Level Order Traversal
- Applications: Expression Trees, Sorting
Types of Binary Trees
Full Binary Tree
Every node has 0 or 2 children
Complete Binary Tree
All levels completely filled except last
Perfect Binary Tree
All internal nodes have 2 children
Balanced Tree
Height difference ≤ 1 for all nodes
Practical Projects
File System Browser
- Tree-based directory navigation
- Implement file operations
- Search files efficiently
- Display hierarchical structure
Expression Evaluator
- Parse mathematical expressions
- Build expression trees
- Evaluate using tree traversal
- Handle parentheses & operators
Auto-Complete System
- Trie data structure implementation
- Prefix-based searching
- Efficient word suggestions
- Real-time updates
Master Tree Data Structures
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