Heap DSA Tutorial - Interactive Learning
Master Heap - DSA Learning Platform 🏔️ Master Heap Priority Queue Complete Binary Tree Learn Heap operations with bubble-up, heapify, and complete tree visualization 📖 Understanding Heap Introduction Max & Min Heap Array Representation Operations Applications What is a Heap? A Heap is a specialized complete binary tree that satisfies the heap property. It's commonly used to implement priority queues, where we need quick access to the maximum or minimum element. Unlike BST, a heap doesn't maintain a sorted order between siblings. Instead, it only guarantees the relationship between parent and children nodes. Heaps are stored as arrays for efficiency, using simple index calculations to find parent and child nodes without needing explicit pointers. 🔑 Key Properties Complete Binary Tree structure Heap property (parent-child relationship) Efficient array representation O(1) access to max/min element O(log n) insert and extract Used in Priority Queues & Heap Sort Max Heap vs Min Heap 📈 Max Heap Parent node is greater than or equal to its children parent ≥ children Root contains the maximum value 📉 Min Heap Parent node is less than or equal to its children parent ≤ children Root contains the minimum value Both types use the same algorithms, just with reversed comparisons. Choose based on whether you need quick access to the largest or smallest element. 📍 Visual Comparison Max Heap: Min Heap: (90) (10) / \ / \ (80) (70) (20) (30) / \ / \ / \ / \ (50)(60)(40)(30) (50)(60)(40)(80) Root = Maximum Root = Minimum Array Representation Heaps are stored in arrays using level-order traversal. This provides efficient memory usage and simple parent-child calculations. Index Formulas (0-based) Parent: (i - 1) / 2 Left Child: 2*i + 1 Right Child: 2*i + 2 ✅ Advantages No pointer overhead, cache-friendly, simple index math 📊 Complete Tree All levels filled except possibly the last (filled left to right) 📍 Tree to Array Mapping Tree View: (50) ← index 0 / \ (30) (40) ← index 1, 2 / \ / (10)(20)(35) ← index 3, 4, 5 Array View: ┌────┬────┬────┬────┬────┬────┐ │ 50 │ 30 │ 40 │ 10 │ 20 │ 35 │ └────┴────┴────┴────┴────┴────┘ 0 1 2 3 4 5 Parent of index 4 = (4-1)/2 = 1 → value 30 Children of index 1 = 2*1+1=3, 2*1+2=4 → values 10, 20 Heap Operations 📥 Insert (Bubble Up) Add element at the end of array Compare with parent Swap if heap property violated Repeat until root or property satisfied 📤 Extract Max/Min (Heapify Down) Save root value (max/min) Move last element to root Compare root with children Swap with larger/smaller child Repeat until leaf or satisfied 🔨 Build Heap Start from last non-leaf node, heapify each node going up. Time: O(n) ⏱️ Time Complexity Insert: O(log n) Extract Max/Min: O(log n) Peek Max/Min: O(1) Build Heap: O(n) Heap Sort: O(n log n) 📊 Space Complexity Array storage: O(n) No extra pointers needed! Real-World Applications 🎯 Priority Queues Task scheduling, event-driven simulations, CPU scheduling 📊 Heap Sort In-place sorting with guaran...
Subject: Data Structures with Animation | Chapter: Heap Data Structure