Data Structures & Algorithms
DSA Part-1
- Introduction to Data Structures
- Asymptotic Notations: Big-O, Omega, and Theta Notations
- Time Complexity and Space Complexity Analysis of Algorithms
- 1D Arrays: Memory Representation and Address Calculation
- 2D Arrays: Row-Major and Column-Major Order Formulas and Numericals
- Array Operations: Traversal, Insertion, and Deletion with Algorithms
- Sparse Matrix: Triplet Representation and Linked Representation
- String Operations, Memory Storage, and Pattern Matching Basics
- Linear Search Algorithm and Complexity Analysis
- Binary Search Algorithm (Iterative and Recursive)
- Bubble Sort Algorithm and Optimization
- Selection Sort Algorithm and Step-by-Step Trace
- Insertion Sort Algorithm and In-Place Analysis
- Merge Sort Algorithm (Divide and Conquer Approach)
- Quick Sort Algorithm and Partitioning Methods
- Counting Sort Algorithm (Non-Comparison Sorting)
- Radix Sort Algorithm and Bucket Distribution
DSA Part-2
- Singly Linked List: Concept and Memory Allocation
- Singly Linked List: Insertion Operations
- Singly Linked List: Deletion Operations
- Singly Linked List: Reversal and Search Operations
- Doubly Linked List: Node Structure and Traversal
- Doubly Linked List: Insertion and Deletion Operations
- Circular Singly Linked List: Concept and Operations
- Circular Doubly Linked List: Concept and Operations
- Header Linked List: Grounded and Circular Header Lists
- Polynomial Representation and Addition using Linked List
DSA Part-3
- Stack Data Structure: Array Implementation
- Stack Implementation using Linked List
- Infix, Prefix, and Postfix Notations
- Infix to Postfix Conversion using Stack
- Infix to Prefix Conversion using Stack
- Evaluation of Postfix Expression using Stack
- Recursion and System Stack (Tower of Hanoi)
- Linear Queue: Array Implementation and Operations
- Drawbacks of Linear Queue and Memory Wastage
- Circular Queue: Array Implementation and Condition Checks
- Queue Implementation using Linked List
- Double-Ended Queue (Deque): Input and Output-Restricted
- Priority Queue: Concept, Array and Heap Representation
DSA Part-4
- Tree Data Structure: Terminology and Basic Concepts
- Binary Trees: Types and Properties
- Binary Tree Traversals: Inorder, Preorder, and Postorder
- Level Order Traversal of Binary Tree
- Binary Search Tree (BST): Concept and Search Operation
- Binary Search Tree (BST): Insertion and Deletion Operations
- AVL Tree: Concept and Balance Factor
- AVL Tree Rotations: LL, RR, LR, and RL Rotations
- Binary Heap: Min-Heap and Max-Heap Properties
- Heap Operations: Heapify, Insertion, and Deletion
- B-Tree: Properties, Structure, and Insertion
- B+ Tree: Structure and Comparison with B-Tree
DSA Part-5
- Graph Data Structure: Terminology and Types
- Graph Representation: Adjacency Matrix and Adjacency List
- Breadth First Search (BFS) Algorithm for Graphs
- Depth First Search (DFS) Algorithm for Graphs
- Hashing: Hash Tables and Hash Functions
- Collision Resolution: Open Addressing Techniques
- Collision Resolution: Separate Chaining Method
B+ Tree: Structure and Comparison with B-Tree
B+ Tree B-Tree ka ek highly popular variation hai jo modern relational database management systems (jaise MySQL InnoDB, PostgreSQL) aur filesystem storage engines me primary indexing structure ke roop me use hota hai.
Key Architectural Differences
- Data Records Only in Leaves: B-Tree me actual data records internal nodes aur leaf nodes dono me store hote the. B+ Tree me internal nodes sirf routing keys / index pointers hold karte hain; actual data records exclusively Leaf Nodes me store hote hain.
- Linked Leaves: B+ Tree ke saare leaf nodes aapas me ek Doubly / Singly Linked List ke zariye connected hote hain. Isse sequential range queries (e.g.
WHERE age BETWEEN 20 AND 30) lightning fast ho jaati hain bina tree ko bar-bar traverse kiye!
Internal Nodes: [ 25 | 50 ]
/ | \
Leaf Nodes: [10, 20] <===> [25, 30, 45] <===> [50, 60, 75]
(Data records) (All leaves linked sequentially for O(k) range scan!)
Comparison Table: B-Tree vs B+ Tree
| Parameter | B-Tree | B+ Tree |
|---|---|---|
| Data Location | Internal aur leaf nodes dono me | Exclusively leaf nodes me |
| Sequential Access | Slow (Inorder tree traversal needed) | Extremely fast via linked leaf chain |
| Node Capacity (Fan-out) | Lower (data records space lete hain) | Higher (internal nodes me sirf keys hoti hain) |
| Search Time | Variable (root ya internal node par mil sakta hai) | Uniform / Constant depth (always reaches leaf) |
Agli post me hum Graphs start karenge: Graph Data Structure: Terminology and Types.