Data Structures & Algorithms

1. Introduction to Data Structures and Algorithms

  • 1.1) Definition and Importance of Data Structures

  • 1.2) Types of Data Structures

  • 1.3) Abstract Data Types (ADT)

  • 1.4) Algorithms – Definition, Characteristics

  • 1.5) Time and Space Complexity

  • 1.6) Asymptotic Notations: Big-O, Omega, Theta

  • 1.7) Recursion and its Applications

  • 1.8) Algorithm Analysis – Best, Worst, Average Case

 

2. Arrays

  • 2.1) Representation and Indexing

  • 2.2) One-Dimensional Arrays

  • 2.3) Multi-Dimensional Arrays

  • 2.4) Operations: Traversal, Insertion, Deletion, Searching

  • 2.5) Applications (e.g., Matrix Operations, Polynomial Representation)

 

3. Strings

  • 3.1) String Representation

  • 3.2) String Operations (Concatenation, Comparison, Substring)

  • 3.3) Pattern Matching Algorithms (Naïve, KMP, Rabin-Karp)

 

4. Linked Lists

  • 4.1) Singly Linked List: Operations and Implementation

  • 4.2) Doubly Linked List

  • 4.3) Circular Linked List

  • 4.4) Applications: Polynomial Arithmetic, Dynamic Memory Allocation

 

5. Stacks

  • 5.1) Stack ADT and Representation

  • 5.2) Operations: Push, Pop, Peek

  • 5.3) Stack Applications: Expression Evaluation, Recursion Conversion (Infix to Postfix), Balanced Parentheses

 

6. Queues

  • 6.1) Queue ADT and Implementation

  • 6.2) Circular Queue

  • 6.3) Deque (Double-Ended Queue)

  • 6.4) Priority Queue

  • 6.5) Applications: CPU Scheduling, Buffer Handling

 

7. Trees

  • 7.1) Terminologies: Node, Degree, Depth, Height, etc.

  • 7.2) Binary Trees and Representations

  • 7.3) Tree Traversals (Inorder, Preorder, Postorder)

  • 7.4) Binary Search Trees (BST)

  • 7.5) AVL Trees (Height-Balanced Trees)

  • 7.6) B-Trees and B+ Trees

  • 7.7) Heap and Heap Sort

  • 7.8) Trie and Applications

 

8. Graphs

  • 8.1) Graph Terminology and Representations (Adjacency Matrix/List)

  • 8.2) Graph Traversal: BFS and DFS

  • 8.3) Minimum Spanning Tree (Prim’s and Kruskal’s Algorithms)

  • 8.4) Shortest Path Algorithms: Dijkstra, Bellman-Ford

  • 8.5) Topological Sort

  • 8.6) Applications: Networking, Map Navigation

 

9. Hashing

  • 9.1) Hash Functions and Techniques

  • 9.2) Collision Resolution Strategies (Chaining, Open Addressing)

  • 9.3) Applications: Symbol Tables, Caching

 

10. Sorting Algorithms

  • 10.1) Bubble Sort

  • 10.2) Selection Sort

  • 10.3) Insertion Sort

  • 10.4) Merge Sort

  • 10.5) Quick Sort

  • 10.6) Heap Sort

  • 10.7) Radix Sort, Counting Sort, Bucket Sort

  • 10.8) Comparison of Sorting Algorithms

 

11. Searching Algorithms

  • 11.1) Linear Search

  • 11.2) Binary Search

  • 11.3) Interpolation Search

  • 11.4) Search in Rotated Sorted Array

 

12. Advanced Topics (Optional / Elective Modules)

  • 12.1) Greedy Algorithms

  • 12.2) Divide and Conquer Algorithms

  • 12.3) Dynamic Programming

  • 12.4) Backtracking

  • 12.5) Branch and Bound

  • 12.6) Amortized Analysis

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