Data Structures and Algorithms Course

1. Introduction to Data Structures and Algorithms

• Definition of Data Structures and Algorithms
• Importance in Problem Solving and Optimization
• Complexity Analysis (Time and Space Complexity)
• Big O Notation, Omega, Theta

2. Mathematics for DSA

• Recursion and Recursive Algorithms
• Time Complexity of Recursion (Master Theorem, Recursion Trees)
• Probability and Combinatorics in Algorithms
• Modular Arithmetic, GCD, and Prime Numbers

3. Arrays

• Definition and Types (1D, 2D, Multi-dimensional)
• Basic Operations (Insertion, Deletion, Traversal)
• Techniques: Sliding Window, Two-pointer technique
• Problems: Kadane’s Algorithm (Maximum Subarray), Searching and Sorting Arrays

4. Linked Lists

• Singly Linked List, Doubly Linked List, Circular Linked List
• Operations: Insertion, Deletion, Reversal
• Detecting and Removing Cycles
• Applications and Problems: Merge Two Sorted Lists, Detecting Cycle (Floyd's Tortoise and Hare)

5. Stacks and Queues

• Stack: LIFO Structure, Operations (Push, Pop, Peek)
• Queue: FIFO Structure, Operations (Enqueue, Dequeue)
• Special Queues: Circular Queue, Deque (Double-Ended Queue), Priority Queue
• Applications: Balanced Parentheses, Stock Span Problem, LRU Cache

6. Hashing

• Hash Functions and Hash Tables
• Collision Resolution Techniques: Chaining, Open Addressing
• Applications: Frequency Counting, Caching, Anagram Problems, Subarrays with Zero Sum

7. Strings

• Basic String Operations (Reversal, Palindrome, Anagram)
• Pattern Searching Algorithms: Naive Search, KMP Algorithm, Rabin-Karp Algorithm
• String Matching Problems: Longest Common Subsequence, Longest Palindromic Substring
• String Compression and Transformation Techniques

8. Sorting Algorithms

• Basic Sorting: Bubble Sort, Selection Sort, Insertion Sort
• Efficient Sorting: Merge Sort, Quick Sort, Heap Sort
• Counting Sort, Radix Sort, Bucket Sort
• Time Complexity and Space Complexity of Sorting Algorithms

9. Searching Algorithms

• Linear Search, Binary Search
• Binary Search Variants: First/Last Occurrence, Peak Element Search
• Ternary Search and Jump Search
• Applications: Search in Rotated Sorted Array, Median of Two Sorted Arrays

10. Recursion and Backtracking

• Basic Recursion Techniques: Base Case, Recursive Case
• Recursion vs Iteration
• Backtracking: N-Queens Problem, Subset Sum Problem, Sudoku Solver
• Memoization and Dynamic Programming

11. Trees

• Binary Trees: Representation and Traversal (Inorder, Preorder, Postorder)
• Binary Search Tree (BST): Insertion, Deletion, Searching
• Balanced Trees: AVL Tree, Red-Black Tree
• Trie (Prefix Tree) and its Applications in String Searching
• Heaps: Min-Heap, Max-Heap, Heap Sort

12. Graph Algorithms

• Graph Representation: Adjacency List, Adjacency Matrix
• Graph Traversal: Depth-First Search (DFS), Breadth-First Search (BFS)
• Shortest Path Algorithms: Dijkstra's Algorithm, Bellman-Ford Algorithm
• Minimum Spanning Tree: Kruskal’s Algorithm, Prim’s Algorithm
• Topological Sorting, Detecting Cycles in a Graph, Strongly Connected Components

13. Greedy Algorithms

• Introduction to Greedy Algorithms
• Problems: Activity Selection, Fractional Knapsack, Job Sequencing with Deadlines
• Huffman Encoding Algorithm
• Greedy vs Dynamic Programming

14. Dynamic Programming (DP)

• Introduction to DP: Memoization, Tabulation
• Classic DP Problems: Fibonacci, Knapsack, Longest Increasing Subsequence
• DP on Trees and Graphs
• Optimization Techniques: Bitmask DP, Matrix Chain Multiplication, DP with State Compression

15. Advanced Data Structures

• Segment Trees, Fenwick Tree (Binary Indexed Tree)
• Union-Find (Disjoint Set Union)
• Sparse Tables, Suffix Arrays
• Heavy-Light Decomposition

16. Advanced Topics

• Bit Manipulation and Applications
• Divide and Conquer Algorithms
• Randomized Algorithms
• Computational Geometry (Convex Hull, Line Intersection)

17. Problem Solving and Optimization

• Analyzing Problems for Data Structure Selection
• Solving Real-World Problems
• Competitive Programming Techniques (Problem Analysis, Brute Force vs Optimal Solutions)
• Practice Problems (LeetCode, Codeforces, HackerRank)