Here’s a detailed course outline for learning Data Structures and Algorithms (DSA):

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📌 Module 1: Introduction to DSA & Complexity Analysis

• Importance of DSA in problem-solving
• Big-O Notation, Omega (Ω), and Theta (Θ)
• Best, Worst, and Average Case Complexity
• Time vs. Space Complexity

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📌 Module 2: Basic Data Structures

1. Arrays

• Static vs. Dynamic Arrays
• Array Operations: Insertion, Deletion, Searching
• Two-pointer technique
• Sliding Window technique

2. Strings

• String operations and manipulation
• Pattern Matching Algorithms (KMP, Rabin-Karp)
• Anagram and Palindrome problems

3. Linked Lists

• Singly, Doubly, and Circular Linked Lists
• Operations: Insert, Delete, Reverse, Merge, Detect Loop
• Fast and Slow Pointer Approach

4. Stacks & Queues

• Stack: Implementation (Array/Linked List), Applications (Undo, Parentheses Matching)
• Queue: Implementation, Circular Queue
• Deque and Priority Queue

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📌 Module 3: Searching and Sorting Algorithms

1. Searching Algorithms

• Linear Search & Binary Search
• Variants: First/Last occurrence, Count occurrences

2. Sorting Algorithms

• Bubble Sort, Selection Sort, Insertion Sort
• Merge Sort, Quick Sort, Heap Sort, Counting Sort
• Sorting Complexities and Best Use Cases

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📌 Module 4: Advanced Data Structures

1. Hashing

• Hash Tables and Hash Maps
• Collision Handling Techniques
• Applications in Caching (LRU Cache)

2. Trees

• Binary Trees: Traversals (Preorder, Inorder, Postorder)
• Binary Search Tree (BST): Insert, Delete, Search
• AVL Tree, Red-Black Tree (Basic understanding)

3. Heaps

• Min Heap & Max Heap
• Heap Sort
• Priority Queues and Applications

4. Graphs

• Graph Representation: Adjacency Matrix & List
• BFS, DFS
• Shortest Path Algorithms (Dijkstra’s, Floyd-Warshall)
• Minimum Spanning Tree (Kruskal’s, Prim’s)

5. Tries

• Prefix Trees
• Auto-Complete & Word Search

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📌 Module 5: Recursion & Backtracking

• Recursion Basics and Stack Memory
• Backtracking: N-Queens, Sudoku Solver
• Subset and Permutation Problems

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📌 Module 6: Dynamic Programming (DP)

• Memoization vs. Tabulation
• Fibonacci, Knapsack Problem
• Longest Common Subsequence (LCS)
• DP on Trees & DP on Graphs

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📌 Module 7: Advanced Topics & Problem Solving

1. Greedy Algorithms

• Activity Selection, Huffman Encoding
• Interval Scheduling

2. Bit Manipulation

• XOR Tricks, Power of Two, Count Set Bits

3. Segment Trees & Fenwick Trees

• Range Queries (RMQ, Lazy Propagation)

4. Disjoint Set Union (DSU)

• Union-Find Algorithm
• Path Compression & Rank

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📌 Module 8: Competitive Programming & System Design Basics

• Solve problems on LeetCode, Codeforces, CodeChef
• Participate in coding contests
• Learn how to handle scalability in real-world applications

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🔹 Project & Practice Plan

• Solve 100+ problems covering all topics
• Take part in contests to improve speed
• Build a small DSA-based project (e.g., Spell Checker using Trie, Graph-based Route Finder)

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This structured roadmap ensures step-by-step mastery of DSA. Would you like specific resources or practice problems for each module? 😊