Data Structures and Algorithms (DSA) form the backbone of efficient software development, technical interviews at top companies, and competitive programming. This structured roadmap takes you from absolute basics to advanced topics used in real-world systems and high-level contests.

Module 1 – Basics & Foundations

1. Introduction to DSA

• What is a Data Structure? Why organization matters
• What is an Algorithm? Characteristics of good algorithms
• Importance of DSA in interviews and real systems
• Common real-world applications (search engines, maps, databases, games)

2. Algorithm Analysis

• Time Complexity vs Space Complexity
• Asymptotic notations: Big-O, Big-Omega (Ω), Theta (Θ)
• Best / Average / Worst case analysis
• Amortized analysis (with simple examples)

3. Recursion

Understanding the call stack, base case, recursive case, tail recursion optimization.

factorial(n):
    if n == 0 or n == 1:
        return 1
    return n * factorial(n-1)

Module 2 – Arrays & Strings

Module 3 – Searching & Sorting

Module 4 – Linked Lists

• Singly, Doubly, Circular Linked List
• Reverse a Linked List (iterative + recursive)
• Detect cycle – Floyd’s Cycle-Finding (Hare & Tortoise)
• Merge two sorted lists
• Remove Nth node from end
• Find intersection point of two lists

Module 5 – Stack & Queue

Module 6 – Hashing

• Hash functions and properties
• Collision resolution: Chaining, Open Addressing
• Load factor and rehashing
• Applications: frequency counting, two-sum, subarray sum, longest substring without repeating characters

Module 7 – Trees

Module 8 – Heap & Priority Queue

• Min Heap / Max Heap & Heapify
• Priority Queue operations
• K largest / K smallest elements
• Find median in a stream

Module 9 – Graphs

• Representation: Adjacency List vs Matrix
• BFS, DFS, Cycle detection
• Shortest Path: Dijkstra, Bellman-Ford, Floyd-Warshall
• Minimum Spanning Tree: Prim’s, Kruskal’s + Union-Find
• Topological Sort, Strongly Connected Components (Kosaraju, Tarjan)

Module 10 – Greedy Algorithms

• Activity Selection Problem
• Fractional Knapsack
• Job Sequencing with Deadline
• Interval Scheduling / Merging
• Huffman Coding (basic idea)

Module 11 – Dynamic Programming (Most Important)

• Memoization vs Tabulation
• 1D DP → 2D DP → Multi-dimensional DP
• Classic problems: 0/1 Knapsack, Unbounded Knapsack, LIS, LCS
• Matrix Chain Multiplication, Coin Change, Edit Distance
• DP on Trees, DP with Bitmask, State compression

Module 12 – Backtracking

• N-Queens Problem
• Sudoku Solver
• Subset Sum / Subsets generation
• Permutations & Combinations
• Combination Sum series

Module 13 – Bit Manipulation

• Bitwise operators & tricks
• XOR based problems (single number, missing number)
• Check power of 2, count set bits
• Generate all subsets using bitmask

Module 14 – Advanced Competitive Programming Topics

• Meet in the Middle
• Mo’s Algorithm
• Square Root Decomposition
• Heavy-Light Decomposition
• Network Flow basics (Ford-Fulkerson, Edmonds-Karp)
• Bipartite Matching, Game Theory introduction

Happy Learning! — from beginner concepts to contest-level mastery