Complete DSA Roadmap for Product-Based Companies

This Data Structures and Algorithms (DSA) roadmap is a step-by-step guide to mastering algorithms and data structures, which will help you perform well in coding interviews at top product-based companies. It is divided into seven phases, covering all the essential topics and their subtopics in detail.

Phase 1: Introduction & Foundation (Day 1-5)

1. Introduction to Data Structures & Algorithms

  • What is a Data Structure?

    • A data structure is a collection of data values and a way of organizing them.
    • Importance in Problem Solving: Organizing data efficiently allows operations like searching, inserting, and deleting to be performed efficiently.

  • What is an Algorithm?

    • An algorithm is a well-defined procedure to solve a problem.
    • Complexity Analysis: Understanding the time complexity (how long the algorithm takes to run) and space complexity (how much memory it uses).

2. Time Complexity & Space Complexity

  • Big-O Notation: Understanding performance in terms of time and space.

    • O(1): Constant time.
    • O(n): Linear time.
    • O(log n): Logarithmic time.
    • O(n²): Quadratic time.
    • O(n log n): Linearithmic time.

  • Understanding Space Complexity: Analyzing how much memory is used.

    • Auxiliary Space: Extra space used by an algorithm apart from the input data.
    • Stack Space: Memory used for recursive calls.

Phase 2: Core Data Structures and Algorithms (Day 6-20)

3. Arrays & Basic Sorting Algorithms (Day 6-8)

  • Arrays:

    • Definition: A collection of elements identified by index.
    • Operations: Insertion, Deletion, Access, Traversal.
    • Common Problems:
    • Find maximum and minimum element.
    • Reverse an array.
    • Rotate an array.

  • Basic Sorting Algorithms:

    • Bubble Sort: Simple, but inefficient (O(n²)).
    • Selection Sort: Efficient in space, but O(n²) time complexity.
    • Insertion Sort: Efficient for small arrays but O(n²) in worst case.

  • Advanced Sorting Algorithms (Later):

    • Merge Sort (O(n log n)).
    • Quick Sort (O(n log n)).

4. Strings (Day 9-10)

  • String Basics:

    • Strings are an array of characters.
    • Operations: Concatenate, Compare, Substring, Slice.

  • Common String Problems:

    • Palindrome Check: Is a string the same forwards and backwards?
    • Anagram Check: Are two strings anagrams of each other?
    • Substring Search: Naive vs KMP (Knuth-Morris-Pratt) Algorithm.

5. Stacks & Queues (Day 11-13)

  • Stack:

    • Definition: A data structure following LIFO (Last-In-First-Out) order.
    • Operations: Push, Pop, Peek, isEmpty.
    • Applications: Expression evaluation, Backtracking.
    • Common Problems:
    • Balanced parentheses.
    • Reverse a stack using recursion.

  • Queue:

    • Definition: A data structure following FIFO (First-In-First-Out) order.
    • Operations: Enqueue, Dequeue, Front, Rear.
    • Applications: BFS (Breadth-First Search), Scheduling.

  • Circular Queue: A queue where the last position is connected back to the first position.

6. Linked Lists (Day 14-16)

  • Types of Linked Lists:

    • Singly Linked List: Each node points to the next node.
    • Doubly Linked List: Each node has pointers to both next and previous nodes.
    • Circular Linked List: Last node points back to the first node.

  • Operations:

    • Insertion, Deletion, Traversal, Reversal.

  • Common Problems:

    • Detecting a cycle in the list (Floyd’s Tortoise and Hare algorithm).
    • Finding the middle element of the linked list.
    • Merging two sorted linked lists.

Phase 3: Advanced Data Structures and Algorithms (Day 17-40)

7. Hashing (Day 17-18)

  • Hash Map:

    • Definition: A collection of key-value pairs for fast retrieval.
    • Hash Function: Maps keys to indexes in the hash table.

  • Applications:

    • Anagram checking.
    • Find duplicates in an array.

  • Common Problems:

    • Find the first non-repeating character in a string.
    • Pair with sum equal to a given value.

8. Trees (Day 19-23)

  • Binary Tree:

    • Definition: A tree where each node has at most two children.
    • Traversal Methods: Pre-order, In-order, Post-order, Level-order (BFS).

  • Binary Search Tree (BST):

    • Definition: A binary tree where left child is smaller, and right child is larger than the parent.
    • Operations: Insert, Delete, Search.

  • Advanced Tree Structures:

    • AVL Tree: Self-balancing binary search tree.
    • Segment Tree: Used for range queries (Sum, Min, Max).
    • Fenwick Tree (Binary Indexed Tree): Efficient for cumulative frequency tables.

  • Common Problems:

    • Finding the Lowest Common Ancestor (LCA) of two nodes.
    • Checking if a tree is balanced (height difference between left and right subtree).

9. Heaps (Day 24-25)

  • Heap:

    • Min-Heap: Root is the minimum element.
    • Max-Heap: Root is the maximum element.

  • Heap Operations:

    • Insert: Insert an element while maintaining heap properties.
    • Delete: Remove the root element.
    • Heapify: Rearrange the heap to maintain the heap property.

  • Applications:

    • Priority Queue: A queue where elements are dequeued based on priority.
    • Heap Sort.

10. Graphs (Day 26-30)

  • Graph Representation:

    • Adjacency Matrix: Matrix representation of graph.
    • Adjacency List: Array of lists (space-efficient for sparse graphs).

  • Graph Traversals:

    • DFS (Depth-First Search): Explore as far as possible along each branch.
    • BFS (Breadth-First Search): Explore all nodes at the present depth level before moving on to nodes at the next depth level.

  • Graph Algorithms:

    • Dijkstra’s Algorithm: Shortest path in a weighted graph.
    • Bellman-Ford Algorithm: Handles graphs with negative weights.
    • Floyd-Warshall Algorithm: All-pairs shortest paths.

  • Common Problems:

    • Cycle Detection: Detect a cycle in a directed or undirected graph.
    • Topological Sort: Linear ordering of vertices in a Directed Acyclic Graph (DAG).

Phase 4: Advanced Algorithmic Techniques (Day 31-50)

11. Divide and Conquer (Day 31-33)

  • Concept: Divide the problem into subproblems, solve them independently, and combine the results.

  • Algorithms:

    • Merge Sort: Divide the array into two halves, recursively sort them, and merge.
    • Quick Sort: Divide the array based on a pivot and sort recursively.
    • Binary Search: Search a sorted array by dividing it into halves.

12. Dynamic Programming (Day 34-40)

  • Concept: Break the problem into overlapping subproblems and solve them optimally by storing intermediate results.

  • Common Problems:

    • Fibonacci Sequence.
    • Knapsack Problem (0/1 Knapsack, Unbounded Knapsack).
    • Longest Common Subsequence (LCS).
    • Coin Change Problem.

13. Greedy Algorithms (Day 41-43)

  • Concept: Make the locally optimal choice at each stage, hoping to find a global optimum.

  • Algorithms:

    • Kruskal’s Algorithm: Minimum Spanning Tree.
    • Prim’s Algorithm: Minimum Spanning Tree.
    • Activity Selection: Select the maximum number of non-overlapping activities.

14. Backtracking (Day 44-45)

  • Concept: Try all possible solutions by making decisions one at a time, undoing them if they don’t lead to a solution.

  • Common Problems:

    • N-Queens Problem.
    • Sudoku Solver.
    • Permutations.
    • Combination Sum.

Phase 5: Advanced Data Structures & Algorithm Design (Day 46-60)

15. Advanced Data Structures (Day 46-50)

  • Trie (Prefix Tree):

    • Efficient for storing strings and performing prefix searches.

  • Segment Tree:

    • Efficient for answering range queries (Sum, Min, Max).

  • Fenwick Tree (Binary Indexed Tree):

    • Efficient for range sum queries and point updates.

  • Union-Find (Disjoint Set Union - DSU):

    • Efficiently keeps track of connected components in a graph.

16. Advanced Graph Algorithms (Day 51-55)

  • Network Flow Algorithms:
    • Ford-Fulkerson Algorithm: Maximum Flow in a flow network.
    • Edmonds-Karp Algorithm: Implementation of Ford-Fulkerson using BFS.

Phase 6: Problem Solving & Practice (Day 56-70)

17. Problem Solving Practice (Day 56-60)

  • Platforms to Practice:

    • LeetCode, GeeksforGeeks, HackerRank, CodeForces.

  • Problem-Solving Patterns:

    • Sliding Window, Two Pointers, Fast and Slow Pointers.
    • Dynamic Programming, Greedy Algorithms, Backtracking.

18. Mock Interviews (Day 61-70)

  • Simulate Interview Conditions: Solve problems in a timed environment.
  • Prepare for System Design: Solve problems like designing a URL shortening service, chat application, etc.

Phase 7: System Design & Final Preparation (Day 71-80)

19. System Design (Day 71-80)

  • Learn About Distributed Systems:

    • Load Balancing, Caching, Database Design (SQL/NoSQL), Microservices, Horizontal Scaling.

  • Real-World System Design:

    • Design systems like chat application, file storage system, social media backend.

Final Tips for Success:

  1. Consistency: Solve 2-3 problems daily to build muscle memory.
  2. Understand Solutions: Don’t just code—focus on understanding the optimal solutions.
  3. Participate in Mock Interviews: Prepare under real-time conditions.
  4. System Design: Practice with real-world scenarios to ace system design interviews.

Good luck, stay consistent, and you’ll be well-prepared for your interviews! 💪