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Data Structures and Algorithms Made Easy Based on the book by Narasimha Karumanchi

A structured roadmap for mastering Data Structures, Algorithms, Problem-Solving Patterns, and Coding Interviews.

Table of Contents

Part I - Foundations

1. Algorithm Analysis

  • Time Complexity
  • Space Complexity
  • Asymptotic Notations
    • Big O
    • Omega
    • Theta
  • Recurrence Relations
  • Amortized Analysis

Part II - Linear Data Structures

2. Arrays

  • Array Fundamentals
  • Hashing
  • Two Pointers
  • Sliding Window
  • Prefix Sum
  • Binary Search on Arrays
  • Kadane's Algorithm
  • Matrix Problems

3. Strings

  • String Fundamentals
  • Pattern Matching
  • String Hashing
  • Sliding Window
  • Two Pointers
  • String Manipulation

4. Linked Lists

  • Singly Linked List
  • Doubly Linked List
  • Circular Linked List
  • Fast & Slow Pointer
  • Cycle Detection
  • Linked List Reversal
  • Merge Lists

5. Stacks

  • Stack Fundamentals
  • Expression Evaluation
  • Monotonic Stack
  • Next Greater Element
  • Histogram Problems

6. Queues

  • Queue Fundamentals
  • Circular Queue
  • Deque
  • Priority Queue
  • Sliding Window Maximum

7. Hashing

  • Hash Tables
  • Collision Resolution
  • Open Addressing
  • Chaining
  • Frequency Maps

Part III - Recursion & Backtracking

8. Recursion

  • Recursion Fundamentals
  • Recursion Trees
  • Divide & Conquer

9. Backtracking

  • Decision Trees
  • Permutations
  • Combinations
  • N-Queens
  • Sudoku Solver
  • Word Search

Part IV - Trees

10. Trees

  • Tree Fundamentals
  • DFS Traversals
  • BFS Traversals
  • Tree Properties
  • Tree Views
  • Diameter Problems

11. Binary Search Trees

  • BST Operations
  • Validation
  • Successor & Predecessor
  • Kth Smallest Element

12. Heaps

  • Min Heap
  • Max Heap
  • Heap Operations
  • Heap Sort
  • Top-K Problems

13. Tries

  • Trie Fundamentals
  • Prefix Search
  • Auto Completion
  • Dictionary Problems

Part V - Searching & Sorting

14. Searching

  • Linear Search
  • Binary Search
  • Variations of Binary Search

15. Sorting

  • Bubble Sort
  • Selection Sort
  • Insertion Sort
  • Merge Sort
  • Quick Sort
  • Heap Sort
  • Counting Sort
  • Radix Sort

16. Divide & Conquer

  • Merge Sort
  • Quick Sort
  • Closest Pair
  • Count Inversions
  • Count Range Sum

Part VI - Graphs

17. Graph Fundamentals

  • Graph Representation
  • Adjacency Matrix
  • Adjacency List

18. Graph Traversal

  • BFS
  • DFS
  • Connected Components

19. Shortest Path Algorithms

  • Dijkstra
  • Bellman-Ford
  • Floyd-Warshall

20. Minimum Spanning Tree

  • Kruskal
  • Prim
  • Union Find

21. Advanced Graph Algorithms

  • Topological Sort
  • SCC
  • Articulation Points
  • Bridges

Part VII - Algorithmic Paradigms

22. Greedy Algorithms

  • Activity Selection
  • Job Scheduling
  • Huffman Coding

23. Dynamic Programming

  • DP Fundamentals
  • Memoization
  • Tabulation
  • 1D DP
  • 2D DP
  • Knapsack
  • LIS
  • LCS
  • Matrix DP

24. Bit Manipulation

  • Bit Operations
  • XOR Tricks
  • Bitmask DP

Part VIII - Advanced Data Structures

25. Disjoint Set Union (Union Find)

  • Path Compression
  • Union by Rank
  • Applications

26. Segment Trees

  • Range Queries
  • Lazy Propagation

27. Fenwick Tree (Binary Indexed Tree)

  • Prefix Queries
  • Update Operations

28. Sparse Table

  • Range Minimum Query

29. Advanced Heaps

  • Indexed Heap
  • Fibonacci Heap

Part IX - Interview Patterns

Array Patterns

  • Hashing
  • Two Pointers
  • Sliding Window
  • Prefix Sum
  • Binary Search

String Patterns

  • Hashing
  • KMP
  • Rabin-Karp
  • Sliding Window

Linked List Patterns

  • Fast & Slow Pointer
  • Reversal
  • Merge

Tree Patterns

  • DFS
  • BFS
  • Tree DP
  • LCA

Graph Patterns

  • BFS
  • DFS
  • Shortest Path
  • Union Find

Dynamic Programming Patterns

  • Knapsack
  • Subsequence DP
  • Grid DP
  • State Machine DP

Advanced Patterns

  • Monotonic Stack
  • Monotonic Queue
  • Sweep Line
  • Divide & Conquer
  • Meet in the Middle

Part X - Revision

Complexity Cheat Sheet

Pattern Cheat Sheet

Interview Checklist

Top 100 Interview Problems

Top 200 LeetCode Mapping

FAANG Interview Roadmap

Recommended Study Order

Arrays
→ Strings
→ Linked Lists
→ Stacks
→ Queues
→ Hashing
→ Recursion
→ Trees
→ BST
→ Heaps
→ Searching
→ Sorting
→ Graphs
→ Greedy
→ Backtracking
→ Dynamic Programming
→ Tries
→ Union Find
→ Segment Trees
→ Advanced Graphs

Goal

Master:

  • Data Structures
  • Algorithms
  • Patterns
  • Complexity Analysis
  • Problem Solving

Focus on understanding patterns and trade-offs, not memorizing solutions.



 Can you help me to create notebook and Readme files with basic notes and theory, solution for problem in each notebook for each topic and sub-topic mentioned above in folder structure? I want to have a clear understanding of each concept and be able to apply it in my coding exercises. Additionally, I would like to include examples, code snippets,mini-projects, and practice problems in each notebook to reinforce my learning.