Basic Level (Foundations in C and Simple DSA Concepts)

1. C Programming Fundamentals

• Data types, variables, operators
• Conditional statements (if, switch)
• Loops (for, while, do-while)
• Functions and recursion
• Arrays and strings
• Pointers and memory management (malloc, free)
• Structures and unions

2. Basic Algorithms

• Linear search,
• Binary search
• Selection sort
• Bubble sort
• Insertion sort
• Counting sort
• Fibonacci recursion examples
• Factorial recursion examples

3. Basic Data Structures

• 1d array
• 2d array
• Singly Linked List (Basic operations: insertion, deletion, traversal)

4. Complexity

• constant
• logarithmic
• linear
• quadratic
• cubic

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Intermediate Level (Core DSA Mastery in C)

5. Linked Lists

• Singly Linked List
• Doubly Linked List
• Circular Linked List

6. Stacks and Queues

• Dynamic Array
• Stack
• Queue
• Circular Queue

7. Recursion & Backtracking

• Recursion
• Backtracking

8. Trees

• Binary Tree and Binary Search Tree (BST)
• Tree traversals (Inorder, Preorder, Postorder)
• Height, diameter, leaf nodes
• Basic tree operations (insertion, deletion, search)

9. Sorting Algorithms (Efficient)

• Merge Sort
• Quick Sort
• Heap Sort (introduction to heaps)

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Advanced Level (Optimizations, Graphs, Complex Problems)

10. Advanced Trees

• AVL Trees
• B-Trees and B+ Trees (basics)
• Segment Tree
• Trie (Prefix Tree)

11. Heaps

• Min Heap and Max Heap implementation
• Heapify and Priority Queue using Heaps

12. Graphs

• Representation (Adjacency Matrix, List)
• Traversal (BFS, DFS)
• Topological Sort
• Shortest Path Algorithms (Dijkstra, Bellman-Ford)
• Minimum Spanning Tree (Prim’s, Kruskal’s)

13. Dynamic Programming (DP)

• Memoization vs Tabulation
• Classic problems:
  • Fibonacci
  • 0/1 Knapsack
  • Longest Common Subsequence (LCS)
  • Matrix Chain Multiplication
  • Coin Change

14. Greedy Algorithms

• Activity Selection
• Huffman Encoding
• Fractional Knapsack

14. Bit Manipulation

• Bitwise operations in C
• Applications (checking power of 2, counting bits)

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Learning Tips:

• Practice problems on each topic (LeetCode, HackerRank, Codeforces)
• Implement every data structure from scratch in C
• Use dry run and visualization tools (like VisuAlgo)
• Participate in contests to sharpen algorithmic thinking

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Expert-Level DSA & Problem Solving (Post-Advanced)

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15. Advanced Graph Algorithms

• Strongly Connected Components (Kosaraju’s, Tarjan’s)
• Union-Find / Disjoint Set Union (DSU) with Path Compression
• Lowest Common Ancestor (Binary Lifting)
• Dijkstra with Binary Heap / Fibonacci Heap
• Floyd-Warshall & Johnson’s Algorithm
• Euler Tour (for tree problems)
• Articulation Points & Bridges
• Network Flow:
  • Ford-Fulkerson
  • Edmonds-Karp
  • Dinic’s Algorithm

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16. Advanced Dynamic Programming

• Bitmask DP
• DP on Trees
• DP with Knuth Optimization
• DP with Divide & Conquer Optimization
• DP on Graphs
• Digit DP
• Convex Hull Trick & Li-Chao Segment Tree

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17. Computational Geometry

• Convex Hull (Graham's scan, Andrew’s monotone chain)
• Line Intersection
• Rotating Calipers
• Sweep Line Algorithms
• Point in Polygon
• Closest Pair of Points

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18. Advanced Data Structures

• Segment Trees with Lazy Propagation
• Persistent Segment Trees
• Binary Indexed Tree (Fenwick Tree)
• Suffix Arrays and LCP Array
• Sparse Tables (for RMQ)
• Treaps, Splay Trees, AVL Trees (Self-balancing BSTs)
• Link-Cut Trees
• Heavy-Light Decomposition (HLD)

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19. Mathematics for CS

• Number Theory:

  • Modular Arithmetic
  • Sieve of Eratosthenes
  • Fermat's Little Theorem
  • Extended Euclidean Algorithm

• Combinatorics:

  • Catalan Numbers
  • Inclusion-Exclusion Principle
  • Pigeonhole Principle

• Fast Exponentiation

• Matrix Exponentiation

• FFT (Fast Fourier Transform)

• Chinese Remainder Theorem

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20. Advanced String Algorithms

• KMP Algorithm
• Z-Algorithm
• Aho-Corasick (Multi-pattern matching)
• Rabin-Karp (Hashing)
• Suffix Trees & Suffix Automaton
• Rolling Hash

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21. Competitive Programming Topics

• Game Theory (Grundy Numbers, Nim Game)
• Mo’s Algorithm (Query Optimization)
• Interactive Problems
• Online Algorithms
• Implicit Treaps & Rope Data Structures

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Tools & Practice Platforms

• Codeforces (div 1/2/3 problems)
• AtCoder (ABC, ARC, AGC)
• TopCoder (SRMs)
• USACO / CSES / SPOJ
• CS Academy, Timus Online Judge
• ICPC problems / CodeChef contests

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Suggested Books

• "Competitive Programming" by Halim Brothers
• "Algorithm Design Manual" by Steven Skiena
• "Introduction to Algorithms" (CLRS)
• "Programming Challenges" by Skiena & Revilla
• "Advanced Data Structures" by Peter Brass

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If you're aiming for research, academia, or very high-level optimization problems, you can also explore:

• Parallel Algorithms
• Approximation Algorithms
• Online Algorithms and Real-Time Systems
• Quantum Algorithms (for theoretical interest)

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