Data Structure and Algorithm (125+ pages)

Full DSA Notes

1. Core definitions of Data Structures and Algorithms

2. The 4-step problem-solving workflow (Understand, Choose Approach, Implement & Optimize, Test & Improve)

3. Abstract Data Type (ADT) definitions as mathematical and structural rules for memory organization

4. Levels of system abstraction and the operational role of interfaces

5. Space Complexity analysis principles

6. Time Complexity classifications (O(1) Constant, O(\log n) Logarithmic, O(n) Linear, O(n \log n) Linearithmic, O(n^2) Quadratic, O(2^n) Exponential)

7. Fundamental searching operations

8. Sorting operations in ascending and descending configurations

9. Structural element insertion operations

10. Data updating and modifying operations

11. Structural element deletion operations

12. Code execution efficiency and resource optimization

13. Software component reusability structures

14. System architectural structural abstraction

15. Core technical engineering application areas (Operating Systems, Databases, Networking, Compiler Design, AI/ML, and Simulations)

16. Primitive Data Structures (int, char, float, double, pointer)

17. Non-Primitive Data Structures and collection clusters

18. Static versus Dynamic allocation memory structures

19. Linear versus Non-Linear storage arrangement models

20. Physical properties of adjacent and contiguous sequential memory allocations

21. Array Indexing configurations (0-based, 1-based, and arbitrary n-based maps)

22. Mathematical 1D address calculation formulas for finding target element byte addresses

23. Multi-dimensional grid configurations (rows and columns representations)

24. Matrix declarations, cell cell-value initializations, and nested iteration loops

25. Row-Major Ordering layout configurations along with its sequential element address calculation formula

26. Column-Major Ordering flat sequential layout mapping configurations

27. Ordered Lists mechanics

28. Singly Linked Lists pointer configurations

29. Stacks architectures (Last-In-First-Out / LIFO sequential pipelines)

30. Queues processing frameworks (First-In-First-Out / FIFO processing blocks)

31. Algorithmic and logic evaluation of mathematical expressions

32. Concurrent execution implementations of Multiple Stacks and Queues within a single array

33. Dynamic Linked Stacks and Linked Queues representation tracks

34. Technical Engineering Application: Executing Polynomial Additions via linear representations

35. Trees (Hierarchical parent-child node structures)

36. Graphs (Interconnected data node and path edge configurations)

37. Hash Tables (Optimized key-value retrieval pairing mapping frameworks)

38. Structural Searching Frameworks: Linear Search versus Binary Search middle-point splits

39. Structural Sorting Frameworks: Operational logic configurations for Bubble Sort, Merge Sort, and Quick Sort

40. Foundational Recursion Core Principles (Base Case conditions, Recursive Cases, and System Call Stack execution frames)

41. Recursion Method Classifications (Direct versus Indirect, Linear versus Tree Recursion, and Tail Space Optimization)

42. Practical Recursion Implementations (Factorial, Fibonacci, GCD, Divide and Conquer phases, and Tree Traversals)

43. Dynamic Programming Mathematical Properties (Overlapping Sub-problems and Optimal Substructure recognition)

44. Dynamic Programming Implementation Approaches (Top-Down Memoization caches and Bottom-Up Tabulation tracking lookups)

45. Standard Dynamic Programming Problems (LCS, LIS, 0/1 Knapsack optimization, Matrix Chain Multiplication, and Floyd-Warshall)

46. Greedy Method Theoretical Framework (The Greedy Choice Property, immediate feasibility, and irreversibility of selections)

47. Greedy Method Implementation Protocols (Sorting-based selections, Priority Queue/Heap tracking, and Mathematical Proofs of Correctness)

48. Standard Greedy Systems Applications (Fractional Knapsack allocation, Kruskal’s/Prim’s Minimum Spanning Trees, Dijkstra’s Shortest Paths, and Huffman Coding)

49. Backtracking Core Mechanics (State Space Tree Generation, Bounding Functions, execution pruning, and stack rollbacks)

50. Backtracking Algorithmic Configurations (Isolating single operational solutions versus enumerating all valid combinations)

51. Standard Backtracking Puzzle and Combinatorial Problems (The N-Queens Problem, Subset Sum optimization, Graph Coloring, Knight’s Tour, and Maze routing paths)