Time & Space Complexity Thinking

Foundations

Understanding the basics of complexity analysis.

1. Why Complexity Matters

• Performance measurement basics
• Input size concept (N)
• Growth rate understanding
• Machine-independent analysis

2. Types of Complexity

• Time complexity
• Space complexity
• Auxiliary space
• Input space

3. Asymptotic Notations

• Big-O notation
• Big-Theta notation
• Big-Omega notation

Common Complexity Orders

Recognizing and comparing complexity classes.

4. Complexity Classes

• O(1)
• O(log N)
• O(N)
• O(N log N)
• O(N²)
• O(2ⁿ)
• O(N!)

5. Growth Comparison

• Constant vs Linear vs Quadratic
• Logarithmic growth intuition
• Polynomial vs Exponential

Complexity Analysis Basics

How to analyze code and determine complexity.

6. Counting Operations

• Loop analysis
• Nested loops
• Sequential statements
• Conditional branches

7. Best, Average, Worst Case

• Case analysis
• Trade-offs

Data Structure Complexity

Understanding complexity of common data structures.

8. Arrays

• Access
• Insert
• Delete
• Search

9. Strings

• Traversal
• Pattern operations

10. Hash Tables

• Average vs worst case

11. Stacks & Queues

12. Linked Lists

13. Trees

• Height-based complexity
• Balanced vs unbalanced trees

14. Heaps

15. Graphs

• BFS
• DFS

Recursion & Mathematical Thinking

Analyzing recursive and mathematical algorithms.

16. Recursion Analysis

• Recursive trees
• Recurrence relations
• Master theorem (basic)

17. Divide & Conquer

• Binary search
• Merge sort
• Quick sort

Optimization Thinking

Techniques for improving algorithm complexity.

18. Reducing Complexity

• Brute force → optimized approach
• Time vs space trade-off
• Precomputation
• Caching / Memoization

19. Amortized Analysis

• Dynamic array resizing
• Aggregate analysis

Advanced Algorithm Thinking

Complex algorithm patterns and their complexity.

20. Sliding Window

21. Two Pointers

22. Prefix Sum

23. Binary Search on Answer

24. Greedy Approaches

25. Dynamic Programming Basics

Space Complexity Optimization

Reducing and optimizing memory usage.

26. In-place Algorithms

27. Memory Reuse

28. Iterative vs Recursive Space Usage

29. Stack Space Analysis

System-Level Complexity Thinking

Complexity analysis in real-world systems.

30. Complexity in Real Systems

• Network latency vs computation
• I/O bound vs CPU bound
• Memory vs speed trade-offs

31. Scalability Thinking

• Handling large datasets
• Horizontal scaling impact
• Caching impact on complexity