Logarithms

5. Binary Logarithm (Base 2)

Most common in CS

6. Common Logarithm (Base 10)

Scientific notation base

7. Natural Logarithm (Base e)

Calculus and growth rates

8. Logarithm of 1 (Special case)

Any base equals zero

9. Logarithm of the Base (Another special case)

Always equals one

10. Product Rule (Multiplication becomes addition)

First logarithm property

11. Quotient Rule (Division becomes subtraction)

Second logarithm property

12. Power Rule (Exponent comes out front)

Third logarithm property

13. Quiz: Logarithm Properties (Knowledge check)

Test your understanding

14. Change of Base Formula (Converting bases)

Switch between any bases

15. Why Bases Don't Matter in Big-O (Constant factor)

All logarithms are equivalent

16. The Halving Pattern (Where log n comes from)

Divide and conquer

17. Binary Search Example (Classic log n algorithm)

Halving the search space

18. Tree Height Example (Another log n pattern)

Balanced binary trees

19. Quiz: Logarithmic Growth (Knowledge check)

Test your understanding

20. Problem - Power Function (Entry problem)

LeetCode 50

21. Power - The Insight (Squaring trick)

Halve the exponent

22. Power - Implementation (The code)

Recursive solution

23. Power - Complexity Analysis (Why it's logarithmic)

Time and space breakdown

24. Lessons from Power (Summary)

What you learned

25. Problem - Search Insert Position (Second problem)

LeetCode 35

26. Search Insert - The Insight (Binary search variant)

Find or insert position

27. Search Insert - Implementation (The code)

Binary search solution

28. Search Insert - Walkthrough (Tracing execution)

Step-by-step example

29. Lessons from Search Insert (Summary)

What you learned

30. Problem - Perfect Squares (Third problem)

LeetCode 279

31. Perfect Squares - The Insight (DP with square roots)

Building from smaller values

32. Perfect Squares - Implementation (The code)

DP solution

33. Perfect Squares - Logarithm Connection (Square roots and logs)

Why logs appear

34. Lessons from Perfect Squares (Summary)

What you learned

35. Logarithms in Merge Sort (Divide and conquer)

Tree height analysis

36. Logarithms in Quicksort (Average case)

Balanced partitions

37. Logarithms in Heaps (Insert and extract)

Heap operations

38. Quiz: Logarithms in Algorithms (Knowledge check)

Test your understanding

39. Problem - Find Kth Smallest (Fourth problem)

LeetCode 378

40. Kth Smallest - The Insight (Binary search on values)

Count elements below threshold

41. Kth Smallest - Implementation (The code)

Binary search solution

42. Lessons from Kth Smallest (Summary)

What you learned

43. Logarithms and Bit Manipulation (Powers of 2)

Binary representation

44. Logarithms and Number of Digits (Base 10)

Counting digits

45. Quiz: Logarithms and Numbers (Knowledge check)

Test your understanding