1. Lecture 3 Algorithm Analysis

2. Motivation Which algorithm to use?

3. Step-Counting Assumptions

4. Step-counting: equal work Adding/Multiplication/Division Trigonometric functions

5. Step-counting: no optimization Unrolling Loops

6. Sample code (simple operations)

7. Sample code (while loop)

8. Sample code (for loop)

9. Sample code: conditionals

11. Which branch do we follow? Best Case Average Case Worst Case

12. Code Sample if (x < 0){ for (i = 0; i < n; i++){ print(n) } else print false

13. Sample Code for (i = 0; i < n; i++){ if (a[i] > x){ for (j = 0; j < n; j++){ b[j] = b[i] } }else{ b[j] = 0 }

14. Limitations of step-counting Recursion Do Constants Matter?

15. Asymptotic Analysis Generalization/Categorization Abstraction

16. Big-O Definition

17. Graph

18. Using Big-O Show 7n+8 = O(n)

19. Using Big-O

20. Show 7n+8 = O(n^2)

21. Using Big-O

22. Upper Bounds

23. Common Labels FunctionNameExample

24. Theorems

27. Function Properties

28. Useful Tool: limits

29. Properties of Big-O and friends Symmetry Transpose Symmetry

30. Properties of Big-O and friends Reflexivity Transitivity

31. Common Misunderstandings Bounds vs. best/worst cases

32. Asymptotic Analysis vs. Running time

33. Lecture 3 Algorithm Analysis

34. Motivation Which algorithm to use?

35. Step-Counting Assumptions

36. Step-counting: equal work Adding/Multiplication/Division Trigonometric functions

37. Step-counting: no optimization Unrolling Loops

38. Sample code (simple operations)

39. Sample code (while loop)

40. Sample code (for loop)

41. Sample code: conditionals

43. Which branch do we follow? Best Case Average Case Worst Case

44. Code Sample if (x < 0){ for (i = 0; i < n; i++){ print(n) } else print false

45. Sample Code for (i = 0; i < n; i++){ if (a[i] > x){ for (j = 0; j < n; j++){ b[j] = b[i] } }else{ b[j] = 0 }

46. Limitations of step-counting Recursion Do Constants Matter?

47. Asymptotic Analysis Generalization/Categorization Abstraction

48. Big-O Definition

49. Graph

50. Using Big-O Show 7n+8 = O(n)

51. Using Big-O

52. Show 7n+8 = O(n^2)

53. Using Big-O

54. Upper Bounds

55. Common Labels FunctionNameExample

56. Theorems

59. Function Properties

60. Useful Tool: limits

61. Properties of Big-O and friends Symmetry Transpose Symmetry

62. Properties of Big-O and friends Reflexivity Transitivity

63. Common Misunderstandings Bounds vs. best/worst cases

64. Asymptotic Analysis vs. Running time