Statistics

Problem Statement

Definition

Class:

SortEstimate

Method:

howMany

Parameters:

int, int

Returns:

double

Method signature:

double howMany(int c, int time)

(be sure your method is public)

Notes

• lg(n) = ln(n)/ln(2) where ln denotes the natural log.
• Your return value must have a relative or absolute error less than 1e-9.

Constraints

• c will be between 1 and 100 inclusive.
• time will be between 1 and 2000000000 inclusive.

Examples

1. 1

   8

   Returns: 4.0

   Given 8 nanoseconds we can sort 4 integers since 1*4*lg(4) = 4*2 = 8

2. 1

   1073741824

   Returns: 4.237868701779632E7

3. 1

   20971520

   Returns: 1048576.0

4. 1

   1744830463

   Returns: 6.7108863963560425E7

5. 2

   16

   Returns: 4.0

   Now that c = 2 we need twice as many nanoseconds to sort 4 integers.

6. 37

   12392342

   Returns: 23104.999312341137

   We can almost sort 23105 integers, but not quite.

7. 1

   2000000000

   Returns: 7.637495090348122E7

   Largest possible return.

8. 15

   183518033

   Returns: 634711.5366691528

9. 94

   528002855

   Returns: 308072.16281298193

10. 22

    1891962415

    Returns: 3926030.802208677

11. 19

    21449736

    Returns: 70129.92471231497

12. 41

    251000508

    Returns: 333658.1565933969

13. 41

    682091086

    Returns: 844976.7106648742

14. 15

    324891869

    Returns: 1080626.000222133

15. 100

    269939035

    Returns: 156438.87972686428

16. 65

    150597632

    Returns: 135872.67212630875

17. 82

    1668460444

    Returns: 1019427.0794480281

18. 94

    698125302

    Returns: 399152.58894443273

19. 73

    537393400

    Returns: 395894.080674982

20. 61

    952343733

    Returns: 796412.1957200351

21. 62

    1668728800

    Returns: 1323517.520513234

22. 67

    1422724322

    Returns: 1060844.4313069163

23. 50

    1302510048

    Returns: 1283769.883887477

24. 72

    1240983207

    Returns: 873315.4015855292

25. 61

    1668868721

    Returns: 1343872.2486778102

26. 70

    672611577

    Returns: 507012.8623876511

27. 41

    844981191

    Returns: 1031674.1952518377

28. 69

    346799919

    Returns: 277924.8297328659

29. 96

    1650394599

    Returns: 871225.0564874781

30. 41

    800275356

    Returns: 980681.0457517206

31. 47

    1751439252

    Returns: 1793764.4273233637

32. 72

    1034087829

    Returns: 736868.1134626163

33. 65

    1405206580

    Returns: 1078722.5591509202

34. 97

    698397013

    Returns: 387824.0070168886

35. 45

    1345840599

    Returns: 1460472.8429022175

36. 92

    1248825953

    Returns: 699151.35947252

37. 22

    1200654528

    Returns: 2563460.5078692725

38. 1

    1999999999

    Returns: 7.637495086728776E7

39. 1

    2000000000

    Returns: 7.637495090348122E7

40. 2

    1999999997

    Returns: 3.962007767021034E7

41. 1

    1

    Returns: 1.5596104694623691

42. 43

    2000000000

    Returns: 2207091.972283502

43. 100

    1

    Returns: 1.0069076686081029

44. 1

    3

    Returns: 2.3884234844993384

45. 100

    2523526

    Returns: 2264.2982128022004

46. 5

    100

    Returns: 7.081840920218569

47. 1

    2

    Returns: 2.0

48. 2

    2000000000

    Returns: 3.962007772642713E7