Statistics

Problem Statement for "MooresLaw"

Problem Statement

Moore's law is a well-known prediction of the growth of computing power over time. This is the formulation we will use in this problem: The speed of new computers grows exponentially and doubles every 18 months. In this problem we will assume that reality precisely obeys this law.

Suppose that you have a hard computational task that would take 14 years to complete on a current computer. Surprisingly, starting its computation as soon as possible is not the best you can do. A better solution: Wait for 18 months and buy a better computer. It will be twice as fast, and therefore solve the task in 7 years. You would have the result 8.5 years from now. In the best possible solution you should wait for slightly over 4 years. The computer you'll be able to buy then will solve the task in approximately 2.2 years, giving a total of 6.2 years.

You have a computational task you want to solve as quickly as possible. You will be given an int years giving the number of years it would take on a computer bought today. Return a double giving the least number of years in which you will have the result of the task if you use the above approach.

Definition

Class:
MooresLaw
Method:
shortestComputationTime
Parameters:
int
Returns:
double
Method signature:
double shortestComputationTime(int years)
(be sure your method is public)

Notes

  • Your return value must have an absolute or relative error less than 1e-9.
  • The computation speed growth is a continuous exponential function satisfying the property from the problem statement.

Constraints

  • years will be between 1 and 1,000,000,000, inclusive.

Examples

  1. 14

    Returns: 6.2044816339207705

    The example from the problem statement.

  2. 3

    Returns: 2.870893001916099

  3. 47

    Returns: 8.82533252835082

  4. 123

    Returns: 10.907221008843223

  5. 1

    Returns: 1.0

  6. 2

    Returns: 2.0

  7. 4

    Returns: 3.4934492508343644

  8. 5

    Returns: 3.976341393165408

  9. 15

    Returns: 6.3537851442471425

  10. 23

    Returns: 7.278792184919884

  11. 37

    Returns: 8.307629299277789

  12. 59

    Returns: 9.317413824877127

  13. 145

    Returns: 11.263312885856767

  14. 172

    Returns: 11.63284638288751

  15. 578

    Returns: 14.255837774585384

  16. 792

    Returns: 14.937484180953778

  17. 2341

    Returns: 17.282813079502382

  18. 7985

    Returns: 19.938064289282256

  19. 22145

    Returns: 22.145489315993384

  20. 19728

    Returns: 21.895384877438623

  21. 74470

    Returns: 24.77000685648385

  22. 135498

    Returns: 26.065317298034948

  23. 603785

    Returns: 29.29896233651874

  24. 2547800

    Returns: 32.414680152491634

  25. 5000000

    Returns: 33.87369424715167

  26. 12345678

    Returns: 35.82970335003532

  27. 87654321

    Returns: 40.0714320647176

  28. 123456789

    Returns: 40.812595650125076

  29. 456789012

    Returns: 43.643878310398875

  30. 912121212

    Returns: 45.14042472529701

  31. 992134572

    Returns: 45.322390118570624

  32. 999912360

    Returns: 45.33928886681244

  33. 999990989

    Returns: 45.339459031538375

  34. 999999947

    Returns: 45.3394784171195

  35. 999999997

    Returns: 45.339478525321624

  36. 999999998

    Returns: 45.33947852748567

  37. 999999999

    Returns: 45.33947852964971

  38. 1000000000

    Returns: 45.339478531813754

  39. 1000000000

    Returns: 45.339478531813754

  40. 1

    Returns: 1.0

  41. 999999999

    Returns: 45.33947852964971

  42. 2

    Returns: 2.0

  43. 999999997

    Returns: 45.339478525321624

  44. 14

    Returns: 6.2044816339207705

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