Statistics

Problem Statement for "FountainOfLife"

Problem Statement

A Fountain of Life is a special fountain that produces the elixir of life at a constant speed of elixir liters per second. A dark mage managed to cast a Curse of Death on the Fountain so in addition to the elixir it now produces a deadly poison at a constant speed of poison liters per second. Both the poison and elixir are collected in an infinitely large pool around the Fountain and form a mixture. The mixture will become deadly once the percentage of poison in the mixture is at least 50%. Your task is to calculate the time at which the mixture will become deadly. At the beginning (0-th second) the pool contains pool liters of 100% elixir.

Your program must return a double, the time in seconds at which the mixture becomes deadly. If the mixture never becomes deadly, return -1.0.

Definition

Class:
FountainOfLife
Method:
elixirOfDeath
Parameters:
int, int, int
Returns:
double
Method signature:
double elixirOfDeath(int elixir, int poison, int pool)
(be sure your method is public)

Notes

  • The returned value must be accurate to within a relative or absolute value of 1E-9.

Constraints

  • elixir will be between 1 and 10000, inclusive.
  • poison will be between 1 and 10000, inclusive.
  • pool will be between 1 and 10000, inclusive.

Examples

  1. 1

    2

    2

    Returns: 2.0

    At t = 0s there are 2 liters of 100% elixir. At t = 1s there are 3 liters of elixir and 2 liters of poison for a total volume of 5 liters. 2 liters of poison is 40% of 5 liters so the mixture is still not deadly. At t = 2s there are 4 liters of elixir and 4 liters of poison for a total volume of 8 liters. 4 liters of poison is exactly 50% of the mixture so it is now deadly.

  2. 200

    100

    1

    Returns: -1.0

    With 200 liters of elixir per second and only 100 liters of poison per second, the mixture never becomes deadly.

  3. 9999

    10000

    10000

    Returns: 10000.0

    It might take a long time for the mixture to become deadly.

  4. 1

    10000

    1

    Returns: 1.0001000100010001E-4

    On the other hand, it might take a short time for the mixture to become deadly.

  5. 40

    43

    41

    Returns: 13.666666666666666

  6. 1000

    999

    1

    Returns: -1.0

  7. 6465

    1234

    123

    Returns: -1.0

  8. 3144

    23

    2459

    Returns: -1.0

  9. 438

    574

    8456

    Returns: 62.1764705882353

  10. 243

    3400

    5234

    Returns: 1.6579030725372188

  11. 2348

    45

    4583

    Returns: -1.0

  12. 3

    4835

    96

    Returns: 0.019867549668874173

  13. 4875

    432

    1267

    Returns: -1.0

  14. 1236

    346

    9864

    Returns: -1.0

  15. 9946

    2231

    9784

    Returns: -1.0

  16. 6321

    32

    1335

    Returns: -1.0

  17. 9875

    32

    8743

    Returns: -1.0

  18. 9123

    24

    5689

    Returns: -1.0

  19. 7575

    5

    2347

    Returns: -1.0

  20. 1231

    2344

    10000

    Returns: 8.984725965858042

  21. 9999

    10000

    9992

    Returns: 9992.0

  22. 10000

    1

    6756

    Returns: -1.0

  23. 1234

    27

    4321

    Returns: -1.0

  24. 7777

    8787

    9898

    Returns: 9.8

  25. 7848

    1438

    2132

    Returns: -1.0

  26. 9876

    9897

    6874

    Returns: 327.3333333333333

  27. 2222

    3333

    7776

    Returns: 6.999099909990999

  28. 1805

    806

    2006

    Returns: -1.0

  29. 174

    806

    2006

    Returns: 3.1740506329113924

  30. 1

    2006

    2005

    Returns: 1.0

  31. 1999

    1998

    2001

    Returns: -1.0

  32. 15

    16

    17

    Returns: 17.0

  33. 19

    19

    20

    Returns: -1.0

  34. 987

    989

    5782

    Returns: 2891.0

  35. 3843

    3843

    806

    Returns: -1.0

  36. 806

    2006

    2005

    Returns: 1.6708333333333334

  37. 1

    1

    12

    Returns: -1.0

  38. 1

    1

    1

    Returns: -1.0

  39. 10000

    10000

    10000

    Returns: -1.0

  40. 1

    10000

    10000

    Returns: 1.000100010001

  41. 1

    10000

    2

    Returns: 2.0002000200020003E-4

  42. 2

    5

    1

    Returns: 0.3333333333333333

  43. 2000

    5000

    1000

    Returns: 0.3333333333333333

  44. 40

    43

    41

    Returns: 13.666666666666666

  45. 1

    1

    1

    Returns: -1.0

  46. 2

    2

    2

    Returns: -1.0

  47. 2

    2

    5

    Returns: -1.0

  48. 1

    10000

    1

    Returns: 1.0001000100010001E-4

  49. 100

    100

    1

    Returns: -1.0

  50. 5

    5

    5

    Returns: -1.0

  51. 5

    5

    2

    Returns: -1.0

  52. 10

    10

    10

    Returns: -1.0

  53. 4

    4

    5

    Returns: -1.0

  54. 1

    1

    100

    Returns: -1.0

  55. 5

    5

    6

    Returns: -1.0

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