Statistics

Problem Statement for "MeasuringTemperature"

Problem Statement

You have a device that measures temperature once a minute. Sadly, the temperature sensor of your device is not 100% reliable, and sometimes it reports wildly inaccurate values.

You don't have the resources to buy a new device so you decide to fix the problem by writing software for your device that will throw away invalid measurements. We consider a measurement invalid if:

  • the value is less than -273, or
  • each value that was measured within 2 minutes before and after this one differs from this value by more than 2

In other words, when deciding whether a measurement is valid, you usually consider the previous two, and the next two measurements.

You are given a int[] measuredValues that contains temperatures measured in the last few minutes. The temperatures are given in chronological order, i.e., the i-th value is the temperature measured i minutes after the device was started. Write a method that computes the average of the valid measurements. If no measurement is valid, return -300.0.

Definition

Class:
MeasuringTemperature
Method:
averageTemperature
Parameters:
int[]
Returns:
double
Method signature:
double averageTemperature(int[] measuredValues)
(be sure your method is public)

Notes

  • The returned value must be accurate to within a relative or absolute error of 1E-9.
  • The lowest possible temperature (in degrees Celsius) is -273.15.
  • It may seem weird that only integer temperatures are used in the input. This is only done to avoid rounding errors.

Constraints

  • measuredValues contains between 2 and 50 elements, inclusive.
  • Each element of measuredValues will be between -1000 and 1000, inclusive.

Examples

  1. {9, 11, 12, 13, 15}

    Returns: 12.0

    All measurements are valid. During this period of time it was getting warmer. The average temperature is (9+11+12+13+15)/5 = 12.

  2. {0, 0, 0, 2, 997, -1, 0}

    Returns: 0.16666666666666666

    The fifth measurement is clearly invalid. The average of the valid ones is slightly positive.

  3. {0, 0, 0, 2, -4, -1, 0}

    Returns: 0.16666666666666666

    This time, the fifth measurement is only slightly off, but still we consider it to be invalid.

  4. {0, 0, 0, 2, -3, -1, 0}

    Returns: -0.2857142857142857

    All the measurements are valid.

  5. {1,2,3,100,100,1,2}

    Returns: 29.857142857142858

    Again, all these measurements are valid. (Sadly, the sensor malfunctioned twice in a row. Our approach can't deal with this situation.)

  6. {1,2,3,4,5,6,7,10}

    Returns: 4.0

    The last measurement is invalid. (The measurements made within 2 minutes from the last measurement gave results 6 and 7, and neither of these values is close enough to 10.)

  7. {-35, -34, -34, -34, -35, 72, -34, 52, -36, -35, -36, 52, -36, -35, 981, -33}

    Returns: -34.75

    It's freezing cold and the sensor is malfunctioning quite often, but luckily we can identify all the wrong measurements (72, 52, 52, and 981) as invalid.

  8. {-273, -273, -274, -273}

    Returns: -273.0

    The third measurement gives a temperature lower than -273, and thus is considered to be invalid.

  9. {10, 20, 30, 40}

    Returns: -300.0

    No valid measurements here.

  10. {0,0}

    Returns: 0.0

  11. {10,12}

    Returns: 11.0

  12. {10,13}

    Returns: -300.0

  13. {12,10}

    Returns: 11.0

  14. {13,10}

    Returns: -300.0

  15. {-10,-12}

    Returns: -11.0

  16. {-10,-13}

    Returns: -300.0

  17. {-12,-10}

    Returns: -11.0

  18. {-13,-10}

    Returns: -300.0

  19. {0,0,-500,0,-500,1}

    Returns: 0.25

  20. {1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000}

    Returns: 1000.0

  21. {1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,-1000,1000,1000}

    Returns: 1000.0

  22. {10,10,13}

    Returns: 10.0

  23. {10,13,10}

    Returns: 10.0

  24. {13,10,10}

    Returns: 10.0

  25. {10,13,16,10}

    Returns: -300.0

  26. {10,13,16,20,10}

    Returns: -300.0

  27. {10,-274,-275,-274,10}

    Returns: -300.0

  28. {-13,12,-14,11,-15,10,-16,9,-17,8,-18,7,6,-19,5,-400,-400,4,-390,-300,-270,3,-12,3,2}

    Returns: -1.0

  29. {47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47}

    Returns: 0.0

  30. {47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,-47,47,47}

    Returns: 1.88

  31. {10,-274,11,12,-275,-286,13}

    Returns: 11.0

  32. {-3,-4,-3,-5,-3,-2,-3}

    Returns: -3.2857142857142856

  33. {-3,-3,-4,-3,-3,-2,-3,-3,-4,-3,-3,-3,-4,-3,-3,-2,-3,-3,-4,-3,-3,-2,-3,-3,-4,-3,-3,-2,-3,-3,-4,-3,-3,-2,-3,-3,-4,-3,-3,-2,-3,-2,-3,-3,-4,-3,-3,-2,-1,0}

    Returns: -2.9

  34. {-274,-273}

    Returns: -273.0

  35. {-274,273}

    Returns: -300.0

  36. {10, 13, 12 }

    Returns: 11.666666666666666

  37. {1, 1, 4 }

    Returns: 1.0

  38. {-273, -273 }

    Returns: -273.0

  39. {2, 10 }

    Returns: -300.0

  40. {10, 20, 30, 40 }

    Returns: -300.0

  41. {0, 0, 0, 2, 997, -1, 0 }

    Returns: 0.16666666666666666

  42. {-274, -275, -276 }

    Returns: -300.0

  43. {-273, -273, -274, -273, -500, -700, 700 }

    Returns: -273.0

  44. {2, -2, -2, -2, -2, 1 }

    Returns: -2.0

  45. {-310, 0, 1, 1 }

    Returns: 0.6666666666666666

  46. {-273, -273, -274, -273 }

    Returns: -273.0

  47. {1, 2 }

    Returns: 1.5

  48. {0, 0 }

    Returns: 0.0

  49. {0, 100 }

    Returns: -300.0

  50. {-272, -274 }

    Returns: -272.0

  51. {-35, -34, -34, -34, -35, 72, -34, 52, -36, -35, -36, 52, -36, -35, 981, -33 }

    Returns: -34.75

  52. {1, 5, 10 }

    Returns: -300.0

  53. {10, 20, 21, 40, 41 }

    Returns: 30.5

  54. {10, 0, 9 }

    Returns: 9.5

  55. {1, 100 }

    Returns: -300.0

  56. {1, 7 }

    Returns: -300.0

  57. {1, 2, 3, 4, 5, 6, 7, 10 }

    Returns: 4.0

  58. {9, 19 }

    Returns: -300.0

  59. {0, 4, 2, 6, 1 }

    Returns: 2.6

  60. {1, 6, 1 }

    Returns: 1.0

  61. {10, 0 }

    Returns: -300.0

  62. {1, 2, 3, 100, 100, 1, 2 }

    Returns: 29.857142857142858

  63. {1, 1, 3, 1, 1 }

    Returns: 1.4

  64. {3, 1, 4, 1, 3 }

    Returns: 2.4

  65. {0, 0, 0, 2, -3, -1, 0, -273, -272 }

    Returns: -60.77777777777778

  66. {50, 10, 11, 12, 13, 14, 70 }

    Returns: 12.0

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