Statistics

Problem Statement for "IncredibleMachineEasy"

Problem Statement

You may remember an old computer game called "The Incredible Machine". It was a game where you could simulate simple processes like balls falling, lasers shooting, or cats pursuing mice. Moreover, you were able to perform these observations with different values for gravitational acceleration.

Imagine a system with some unknown acceleration of gravity. There are N balls, each fixed initially at some height above the ground. You are given a int[] height, where the i-th element is the height of the i-th ball above the ground. At time 0, the first ball is set loose and it starts falling. When it reaches the ground, the second ball is instantly set loose, and so on. This continues until the last ball reaches the ground at time T.

Return the acceleration of gravity in this system. Neglect air resistance and any other resisting factors. The distance d travelled by an object falling for time t with no initial velocity in a system with gravitational acceleration g and no resisting factors is equal to d = 0.5 * g * t^2.

Definition

Class:
IncredibleMachineEasy
Method:
gravitationalAcceleration
Parameters:
int[], int
Returns:
double
Method signature:
double gravitationalAcceleration(int[] height, int T)
(be sure your method is public)

Notes

  • The returned value must have an absolute or relative error less than 1e-9.

Constraints

  • height will contain between 1 and 50 elements, inclusive.
  • Each element of height will be between 1 and 100, inclusive.
  • T will be between 1 and 100, inclusive.

Examples

  1. {16,23,85,3,35,72,96,88,2,14,63}

    30

    Returns: 9.803799620759717

    That's an acceleration of gravity that might be somewhere on Earth's surface.

  2. {6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,5}

    12

    Returns: 26.73924541044107

    And this is likely on Jupiter.

  3. {8,8}

    3

    Returns: 7.111111111111111

    That's a light one.

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

    12

    Returns: 0.7192306901503684

    You could nearly fly under such conditions.

  5. {100}

    8

    Returns: 3.1250000000000004

  6. {100}

    100

    Returns: 0.020000000000000004

  7. {100}

    1

    Returns: 200.00000000000003

  8. {1}

    100

    Returns: 2.0000000000000004E-4

  9. {100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100}

    1

    Returns: 500000.00000000006

  10. {88,99,44,21,38,98,49,48,83,63,16,78,30,14,15,91,58,97,61,40,75,23,40,88,63,94,57,21,89,24,29,4,81,42,16,24,53,59,57,19,57,32,21,90,61,72,27,27,23,48}

    1

    Returns: 234244.23074443493

  11. {48,47,21,15,96,66,4,58,26,66,10,38,63,3,60,85,35,31,57,23,56,6,65,84,95,83,66,58,29,65,87,83,76,71,7,35,100,90,71,71,57,16,89,26,1,35,15,41,45,28}

    26

    Returns: 329.56013707429355

  12. {6,9,3,1,7,3,7,8,9,7,8,2,3,10,3,7,6,7,5,1,10,9,2,8,7,3,6,10,8,3,5}

    21

    Returns: 23.980375807383616

  13. {26,50,3,42,22,41,8}

    99

    Returns: 0.24014334371779925

  14. {49,79,25,71,93,41,95,90,4,50,15,40,51,76,88,4,79,33,6,82,6,72,54,57,64,44,20,84,64,28,94,90,63,37,41,73,32,92,31,46,33,76,46,27,21,44,7}

    59

    Returns: 59.08638183287904

  15. {49,79,25,71,93,41,95,90,4,50,15,40,51,76,88,4,79,33,6,82,6,72,54,57,64,44,20,84,64,28,94,90,63,37,41,73,32,92,31,46,33,76,46,27,21,44,7}

    100

    Returns: 20.567969516025194

  16. {49,79,25,71,93,41,95,90,4,50,15,40,51,76,88,4,79,33,6,82,6,72,54,57,64}

    100

    Returns: 5.853270739330036

  17. {93,81,9,24,85,49,37,97,71,11,54,49,85,65,13,100,62,59,49,54,37,43,73,75,54,96,8,25,88}

    10

    Returns: 880.1207531416899

  18. {93,81,9,24,85,49,37,97,71,11,54,49,85,65,13,100,62,59,49,54,37,43,73,75,54,96,8,25,88,48,59,30,5,63,92,78,88,59,28}

    70

    Returns: 32.186089439108216

  19. {28,25,3}

    4

    Returns: 18.070729634600493

  20. {28,25,3,8,26,15,12,29,22,4,16,15,26,20,4,30,19,18,15,16,11,13,22,23,17,29,3,8,27,15,18,9,2,19,28,24,27,18}

    2

    Returns: 11696.987201004398

  21. {9,38,58,57,18,50,18,2}

    27

    Returns: 4.679666016210067

  22. {1,3,5,5,2,4,2,1,1,5,3,4,3,4,4,5,3,3,3,1,3,1,5,1,5,1,4,1,2,5,3,4,5,1,4,1,3,1}

    29

    Returns: 9.354942840461625

  23. {2,4,1,2}

    15

    Returns: 0.30196055776424113

  24. {9,9,20,16,22,42,56,29,5,19,51,53,56}

    75

    Returns: 1.5966412313678775

  25. {45,21,49,43,26,33,21,12,22,49,57,29,18,13,55,49,16,50,10,42,42,46,17}

    78

    Returns: 5.447415660683728

  26. {3,7,1,1,2,4,4,1,6,4,4}

    8

    Returns: 11.569860342929067

  27. {7,4,2,37,28,24,11,22,9,5,19,37}

    14

    Returns: 21.60871875973662

  28. {18,13,33,35,81,28,40,5,52,72,54,28,10,34,52,34,31,16,40,31,20,57,55,34,41,69,80,72,53,12,87,63}

    50

    Returns: 31.87530596099118

  29. {6,4,11,11,26,9,13,2,17,23,17,9}

    50

    Returns: 1.2956357124584472

  30. {26,9,24,19,3,18,1,8,1,3,23,4,1,18,21,22,3,5,7}

    56

    Returns: 2.1319208377222325

  31. {89,29,79,63,8,59,1,26,3,9,78,12,4,62,71,74,10,16,23,13,81,55,64}

    92

    Returns: 4.127404384472292

  32. {17,8,4,92,70,58,27,54,21,11,48,91,51,79,21,33,32,88,54}

    15

    Returns: 128.3840801877069

  33. {73,42,76,2}

    27

    Returns: 1.7362479206283623

  34. {57,68,67,73,54,28,70,30}

    66

    Returns: 1.5987537521565605

  35. {52,79,88,67,5,85,84,14}

    97

    Returns: 0.7157482123949152

  36. {63,33,15,35,53,90,18,16,81,51,81,10,28,31,60}

    9

    Returns: 224.67007927918206

  37. {41,65,15,16,27,35,56,21}

    95

    Returns: 0.4591137241934603

  38. {24,37,36,75,8,75}

    81

    Returns: 0.4202673953790659

  39. {44,57,50,55,38,59,64,88}

    100

    Returns: 0.7175239305102875

  40. {46,30,6,79,73,44,10,38,76,32,54,8,85,62,5,10,68,72}

    86

    Returns: 3.384604400925884

  41. {64,80,39,85,37,16,19,64,44}

    61

    Returns: 2.0318454671064146

  42. {78,87,36,89,61,70,50,89,67,8}

    54

    Returns: 4.09709093255552

  43. {51,20,88,56,80,6,78,45,26,35,3,15}

    86

    Returns: 1.4030684586400395

  44. {57,63,89,11,15,35,28,85}

    70

    Returns: 1.1266207761790947

  45. {44,32,9,58,61}

    82

    Returns: 0.2806307061400362

  46. {48,83,25}

    68

    Returns: 0.19144647006863064

  47. {31,67,80,52,80}

    95

    Returns: 0.3345234863211787

  48. {92,69,8,90,88,3,33,52,19}

    69

    Returns: 1.4445562346882057

  49. {59,38,33,41,74,40,54,12}

    47

    Returns: 2.423062063516802

  50. {12,48,43,11,44,16,81,55,30,66,9,22,40,38,6,58,89,89}

    7

    Returns: 494.1441947053054

  51. {3,40,76,78}

    57

    Returns: 0.40361691593049

  52. {81,91,41,19,35,91,45,44,76,58,14,72,28,13,14,83,53,89,56,37,69,21}

    25

    Returns: 73.52223032287273

  53. {5,8,70}

    66

    Returns: 0.08282567620441224

  54. {83,23,10,60,30,10,4,11,60}

    86

    Returns: 0.5851255986453214

  55. {31,72,37,71,72,6,89,30,82,37,50,20,83}

    49

    Returns: 6.777167552412185

  56. {45,17,56,42,62,20,73,5,27,68,58}

    30

    Returns: 10.573780905113395

  57. {81,24,38,55,22,31,18,59,41,4,80,67,1,78,74,59,3,60,91}

    60

    Returns: 8.043652566145424

  58. {18,59,85,21,21,6,9,53,88,72,68,62,4,15,24,72,89,63,52,41,62}

    15

    Returns: 162.338883921523

  59. {29,1,68,90,3,24,58,37,32,86,56,45,71,17}

    1

    Returns: 14832.971837778898

  60. {51,3,25,2,56,16,44,85,73,59,42}

    54

    Returns: 2.927276152877925

  61. {14,24,57,64}

    36

    Returns: 0.9030538612412858

  62. {92,70,23,60,86,56,66}

    80

    Returns: 0.9584558870161284

  63. {48,13,19,29,82}

    62

    Returns: 0.44767784671496486

  64. {15,28,18,42,83,33,14,91}

    42

    Returns: 2.6148483196798473

  65. {8,58,78,1,33,83,44,27,65,77,24,78}

    18

    Returns: 37.102720266892746

  66. {63,24,48,7,73,77,87,17,59,66,35,86,26,32}

    23

    Returns: 34.07100290383988

  67. {20,62,44}

    22

    Returns: 1.4885015462851492

  68. {32,44,46,83,54,36,25,34,85,67}

    55

    Returns: 3.2181555085976985

  69. {51,82,77,8,15,37,68}

    1

    Returns: 4232.39785535723

  70. {7,71,4,89,89,56,52,65,36,61,66,7,25,61,38}

    85

    Returns: 2.6721955583786694

  71. {55,41,52,57,71,55,4,52,15,64,37,71,56,46,77,39}

    42

    Returns: 13.545073959102576

  72. {33,27,35,16,71,72,29,80}

    88

    Returns: 0.7009727429140311

  73. {31,47,84,9,5}

    73

    Returns: 0.27005487767677866

  74. {43,72,85}

    93

    Returns: 0.13612151038787065

  75. {7,56,86}

    77

    Returns: 0.12699078054146318

  76. {22,87,62,38}

    11

    Returns: 13.010765205788962

  77. {72,11,70,42,80,89,86,28,16,51,11,15,13,3}

    78

    Returns: 2.2789077600779404

  78. {28,58,2,27,58,29,49}

    7

    Returns: 63.74359737396458

  79. {92,44,37,12,3,87,45,83,59,82,7,30}

    2

    Returns: 3003.849817311856

  80. {55,39,82,41,83,27,83,47,35,70,75,79,30,17,24,78,15,40,15,89,70,3,8}

    26

    Returns: 67.44621581868176

  81. {44,44,19,14,88,61,4,53,24,61,9,35,58,3,56}

    28

    Returns: 18.99687308284069

  82. {1,1,2,2}

    3

    Returns: 5.180824110885502

  83. {12,9,12,13,16}

    6

    Returns: 17.079585948196677

  84. {25}

    61

    Returns: 0.013437248051599035

  85. {95}

    2

    Returns: 47.5

  86. {16, 23, 85, 3, 35, 72, 96, 88, 2, 14, 63 }

    30

    Returns: 9.803799620759717

  87. {6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5 }

    12

    Returns: 26.73924541044107

  88. {100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100 }

    1

    Returns: 500000.00000000006

  89. {3, 1, 3, 1, 3 }

    12

    Returns: 0.7192306901503684

  90. {8, 8 }

    3

    Returns: 7.111111111111111

  91. {100, 100, 100, 100, 100, 100, 100, 100, 100 }

    1

    Returns: 16200.000000000002

  92. {1, 4 }

    3

    Returns: 2.0000000000000004

  93. {98 }

    10

    Returns: 1.96

  94. {7 }

    4

    Returns: 0.875

  95. {1, 2, 3, 4, 5, 6, 7, 100, 4, 67, 34, 12, 56, 78, 90, 29 }

    97

    Returns: 1.1685596558152092

  96. {10 }

    30

    Returns: 0.022222222222222227

  97. {1, 4 }

    5

    Returns: 0.7200000000000002

  98. {2, 9 }

    12

    Returns: 0.2706289079755357

  99. {16, 23, 85, 3, 35, 72, 96, 88, 2, 14, 63, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 10, 100, 1, 100 }

    1

    Returns: 72643.74527753238

  100. {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }

    1

    Returns: 4999.999999999993

  101. {100 }

    1

    Returns: 200.00000000000003

  102. {100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100 }

    1

    Returns: 480200.00000000006

  103. {100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 10, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100 }

    1

    Returns: 486418.06421393016

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