Statistics

Problem Statement for "PillarsDivTwo"

Problem Statement

On a horizontal line, there are N uniformly spaced vertical pillars. The pillars are numbered 0 through N-1, in order. For each i, the distance between the bottoms of pillars i and i+1 is exactly w. For each i, the height of pillar i (0-based index) is an integer between 1 and heights[i], inclusive. We want to take a single piece of rope and use it to join the top ends of all pillars, in order. (Once in place, the rope will have the shape of a polyline consisting of N-1 segments.) What is the shortest length of rope that is guaranteed to be sufficient, regardless of the actual pillar heights?

You are given the int[] heights and the int w. Compute and return the answer to the above question. In other words, find a sequence of pillar heights (within the given constraints) for which the length of the rope we need is maximized, and return that maximum.

Definition

Class:
PillarsDivTwo
Method:
maximalLength
Parameters:
int[], int
Returns:
double
Method signature:
double maximalLength(int[] height, int w)
(be sure your method is public)

Notes

  • Your return value must have a relative or an absolute error of less than 1e-9.

Constraints

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

Examples

  1. {3,3,3}

    2

    Returns: 5.656854249492381

  2. {1,1,1,1}

    100

    Returns: 300.0

  3. {100,2,100,2,100}

    4

    Returns: 396.32310051270036

    We will need the most rope if columns 0, 2, and 4 have height 100 each, and columns 1 and 3 have height 1 each.

  4. {2,1,1,2}

    1

    Returns: 3.82842712474619

  5. {5,6,7,8,9,10,11,12,13,14,15}

    20

    Returns: 221.02070848731498

  6. {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}

    100

    Returns: 6895.085278660454

  7. {100,1,100}

    97

    Returns: 277.2002886001384

  8. {1,100,4}

    93

    Returns: 271.6615541441225

  9. {42,68,35,1,70,25,79,59,63,65,6,46,82,28,62,92,96,43,28,37,92,5,3,54,93,83,22,17,19,96,48,27,72,39,70,13,68,100,36,95,4,12,23,34,74,65,42,12,54,69}

    97

    Returns: 5697.585698318906

  10. {92,98,43,46,30,10,72,1,25,43,19,44,14,38,43,94,70,25,86,59,99,51,4,68,100,4,57,92,12,95,43,61,92,5,94,15,4,13,78,42,31,100,59,74,64,17,51,20,36,9}

    23

    Returns: 3227.74775802847

  11. {61,39,43,56,60,68,98,64,20,5,13,69,78,63,27,46,91,38,63,57,49,71,35,2,51,62,84,1,88,98,94,81,31,18,78,71,6,74,33,1,83,39,19,15,80,74,36,39,14,28}

    49

    Returns: 3762.30612268847

  12. {42,68,35,1,70,25,79,59,63,65,6,46,82,28,62,92,96,43,28,37,92,5,3,54,93,83,22,17,19,96,48,27,72,39,70,13,68,100,36,95,4,12,23,34,74,65,42,12,54,69}

    48

    Returns: 3851.8189701668684

  13. {45,63,58,38,60,24,42,30,79,17,36,91,43,89,7,41,43,65,49,47,6,91,30,71,51,7,2,94,49,30,24,85,55,57,41,67,77,32,9,45,40,27,24,38,39,19,83,30,42,34}

    16

    Returns: 2844.926773074714

  14. {40,59,5,31,78,7,74,87,22,46,25,73,71,30,78,74,98,13,87,91,62,37,56,68,56,75,32,53,51,51,42,25,67,31,8,92,8,38,58,88,54,84,46,10,10,59,22,89,23,47}

    7

    Returns: 2950.092492769286

  15. {31,14,69,1,92,63,56,11,60,25,38,49,84,96,42,3,51,92,37,75,21,97,22,49,100,69,85,82,35,54,100,19,39,1,89,28,68,29,94,49,84,8,22,11,18,14,15,10,17,36}

    52

    Returns: 4049.5657504383657

  16. {1,50,20,57,99,4,25,9,45,10,90,3,96,86,94,44,24,88,15,4,49,1,59,19,81,97,99,82,90,99,10,58,73,23,39,93,39,80,91,58,59,92,16,89,57,12,3,35,73,56}

    29

    Returns: 3524.900000318473

  17. {47,63,87,76,34,70,43,45,17,82,99,23,52,22,100,58,77,93,90,76,13,1,11,4,70,62,89,2,90,56,24,3,86,83,86,89,27,18,58,33,33,70,55,22,90,77,30,69,93,26}

    56

    Returns: 4213.296072802553

  18. {35,50,42,13,46,61,19,54,40,24,80,97,88,30,50,38,67,50,94,96,98,17,87,6,89,83,56,35,15,2,17,72,87,64,14,56,86,54,13,9,33,46,14,57,22,59,47,83,82,45}

    97

    Returns: 5645.772838902263

  19. {23,30,62,36,51,74,67,45,60,93,40,54,25,55,11,46,50,87,14,75,23,69,19,88,6,59,92,3,26,78,15,15,25,35,75,73,60,34,71,88,98,19,78,74,71,64,69,93,86,3}

    81

    Returns: 5143.7240088784765

  20. {14,28,3,100,28,26,44,25,24,73,62,82,4,33,6,94,26,32,93,43,23,87,65,1,88,61,14,75,71,71,36,34,12,61,97,68,86,51,41,95,96,25,20,26,77,95,59,3,72,67}

    79

    Returns: 5012.8427487849

  21. {94,52,85,19,65,20,53,1,88,61,27,11,58,71,16,77,28,44,59,65,10,83,87,66,88,78,75,26,28,30,29,24,21,3,63,24,97,38,62,96,26,65,61,3,17,31,27,12,72,12}

    48

    Returns: 3761.538515581392

  22. {54,21,91,25,89,64,41,52,63,30,1,14,59,79,66,8,78,1,59,40,4,61,58,25,78,9,14,88,2,51,61,29,94,85,6,41,12,5,36,57,73,51,24,86,57,17,27,58,27,58}

    38

    Returns: 3347.0754719268034

  23. {72,70,62,97,23,18,13,18,97,86,42,24,30,30,66,60,33,97,56,54,63,85,35,55,73,58,70,33,64,8,84,12,36,68,49,76,39,24,43,55,12,42,76,60,26,22,71,27,35,6}

    84

    Returns: 5086.827402571348

  24. {51,99,80,2,94,35,38,35,57,94,77,6,63,49,82,1,14,42,56,56,43,63,12,78,25,79,53,44,97,74,41,14,76,73,19,11,18,33,13,96,70,32,41,89,86,91,98,90,91,46}

    54

    Returns: 4138.221466339355

  25. {15,52,41,45,59,36,60,93,6,65,82,4,30,76,9,93,98,50,57,62,28,68,42,30,41,14,75,2,78,16,84,14,93,25,2,93,60,71,29,28,85,76,87,99,71,88,48,5,4,22}

    64

    Returns: 4475.562028763542

  26. {7,64,11,72,90,41,65,43,20,14,92,5,19,33,51,6,76,40,4,23,99,48,85,49,72,65,14,76,46,13,47,79,70,63,20,86,90,45,66,41,46,9,19,71,2,24,33,73,53,88}

    71

    Returns: 4603.814856077139

  27. {64,2,4,24,28,1,70,16,66,29,44,48,89,44,38,10,64,50,82,89,43,9,61,22,59,55,89,47,91,50,44,31,21,49,68,37,84,36,27,86,39,54,30,25,49,24,60,58,67,45}

    56

    Returns: 3993.840621897657

  28. {19,27,12,26,56,2,50,97,85,16,65,43,76,14,43,97,49,73,27,7,74,30,5,6,27,13,76,94,66,37,37,42,15,95,57,53,37,39,83,56,16,32,31,42,26,12,38,87,91,51}

    63

    Returns: 4146.494525759854

  29. {35,94,54,17,53,9,63,34,55,4,35,4,57,49,25,18,14,10,29,1,81,19,59,51,56,62,65,4,77,44,10,3,62,90,49,83,54,75,21,3,24,32,70,79,60,9,20,72,4,46}

    82

    Returns: 4874.647346475028

  30. {5,93,86,14,99,90,23,39,38,11,62,35,9,62,60,94,16,70,38,70,59,1,72,65,18,16,56,16,31,40,13,89,83,55,86,11,85,75,81,16,52,42,16,80,11,99,74,89,78,33}

    57

    Returns: 4214.483768834308

  31. {90,14,9,42,91,24,64,29,85,79,1,72,86,75,72,34,68,54,96,69,26,77,30,51,99,10,94,87,81,17,50,68,29,80,65,22,6,27,17,17,27,67,88,82,65,41,87,22,63,22}

    65

    Returns: 4541.267361569381

  32. {10,16,3,74,25,42,46,63,24,32,7,69,19,3,8,8,82,13,37,31,15,10,85,57,91,94,97,53,55,46,9,49,92,13,32,15,40,59,23,5,96,53,70,80,39,24,19,67,60,99}

    87

    Returns: 5138.717089235266

  33. {97,63,34,59,23,47,93,38,26,48,59,3,8,99,31,93,1,79,100,53,49,83,41,16,76,63,68,37,98,19,98,29,52,17,31,50,26,59,30,21,41,61,48,63,56,76,93,62,55,99}

    47

    Returns: 3936.215255729578

  34. {15,47,89,70,39,64,76,16,22,76,16,29,35,71,6,65,58,63,62,25,50,70,31,24,51,34,26,11,38,37,38,79,94,37,15,65,92,50,36,6,38,5,38,24,65,71,9,69,82,86}

    53

    Returns: 3721.8263629029

  35. {74,53,95,77,27,97,73,50,41,75,20,44,12,42,90,20,66,6,86,17,51,16,10,65,67,94,75,10,1,96,74,90,62,73,69,59,32,69,27,11,23,75,80,11,53,83,92,96,65,75}

    65

    Returns: 4608.578068254262

  36. {3,56,61,75,73,22,23,48,78,90,6,96,95,51,44,55,82,13,73,40,29,13,63,68,9,16,9,24,60,35,5,87,20,59,46,7,67,1,68,93,88,33,57,75,48,22,84,23,32,77}

    84

    Returns: 5069.750569832345

  37. {49,24,83,19,77,21,12,83,57,91,26,25,87,78,70,44,35,78,69,69,92,97,84,29,28,27,72,98,13,4,28,9,46,9,86,39,38,44,14,2,51,29,12,51,50,93,55,70,82,66}

    68

    Returns: 4539.631995764839

  38. {14,94,35,73,73,31,2,43,78,78,71,3,65,82,91,24,38,24,80,96,70,28,43,11,83,59,27,88,71,29,52,59,14,61,84,87,43,11,73,29,35,42,19,4,68,66,39,82,58,51}

    15

    Returns: 2995.169090435318

  39. {99,59,62,64,57,8,79,90,36,66,76,87,87,34,61,31,49,29,93,34,41,67,36,11,100,38,93,83,29,53,70,45,95,9,53,48,33,36,9,65,98,44,50,16,42,90,1,13,49,24}

    52

    Returns: 4036.1298009018233

  40. {75,34,92,1,55,91,98,20,81,79,32,45,41,88,100,26,84,39,93,94,53,12,61,35,41,98,86,30,41,6,92,93,11,50,79,80,72,78,74,94,21,98,27,77,91,83,79,60,19,90}

    60

    Returns: 4613.392057360121

  41. {50,25,73,81,9,68,9,78,4,71,8,97,75,23,12,20,62,57,91,64,84,17,33,53,42,55,14,63,97,61,16,5,100,37,81,99,33,88,85,41,18,7,71,42,83,50,24,59,6,22}

    96

    Returns: 5695.095225480062

  42. {97,17,79,79,80,59,78,51,8,30,82,96,79,77,54,100,85,66,94,9,73,44,30,15,69,56,92,74,23,49,52,87,45,47,78,18,30,17,75,92,70,13,47,94,92,16,50,58,41,53}

    37

    Returns: 3701.285980331424

  43. {52,88,27,63,56,84,95,81,98,66,66,14,62,79,79,79,41,12,48,46,71,76,90,51,50,34,66,15,83,8,33,97,68,23,83,11,42,32,88,6,80,22,39,52,48,9,47,77,60,90}

    23

    Returns: 3423.257432740588

  44. {67,87,56,29,15,61,54,78,49,4,62,32,83,56,98,7,53,22,97,82,22,56,48,25,19,36,77,75,60,99,75,54,23,36,44,89,54,33,48,81,27,79,51,2,62,100,56,64,17,74}

    62

    Returns: 4400.964779878813

  45. {46,74,75,51,54,82,88,100,11,44,66,73,30,82,13,77,82,48,91,72,6,73,33,90,21,66,32,59,94,7,79,49,7,72,67,97,98,21,95,30,89,10,85,70,79,18,16,27,85,69}

    7

    Returns: 3440.8269950782324

  46. {29,98,19,91,100,86,87,100,21,11,72,14,16,86,19,81,32,68,88,45,87,8,61,28,75,32,53,72,69,94,86,38,12,5,78,7,69,23,14,1,43,38,39,89,56,90,48,82,94,85}

    88

    Returns: 5558.977635800158

  47. {62,94,18,2,83,48,66,54,5,85,96,26,22,65,82,73,7,57,44,94,81,81,69,12,14,69,52,17,80,69,41,32,34,80,64,60,54,37,96,66,75,21,36,81,77,56,26,72,9,60}

    57

    Returns: 4212.1177983213665

  48. {3,33,6,41,76,63,86,63,81,37,98,3,9,81,41,77,59,94,41,47,75,74,98,81,36,73,1,8,56,67,42,89,82,69,16,97,26,10,13,37,56,63,44,43,22,23,13,49,19,69}

    18

    Returns: 3132.125123376149

  49. {15,51,91,36,60,70,96,4,41,80,100,6,92,62,82,53,54,34,30,88,43,54,84,21,15,19,45,64,30,53,65,70,71,6,48,95,88,27,77,24,41,80,91,89,11,72,46,22,71,84}

    90

    Returns: 5519.1645016944785

  50. {56,79,80,7,63,36,88,97,34,89,36,80,94,91,63,66,2,6,8,68,70,35,72,58,99,46,98,19,39,45,73,64,29,65,2,24,91,5,2,28,98,93,72,64,2,64,22,66,22,46}

    11

    Returns: 3155.4891309934756

  51. {96,42,23,13,52,16,56,94,39,80,83,9,55,23,8,46,39,45,91,40,55,5,24,26,79,25,82,31,34,24,95,31,47,88,46,6,17,51,90,39,64,36,98,10,31,25,9,38,75,21}

    73

    Returns: 4649.080920198726

  52. {94,56,35,62,57,7,85,76,83,20,42,33,85,80,80,84,68,37,26,19,38,29,20,78,38,92,57,96,61,2,94,33,37,81,76,8,85,75,20,91,77,42,52,30,91,75,73,92,90,88}

    91

    Returns: 5599.94889235557

  53. {40,94,54,64,82,4,6,77,80,96,40,69,99,84,40,16,22,94,27,23,39,29,82,100,79,92,24,44,35,44,50,3,8,3,42,88,47,92,38,14,1,17,91,63,36,27,11,78,83,61}

    90

    Returns: 5414.974253146997

  54. {6,75,64,23,96,67,61,39,89,12,46,68,26,68,90,43,64,48,3,18,100,24,27,4,49,52,71,37,59,68,57,6,32,63,20,76,57,32,96,45,92,4,89,16,51,20,73,92,84,34}

    76

    Returns: 4963.683542239594

  55. {43,70,1,55,79,86,58,34,94,91,4,51,34,23,72,12,91,39,42,59,48,53,59,80,3,84,91,3,69,23,96,36,9,62,43,95,100,89,79,43,58,42,48,70,46,81,14,65,11,62}

    86

    Returns: 5349.152628770879

  56. {74,5,63,4,3,70,55,30,53,75,50,31,45,45,50,19,66,64,53,74,71,32,48,12,70,99,99,4,53,80,54,44,23,89,64,35,51,23,41,12,93,52,81,78,17,77,79,21,16,49}

    99

    Returns: 5683.230350379701

  57. {80,36,58,84,63,3,63,21,71,23,74,42,87,89,18,18,93,99,68,50,66,90,33,20,82,4,31,29,32,90,53,31,73,65,8,96,29,82,91,11,78,72,37,60,44,41,34,38,94,31}

    75

    Returns: 4869.419994991303

  58. {94,83,4,62,91,63,8,98,52,24,91,18,41,4,67,84,62,60,46,87,52,66,2,41,10,98,84,51,59,22,76,82,88,72,88,100,5,80,39,1,31,62,19,6,41,29,60,23,99,61}

    99

    Returns: 5883.412415138644

  59. {36,82,15,68,94,97,62,47,39,71,39,77,56,18,72,61,53,59,34,56,66,27,2,35,60,94,49,74,93,94,34,38,4,91,12,95,69,28,99,90,49,80,48,50,32,70,76,99,50,37}

    100

    Returns: 5959.549729629215

  60. {24,44,32,55,62,35,86,68,17,94,5,67,54,9,24,85,93,68,49,70,31,12,15,91,28,44,5,100,75,96,7,59,90,59,10,90,48,41,19,65,76,27,90,4,67,13,41,71,77,96}

    42

    Returns: 3799.667114248842

  61. {87,52,10,88,84,86,91,51,87,56,82,29,3,78,63,25,66,73,33,86,29,47,90,79,84,26,66,61,46,79,22,56,21,28,74,35,52,76,37,35,2,38,11,75,91,57,72,81,36,46}

    83

    Returns: 5182.929781607518

  62. {100}

    4

    Returns: 0.0

  63. {5, 10, 10, 10 }

    5

    Returns: 30.886890422961002

  64. {34, 62, 79, 29, 38, 38, 5, 39, 57, 25, 24, 27, 24, 83, 54, 72, 12, 95, 11, 65, 62, 65, 98, 62, 63, 42, 63, 5, 64, 78, 3, 1, 92, 60, 98, 27, 92, 44, 67, 1, 9, 29, 28, 14, 18, 94, 64, 19, 66, 68 }

    3

    Returns: 2767.087523846886

  65. {100, 10, 1, 1, 10, 100, 100, 10, 1, 1, 10, 100, 100, 10, 1, 1, 10, 100, 100, 10, 1, 1, 10, 100, 100, 10, 1, 1, 10, 100, 100, 10, 1, 1, 10, 100, 100, 10, 1, 1, 10, 100, 100, 10, 1, 1, 10, 100 }

    10

    Returns: 1950.4110370245667

  66. {100, 1, 100, 100, 1, 1 }

    95

    Returns: 601.62361448294

  67. {100, 2, 100, 2, 100 }

    4

    Returns: 396.32310051270036

  68. {1, 51, 100, 1 }

    10

    Returns: 209.00753754569197

  69. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50 }

    100

    Returns: 5089.709782605168

  70. {1, 2, 8, 100, 98, 10, 100, 34, 12, 100, 99, 100, 19, 43, 13, 12, 100, 100, 100, 100, 100, 100, 100, 100, 100, 9, 2, 100, 100, 29, 10 }

    43

    Returns: 2639.5685714652464

  71. {1, 2, 4 }

    2

    Returns: 5.60555127546399

  72. {2, 1, 1, 2 }

    1

    Returns: 3.82842712474619

  73. {1, 100, 1, 100 }

    10

    Returns: 298.51130631853795

  74. {1, 2, 5, 100, 1, 3, 100, 2, 1, 100, 5, 40, 100, 12, 100, 99, 1, 15, 100, 60, 50, 100, 1, 12 }

    14

    Returns: 1529.6658157576385

  75. {100, 99, 88, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 60, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 52, 52, 51 }

    100

    Returns: 6122.496143467997

  76. {36, 2, 1, 4, 5, 8, 96, 65, 5, 6 }

    5

    Returns: 261.23081191346324

  77. {100, 2, 100, 2, 100, 33, 44, 5, 55, 66, 77, 55, 88 }

    7

    Returns: 932.1960719164986

  78. {1, 10, 100 }

    10

    Returns: 109.50376877284599

  79. {1, 10, 10, 1 }

    1

    Returns: 19.110770276274835

  80. {3, 50, 80, 90, 6 }

    2

    Returns: 276.1265368295624

  81. {2, 2, 1, 3, 4 }

    5

    Returns: 21.02899092203087

  82. {3, 2, 1 }

    2

    Returns: 4.82842712474619

  83. {100, 1, 1, 100 }

    1

    Returns: 199.01010075246163

  84. {1, 2, 3 }

    2

    Returns: 4.82842712474619

  85. {5, 3 }

    1

    Returns: 4.123105625617661

  86. {50, 45, 1 }

    10

    Returns: 90.24411338142782

  87. {16, 25, 12, 13, 51, 12, 6, 89, 6, 86, 54, 58, 14, 32, 27, 4, 66, 7, 93, 2, 74, 29, 47, 66, 14, 98, 93, 88, 88, 8, 49, 12, 78, 26, 8, 98, 51, 24, 52, 22, 76, 37, 35, 49, 61, 63, 11, 19, 28, 52 }

    97

    Returns: 5611.37850356068

  88. {2, 100, 2, 100, 50, 100 }

    10

    Returns: 497.51884386422995

  89. {90, 1, 35, 70, 99, 10, 50, 11, 13, 33, 60, 50, 40, 30, 10, 99, 55, 16, 60, 53, 57, 63, 16, 1, 10, 5, 2, 3, 4, 5, 6, 7, 7, 8, 9, 16, 95, 16, 32, 32, 66, 13, 15, 15, 16, 19, 20, 25, 33 }

    95

    Returns: 5060.868086519161

  90. {100, 2, 2, 100 }

    1

    Returns: 199.01010075246163

  91. {1, 100, 1, 1, 100, 1 }

    20

    Returns: 424.0

  92. {10, 50, 100 }

    1

    Returns: 108.06043551436824

  93. {100, 100, 100, 100, 100 }

    5

    Returns: 396.50472884948044

  94. {10, 9 }

    1

    Returns: 9.055385138137417

  95. {2, 10, 10, 5 }

    1

    Returns: 22.233875901892496

  96. {20, 40, 60, 70, 80, 90, 10, 60, 55, 3, 99, 99, 99, 40 }

    99

    Returns: 1607.1064447643892

  97. {100, 1, 100, 100, 1, 1, 2, 2, 3, 4, 4, 2, 100, 100, 99, 90, 100, 100, 100, 90, 80, 90, 80, 90, 100, 10, 100, 1, 10, 100 }

    95

    Returns: 3543.256352118813

  98. {50, 15, 8, 20, 50, 19, 38, 30, 45, 1, 1, 1, 1, 1, 50, 12, 48, 32, 45, 11, 43, 100, 1, 12, 88 }

    3

    Returns: 908.6756534435257

  99. {1, 10, 100, 84, 34, 75, 34, 88, 11, 1, 22, 33, 44, 55, 100, 88, 15, 45, 75 }

    4

    Returns: 971.9020717717231

  100. {10, 8, 5 }

    2

    Returns: 14.560219778561036

  101. {5, 5, 2 }

    1

    Returns: 8.246211251235321

  102. {1, 4, 6 }

    2

    Returns: 7.385164807134504

  103. {3, 4, 88 }

    5

    Returns: 92.52872452327188

  104. {2, 3, 100, 2, 100 }

    2

    Returns: 299.29666785570646

  105. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 47, 48, 49 }

    4

    Returns: 1227.9369749565783

  106. {1, 46, 91, 100, 1, 46, 91, 5, 100 }

    2

    Returns: 569.1938838734787

  107. {50, 30, 59, 30, 49, 49, 39, 39, 30, 10, 10, 1, 39, 40, 20, 30, 40, 30, 40, 29, 99, 88, 69, 4, 3, 2, 6, 7, 1, 3, 6, 29, 30, 44, 58, 38, 30, 10, 10, 10, 10, 10, 10 }

    100

    Returns: 4505.53649020157

  108. {100, 2, 1, 1, 2, 100 }

    1

    Returns: 201.01010075246163

  109. {4, 2, 3, 4 }

    1

    Returns: 7.63441361516796

  110. {1, 2 }

    100

    Returns: 100.00499987500625

  111. {100, 1, 2, 3, 4, 1, 1, 1, 1, 100 }

    100

    Returns: 981.5320316993422

  112. {1, 2, 3 }

    1

    Returns: 3.23606797749979

  113. {1, 2, 3, 3 }

    1

    Returns: 5.47213595499958

  114. {5, 1, 4, 3, 4, 5 }

    20

    Returns: 101.29107171899787

  115. {1, 2, 3, 4, 5, 4, 3, 2, 1, 1, 2, 1, 1, 1, 2, 3, 4, 3, 2, 1, 100, 1, 1, 1, 2, 3, 4, 5, 6, 6, 6, 6, 4, 3, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 3, 2, 1, 100 }

    100

    Returns: 5023.327596290844

  116. {2, 1, 1, 2, 2, 1, 1, 3, 2, 1, 1, 1, 2, 1, 3, 8, 24, 56 }

    1

    Returns: 87.69442954849627

  117. {50, 15, 8, 20, 50, 19, 38, 30, 45, 1, 1, 1, 1, 1, 50, 12, 48, 32, 45, 11, 43, 100, 1, 12, 88, 99, 12, 1, 15, 38, 39, 57, 68, 88, 89, 97, 33, 92, 34, 100, 100, 100, 100, 2, 3 }

    7

    Returns: 2234.9825228448544

  118. {100, 1, 100, 100, 1, 10, 50, 19, 90, 98, 100, 15, 17, 100, 90, 90, 90, 90, 80, 70, 60, 20, 10, 100, 90, 18, 20, 20 }

    95

    Returns: 3233.2064416800113

  119. {1, 67, 3, 45, 78, 90, 23, 12, 34, 72, 91, 87, 52, 58, 24, 51, 74 }

    93

    Returns: 1795.3221382497823

  120. {2, 1, 1, 2, 1, 3, 8, 24, 49, 100 }

    1

    Returns: 154.763284751235

  121. {2, 1, 1, 3 }

    2

    Returns: 7.06449510224598

  122. {3, 16, 17, 39, 12, 88, 80, 98, 73, 89, 4, 1, 92, 13, 2, 65, 7, 3, 69, 76 }

    5

    Returns: 1115.1380910781872

  123. {2, 3, 100, 3, 2, 100, 2, 3 }

    2

    Returns: 403.1452949398549

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