Statistics

Problem Statement for "IncredibleMachine"

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.

We are observing a system with some unknown acceleration of gravity. There is a slope which has the form of a polyline with N vertices. Each vertex of the polyline is positioned lower and to the right of the previous one. At time 0, a ball is placed at the first vertex. The ball is small enough to be considered a single point. Assume that there's no friction between the slope and the ball, the ball is absolutely nonelastic, and the direction of its velocity changes instantly at the polyline's vertices. Under these conditions, the ball will follow the polyline without ever losing contact with it. The ball reaches the final vertex at time T.

You are given int[]s x and y, where (x[i], y[i]) are the coordinates of the i-th vertex. Return the gravitational acceleration in this system. A body rolling down an inclined plane of angle alpha (measured between the plane and horizontal direction) under gravitational acceleration g has a constant acceleration of a = g * sin(alpha). The distance d travelled by an object during time t moving with initial velocity v0 and with constant acceleration a is equal to d = v0 * t + 0.5 * a * t^2. The velocity v1 of the object after time t has passed is equal to v1 = v0 + a * t.

Definition

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

Notes

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

Constraints

  • x will contain between 2 and 50 elements, inclusive.
  • Elements of x will be strictly ascending.
  • Elements of x will be between 0 and 100, inclusive.
  • x and y will contain the same number of elements.
  • Elements of y will be strictly descending.
  • Elements of y will be between 0 and 100, inclusive.
  • T will be between 1 and 100, inclusive.

Examples

  1. {0,6}

    {100,22}

    4

    Returns: 9.807692307692307

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

  2. {0,26,100}

    {50,26,24}

    4

    Returns: 26.743031720603582

    And this is likely on Jupiter.

  3. {0,100}

    {100,0}

    8

    Returns: 6.250000000000003

  4. {0,7,8}

    {10,6,0}

    7

    Returns: 1.1076837407708007

    Note that in spite of the angle at vertex (7,6), the body won't fly off the slope and will follow the segment (7,6)-(8,0).

  5. {0,100}

    {1,0}

    1

    Returns: 20002.000000000004

  6. {0,1}

    {100,0}

    100

    Returns: 0.020002

  7. {4,8,19,20,23,26,29,31,35,39,42,47,50,52,55,60,63,67,69,70,74,76,79,80,82,85,86,88,89,90,95,98}

    {100,99,94,92,91,89,86,84,81,78,72,67,64,63,62,60,59,58,53,48,45,42,37,35,22,15,12,9,8,7,5,3}

    44

    Returns: 0.3508891171443518

  8. {4,6,8,9,21,27,34,38,41,43,53,55,56,58,67,68,70,72,75,76,80,89,92,94,96,97}

    {98,95,89,84,78,77,76,70,66,64,62,59,58,55,54,47,44,40,31,28,26,24,23,16,10,6}

    71

    Returns: 0.08590581355212065

  9. {3,6,7,12,13,14,15,18,23,25,26,28,29,31,33,37,40,41,42,46,47,48,49,52,53,57,58,63,64,67,69,71,73,76,85,87,92,93,94,98,99,100}

    {100,97,94,93,87,83,77,76,75,74,73,68,66,61,60,58,54,52,51,49,47,43,42,35,34,32,31,30,28,27,24,23,22,21,16,15,14,10,9,6,5,3}

    65

    Returns: 0.10159426713033466

  10. {2,7,9,23,31,32,43,45,51,56,57,66,68,70,72,75,78,91,100}

    {99,96,87,85,84,79,75,73,72,58,53,42,38,35,32,31,21,15,7}

    77

    Returns: 0.09227475125261662

  11. {4,5,10,13,19,21,22,23,24,26,29,38,39,41,42,43,44,46,49,50,53,56,57,58,59,60,62,63,64,66,68,73,75,77,78,79,80,85,86,88,89,93,94,96,99,100}

    {98,97,94,93,90,89,85,84,82,77,76,75,73,72,70,67,66,63,62,61,58,57,56,50,46,45,44,42,41,40,39,35,34,30,26,25,23,21,19,15,14,13,11,8,7,6}

    48

    Returns: 0.21327037314389624

  12. {1,3,4,8,11,12,17,18,22,24,29,39,41,42,43,44,46,47,50,53,54,57,63,66,67,70,71,73,74,76,79,80,82,83,84,85,86,89,91,93,94,96,100}

    {100,93,91,89,88,86,84,82,80,72,69,65,64,61,59,58,56,55,51,48,47,45,44,42,41,40,39,36,35,34,32,31,30,28,27,24,22,19,16,14,9,3,1}

    81

    Returns: 0.06286695631251715

  13. {11,13,14,15,20,22,24,25,29,34,35,37,38,41,45,51,52,56,57,59,61,62,64,65,66,74,75,77,78,79,80,87,88,90,91,96}

    {100,98,94,93,92,90,84,78,77,76,72,62,59,58,51,48,47,46,44,37,35,33,31,30,29,25,23,22,21,20,17,12,9,8,5,2}

    29

    Returns: 0.47505200669869774

  14. {6,11,15,18,19,21,22,24,28,32,34,38,39,40,45,47,50,53,56,58,59,61,62,66,67,69,70,71,72,73,74,76,77,80,82,87,93,96,98}

    {98,95,94,89,88,86,84,82,77,76,73,72,71,65,61,59,53,50,49,48,47,45,44,41,40,38,37,35,34,32,31,25,20,19,16,13,7,2,1}

    20

    Returns: 1.1872814409449153

  15. {9,86,96}

    {68,64,32}

    59

    Returns: 1.049661828204787

  16. {3,11,16,28,30,36,37,46,55,62,63,85,87,96,99}

    {90,85,73,70,68,60,49,40,38,26,22,19,16,15,7}

    16

    Returns: 1.8122286644545182

  17. {2,4,5,6,7,10,14,19,20,22,25,26,32,33,35,36,37,38,42,51,52,53,59,61,63,70,71,72,73,75,82,83,87,90,92,93}

    {99,97,95,90,87,86,85,83,80,78,76,73,68,67,66,65,64,63,61,55,50,43,42,41,39,36,31,23,22,18,15,12,5,4,3,1}

    31

    Returns: 0.4379617599463084

  18. {7,14,15,19,21,50,56,60,77,86,88}

    {80,78,72,69,68,48,39,31,26,10,3}

    50

    Returns: 0.20427114727192094

  19. {1,2,4,9,14,17,24,29,39,41,44,48,60,67,72,81,84,89,91,96,99,100}

    {90,88,78,77,70,67,63,51,50,48,41,39,38,28,26,25,16,13,11,9,7,1}

    2

    Returns: 100.88545887226479

  20. {2,4,6,9,12,13,14,17,18,19,21,22,24,26,27,29,32,33,38,41,43,45,46,50,53,54,55,56,57,58,59,60,61,62,64,66,71,77,79,80,82,83,85,89,92,93,95,96,97,98}

    {100,99,97,96,95,93,90,88,86,84,83,81,80,75,74,73,71,69,66,64,60,57,53,52,51,50,48,47,46,45,43,41,39,38,37,36,35,34,33,27,25,21,18,17,16,14,12,9,4,3}

    85

    Returns: 0.06994564382209403

  21. {2,3,4,7,9,11,14,16,17,20,25,26,27,28,30,31,32,33,38,44,45,46,53,55,58,61,63,65,66,68,69,72,76,79,80,83,86,87,88,89,95,96,99,100}

    {98,97,95,94,93,90,82,81,80,77,74,73,72,71,68,67,66,65,58,55,54,52,51,49,47,40,38,37,36,35,34,32,31,30,29,26,24,23,20,19,17,16,10,8}

    51

    Returns: 0.15880913400551766

  22. {4,9,15,18,29,30,31,38,41,42,43,44,48,49,52,55,57,59,61,63,64,65,68,70,74,79,80,85,94,95,96,97,98,99}

    {97,91,90,87,83,81,79,77,76,74,72,58,53,52,50,48,47,46,43,42,38,36,34,28,26,23,22,21,20,19,10,9,6,5}

    87

    Returns: 0.06387348338471038

  23. {7,14,33,36,95}

    {71,49,33,26,15}

    97

    Returns: 0.030768022040635404

  24. {1,3,4,6,9,13,17,18,20,24,28,34,38,43,47,54,66,68,71,74,77,80,82,85,86,87,89,90,98}

    {98,97,90,88,85,84,82,80,77,73,69,68,65,63,54,53,49,48,35,33,31,27,22,20,18,16,10,5,2}

    43

    Returns: 0.25842956188197036

  25. {13,18,31,46,48,55,69,76}

    {93,87,82,67,53,31,12,4}

    97

    Returns: 0.035724650600767176

  26. {1,4,5,8,9,14,17,18,22,29,34,40,45,49,59,60,62,65,67,71,72,84,87,88,90,91,92,95,97,100}

    {96,95,94,86,82,74,72,71,68,66,64,61,59,55,52,50,47,45,44,40,38,35,28,26,22,17,16,14,5,1}

    15

    Returns: 2.318545440342977

  27. {1,2,4,6,7,9,10,12,14,15,16,19,22,24,25,26,27,28,29,32,34,40,41,44,45,48,53,54,57,60,62,73,74,76,77,78,81,82,85,89,90,92,94,95,97,98}

    {97,88,85,84,83,81,80,79,78,77,74,72,70,69,68,67,66,63,58,57,56,53,52,47,40,39,38,37,36,34,33,27,26,25,24,21,20,14,13,10,9,7,5,4,2,1}

    71

    Returns: 0.07465116494648613

  28. {3,4,6,9,10,17,18,20,24,26,27,32,33,45,56,60,61,62,65,69,72,74,81,86,87,89,91}

    {99,98,93,91,88,85,84,80,73,57,53,48,47,45,43,42,40,38,37,36,31,28,25,20,19,10,5}

    58

    Returns: 0.1173782021693497

  29. {21,38}

    {40,15}

    9

    Returns: 0.9027160493827163

  30. {4,5,7,9,10,11,13,15,16,17,19,21,23,25,27,28,29,30,31,36,37,40,41,42,44,47,48,50,60,61,63,66,76,80,82,83,85,87,88,89,91,92,96,97,98,100}

    {100,97,95,89,88,87,85,83,82,80,79,77,76,75,74,73,71,65,64,62,60,55,53,50,44,43,41,38,36,34,33,30,27,26,24,23,22,20,19,18,17,15,11,9,6,5}

    22

    Returns: 0.7671971639721655

  31. {2,3,7,15,22,43,48,62,85}

    {90,63,61,58,34,30,26,9,7}

    60

    Returns: 0.08931359313505766

  32. {1,6,32,39,40,41,52,63,66,71,84,85,89,95}

    {89,84,79,77,67,61,53,36,35,22,20,17,10,6}

    32

    Returns: 0.5447044021596468

  33. {2,4,6,9,11,14,15,16,18,19,25,27,31,32,33,34,43,44,45,46,48,50,51,52,54,55,56,59,62,63,64,67,68,70,71,73,74,75,76,77,81,82,83,85,89,93,96,100}

    {99,97,95,93,92,91,89,88,87,86,85,83,81,80,78,76,73,72,68,65,63,61,58,57,55,54,51,50,49,40,38,34,31,28,27,22,21,20,19,18,15,13,12,9,8,5,4,2}

    14

    Returns: 2.448125753991936

  34. {3,26,44,47,56,57,64,74,84,85,90,98,99}

    {95,81,79,75,65,58,50,48,30,28,15,6,2}

    69

    Returns: 0.1196240519779429

  35. {39,58,63,73,98}

    {83,82,77,17,1}

    85

    Returns: 0.22574063895865865

  36. {1,6,8,9,10,13,15,16,17,19,23,27,28,29,30,31,35,36,39,40,45,47,49,52,55,56,62,64,65,67,69,70,73,77,81,82,87,88,91,92,99}

    {97,95,91,90,89,88,86,77,73,72,71,69,61,60,59,58,50,49,48,43,39,38,35,32,28,27,24,23,22,20,19,18,14,12,11,10,9,8,4,3,2}

    9

    Returns: 6.238148082542964

  37. {2,6,9,11,19,20,21,24,25,26,27,36,39,43,45,54,60,68,69,72,73,76,78,82,84,86,87,88,92,97}

    {97,92,85,82,81,79,77,71,68,60,58,53,51,50,49,46,42,40,39,37,31,29,27,23,22,20,13,12,2,1}

    54

    Returns: 0.142418794820918

  38. {1,11,15,21,29,52,63,84,85,89,90,95}

    {93,84,70,57,55,48,38,36,31,26,14,8}

    70

    Returns: 0.08643255917047979

  39. {3,4,6,8,9,10,11,12,14,16,17,18,24,26,27,28,31,35,36,37,40,44,45,49,51,52,55,60,61,62,66,67,71,72,74,75,79,80,83,88,89,96,97}

    {96,94,91,85,84,82,81,72,71,65,62,61,60,59,57,54,53,51,48,47,44,43,42,37,35,34,30,27,25,24,23,21,19,18,14,13,12,11,10,9,8,7,5}

    6

    Returns: 9.86035382854815

  40. {4,5,8,20,22,23,27,33,36,42,43,44,53,54,55,56,57,58,59,60,86,91,96}

    {97,96,92,91,89,88,86,84,83,82,77,73,70,63,57,51,47,41,19,15,14,8,7}

    21

    Returns: 1.3376296399818641

  41. {2,4,5,9,14,16,20,26,27,28,32,57,68,93}

    {100,99,96,85,82,80,70,65,59,58,52,40,27,1}

    21

    Returns: 0.9043226816748323

  42. {3,4,5,8,10,12,18,19,21,22,23,24,26,27,31,32,33,34,35,36,37,38,48,50,51,53,54,55,56,59,61,64,65,67,70,71,75,76,77,79,82,88,90,91,92,94,97,98,100}

    {97,91,90,89,88,84,81,80,75,74,72,71,70,66,65,61,60,59,58,57,55,52,51,50,46,45,42,40,39,38,36,35,33,31,29,28,27,25,23,21,18,13,11,10,8,6,5,3,2}

    96

    Returns: 0.04284539299719726

  43. {12,13,14,16,24,31,32,33,34,35,42,47,49,53,62,70,71,72,78,81,89,90,93,94,98,100}

    {100,91,90,85,82,79,76,74,71,65,64,60,50,49,43,42,40,29,28,26,25,24,11,7,5,3}

    94

    Returns: 0.04456806202935621

  44. {1,5,7,9,12,21,26,35,38,39,41,44,45,47,50,51,56,58,60,67,69,70,71,73,74,75,79,80,81,84,85,89,90,93,96,100}

    {99,97,96,95,93,90,81,80,79,77,75,73,69,68,63,58,57,52,50,48,47,43,38,37,34,32,30,23,19,14,13,11,5,3,2,1}

    40

    Returns: 0.3810861110507062

  45. {2,4,9,10,12,14,16,17,19,22,23,25,26,27,28,29,30,31,32,33,39,40,42,43,52,56,57,58,60,61,62,66,67,69,71,72,73,74,77,78,81,85,90,93,94,96,98,100}

    {100,97,94,93,90,88,85,80,76,74,71,68,65,64,63,62,61,59,56,55,53,50,46,44,39,37,35,32,31,29,28,27,26,25,24,23,22,20,18,17,15,13,11,9,8,5,2,1}

    55

    Returns: 0.13052012987318598

  46. {5,6,8,9,14,16,19,21,22,23,26,36,40,41,43,44,47,50,51,52,56,58,62,63,65,73,74,75,76,77,78,79,80,81,86,87,91,94,95,97}

    {100,97,91,88,84,83,71,69,67,66,64,63,62,60,58,55,52,51,47,46,45,43,42,40,34,33,32,31,30,26,24,21,15,14,13,12,9,5,4,2}

    34

    Returns: 0.3289154299018763

  47. {7,8,9,10,17,19,28,32,34,39,49,50,58,59,63,65,67,73,74,78,80,90,93,94,96}

    {91,90,82,81,79,78,76,75,74,72,66,64,59,56,55,53,45,38,31,28,27,26,17,15,5}

    61

    Returns: 0.12158824132087609

  48. {1,3,4,7,12,16,18,19,22,25,26,27,30,31,35,37,38,44,45,47,48,50,59,64,69,70,75,78,83,84,85,86,90,92,95,97}

    {95,94,89,88,85,82,81,78,73,71,70,62,61,60,57,56,53,52,49,45,41,40,36,35,33,28,26,25,22,21,20,17,16,13,8,6}

    92

    Returns: 0.05436201552371344

  49. {1,7,9,10,12,15,18,22,27,29,30,36,39,42,43,44,48,51,52,61,62,65,70,75,76,78,82,84,85,89,95,98}

    {98,93,91,90,89,88,86,81,68,66,63,62,61,53,51,45,44,36,35,32,31,26,25,24,17,16,14,11,8,6,5,2}

    51

    Returns: 0.17505369824038333

  50. {4,6,9,11,13,14,18,19,20,24,27,38,40,41,43,48,50,53,55,56,62,63,65,66,68,71,73,81,88,92,97,100}

    {97,95,94,93,91,86,85,84,78,75,69,66,65,64,60,47,43,40,34,33,32,30,26,25,24,21,20,19,17,14,6,1}

    12

    Returns: 3.1872783149906616

  51. {8,16,22,31,51,62,73,74,97}

    {93,79,75,69,68,53,38,37,12}

    21

    Returns: 0.8352310087885916

  52. {3,4,8,10,13,20,24,25,33,35,38,40,41,44,45,55,59,63,66,67,69,71,72,80,88,90,91,97,99}

    {100,97,96,92,87,85,65,55,52,50,46,44,43,42,40,37,36,32,30,29,27,26,25,23,16,10,9,8,5}

    7

    Returns: 8.424311414202764

  53. {1,2,7,13,22,25,36,37,38,53,60,85,90,96,99}

    {100,88,85,81,67,66,64,59,58,57,55,51,47,26,17}

    59

    Returns: 0.11981816031169423

  54. {3,4,16,17,18,19,23,25,26,27,31,33,38,41,46,50,51,56,58,61,69,75,79,83,85,88,91,93,94,97,98,99}

    {100,95,92,91,86,84,82,77,76,75,74,71,67,66,64,60,57,55,54,49,42,41,40,32,29,22,19,15,13,12,7,2}

    53

    Returns: 0.16217985398399193

  55. {1,2,7,12,16,25,28,31,37,41,45,48,50,52,57,59,61,62,67,71,75,80,83,86,87,90,91,96}

    {98,96,84,82,79,69,66,61,60,58,55,43,37,36,33,31,30,29,27,25,23,15,14,11,5,4,3,1}

    4

    Returns: 23.515327900457642

  56. {1,2,4,5,7,8,10,11,13,14,15,16,21,27,28,32,33,36,39,40,44,45,49,51,52,53,54,56,59,64,67,69,70,71,76,77,78,82,83,84,86,93,95,98,99,100}

    {100,96,94,89,88,87,84,83,80,79,77,76,75,74,73,70,69,68,67,66,62,61,57,52,51,48,43,41,40,39,38,37,35,31,30,29,27,26,22,21,20,18,14,12,7,2}

    69

    Returns: 0.08681803169298105

  57. {26,33,47}

    {76,15,3}

    58

    Returns: 0.048039159635711204

  58. {19,23,93}

    {65,22,6}

    86

    Returns: 0.036567872214892286

  59. {44,52,57,58,75}

    {100,86,85,71,57}

    25

    Returns: 0.22253374276602436

  60. {18,22,24,56,67,77}

    {94,86,41,40,34,20}

    16

    Returns: 1.0675177705514436

  61. {4,8,39,57,72,97}

    {97,77,70,66,61,8}

    27

    Returns: 0.5948190923208516

  62. {9,47,48,50,54,66}

    {95,77,63,51,34,33}

    31

    Returns: 0.4252969591873462

  63. {26,39}

    {82,40}

    78

    Returns: 0.015129457437149748

  64. {7,14,33,36,85,95}

    {90,71,49,33,26,15}

    66

    Returns: 0.07275988372083177

  65. {21,38,46,93}

    {40,33,15,5}

    7

    Returns: 7.916833880764825

  66. {24,93,100}

    {76,65,60}

    59

    Returns: 0.2842507380286895

  67. {76,78}

    {46,12}

    42

    Returns: 0.03868213952247567

  68. {13,17,64,85,98}

    {73,46,35,27,9}

    41

    Returns: 0.19309499238142558

  69. {33,61,81}

    {94,28,21}

    89

    Returns: 0.025737309019335648

  70. {49,66,71,84,89}

    {91,88,68,24,8}

    49

    Returns: 0.2588548175845644

  71. {43,81,94,96}

    {94,56,55,26}

    85

    Returns: 0.03837721943363127

  72. {13,46,58,66,80}

    {93,85,72,57,26}

    38

    Returns: 0.4687530887192758

  73. {9,21,35,60,96,100}

    {97,77,75,57,11,3}

    28

    Returns: 0.4838396931954325

  74. {42,70}

    {92,87}

    11

    Returns: 2.6743801652892563

  75. {26,32,53,94,95,98}

    {100,68,53,35,28,4}

    8

    Returns: 4.937427205466061

  76. {25,49,93,95}

    {90,79,71,41}

    58

    Returns: 0.16056039932868243

  77. {1,9,10,17,19,20,23,27,28,31,34,37,39,43,45,46,48,58,61,67,69,73,74,76,77,80,81,90,93,94,97,100}

    {97,96,90,87,86,82,76,73,72,71,69,67,65,62,61,57,56,52,42,40,37,27,26,23,19,15,13,12,8,7,5,1}

    6

    Returns: 24.284185842266385

  78. {4,9,10,14,16,17,19,22,23,25,26,28,29,30,31,32,33,40,42,43,52,56,57,58,60,61,62,66,67,69,71,72,73,74,77,78,81,85,94,96,98}

    {100,97,94,93,90,88,85,80,76,74,71,68,65,64,63,61,56,55,53,50,46,39,37,35,31,29,28,27,26,25,24,23,22,18,17,15,11,9,8,5,2}

    6

    Returns: 12.647034758636012

  79. {3,6,8,9,10,14,17,19,22,25,26,28,32,34,36,38,45,47,48,49,50,52,53,64,65,68,73,82,84,86,90,94,95,96,98,100}

    {100,97,90,76,73,71,70,68,66,64,61,57,55,54,53,50,48,46,43,41,38,37,36,35,33,31,30,28,26,25,22,17,14,8,4,1}

    2

    Returns: 102.95870245424061

  80. {2,5,15,19,20,22,27,31,34,36,39,52,53,54,55,59,61,64,65,69,70,71,74,75,77,82,91,92,95,96,97,100}

    {98,86,84,83,82,79,78,74,71,66,63,61,55,54,51,50,49,48,47,46,45,44,35,30,28,24,22,17,16,6,4,2}

    8

    Returns: 7.130433793809195

  81. {1,5,7,9,12,21,26,35,38,39,41,44,45,47,50,51,56,60,67,69,70,71,73,75,79,80,81,84,85,89,90,93,96,100}

    {99,97,95,93,90,81,80,79,77,75,73,69,68,63,58,57,52,50,48,43,38,37,34,32,30,23,19,14,13,11,5,3,2,1}

    9

    Returns: 6.581969715632265

  82. {1,2,3,4,9,14,16,17,23,26,29,30,34,38,39,41,44,47,48,50,51,56,59,60,63,64,65,67,74,78,79,81,84,85,86,88,90,91,96,99}

    {100,99,98,95,90,89,88,84,81,78,77,75,72,70,68,67,64,58,57,56,50,48,44,41,39,35,34,32,28,26,25,24,15,13,11,9,7,6,5,1}

    8

    Returns: 6.92297600829009

  83. {4,6,9,10,11,13,14,18,19,20,24,27,29,32,35,38,40,41,43,48,50,52,53,55,56,58,62,63,65,66,68,71,73,81,82,88,92,94,97,100}

    {100,99,97,95,94,93,91,89,86,85,84,78,75,69,66,65,64,60,54,49,47,43,40,35,34,33,32,30,26,25,24,21,20,19,17,14,13,11,6,1}

    3

    Returns: 53.12415117086146

  84. {4,8,10,16,17,21,22,25,28,31,32,34,40,47,51,52,60,62,65,73,74,79,81,83,86,90,97}

    {93,89,79,75,69,68,66,61,59,53,51,48,44,43,42,40,38,37,30,26,21,15,12,9,6,2,1}

    8

    Returns: 6.0812596035319775

  85. {1,2,3,4,5,7,13,16,17,21,22,23,24,25,27,33,34,35,36,37,38,41,42,46,53,59,60,69,73,74,76,82,85,90,95,96,99,100}

    {100,97,95,89,88,86,85,82,81,78,73,72,69,67,66,64,62,60,59,58,57,55,51,49,47,34,33,32,29,26,25,20,17,16,12,9,3,1}

    7

    Returns: 8.217213341155478

  86. {2,3,8,9,11,13,14,17,21,27,29,30,31,32,35,36,37,42,46,47,48,49,50,53,56,57,58,60,62,68,73,79,80,86,88,90,91,92,93,97,100}

    {100,99,97,96,95,88,86,85,83,79,77,73,72,69,68,67,66,62,58,56,55,54,48,47,43,42,40,34,28,27,26,23,22,20,19,18,12,10,9,7,5}

    2

    Returns: 118.40208864369161

  87. {4,5,6,7,15,21,25,31,32,33,36,37,42,44,49,51,57,68,72,79,84,88,93,94,95}

    {92,90,82,79,76,73,71,68,64,63,55,54,50,49,46,45,44,41,40,33,28,27,20,19,4}

    8

    Returns: 6.101432089900507

  88. {3,4,9,11,12,16,17,24,25,26,27,28,30,32,36,37,39,42,46,49,51,54,55,59,62,63,71,74,75,76,78,79,85,87,89,96,98,99}

    {90,85,84,81,73,70,69,68,60,58,56,55,50,49,48,40,38,37,32,30,27,26,22,21,20,19,17,16,15,13,12,9,8,7,6,5,3,2}

    8

    Returns: 6.27262066668572

  89. {1,6,9,10,14,18,22,24,29,32,34,35,37,38,39,44,45,49,50,52,55,56,59,60,61,65,68,70,71,75,77,79,80,81,86,87,88,89,90}

    {98,96,93,91,88,87,86,82,81,80,77,73,70,68,65,59,56,55,53,52,47,44,42,38,36,32,31,28,23,20,19,18,17,16,13,11,7,4,3}

    6

    Returns: 14.789814644625674

  90. {1,2,5,7,14,15,16,17,19,20,21,22,23,26,28,29,30,36,38,40,43,50,51,52,53,56,59,60,62,64,66,67,71,72,77,78,79,84,86,88,93,96,97,98}

    {100,98,97,93,90,88,84,80,78,77,76,72,70,69,68,67,52,51,49,48,47,46,45,43,41,39,38,37,35,34,31,27,26,25,24,19,16,15,14,11,10,4,3,2}

    2

    Returns: 111.39064925950503

  91. {4,15,16,19,24,25,26,27,30,32,38,40,42,44,45,46,49,53,56,57,58,60,61,63,67,72,75,83,86,88,95}

    {99,98,97,96,94,91,90,89,88,81,78,77,71,70,64,63,59,57,54,48,44,42,40,29,28,27,23,21,16,14,1}

    3

    Returns: 132.65932312713576

  92. {5,8,9,10,12,14,16,19,23,25,26,28,29,33,37,39,40,42,43,45,46,47,49,50,52,53,56,58,61,62,68,70,72,73,77,78,81,83,84,88,89,96,97,98}

    {97,95,90,89,85,84,83,82,80,78,76,74,72,69,67,66,63,62,60,58,57,54,53,50,49,48,47,46,45,42,38,32,27,26,20,15,14,12,11,7,5,4,2,1}

    7

    Returns: 8.807975196710327

  93. {1,2,3,7,9,11,13,17,18,22,24,28,29,31,32,33,36,37,40,43,45,46,47,48,55,58,63,64,65,67,68,69,72,73,76,86,87,92,93,94,95,96,98,99,100}

    {99,96,95,93,92,89,88,87,86,82,81,79,75,74,72,71,69,67,63,61,57,56,53,52,46,44,37,35,31,28,26,25,23,22,19,17,16,15,14,13,12,9,7,5,4}

    4

    Returns: 26.246963988470142

  94. {4,8,9,10,11,15,21,25,28,30,35,38,39,42,44,45,46,52,53,54,55,56,57,58,63,65,66,73,75,76,82,85,86,88,92,94,100}

    {100,99,97,94,93,89,86,85,83,81,80,77,76,75,74,73,71,69,68,67,62,61,58,57,52,51,45,44,42,40,33,30,16,11,10,8,7}

    1

    Returns: 613.8564972992187

  95. {2,3,6,11,14,15,20,25,27,29,36,45,49,50,53,55,67,72,77,78,81,82,86,87,88,89,91,92,93,96}

    {98,97,96,90,85,81,79,78,68,61,56,54,51,50,47,46,45,41,37,30,24,19,18,14,13,11,10,8,3,1}

    3

    Returns: 52.314947976919036

  96. {2,3,4,7,9,21,22,23,38,45,49,50,54,57,63,64,67,68,69,72,75,78,79,88,90,91,94,95,96,100}

    {96,95,87,83,82,79,78,73,70,69,65,64,63,61,60,57,56,53,51,39,37,36,32,24,19,13,8,6,5,1}

    7

    Returns: 9.858868328136493

  97. {88,92,96,97}

    {96,94,93,90}

    3

    Returns: 6.076100865462094

  98. {88,89,90,91,92,93,94,95,96,97}

    {97,96,95,94,93,92,91,90,89,88}

    1

    Returns: 35.99999999999999

  99. {88,92,93,94,95,96}

    {97,96,94,93,90,88}

    1

    Returns: 81.84947220970487

  100. {91,93}

    {96,95}

    1

    Returns: 10.000000000000004

  101. {90,94,95,96}

    {97,95,93,91}

    2

    Returns: 9.330127018922193

  102. {1,2,6}

    {56,5,4}

    7

    Returns: 2.2533066454881383

  103. {1,3}

    {96,4}

    1

    Returns: 184.08695652173915

  104. {1,2,3}

    {96,5,4}

    1

    Returns: 184.85377649576782

  105. {0, 100 }

    {1, 0 }

    1

    Returns: 20002.000000000004

  106. {0, 100 }

    {100, 99 }

    1

    Returns: 20002.000000000004

  107. {0, 1 }

    {100, 0 }

    1

    Returns: 200.02

  108. {0, 100 }

    {2, 1 }

    1

    Returns: 20002.000000000004

  109. {0, 1, 2, 3, 4, 5, 6, 7 }

    {100, 97, 90, 82, 71, 51, 20, 10 }

    10

    Returns: 1.8485407796269264

  110. {0, 99, 100 }

    {100, 99, 0 }

    1

    Returns: 23330.38016528926

  111. {0, 7, 8 }

    {10, 6, 0 }

    7

    Returns: 1.1076837407708007

  112. {2, 3, 10, 12, 16, 18, 19, 20, 24, 25, 26, 31, 34, 35, 37, 38, 39, 40, 41, 43, 44, 47, 48, 49, 50, 52, 53, 54, 55, 56, 59, 61, 62, 64, 65, 67, 69, 71, 72, 76, 77, 80, 82, 87, 88, 89, 91, 92, 95, 96 }

    {100, 97, 94, 93, 89, 85, 84, 83, 80, 79, 74, 72, 71, 70, 69, 67, 66, 64, 61, 59, 55, 54, 52, 51, 49, 48, 46, 45, 44, 42, 39, 38, 37, 32, 31, 29, 28, 27, 26, 25, 23, 20, 18, 13, 12, 11, 10, 9, 5, 3 }

    1

    Returns: 411.146418676107

  113. {0, 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, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 }

    1

    Returns: 196.00000000000017

  114. {1, 2, 3, 4, 5, 6, 7, 8, 9, 50 }

    {100, 90, 80, 77, 60, 50, 40, 30, 20, 10 }

    1

    Returns: 254.90587438498275

  115. {0, 100 }

    {100, 0 }

    1

    Returns: 400.00000000000017

  116. {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 }

    {49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 }

    1

    Returns: 196.00000000000017

  117. {0, 1 }

    {100, 0 }

    100

    Returns: 0.020002

This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2024, TopCoder, Inc. All rights reserved.
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