Statistics

Problem Statement for "YetAnotherRobotSimulation"

Problem Statement

Manao has constructed a robot which can move on a plane and has a remote control device. The only instructions the robot understands are "UP", "DOWN", "LEFT" and "RIGHT". If (x, y) is the robot's current location, then after receiving an "UP" instruction, it will move to (x, y+1). Similarly, after receiving "DOWN", "LEFT" and "RIGHT" instructions, it will move to (x, y-1), (x-1, y) and (x+1, y), correspondingly. Unfortunately, it seems that the robot's receiving device sometimes malfunctions. When an instruction is sent to the robot, there is a 1/2 probability that it receives an instruction and performs it, and there is a 1/2 probability that its receiving device malfunctions, in which case the robot will remain in its current position.

The robot is initially located in (0,0). You are given a set of points on the plane. The coordinates of the i-th point are (locationsX[i], locationsY[i]). Manao wants to get his robot in one of these locations. In order to do it, he will choose a fixed sequence containing exactly L instructions and will send all of them, in order, to the robot (some of the instructions might be performed by the robot and some might be ignored due to the malfunction). The quality of a sequence is defined as the probability that the robot finishes in one of the given locations after Manao sends the entire sequence of instructions. Return the maximum possible quality of a sequence of length L.

Definition

Class:
YetAnotherRobotSimulation
Method:
getMaximumProbability
Parameters:
int, int[], int[]
Returns:
double
Method signature:
double getMaximumProbability(int L, int[] locationsX, int[] locationsY)
(be sure your method is public)

Notes

  • The returned value must have an absolute or relative error less than 1e-9.
  • You can assume that when Manao sends an instruction to the robot, whether its receiving device will malfunction or not does not depend on the robot's behaviour for each of the previously sent instructions.

Constraints

  • L will be between 1 and 50, inclusive.
  • locationsX will contain between 1 and 50 elements, inclusive.
  • Each element of locationsX will be between -100 and 100, inclusive.
  • locationsY will contain the same number of elements as locationsX.
  • Each element of locationsY will be between -100 and 100, inclusive.
  • Points (locationsX[i], locationsY[i]) will be distinct.

Examples

  1. 3

    {1,2,2}

    {1,1,0}

    Returns: 0.5

    One of the optimal sequences is {"UP","RIGHT","RIGHT"}. If the robot's receiving device malfunctions at the first instruction, then the remaining two instructions should surely be performed in order to reach location 2. The probability of this case is 1/8. On the other hand, if the first instruction is successfully accomplished, only failing both of the remaining instructions will get the robot nowhere, which means a 3/8 success chance. Summing these up, we obtain 1/2.

  2. 5

    {0,0,0,0}

    {0,1,2,3}

    Returns: 0.9375

    A possible strategy is pushing "UP" four times and "DOWN" once.

  3. 1

    {0}

    {0}

    Returns: 0.5

    Sometimes malfunctioning is desirable.

  4. 8

    {2,3,3}

    {1,1,0}

    Returns: 0.41015625

  5. 36

    {6,7,12,-21,5,5,2,4}

    {4,5,-2,4,5,12,5,7}

    Returns: 0.1323284485260956

  6. 1

    {1}

    {-1}

    Returns: 0.0

  7. 1

    {1,-1,0}

    {0,0,-1}

    Returns: 0.5

  8. 2

    {1,-1,0}

    {0,0,-1}

    Returns: 0.5

  9. 50

    {1,-1,0}

    {0,0,-1}

    Returns: 0.2159137935754174

  10. 37

    {0,1,2}

    {1,0,2}

    Returns: 0.1285853206354659

  11. 20

    {-5,-2,-3,-4,5,4,2,1,3}

    {0,0,0,0,0,0,0,0,0}

    Returns: 0.7574987411499023

  12. 3

    {0,1,2,3}

    {0,0,0,0}

    Returns: 1.0

  13. 14

    {9,-3,35,40,14,-14,48,-21,-50,-40,30,35,9,-47,1,42,-28,21,-5,15,9,-31,19,-28,-49,-13,26,-18,-5,-16,17,43,-21,46,-22,15,19,31,0,-39,5,-11,-45,-43,4,-22}

    {46,-37,45,27,-1,23,14,-17,-27,11,-13,46,-7,-1,48,-37,41,11,-45,16,10,-11,-28,27,28,-43,-22,29,-37,47,30,-26,-18,20,-4,20,-12,-31,-7,-3,-4,5,-16,-34,4,-48}

    Returns: 0.20947265625

  14. 17

    {27,20,-32,9,-18,-20,-5,-38,3,-17,10,29,-8,-18,-41,-6,-20,-2,-48,-34,-35,-22,-27,44,22,-35,-14,-7,-39,-3,35,-36,4,-46,10,4,6,-50,19,39,38,37,7}

    {-5,2,2,45,-13,-4,-9,-16,20,13,6,39,-48,17,49,25,33,27,-25,4,-14,-30,-20,-30,-2,29,-13,29,-15,-43,-50,-19,-44,-14,-33,28,-31,37,-41,33,-38,5,-41}

    Returns: 0.0025177001953125

  15. 26

    {25,3,-4,8,19,-9,20,-18,-14,5,-27,-39,16,-31,-35,28,33,6,-21,-22,-29,-26,-39,37,11,12,-20,-46,49,-40,1,7,35,1,-22,18,2,-44,43,-3,-14,29,47,40,-4,-19}

    {7,47,-4,39,-13,10,32,45,-24,23,-13,1,12,43,29,29,10,38,-31,-18,-1,26,48,29,-23,-24,14,38,13,-50,12,-35,-44,19,-13,-24,40,-25,-34,49,-10,26,-30,43,-38,40}

    Returns: 0.08185684680938721

  16. 34

    {-19,39,-11,-20,-48,-30,3,-48,46,7,47,42,36,-35,20,26,5,49,4,-23,22,-41,-35,1,-7,0,30,-20,2,-4,-14,-1,5,-7,-49,-19,27,-13,5}

    {-44,-9,-23,-28,1,-36,39,33,40,-48,-2,43,-32,18,29,-28,-37,-38,9,-50,38,-22,32,-3,36,-45,-19,33,-22,-28,20,-45,38,-36,-20,37,38,42,35}

    Returns: 0.06997496704570949

  17. 50

    {-23,-33,0,-2,16,-35,29,-11,-18,38,40,39,48,-16,-40,45,7,-46,42,-6,-6,-22,15,6,17,18,-39,-28,-31,41,-2,-9,43,25}

    {-24,29,-7,47,-6,-10,31,-7,-14,-17,-25,-45,2,-27,48,10,-25,28,11,-17,25,-5,46,-22,-7,-7,-27,49,-43,-35,23,42,48,31}

    Returns: 0.11227517265921705

  18. 50

    {-49,-21,-27,27,27,-20,-3,33,-20,26,-39,18,-33,23,28,48,-31,10,-24,-46,-26,22,-4,42,-18,14,-43,-9,29,-11,40,-24,37,-2,-34,12,26,-6,-46}

    {23,-39,30,-18,22,-2,-2,-49,8,-43,-17,-32,-8,23,-3,-11,-31,19,44,4,44,11,-30,39,43,-32,49,32,37,-44,-11,-6,-22,18,21,-10,22,-13,15}

    Returns: 0.043876582870540304

  19. 43

    {29,-9,14,24,35,-4,24,-43,43,28,24,30,33,-22,20,-46,5,-35,36,42,-39,-46,23,-45,31,14,7,27,-22,47,22,21,-44,-28,13,15,12,-38,20,23,-49,-35}

    {47,-25,-1,-17,20,34,48,35,-15,-2,13,47,7,46,-46,27,-12,10,19,-21,-23,15,24,25,-20,11,3,-22,11,3,-22,48,46,-20,9,29,-48,-13,39,10,17,19}

    Returns: 0.061195391524506704

  20. 38

    {41,-12,7,13,20,-5,5,-46,41,-48,33,-44,-8,24,49,-50,-24,39,-40,8,14,-24,20,-11,2,-39,-17,-41,42,10,28}

    {-4,13,47,-15,-37,23,46,-14,-9,18,29,35,-6,-39,-18,33,18,-9,-24,-13,-39,-25,-4,10,31,-33,24,-45,35,-31,2}

    Returns: 0.034961538040079176

  21. 11

    {9,-40,-28,33,7,-19,12,-15,37,15,-42,10,-35,5,45,-13,-14,-4,-6,-40,-24,46,-15,29,18,-29,-11,3,11,40,-38,39}

    {47,9,-4,7,-8,32,-15,21,-42,19,5,-29,-11,-26,-18,-48,-32,-38,-29,25,-33,7,12,-2,41,12,36,34,-39,-29,11,4}

    Returns: 0.0

  22. 41

    {21,34,-19,19,40,43,45,23,-35,-46,-36,14,39,13,11,37,-16,-50,-10,-41,30,6,-7,32,-38,16,-33,-18,-5,4,20,0,-14,-38,-17,18,34,26,-9}

    {49,-36,17,49,34,-48,24,27,30,-43,-46,-19,-32,-46,39,47,-46,-22,-26,-1,5,49,2,20,9,-6,-42,14,40,8,10,-15,-44,-33,33,43,44,-11,0}

    Returns: 0.12238567124768451

  23. 47

    {9,8,20,-16,39,-4,-27,7,-10,22,-39,-27,-15,41,-7,-30,-33,49,26,39,30,47,1,33,-16,-10,-12,20,-9,-17,33,-1,-44,23,-19,43,-7,-10}

    {49,-26,-20,17,-29,-4,-6,-18,-25,16,45,-10,7,-27,-11,19,10,-9,-10,39,-37,-25,-1,-50,28,41,-35,34,-30,-48,-46,44,16,15,47,-36,-50,-31}

    Returns: 0.05850204393880176

  24. 47

    {40,7,-31,-36,-34,42,44,23,12,-31,-40,12,19,-17,33,-19,5,-18,24,-50,-42,32,3,47,8,-22,19,13,9,-30,5,49,40,44,-3,-32,19,-34,-42,-41,-13}

    {-25,-17,28,-9,42,-17,-17,14,-35,-20,-24,-39,43,-26,39,-44,-32,-50,32,-32,-27,-34,23,-33,10,-36,10,7,43,-5,-8,-21,-12,-5,43,49,-48,-32,36,-20,46}

    Returns: 0.031941047887791285

  25. 39

    {-44,12,18,-37,12,10,8,-37,-12,-15,-19,0,18,-7,44,-23,-43,14,2,22,0,35,39,13,-2,40,-45,11,40,38,32}

    {48,-6,43,12,49,28,43,31,-32,-24,-6,-5,-32,-38,8,39,-13,-21,-10,-38,-46,2,-9,22,23,45,31,20,-34,-48,-23}

    Returns: 0.12537068761957926

  26. 50

    {-10,2,-33,-46,23,-38,13,-12,15,0,-10,29,-3,18,-40,11,-2,-50,-18,26,-47,36,23,31,43,-29,39,20,42,7,23}

    {-29,-35,14,44,-38,23,19,15,-39,30,42,-27,-23,29,-4,-48,-12,45,7,-7,-34,3,-39,-12,-32,44,-33,17,34,14,-7}

    Returns: 0.044014771237694816

  27. 25

    {-33,-19,-13,-33,33,0,-35,-21,16,-15,-24,4,-18,-45,29,34,49,42,34,7,5,-39,-26,-48,-24,-10,-11,-12,14,16,23,-38,49,27,21,0,38,-39,0,11,12,40,15}

    {0,-35,-45,-22,-8,-44,-2,17,12,36,25,-27,-15,40,-14,8,34,-28,22,-16,23,38,12,-42,-40,-46,-3,23,32,-21,15,36,11,26,-45,-48,49,-23,-13,36,43,-8,-40}

    Returns: 0.15498101711273193

  28. 22

    {21,-43,-4,-49,-48,12,-24,11,-1,-3,20,49,-33,-48,2,44,21,26,-40,-25,-10,19,49,13,38,-45,-42,11,7,45,18,-10,-23}

    {-14,-50,5,49,-3,41,-21,33,-16,-37,-17,-49,17,-39,-34,-34,41,-10,18,25,5,37,-38,-9,-26,42,19,-29,-47,-35,-22,-19,-32}

    Returns: 0.057277679443359375

  29. 50

    {46,37,22,-8,46,5,-37,0,-34,-31,34,-17,-9,-21,-2,-10,-1,-5,-44,37,29,3,-30,22,8,-2,-45,45,-31,-19,41,-11,23,26,20,-48,-41,14,27,7,-20,32,15,30,11,-3,35}

    {39,9,-18,-42,-30,49,-3,21,48,-20,-29,10,-13,-33,-27,-19,39,32,-12,-25,-3,4,-42,-13,-46,-2,-20,-48,19,10,-18,-49,-49,31,-42,38,-18,6,26,42,20,-10,34,6,-42,-12,38}

    Returns: 0.11227517265921705

  30. 43

    {46,44,-28,18,-43,-35,10,19,7,-38,-44,14,-28,-10,-10,46,18,-35,-9,-19,38,-18,-5,-17,-14,-8,-21,-2,-22,-38}

    {32,47,16,-9,17,-9,19,-22,-9,47,-2,6,28,-15,2,40,-48,47,2,-31,28,36,12,5,36,-19,-47,-49,-30,10}

    Returns: 0.09402801571468444

  31. 49

    {-18,-20,21,18,-36,17,9,-19,-22,9,-2,-34,-18,20,-8,45,-26,-7,4,1,22,-40,-50,-10,-41,-8,-11,-8,-48,31,44,-22,4,33,-50,-44,-48,16,15,-11,44,3,7,-5,34,-16,-13,-35,25}

    {7,44,-28,21,-19,-47,6,-3,37,49,-44,-48,13,-34,40,-45,-26,14,-6,35,30,41,11,-45,39,35,10,46,8,5,-23,-32,30,-49,12,18,11,35,-41,-6,-26,-12,10,-15,49,25,20,-38,-7}

    Returns: 0.04534845938012566

  32. 47

    {-46,-36,-34,-18,6,12,25,-27,7,35,-38,44,-16,35,-38,44,-31,-22,-1,13,41,-25,-29,-43,28,29,-32,-8,48,-45,-21}

    {-48,-31,35,25,-28,26,-26,12,21,-39,-36,-4,34,-13,27,32,-45,-34,33,-2,47,43,-22,26,-21,-30,32,-33,16,-49,-10}

    Returns: 0.04485156701974802

  33. 25

    {36,-30,-33,-7,-3,-2,-13,25,14,44,-47,-6,-30,-27,0,43,18,28,-40,-36,33,23,36,8,-28,-46,-23,10,-37,-34,-37,-32,-35,43,-4,-45}

    {-25,33,19,46,42,-44,24,-3,31,-27,-47,49,11,-42,-24,2,10,35,-31,-19,-50,-48,18,13,-29,-23,7,36,23,-33,-40,-2,9,29,40,-13}

    Returns: 1.5020370483398438E-4

  34. 26

    {-7,-31,32,-16,30,2,-27,-46,-41,-23,-8,-2,-28,28,-16,34,-38,-46,20,-6,2,4,-25,33,1,6,30,8,-39,-28,-35,-43,11,-37,-38,-5,-6,2}

    {-13,-42,48,2,4,-42,4,29,26,13,11,-4,19,17,6,1,-28,-15,29,19,-43,-1,-45,40,9,-31,30,-17,-36,-2,-12,-24,-40,22,-50,-12,-19,46}

    Returns: 0.0805901288986206

  35. 30

    {10,48,-4,-5,-39,-3,42,28,30,-48,34,-24,9,-22,2,-23,18,-4,3,-2,17,-24,41,5,-32,-6,4,9,10,48,-4,15,-6,-39,25,-7}

    {8,-47,-32,-6,-1,14,9,27,39,-24,46,40,3,-39,-26,-5,13,-23,-22,-44,11,-8,3,-6,22,34,-38,42,11,-40,-21,38,7,-48,-25,-48}

    Returns: 0.05036883056163788

  36. 40

    {-26,41,-35,-11,42,-33,19,-9,29,29,-4,13,19,-34,-26,28,-28,-9,13,-23,-10,-31,33,-6,-44,-7,-1,48,22,24,41,-3,15,-27,49,43,-4,-35,19,21}

    {25,-26,-43,19,-46,-36,21,-9,-49,-7,-41,8,13,0,-5,49,32,-2,-3,-14,46,-31,-47,-15,-29,13,49,-1,10,-1,-14,8,14,-37,-12,-26,47,38,14,-4}

    Returns: 0.04952272483933484

  37. 40

    {-22,28,-48,6,8,45,-31,22,-8,-20,-49,49,28,-20,41,11,15,41,-31,38,1,49,34,-49,-21,24,-19,10,-2,-49,-23,27,-2}

    {-2,47,-19,30,-16,-5,37,47,-41,-28,-17,40,-36,8,8,30,-40,10,-28,23,25,33,1,-26,33,5,27,-13,32,-24,-15,-49,-47}

    Returns: 0.026788832585225464

  38. 48

    {5,33,-7,24,-18,-44,14,-17,-45,-16,48,-9,19,26,35,9,-25,-12,15,-22,-26,-48,-16,18,-5,17,-35,43,30,28,-18,-48,-25,-40,48,34,46,11,-4,13}

    {-23,-42,-14,-19,-49,17,6,-47,-1,-14,-11,31,-28,8,-41,37,-15,-5,-48,-44,-14,-26,-33,-48,25,-34,-49,26,19,-30,-4,12,23,-16,-5,-48,45,-1,-13,10}

    Returns: 0.05850204393880176

  39. 47

    {-24,47,-17,-4,5,-18,-42,12,-49,26,-46,-49,41,12,18,15,-10,7,-17,11,-11,2,-43,-44,-2,-21,-22,5,-17,20,-39,-25,-25,9}

    {33,18,21,22,15,2,-50,-2,-25,-42,-48,-31,38,-8,-22,33,9,-32,-39,-40,-40,-45,-1,16,-4,-40,-5,-7,-34,-7,47,-7,38,8}

    Returns: 0.04485259736720337

  40. 25

    {3,27,46,20,28,-48,-14,0,37,32,19,-16,-1,7,-4,-45,15,13,35,-15,28,-28,-13,43,2,-46,-1,11,0,-18,45,-42,43,26,-25,-35,7,7,32,4,24,17,8,16}

    {27,13,28,-6,29,19,-34,16,25,0,-13,8,-34,-19,24,-45,-12,26,-14,22,41,-16,17,27,-4,-24,26,19,2,0,-20,34,-42,40,32,27,12,-11,29,24,22,22,18,10}

    Returns: 0.15498101711273193

  41. 45

    {38,-10,39,-31,-28,13,-17,38,-18,-11,-46,34,-12,-33,-43,-22,-18,22,-3,3,11,48,-23,-45,45,-36,13,-9,-48,-26,18,43,-47,-47}

    {9,46,33,-17,32,28,41,-25,-3,-24,-10,38,12,-21,-13,-10,19,13,21,-18,18,19,28,44,-41,-43,-23,-15,43,49,39,-12,-34,-21}

    Returns: 0.03917833988111852

  42. 33

    {-20,-38,-18,16,-33,-37,-14,-22,2,-45,30,43,19,12,33,-6,-12,-29,43,33,41,-31,-41,17,-6,46,27,-5,30,-10,-36,47,-18,-45,-18,-46,16,-27,1,-42,15}

    {14,14,30,49,13,8,0,32,47,-39,-14,-50,23,44,27,37,38,-4,-25,44,-39,-24,3,3,13,-11,-13,-1,25,24,-2,28,27,8,11,42,-31,-37,35,-23,21}

    Returns: 0.13583375955931842

  43. 34

    {7,1,44,-31,-42,-26,13,17,14,-14,17,-34,22,-25,-28,16,-28,5,-25,30,-45,-1,31,40,-9,-8,20,-6,11,1}

    {-19,-20,-8,16,25,9,17,-44,5,-10,9,-39,38,-45,33,-30,5,-14,16,-24,-21,10,-48,41,30,-46,-24,28,0,10}

    Returns: 0.13583375955931842

  44. 44

    {26,48,-24,1,11,-13,0,29,-40,47,2,-39,33,29,38,-14,-3,34,-34,27,8,-34,2,17,-36,-40,30,-39,-4,-33,-34,36,27,-29,-12,23,23,22,-5,48,-4,6}

    {-29,42,-27,-19,11,40,44,-19,41,-38,25,-18,-11,-30,9,-12,19,15,43,-31,37,-50,34,-5,37,46,-35,-50,-5,37,41,49,27,0,9,10,-24,-45,-4,41,-10,37}

    Returns: 0.07267286449632593

  45. 50

    {-26,36,-9,-21,-48,12,-23,4,38,8,-15,8,32,45,7,8,33,8,-47,-47,-9,0,-14,46,14,-8,-22,16,18,42}

    {-13,44,-11,37,-32,44,5,-23,-33,25,-22,-30,-17,-19,-14,26,34,16,25,33,22,26,25,-14,46,-50,8,5,-30,-48}

    Returns: 0.1079568967877087

  46. 28

    {16,31,-38,25,40,-17,-16,18,22,14,-25,22,12,-4,-36,-21,8,22,23,-2,13,15,17,-17,-25,-42,30,14,1,14,-24,36,-35,-17}

    {36,-4,-14,35,-12,17,6,40,2,2,35,25,34,29,-46,-7,-38,-35,-18,-24,-2,32,-22,-36,-31,44,0,-31,-7,-17,-14,-20,-39,-1}

    Returns: 0.07749050855636597

  47. 41

    {-48,35,14,41,34,6,-46,-26,6,-26,39,21,-49,49,-49,42,-23,48,44,42,-1,-47,-7,-40,24,-6,12,0,26,44,20,-20,-27,12,-42,33,-35,-29,-12,-25,-4,-30}

    {45,46,16,20,-27,-32,-13,20,21,24,-10,40,-20,7,18,48,48,-8,35,12,29,21,43,-27,-33,3,19,13,-35,22,-35,-30,-18,11,-2,41,3,-44,-31,-50,35,8}

    Returns: 0.12238567124768451

  48. 50

    {-7,-9,-23,36,33,-27,-50,-47,-47,18,3,-20,-42,-11,18,42,-38,-38,-9,16,-33,-46,-45,-41,42,-28,-30,0,27,-33,1,-32,7,-27,-38,-7,34,-9,-10,-4,-6,41,-28,-41,23,-11,-38,47}

    {18,19,-7,-22,18,16,-11,-4,-48,-16,-32,-25,-18,-26,46,-40,-34,-26,-17,36,-14,7,45,6,32,-24,-15,17,-40,-1,20,-31,-5,-2,-40,8,-32,45,2,-1,-5,-33,6,13,39,-17,12,-11}

    Returns: 0.11227517265921705

  49. 31

    {22,5,-42,41,-41,38,25,35,-44,-45,4,46,-27,36,-41,-29,46,-5,-48,-30,43,33,29,36,-36,-6,-4,44,26,7,35}

    {26,29,13,41,47,-49,10,42,-26,32,-3,45,7,4,5,14,1,-44,7,-34,-5,-15,8,-27,-34,-32,38,-5,-44,7,29}

    Returns: 0.04843156784772873

  50. 42

    {16,0,-12,-5,30,-25,-50,-38,-6,21,-28,5,-44,20,8,-15,14,21,38,8,-21,-37,13,40,29,31,6,49,-9,23,3,-42,-18,-48,-4,37,-2,-16,-40,-37,35,-16,25}

    {4,-45,28,-11,-2,-27,9,14,-41,7,42,-28,-3,-46,-2,12,38,-20,-6,-37,24,-21,4,37,-39,25,-48,-50,-46,36,-40,25,-2,27,-1,-49,3,-47,-28,8,-20,-49,29}

    Returns: 0.06513887652454287

  51. 32

    {-12,9,33,-18,-23,-38,-11,-11,-41,-27,13,5,-23,-47,43,29,-40,5,-11,-7,-21,-10,-4,-19,22,36,48,-41,-21,1,30,-45,-13,35,-18,38,-24,-9,35,-33,3,-13,0}

    {-31,44,-19,24,48,-6,-32,11,-47,31,40,-15,49,3,22,46,18,-46,-29,41,-49,5,30,-11,-47,20,36,-3,-41,0,6,-47,-2,-15,27,-34,26,-29,20,-9,34,-29,49}

    Returns: 0.13994993409141898

  52. 43

    {-42,-3,-37,-6,-7,2,18,29,1,6,7,44,46,-20,5,18,-46,-43,-41,39,12,-14,-2,12,-42,-42,-28,11,-36,-46,-26,-37,-27,42,-23,-27,36,16,-28,21,-46,39}

    {-16,22,-50,-30,-43,-16,20,48,15,24,8,38,24,-31,-32,41,-7,-5,10,34,-37,-2,-48,33,48,25,1,38,18,-47,42,45,38,21,-24,-32,-27,-27,23,6,48,-49}

    Returns: 0.06119283562384226

  53. 50

    {41,41,6,28,24,27,36,23,43,38,5,25,46,36,27,14,8,49,35,13,15,46,47,21,26,32,4,49,21,13,22,11,2,44,37,17,10,6,29,19,19,21,18,18,40}

    {36,6,38,15,22,45,5,2,14,41,49,27,43,35,29,10,3,20,2,20,18,25,10,16,33,30,35,5,31,48,33,20,4,32,41,46,24,45,4,31,22,25,29,43,29}

    Returns: 0.04550259531293488

  54. 50

    {27,38,12,1,29,13,21,47,19,19,38,23,23,30,44,4,16,14,6,22,3,29,43,46,29,15,2,29,44,49,14,9,41,34,22,38,31,11,31,37,46,27,1,31,44,9,37}

    {35,10,19,48,5,1,33,45,6,48,2,10,22,36,44,23,24,15,4,36,26,28,29,11,27,39,30,15,3,21,30,36,47,22,22,13,33,49,3,3,31,24,34,14,39,21,19}

    Returns: 0.05728325135674339

  55. 37

    {46,7,2,35,2,10,2,10,29,27,49,28,24,44,40,29,46,14,44,43,46,24,21,15,20,31,49,38,33,21,33,16,40,4,14,41,26,11,8,14,14,21,37,34,45,35}

    {9,12,48,25,17,13,38,16,6,31,33,25,41,0,28,26,26,43,32,12,49,11,26,30,16,17,31,35,47,42,32,11,26,9,25,49,18,43,5,28,6,29,42,44,25,15}

    Returns: 0.05121827241964638

  56. 46

    {0,4,4,1,45,25,45,24,35,12,5,12,21,38,44,1,17,30,29,49,46,40,30,15,40,2,22,28,32,19,7,25,0,4,0,14,7,0,2,9,31,22,41,28,18,19}

    {21,49,27,24,35,35,21,19,14,48,3,6,27,39,41,49,42,37,39,11,22,18,36,12,31,10,38,37,34,41,28,25,3,48,16,34,32,27,43,4,46,11,33,32,49,5}

    Returns: 0.18564423772667737

  57. 48

    {27,5,47,5,21,32,30,30,20,48,25,16,43,45,27,11,26,47,34,22,43,41,36,46,38,14,4,30,38,39,35,24,7,20,9,27,40,25,6,27,22,38,29,11,29,44,13,10}

    {23,4,41,28,49,27,14,40,30,47,37,36,45,25,40,30,18,40,33,26,13,37,10,5,36,8,11,34,37,49,45,8,14,10,33,10,6,25,11,30,1,22,23,6,5,40,15,4}

    Returns: 0.06627126996075461

  58. 49

    {46,2,4,16,12,15,28,29,40,17,47,10,19,12,26,41,49,44,30,25,6,23,7,11,13,28,47,48,0,31,24,37,34,27,40,6,21,10,45,16,30,48,26,43,25,0,26,13}

    {32,26,47,0,24,19,17,26,34,20,35,11,34,46,28,6,19,36,13,12,8,35,9,21,12,38,24,14,17,48,19,40,1,42,14,0,49,12,31,42,19,17,43,19,36,15,15,37}

    Returns: 0.2159137935754174

  59. 50

    {-24,-23,-22,-25,-14,-25,-24,-6,-5,-22,-23,-5,-5,-16,-13,-8,-17,-12,-21,-12,-9,-22,-7,-6,-14,-1,-16,-6,-19,-17,-19,-16,-14,-15,-22,-1,-2,-3,-19,-2,-14,-2,-16,-12,-23,-3,-14,-12}

    {14,6,10,21,24,12,7,3,4,12,10,6,13,0,1,21,4,0,5,20,24,9,6,16,17,0,17,24,11,24,8,2,22,22,7,13,18,21,13,20,9,22,3,13,1,13,7,15}

    Returns: 0.19203119661730383

  60. 50

    {-59,57,-61,-33,-87,-80,72,29,10,-79,-100,57,14,23,20,97,35,-96,-88,60,-1,22,-88,76,49,-86,62,-33,-73,21,-52,-58,50,-62,54,62,33,-100,14,85,94,93,26,-74,-23}

    {-70,97,-96,-15,-52,-45,41,-28,87,-99,-85,-21,-67,-1,10,98,24,32,-47,-59,-36,-87,-84,80,-30,19,75,-48,-97,-16,-22,60,64,-9,-39,49,-90,-22,-34,-15,89,-97,-13,-61,11}

    Returns: 0.05728325135674339

  61. 50

    {1,16,73,96,53,5,44,-5,-90,11,42,15,4,-51,-50,-33,-30,23,37,-47,14,-57,11,21,70,-81,-92,85,55,27,-45,-37,-19,33,-17,23,-65,-6,30,-31,-28,-6,6,-12,37,46,-34,77,75,26}

    {80,56,-62,-49,-37,-46,-82,87,34,65,-44,40,-26,54,80,-65,47,-85,-6,-1,-38,44,-68,98,-34,89,88,-79,-26,45,75,98,46,66,-52,-49,-65,-32,-67,94,-94,6,88,60,57,-6,-46,78,26,55}

    Returns: 0.029007040104289672

  62. 50

    {-86,87,38,-50,16,-11,64,9,79,-47,-62,79,-57,49,-79,23,-20,-58,43,-98,22,14,24,52,-76,-51,-1,84,34,49,-55,-51,51,6,-57,-23,88,-81,60,-92,99,-34,-95,-21}

    {58,-71,-46,72,23,93,4,33,7,4,40,-48,-84,72,-21,-58,40,3,68,-49,46,-84,65,-77,-97,-57,-55,22,-69,55,-18,78,98,-48,-53,-78,-93,54,-24,62,63,94,-57,39}

    Returns: 8.76050432196962E-6

  63. 47

    {-46,94,-10,62,69,-97,-54,-70,59,-16,3,-61,79,-82,64,-98,14,32,34,56,-88,-93,-23,-94,-38,67,-95,70,-7,-87,21,64,-25,-90,77,14,-21,-21,-17,-82,-33,-3,28,-54}

    {8,-75,-61,-54,69,-2,-30,62,41,99,99,1,65,86,-48,54,43,88,-36,-57,19,37,-22,-48,6,-71,47,-68,74,58,82,79,-17,-99,55,-32,90,8,96,38,94,69,98,-93}

    Returns: 0.0084861191788832

  64. 49

    {55,1,69,7,-41,-41,-61,41,-43,-20,-26,24,46,74,-12,-74,33,-15,16,-17,39,-78,-61,-26,85,-10,23,47,-75,-97,-44,96,-38,39,51,-48,-94,-98,-98,-92,-78,-55,62,-67,24,-69}

    {85,-85,-92,51,50,-78,74,-83,-12,59,-29,34,-96,25,57,-73,58,-21,-29,-53,-18,-22,-14,45,9,20,52,-84,-84,52,-60,-68,48,-34,16,69,29,52,9,-43,-95,23,30,-18,-45,-9}

    Returns: 0.008153330191476016

  65. 50

    {0}

    {50}

    Returns: 8.881784197001252E-16

  66. 50

    {0}

    {51}

    Returns: 0.0

  67. 8

    {0,1,2,3,4,5,6}

    {9,8,7,6,5,4,3}

    Returns: 0.0

  68. 5

    {0,0,0,1,1,1,2,2,2}

    {0,1,2,0,1,2,0,1,2}

    Returns: 0.875

  69. 10

    {0,0,0,1,1,1,2,2,2}

    {0,1,2,0,1,2,0,1,2}

    Returns: 0.7109375

  70. 25

    {0,0,0,1,1,1,2,2,2}

    {0,1,2,0,1,2,0,1,2}

    Returns: 0.4587438106536865

  71. 47

    {-5,-5,-1,3,2,-9,-1,-8,-7,-10,7,1,5,5,-2,-3,8,8,-10,-10,5,9,-2,-9,-7,4,-7,7,9,0,-1,7,2,4,-5,2,-4,8,-9,-7,3,-3,-7,-2}

    {4,-2,-4,9,7,-9,-9,-3,-9,-4,-2,-5,4,2,8,3,4,-8,9,-5,3,-3,9,7,7,9,6,-7,-9,-6,-10,6,2,-7,3,-3,0,7,1,8,0,-9,0,-5}

    Returns: 0.2161429200455771

  72. 49

    {9,6,-6,1,-5,9,-2,-1,-3,-10,-8,-7,3,-3,9,-4,4,2,1,5,1,9,-3,-2,-3,2,2,9,7,5,4,-8,-9,-2,7,7,-2,7,-2,-4,4,9,-9}

    {3,-4,6,9,8,-2,4,0,1,0,-9,4,-1,7,0,5,8,-7,0,-9,3,7,-8,-2,3,3,4,2,2,3,1,9,5,-5,6,0,-3,-10,6,-9,-9,-10,-7}

    Returns: 0.24605873222782115

  73. 48

    {0,-1,-3,3,-6,5,8,-6,-8,1,3,0,1,-10,-1,-8,-7,5,0,-4,3,3,-9,9,0,2,0,-7,-3,-3,2,0,7,3,4,-3,0,-7,6,-2,-9,-10,1,-9,5,5,-10,7}

    {-4,-6,3,0,8,3,1,2,8,8,6,-5,7,7,-7,2,7,-10,1,5,-7,-3,5,-5,-9,-10,-3,4,-1,-2,-7,7,-10,2,4,-10,3,3,2,6,-6,-8,4,-8,-4,-5,6,0}

    Returns: 0.4349538847345542

  74. 47

    {1,3,8,17,11,6,8,5,2,11,9,16,1,19,11,11,15,14,16,0,18,2,3,0,10,6,11,14,11,1,15,10,12,14,18,17,13,10,19,5,5,9,5,4,1,2,18,15,16,7}

    {1,7,10,14,14,7,13,16,3,8,12,0,0,2,13,6,13,5,6,3,13,9,1,4,10,6,0,6,18,14,19,7,3,15,6,9,17,3,1,15,17,18,3,15,17,13,14,7,17,9}

    Returns: 0.22913300542697357

  75. 48

    {17,0,3,10,8,9,18,8,14,11,7,1,16,15,3,16,12,8,15,19,16,7,16,18,8,2,14,13,4,19,5,12,6,4,9,3,5,16,2,5,17,14,13,2,8,17,6,18,10,18}

    {15,11,12,18,19,7,9,14,17,6,0,10,6,16,0,8,15,6,9,13,16,6,0,0,12,6,8,15,6,9,3,17,15,15,12,3,16,13,18,0,3,12,10,19,2,14,9,2,11,3}

    Returns: 0.30991899427611713

  76. 50

    {16,5,18,2,10,8,10,7,3,8,10,0,12,9,3,12,0,17,16,13,4,15,16,17,10,15,18,8,12,3,1,18,8,19,16,9,11,13,9,12,4,19,9,5,1,13,15,5,0,6}

    {16,4,0,0,8,11,1,9,19,17,7,1,0,10,3,11,6,6,18,0,1,6,4,1,4,10,5,0,18,14,2,10,15,7,9,6,10,4,17,8,16,5,11,14,15,17,2,18,4,15}

    Returns: 0.3090358950920553

  77. 50

    {3,5,12,17,8,17,2,1,6,18,8,13,18,19,19,1,0,13,8,0,12,2,19,14,16,12,10,15,3,4,16,12,6,11,19,1,4,11,1,2,11,12,14,15,8,6,4,9,3,2}

    {2,0,14,11,4,14,0,18,1,18,9,10,15,17,12,1,16,15,1,1,19,16,4,4,9,12,3,16,4,5,3,17,15,19,10,9,8,14,12,17,7,2,15,19,18,17,10,11,11,3}

    Returns: 0.2517221567135408

  78. 49

    {6,8,0,1,0,12,13,11,5,11,9,5,8,16,4,14,17,3,14,13,0,8,0,10,2,1,8,4,19,2,4,8,13,6,5,14,4,14,15,17,0,16,18,16,9,18,4,7,6,12}

    {14,12,16,18,3,19,19,18,1,16,1,18,10,4,13,10,14,9,19,8,5,14,15,18,14,1,2,15,10,0,4,3,15,16,10,11,18,18,16,11,4,16,7,3,11,11,11,16,4,3}

    Returns: 0.32985491478050477

  79. 50

    {-100,-100,100,100,0}

    {-100,100,-100,100,0}

    Returns: 0.11227517265921705

  80. 50

    {0,1,2,3,4,5,25,50,60,70,100}

    {0,1,2,3,4,5,25,0,100,100,100}

    Returns: 0.11227517265921705

  81. 50

    {-100,-100,100,100}

    {100,-100,-100,100}

    Returns: 0.0

  82. 50

    {-100, -99, -98 }

    {1, 2, 3 }

    Returns: 0.0

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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