Statistics

Problem Statement for "CardDrawGame"

Problem Statement

You have a deck of cards. Each card has a small nonnegative integer written on it. You are given the int[] count, where count[x] indicates the number of cards that contain the integer x.

You are playing a game in which the goal is to end with three cards whose total is target. The game is played as follows:

  1. The deck is randomly shuffled.
  2. You draw the top three cards.
  3. You decide which of the three cards in your hand you want to keep and which ones you want to discard. You may keep any subset of cards, including none or all of them.
  4. You discard the chosen cards onto a separate pile. (The discarded cards do not go back into the deck.)
  5. You draw more cards from the deck until you have three cards in your hand again.
  6. If the sum of your cards is target, you win. Otherwise, you lose.

You also lose the game whenever you try to draw a card from an empty deck.

Assuming you play optimally, what is the probability of winning the game?

Definition

Class:
CardDrawGame
Method:
winChance
Parameters:
int, int[]
Returns:
double
Method signature:
double winChance(int target, int[] count)
(be sure your method is public)

Notes

  • The returned value must be within 1e-9 absolute or relative error of the actual value to be accepted.

Constraints

  • target will be between 0 and 50, inclusive.
  • count will contain between 1 and 20 elements, inclusive.
  • Each element of count will be between 0 and 100, inclusive.

Examples

  1. 3

    {0, 3}

    Returns: 1.0

    The deck has three cards, each of which is a 1. You're guaranteed to get a total of 3 on the initial draw of 3 cards.

  2. 10

    {3, 3}

    Returns: 0.0

    There's six cards in the deck, but none of them are larger than a 1, so getting a total of 10 is impossible.

  3. 3

    {1, 3}

    Returns: 1.0

    One of the four cards is a 0 and the other three are 1s. If you draw all three 1s, you win. If you draw two 1s and the 0, the optimal play is to discard the 0 and to draw the remaining card: the third 1.

  4. 6

    {1, 1, 3}

    Returns: 0.7000000000000001

    There's a 0.1 chance of getting 2-2-2 on the initial draw, and not needing to draw any cards. There's a 0.3 chance of getting 0-1-2 on the first three cards (in any order), after which redrawing two cards for the 0 and 1 is guaranteed to end up a winning hand. There's a 0.3 chance of getting 0-2-2, and a 0.3 chance of getting 1-2-2; in either case, redrawing one card gives a 0.5 chance of getting the winning hand. Thus, the answer is 0.1 + 0.3 * 1.0 + 0.6 * 0.5 = 0.7

  5. 12

    {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

    Returns: 0.003681666273366085

  6. 3

    {0,0,0,2}

    Returns: 0.0

    There are only two cards. You will lose the game almost immediately, as you are unable to draw the initial three-card hand.

  7. 0

    {3, 3}

    Returns: 0.39999999999999997

    You always want to keep all the 0s you have and discard all the 1s. In particular, if your initial draw is three 1s, the optimal strategy is to discard the whole hand.

  8. 5

    {1,2,1,1,1}

    Returns: 0.6333333333333331

  9. 50

    {100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100}

    Returns: 0.022323614316228788

  10. 3

    {0,0,0,1}

    Returns: 0.0

  11. 14

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

    Returns: 0.09437229437229548

  12. 15

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

    Returns: 0.11679197994987402

  13. 30

    {0, 1, 2, 0, 2, 3, 2, 0, 1, 2, 1, 3, 0, 3, 2, 2, 1, 2, 2, 0}

    Returns: 0.12354237716306858

  14. 35

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

    Returns: 0.06106749462012641

  15. 1

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

    Returns: 0.0

  16. 6

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

    Returns: 0.007791208065094629

  17. 11

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

    Returns: 0.05533014947633677

  18. 35

    {8, 5, 0, 3, 0, 6, 1, 0, 1, 4, 0, 8, 4, 3, 8, 2}

    Returns: 0.06949851638768732

  19. 32

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

    Returns: 0.10363384969083182

  20. 10

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

    Returns: 0.10026957491148072

  21. 49

    {0, 9, 1, 10, 7, 7, 4, 10, 8, 10, 11, 11, 0, 8, 3, 10, 4, 0}

    Returns: 0.0

  22. 19

    {8, 7, 6, 1, 11, 12, 1, 8, 11, 9, 9, 7, 8, 11, 12, 5, 9}

    Returns: 0.09762082539047387

  23. 5

    {12, 10, 3, 11, 10, 1, 1, 8, 12, 4, 6, 5, 8, 13, 5, 13, 1, 13}

    Returns: 0.028002380594647425

  24. 42

    {11, 6, 5, 0, 5, 9, 13, 0, 14, 6, 10, 12, 4, 4, 3, 4, 3, 7, 13}

    Returns: 0.04990834038245657

  25. 27

    {14, 14, 10, 1, 4, 15, 0, 0, 13, 14, 14, 8, 9, 3, 9, 3, 5}

    Returns: 0.11241266518540505

  26. 26

    {15, 13, 7, 16, 16, 8, 10, 0, 12, 14, 5, 12, 1, 5, 5, 2, 15}

    Returns: 0.0995037542739025

  27. 32

    {7, 14, 5, 12, 0, 4, 2, 17, 12, 0, 12, 15, 14, 11, 3}

    Returns: 0.09929790562789585

  28. 25

    {3, 2, 13, 13, 17, 3, 5, 15, 15, 14, 2, 12, 16, 16, 10, 13, 6, 10}

    Returns: 0.11459931004334731

  29. 41

    {4, 15, 10, 3, 8, 15, 2, 11, 0, 12, 19, 2, 19, 7, 16}

    Returns: 0.011466663352341717

  30. 37

    {16, 8, 9, 16, 19, 3, 17, 1, 9, 5, 15, 7, 12, 19, 15, 0}

    Returns: 0.04877159991280091

  31. 4

    {19, 7, 20, 17, 11, 3, 10, 2, 5, 18, 3, 7, 5, 2, 4, 16, 5, 5}

    Returns: 0.057241622398269576

  32. 6

    {4, 18, 12, 11, 3, 13, 9, 17, 20, 7, 21, 11, 2, 20, 10}

    Returns: 0.025053194981367644

  33. 33

    {6, 17, 4, 10, 2, 10, 22, 21, 13, 16, 17, 18, 21, 11, 16}

    Returns: 0.09361826278967182

  34. 6

    {20, 14, 13, 21, 13, 23, 15, 0, 6, 10, 1, 19, 13, 3, 14, 24, 18, 3}

    Returns: 0.04837891209714356

  35. 12

    {13, 23, 1, 10, 25, 24, 5, 21, 13, 15, 23, 16, 15, 22, 16, 3, 7}

    Returns: 0.07249383877637472

  36. 16

    {0, 17, 15, 10, 4, 21, 5, 24, 9, 2, 1, 23, 26, 19, 9, 1, 20, 19, 21, 0}

    Returns: 0.053973795724048465

  37. 26

    {6, 17, 6, 11, 11, 4, 6, 14, 19, 1, 25, 23, 26, 9, 19, 21, 9}

    Returns: 0.1268338615400366

  38. 25

    {13, 26, 13, 11, 24, 15, 8, 1, 23, 18, 23, 22, 15, 7, 8}

    Returns: 0.12166295571575503

  39. 21

    {27, 0, 12, 6, 24, 13, 11, 16, 2, 11, 23, 27, 19, 28, 20}

    Returns: 0.12153347130663096

  40. 7

    {27, 26, 2, 28, 2, 15, 8, 2, 5, 6, 7, 29, 13, 15, 25, 6, 9, 0}

    Returns: 0.0566658942514588

  41. 2

    {0, 16, 13, 23, 30, 13, 21, 25, 2, 26, 20, 22, 0, 6, 1, 19, 3, 13, 0}

    Returns: 0.0

  42. 16

    {3, 24, 29, 12, 5, 17, 25, 32, 22, 2, 4, 19, 19, 3, 28, 29, 26, 21, 5}

    Returns: 0.07210693919575178

  43. 9

    {23, 6, 24, 24, 11, 18, 1, 1, 12, 8, 14, 5, 0, 27, 27, 26, 27, 8}

    Returns: 0.04027915845981246

  44. 50

    {24, 34, 29, 16, 9, 4, 2, 15, 8, 4, 1, 8, 7, 33, 8, 18, 26, 31, 1, 10}

    Returns: 0.027990005742028024

  45. 23

    {34, 9, 14, 7, 9, 18, 30, 31, 29, 19, 26, 28, 11, 0, 27, 31, 31, 26, 21}

    Returns: 0.09688467833145016

  46. 22

    {19, 19, 25, 24, 2, 33, 17, 9, 29, 25, 6, 6, 2, 23, 21, 36, 9, 0, 16}

    Returns: 0.11005274018995426

  47. 44

    {2, 26, 30, 20, 9, 17, 16, 21, 26, 7, 13, 11, 14, 18, 15, 29}

    Returns: 0.011575481021994799

  48. 48

    {21, 9, 33, 23, 7, 9, 11, 36, 14, 34, 36, 33, 20, 34, 13, 15, 2, 23, 24}

    Returns: 0.016645465308232604

  49. 42

    {31, 38, 10, 12, 25, 3, 30, 20, 35, 34, 4, 16, 6, 8, 32, 37}

    Returns: 0.016327261021177267

  50. 36

    {17, 38, 24, 7, 16, 35, 22, 7, 24, 23, 34, 14, 18, 16, 38, 20}

    Returns: 0.05576784416526737

  51. 2

    {39, 13, 18, 28, 20, 7, 9, 37, 11, 16, 21, 17, 6, 18, 13}

    Returns: 0.02781416882770267

  52. 26

    {39, 41, 13, 12, 31, 31, 4, 24, 41, 1, 41, 37, 9, 6, 26, 19, 14}

    Returns: 0.1209309657979036

  53. 29

    {5, 13, 41, 40, 42, 14, 35, 5, 35, 26, 19, 20, 23, 7, 5, 20}

    Returns: 0.08440321640725144

  54. 49

    {7, 41, 5, 34, 42, 21, 36, 44, 30, 14, 3, 20, 19, 42, 24, 16}

    Returns: 0.0

  55. 36

    {3, 4, 16, 29, 32, 14, 32, 32, 31, 18, 20, 27, 33, 15, 39, 43, 44, 41, 21}

    Returns: 0.11013615346240806

  56. 21

    {13, 36, 11, 12, 15, 2, 1, 44, 38, 32, 38, 16, 38, 18, 12, 21, 37, 38, 40, 35}

    Returns: 0.06641637582641251

  57. 44

    {11, 47, 20, 23, 11, 10, 42, 46, 31, 4, 2, 25, 29, 44, 28, 18, 39, 6, 40}

    Returns: 0.049256310677844584

  58. 23

    {40, 17, 21, 18, 44, 13, 44, 27, 4, 16, 39, 24, 20, 29, 18, 10, 15, 11}

    Returns: 0.12020149965823343

  59. 15

    {19, 2, 13, 44, 36, 30, 1, 22, 0, 40, 18, 17, 35, 26, 48, 33}

    Returns: 0.07341070180531228

  60. 1

    {29, 3, 5, 46, 8, 46, 25, 28, 11, 15, 2, 25, 43, 28, 34, 33, 6, 35}

    Returns: 7.078700465649993E-4

  61. 17

    {28, 34, 31, 37, 10, 10, 50, 48, 15, 17, 42, 20, 12, 35, 43, 31, 32, 51, 47}

    Returns: 0.06596556967723079

  62. 45

    {16, 21, 33, 7, 14, 48, 16, 50, 14, 2, 50, 8, 15, 44, 47, 45, 28, 47}

    Returns: 0.054447314743458604

  63. 23

    {20, 46, 35, 47, 41, 41, 13, 20, 40, 6, 50, 16, 33, 10, 17}

    Returns: 0.12336870725404238

  64. 6

    {47, 10, 5, 11, 52, 3, 54, 49, 32, 11, 38, 41, 51, 35, 39, 39}

    Returns: 0.01882722396622517

  65. 49

    {2, 51, 20, 11, 5, 28, 17, 6, 19, 12, 37, 48, 48, 31, 39, 46, 9}

    Returns: 0.0

  66. 1

    {15, 45, 34, 54, 15, 38, 19, 16, 43, 47, 29, 51, 1, 19, 12, 47}

    Returns: 0.0017117102714796653

  67. 3

    {11, 17, 56, 44, 31, 12, 28, 0, 23, 40, 15, 25, 32, 11, 50, 11, 11, 38}

    Returns: 0.005176037828523804

  68. 19

    {20, 39, 25, 41, 19, 46, 17, 40, 5, 19, 14, 2, 35, 30, 57, 52}

    Returns: 0.1146638725754302

  69. 2

    {18, 53, 29, 11, 11, 35, 19, 50, 29, 18, 18, 39, 47, 3, 53, 19}

    Returns: 0.011723613224677878

  70. 11

    {55, 4, 39, 38, 25, 36, 32, 27, 9, 24, 24, 42, 34, 14, 33, 35, 26, 44, 28, 34}

    Returns: 0.045233370459060174

  71. 1

    {25, 20, 58, 21, 57, 7, 24, 27, 8, 5, 47, 27, 15, 15, 0, 16, 34}

    Returns: 0.0037508368964494707

  72. 5

    {25, 55, 34, 19, 62, 45, 12, 16, 62, 4, 43, 3, 15, 11, 39, 22, 22}

    Returns: 0.04169450875102753

  73. 17

    {63, 33, 35, 47, 26, 6, 33, 62, 29, 13, 39, 23, 50, 35, 25, 35, 20, 20, 40, 19}

    Returns: 0.08323603297238352

  74. 12

    {12, 36, 33, 19, 50, 28, 28, 22, 11, 37, 18, 59, 37, 4, 13, 28, 26, 13}

    Returns: 0.06673383632838645

  75. 1

    {49, 38, 32, 1, 42, 46, 53, 12, 11, 42, 33, 29, 17, 31, 63, 25, 4, 21}

    Returns: 0.01050296103254241

  76. 39

    {40, 29, 46, 29, 31, 62, 47, 25, 54, 23, 59, 28, 4, 52, 59, 29, 54, 2, 54}

    Returns: 0.06794268046890174

  77. 13

    {8, 62, 24, 50, 24, 0, 30, 63, 66, 1, 37, 61, 40, 39, 66, 64, 48, 28, 6}

    Returns: 0.04091242253751325

  78. 9

    {62, 56, 63, 51, 51, 17, 53, 45, 1, 67, 43, 13, 46, 65, 49, 33}

    Returns: 0.07023487522060957

  79. 46

    {27, 6, 33, 33, 22, 47, 47, 29, 17, 30, 13, 17, 46, 6, 18}

    Returns: 0.0

  80. 17

    {49, 34, 66, 8, 68, 19, 30, 41, 58, 66, 33, 12, 44, 32, 1, 70}

    Returns: 0.12238711559813212

  81. 47

    {34, 59, 67, 59, 19, 46, 17, 26, 2, 12, 6, 49, 63, 26, 67, 20, 47, 7, 71}

    Returns: 0.0320322034466686

  82. 10

    {70, 30, 61, 61, 54, 7, 63, 29, 65, 41, 65, 28, 49, 58, 17, 21}

    Returns: 0.08110838168671618

  83. 25

    {42, 0, 66, 25, 70, 57, 20, 37, 66, 55, 60, 70, 55, 2, 21, 54}

    Returns: 0.13025999837128233

  84. 17

    {71, 6, 7, 13, 26, 61, 24, 70, 4, 68, 15, 2, 42, 33, 61}

    Returns: 0.1156587218649779

  85. 44

    {14, 45, 61, 1, 35, 73, 58, 57, 23, 15, 33, 47, 59, 6, 62}

    Returns: 0.0

  86. 50

    {54, 10, 26, 47, 25, 29, 74, 18, 26, 63, 65, 13, 37, 69, 12}

    Returns: 0.0

  87. 43

    {24, 4, 19, 64, 33, 18, 35, 47, 18, 42, 68, 47, 16, 18, 54, 52, 73, 40}

    Returns: 0.058633542010488676

  88. 4

    {77, 48, 2, 13, 54, 21, 8, 12, 16, 13, 9, 27, 3, 23, 49, 12}

    Returns: 0.0955836467757473

  89. 27

    {61, 2, 15, 22, 42, 16, 16, 35, 28, 17, 6, 49, 20, 53, 70, 3, 9, 31, 64}

    Returns: 0.10328474858290537

  90. 23

    {80, 76, 8, 45, 31, 45, 34, 24, 5, 39, 5, 22, 7, 67, 39, 39, 55, 43, 6}

    Returns: 0.10122130471786495

  91. 26

    {76, 32, 81, 23, 66, 80, 20, 24, 79, 3, 68, 59, 29, 33, 53, 61, 0, 6, 43, 79}

    Returns: 0.10215599476591644

  92. 16

    {9, 79, 43, 26, 33, 43, 15, 79, 19, 76, 57, 48, 74, 43, 25}

    Returns: 0.10675619693896607

  93. 28

    {58, 31, 61, 22, 73, 52, 49, 25, 4, 41, 5, 30, 8, 14, 35, 30, 61}

    Returns: 0.07968251672623021

  94. 30

    {79, 12, 1, 75, 42, 36, 72, 5, 33, 47, 47, 46, 20, 11, 32, 11}

    Returns: 0.07184330979113523

  95. 41

    {64, 59, 85, 43, 77, 49, 20, 37, 15, 57, 54, 74, 33, 31, 30, 5, 20, 4, 39}

    Returns: 0.02289682520730049

  96. 11

    {63, 31, 27, 7, 34, 74, 74, 27, 65, 4, 41, 35, 17, 53, 15, 14, 29, 67}

    Returns: 0.06790510025328748

  97. 42

    {78, 23, 77, 14, 50, 41, 34, 0, 64, 68, 34, 22, 65, 1, 80, 65, 75, 39, 73, 38}

    Returns: 0.07284281360902356

  98. 29

    {73, 74, 47, 42, 31, 36, 27, 87, 88, 43, 51, 47, 87, 27, 17, 45, 65, 3}

    Returns: 0.10085709941010385

  99. 23

    {69, 45, 50, 11, 11, 9, 71, 53, 64, 19, 85, 23, 21, 57, 8, 27}

    Returns: 0.13767893530880318

  100. 23

    {49, 24, 63, 89, 9, 80, 71, 63, 25, 7, 2, 41, 71, 24, 48, 1, 17, 71, 85, 50}

    Returns: 0.10111948004772912

  101. 49

    {13, 31, 25, 49, 32, 75, 59, 50, 53, 61, 4, 21, 19, 24, 45, 76}

    Returns: 0.0

  102. 46

    {68, 44, 18, 88, 6, 82, 4, 16, 81, 23, 22, 6, 1, 89, 45, 26, 2, 64, 17, 3}

    Returns: 0.015369098141528275

  103. 26

    {32, 38, 53, 18, 57, 92, 56, 20, 84, 20, 67, 54, 1, 16, 23, 62, 16}

    Returns: 0.12316458751784776

  104. 37

    {3, 1, 74, 58, 26, 38, 21, 35, 66, 92, 39, 84, 78, 53, 23, 41, 12}

    Returns: 0.06740596615973286

  105. 23

    {70, 84, 28, 92, 26, 78, 58, 56, 23, 28, 83, 35, 3, 80, 12, 50, 6}

    Returns: 0.12214899867814244

  106. 3

    {81, 7, 56, 4, 13, 32, 43, 84, 27, 47, 1, 44, 28, 27, 25, 23, 43, 30, 49}

    Returns: 0.005497500306578259

  107. 29

    {14, 16, 78, 65, 79, 53, 41, 46, 57, 62, 59, 63, 75, 21, 97, 4, 53, 75, 64, 69}

    Returns: 0.09749147390260593

  108. 15

    {47, 55, 21, 66, 83, 70, 68, 29, 63, 52, 95, 5, 44, 38, 79, 31, 60}

    Returns: 0.09055832640858527

  109. 1

    {11, 63, 84, 48, 74, 27, 63, 3, 41, 31, 24, 42, 93, 75, 66, 28}

    Returns: 3.209488418479873E-4

  110. 6

    {90, 5, 65, 74, 42, 71, 69, 41, 44, 81, 65, 58, 79, 4, 73, 76, 23, 96}

    Returns: 0.023421055814851443

  111. 35

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

    Returns: 0.0

  112. 39

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

    Returns: 0.0

  113. 16

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

    Returns: 0.0

  114. 33

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

    Returns: 0.0

  115. 35

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

    Returns: 0.0

  116. 50

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

    Returns: 0.0

  117. 21

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

    Returns: 0.0

  118. 34

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

    Returns: 0.0

  119. 44

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

    Returns: 0.0

  120. 49

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

    Returns: 0.0

  121. 22

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

    Returns: 0.0

  122. 16

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

    Returns: 0.0

  123. 31

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

    Returns: 0.0

  124. 4

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

    Returns: 0.0

  125. 41

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

    Returns: 0.0

  126. 13

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

    Returns: 0.0

  127. 8

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

    Returns: 0.0

  128. 36

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

    Returns: 0.0

  129. 41

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

    Returns: 0.0

  130. 2

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

    Returns: 0.0

  131. 50

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

    Returns: 0.0

  132. 34

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

    Returns: 0.0

  133. 45

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

    Returns: 0.0

  134. 3

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

    Returns: 0.0

  135. 35

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

    Returns: 0.0

  136. 31

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

    Returns: 0.0

  137. 19

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

    Returns: 0.0

  138. 29

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

    Returns: 0.0

  139. 48

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

    Returns: 0.0

  140. 32

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

    Returns: 0.0

  141. 3

    {3, 3 }

    Returns: 0.39999999999999997

  142. 50

    {96, 93, 92, 94, 96, 94, 93, 97, 90, 98, 97, 92, 99, 90, 96, 93, 99, 93, 97, 93 }

    Returns: 0.022519923607622283

  143. 30

    {100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100 }

    Returns: 0.08472762786772521

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