Statistics

Problem Statement for "Straights"

Problem Statement

You are playing a game of cards in which the number of straights, i.e., sets of consecutive-valued cards, determines the strength of your hand. You will be given a int[] hand, where the i-th element of hand is the number of cards of value i in your hand. You should return the number of straights of length k. For example, suppose you have the hand:
  • 2 of spades
  • 2 of diamonds
  • 2 of clubs
  • 3 of clubs
  • 4 of hearts
  • 4 of clubs
You would be given hand = { 0, 3, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0 }. The number of two-card straights is 5:
  • 2 of spades, 3 of clubs
  • 2 of diamonds, 3 of clubs
  • 2 of clubs, 3 of clubs
  • 3 of clubs, 4 of hearts
  • 3 of clubs, 4 of clubs

Definition

Class:
Straights
Method:
howMany
Parameters:
int[], int
Returns:
int
Method signature:
int howMany(int[] hand, int k)
(be sure your method is public)

Notes

  • Straights do not wrap around: if hand is {1,0,0,0,0,0,0,0,0,0,0,0,1}, you have no straights of length 2.

Constraints

  • hand will contain exactly 13 elements.
  • Each element of hand will be between 0 and 4 inclusive.
  • k will be between 1 and 13 inclusive.

Examples

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

    2

    Returns: 5

    The example given.

  2. {1,1,1,1,1,1,1,1,1,1,1,1,1}

    5

    Returns: 9

    Say hand[0] references Aces. There are 9 ways to make a straight of length 5: Ace-Five up to Nine-King.

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

    13

    Returns: 67108864

  4. {4,0,4,0,4,0,4,0,4,0,4,0,4}

    2

    Returns: 0

    Straights do not wrap around; we have no straights here.

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

    1

    Returns: 31

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

    3

    Returns: 79

  7. {2,2,3,0,1,1,4,2,2,3,2,1,3}

    10

    Returns: 0

  8. {4,2,3,4,4,3,2,4,3,4,2,3,1}

    8

    Returns: 47808

  9. {0,2,3,4,4,2,0,0,1,0,3,2,4}

    13

    Returns: 0

  10. {2,4,2,0,3,4,4,1,1,1,1,0,1}

    5

    Returns: 68

  11. {1,4,1,4,1,3,3,1,4,3,4,0,2}

    6

    Returns: 912

  12. {4,0,2,3,0,1,1,1,0,0,4,2,3}

    12

    Returns: 0

  13. {0,0,3,2,0,4,4,3,2,0,3,2,2}

    11

    Returns: 0

  14. {4,1,1,4,4,3,4,3,2,1,2,3,0}

    4

    Returns: 536

  15. {0,3,4,2,1,2,2,4,0,4,2,2,3}

    10

    Returns: 0

  16. {1,1,0,0,0,4,1,4,2,2,1,4,3}

    6

    Returns: 320

  17. {1,1,2,2,0,2,0,0,3,3,0,2,1}

    8

    Returns: 0

  18. {1,1,2,3,1,1,4,3,3,2,3,3,4}

    2

    Returns: 71

  19. {2,0,0,3,4,1,1,0,3,4,4,4,1}

    6

    Returns: 0

  20. {1,4,0,3,4,1,2,1,4,4,1,4,3}

    12

    Returns: 0

  21. {0,1,1,1,0,3,1,1,0,3,2,4,3}

    11

    Returns: 0

  22. {4,4,4,3,4,0,0,3,1,2,4,4,4}

    11

    Returns: 0

  23. {3,3,1,3,0,3,2,3,1,1,2,0,2}

    4

    Returns: 57

  24. {1,3,3,3,3,3,0,4,3,1,3,3,2}

    10

    Returns: 0

  25. {1,2,4,0,1,1,2,3,1,2,3,0,0}

    7

    Returns: 36

  26. {0,4,3,3,2,2,2,2,1,1,1,4,0}

    13

    Returns: 0

  27. {3,0,1,3,4,1,4,0,2,0,4,3,4}

    5

    Returns: 48

  28. {3,3,0,0,2,1,0,3,0,3,3,2,2}

    13

    Returns: 0

  29. {0,4,1,2,4,2,3,3,1,4,3,2,0}

    7

    Returns: 2592

  30. {3,0,4,0,4,2,3,0,2,1,4,0,1}

    4

    Returns: 0

  31. {0, 3, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    2

    Returns: 5

  32. {1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1 }

    1

    Returns: 31

  33. {4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 }

    13

    Returns: 67108864

  34. {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }

    5

    Returns: 288

  35. {0, 3, 1, 2, 3, 2, 2, 0, 0, 0, 0, 0, 0 }

    4

    Returns: 54

  36. {1, 2, 3, 4, 4, 3, 2, 1, 4, 2, 4, 2, 3 }

    5

    Returns: 1232

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