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Problem Statement for "SetPartialOrder"

Problem Statement

In math, we sometimes define a partial order on some objects. In this problem we will take a look at one possible way how to define a partial order on sets of integers.

Consider two sets of integers: X and Y. These two sets can be related to each other in four possible ways:

  • X is equal to Y if each element of X is also an element of Y and vice versa.
  • X is less than Y if X is not equal to Y (see previous item) and each element of X is also an element of Y.
  • X is greater than Y if Y is less than X.
  • In all other cases X and Y are incomparable.

In other words: X is less than Y if and only if X is a proper subset of Y. Two sets are incomparable if neither is a subset of the other.

You are given two int[]s a and b. The elements of a form the set X. The elements of b form the set Y. Compare X to Y and return the correct one of the following four strings: "EQUAL", "LESS", "GREATER", or "INCOMPARABLE".

(The string "LESS" means that X is less than Y, the string "GREATER" means that X is greater than Y. Quotes are for clarity only. Note that the return value is case-sensitive.)

Definition

Class:
SetPartialOrder
Method:
compareSets
Parameters:
int[], int[]
Returns:
String
Method signature:
String compareSets(int[] a, int[] b)
(be sure your method is public)

Constraints

  • Each of arrays a and b will have length between 1 and 50, inclusive.
  • Each element of arrays a and b will be between 1 and 100, inclusive.
  • In each of arrays a and b all elements are distinct.

Examples

  1. {1, 2, 3, 5, 8}

    {8, 5, 1, 3, 2}

    Returns: "EQUAL"

    The order of elements in a and b does not matter. The two sets X and Y are equal.

  2. {2, 3, 5, 7}

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

    Returns: "LESS"

    Each number that occurs in a does also occur in b.

  3. {2, 4, 6, 8, 10, 12, 14, 16}

    {2, 4, 8, 16}

    Returns: "GREATER"

  4. {42, 23, 17}

    {15, 23, 31}

    Returns: "INCOMPARABLE"

  5. {1}

    {1}

    Returns: "EQUAL"

  6. {5}

    {4}

    Returns: "INCOMPARABLE"

  7. {100}

    {95}

    Returns: "INCOMPARABLE"

  8. {4, 5, 6}

    {9, 1, 4}

    Returns: "INCOMPARABLE"

  9. {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98}

    {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98}

    Returns: "EQUAL"

  10. {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98}

    {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99}

    Returns: "INCOMPARABLE"

  11. {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99}'

    {51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99}

    Returns: "INCOMPARABLE"

  12. {1 }

    {2, 3, 4 }

    Returns: "INCOMPARABLE"

  13. {1, 2, 3 }

    {1, 4, 5, 6 }

    Returns: "INCOMPARABLE"

  14. {2, 3 }

    {4, 1 }

    Returns: "INCOMPARABLE"

  15. {42, 23, 17, 50 }

    {15, 23, 31 }

    Returns: "INCOMPARABLE"

  16. {1, 2, 3, 5, 8 }

    {1 }

    Returns: "GREATER"

  17. {1, 2 }

    {2, 3, 4 }

    Returns: "INCOMPARABLE"

  18. {3, 4, 5 }

    {1, 2 }

    Returns: "INCOMPARABLE"

  19. {1, 2, 3, 5, 8 }

    {8, 5, 1, 3, 2 }

    Returns: "EQUAL"

  20. {1, 2 }

    {1, 2 }

    Returns: "EQUAL"

  21. {2, 3, 5, 15 }

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

    Returns: "INCOMPARABLE"

  22. {2, 4, 6, 8, 10, 12, 14, 16 }

    {2, 4, 8, 16 }

    Returns: "GREATER"

  23. {2, 3, 5, 7 }

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

    Returns: "LESS"

  24. {1, 2, 4, 7, 8 }

    {1, 4, 3 }

    Returns: "INCOMPARABLE"

  25. {100, 99 }

    {99, 88 }

    Returns: "INCOMPARABLE"

  26. {1, 2, 3, 4, 5, 6, 7, 8 }

    {13 }

    Returns: "INCOMPARABLE"

  27. {1, 2, 3 }

    {1, 2 }

    Returns: "GREATER"

  28. {1, 2, 3 }

    {4, 5 }

    Returns: "INCOMPARABLE"

  29. {1, 2, 3, 5, 8, 100 }

    {8, 5, 1, 3, 2, 100, 99 }

    Returns: "LESS"

  30. {1, 100 }

    {8, 5, 1, 3, 2 }

    Returns: "INCOMPARABLE"

  31. {1, 2, 3, 7, 6, 9 }

    {8, 5, 1, 3, 2 }

    Returns: "INCOMPARABLE"

  32. {1, 2, 3, 5 }

    {2, 4, 8, 9, 11 }

    Returns: "INCOMPARABLE"

  33. {2, 3, 4, 5, 6, 7, 8 }

    {13 }

    Returns: "INCOMPARABLE"

  34. {1, 3, 4 }

    {1, 2 }

    Returns: "INCOMPARABLE"

  35. {1, 2 }

    {3 }

    Returns: "INCOMPARABLE"

  36. {2, 4, 6, 8 }

    {2, 4, 6 }

    Returns: "GREATER"

  37. {42, 23, 17 }

    {15, 23, 31 }

    Returns: "INCOMPARABLE"

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