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, 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, 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.{2, 4, 6, 8, 10, 12, 14, 16}{2, 4, 8, 16}Returns: "GREATER"
{42, 23, 17}{15, 23, 31}Returns: "INCOMPARABLE"
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