CPEN 221 / Fall 2017

• Can you solve the provided question in one hour?
• Skeleton code can be obtained by cloning this repository. Add JUnit to your build path in Eclipse.

The skeleton source code for this question is in the package additionClosure. You have to implement the methods isClosed.

You are given a List of Integers, listInt, and another integer n. We will define closure under addition for listInt to mean that for two distinct values of i and j, (listInt[i]+listInt[j]) % n is in listInt or k * n + (listInt[i]+listInt[j]) % n (for some int k) is in listInt.

Your goal is to determine if a given List of Integers is closed under addition for some modulus n. You will implement a method, isClosed, that will return true if a List is closed under addition for a given n and false otherwise.

• input list: [-1, 0, 1]; n = 2

  • Returns: true
  • (-1 + 0) % 2 = -1; (-1 + 1) % 2 = 0, (0 + 1) % 2 = 1.

• input list: [-2, 3]; n = 4

  • Returns: false

• input list: [1, 1, 0]; n = 2

  • Returns: true

• input list: [1, 1]; n = 3

  • Returns: false

• input list: [1, 1, 2]; n = 2

  • Returns: true

• input list: [0, 1, 1, 2]; n = 2

  • Returns: true

• input list: [0, 1, 100, 50, 50], n = 100

  • Return: false

• input list: [0, 1, 100, 50, 50], n = 50

  • Return: true