This assignment should help you gain practice with creating and editing basic Java classes based on given specifications.

Task

Do the following exercises, each in a different file. Your filenames should be

• java
• java

Each file should have a comment including your name at the top of the file. Each file should also have appropriate comments throughout the program. When adding to a pre-supplied file, clearly indicate, using comments, which parts are your additions.

Integer Set

Filename: IntegerSet.java

• Create class IntegerSet in its own file
• An IntegerSet object holds integers in the range 0-100
• This is represented by an array of boolean Array element i is set to true if the integer i is in the set and false otherwise.
• Create these methods for the class (these should be the only public methods)

IntegerSet() public IntegerSet union(IntegerSet iSet) public IntegerSet intersection(IntegerSet iSet) public IntegerSet insertElement(int data) public IntegerSet deleteElement(int data) public boolean isEqualTo(IntegerSet iSet) public String toString()

• The constructor (no arguments) initializes the array to represent the empty set (no integers in the set)
• Method union creates and returns a new set that is the set-theoretic union of the two existing sets (the calling object and the parameter). An element is in the union if it is in either of the two starting sets
• Method intersection creates and returns a new set that is the settheoretic intersection for he two existing sets. An element is in the intersection if its in both of the starting sets.
• Method insertElement adds the argument(an integer) to the set (the calling object) and should also return that set (this allows calls to be cascaded)
• Method deleteElement removes the argument from the set and should also return the set, to allow cascading
• Method isEqualTo returns true if the two sets are equal (if they have all the same elements) and false otherwise
• Method toString returns a string containing the set elements as a list of numbers in ascending order, separated by spaces. Include only the elements present in the set. Use to represent an empty set

Fraction class

Filename: Fraction.java

Begin with this Fraction class, as discussed in the lecture and add the following features:

• You will create methods with the following signatures:

public Fraction simplify() public Fraction add(Fraction f) public Fraction subtract(Fraction f) public Fraction multiply(Fraction f) public Fraction divide(Fraction f)

• The simplify method will return a simplified version of the calling object. This method should return a new Fraction (simplified), but not change the original one. The fractions in the form should have a simplified form of . Any other fraction has the usual mathematical definition of simplified form. This will require finding the GCD of the numerator and denominator. One useful algorithm for doing so is Euclids algorithm/the Euclidean algorithm.
• Methods add, subtract, multiply, divide should take in a Fraction as a parameter and perform the given computation between the calling object and the parameter object (The calling object is always the first operand). The result of each operation should always be a fraction returned in simplified form. Example calls: add(f2) means to return the value f1 + f2, f1.divide(f2) means to return the value f1/f2.
• In divide, if an attempt is made to divide by a fraction with the numerator 0, default the result to . This division is actually undefined, but we need to return something from the method and this is a sane value
• Be sure that your new methods enforce the same rules on the data as the original methods do the denominator must always be non-negative (negative fractions have the negative sign in the numerator) and the denominator must never be zero

Testing

Ive provided a file to help you get started with testing. This is not a comprehensive set of tests (so make sure you do some of your own), but will get you started. Also, you will need to include the HW2Tester class (unchanged) in your jar file when you submit, as indicated at the end of this.

Here is the HW2Tester.java file which contains some tests for both the IntegerSet and Fraction classes.

Sample Run of HW2Tester

After set1.insertElement(10), set1 = 0 2 8 10 default IntegerSet is =

set1 = 0 2 4 6 8 10 12 95 100 set2 = 0 3 6 9 12 set1.union(set2) = 0 2 3 4 6 8 9 10 12 95 100 set1.intersection(set2) = 0 6 12 set1.deleteElement(2) = 0 4 6 8 10 12 95 100 set1.isEqualTo(set1) = true set1.isEqualTo(set2) = false

Fraction tests:

4/6 simplified = 2/3

75/175 simplified = 3/7 -6/17 simplified = -6/17 f1 = 4/6 f2 = 75/175 f3 = -6/17

4/6 + 75/175 = 23/21

4/6 75/175 = 5/21

4/6 * 75/175 = 2/7

4/6 / 75/175 = 14/9

75/175 + -6/17 = 9/119

75/175 -6/17 = 93/119

75/175 * -6/17 = -18/119

75/175 / -6/17 = -17/14

75/175 / 0/1 = 0/1