Homework 5

From the book, p. 606, q. 10.

Skills needed to complete this assignment:

(See rectangle.cpp for an example from class that’s similar to this assignment.)

Write a rational number class. This problem is revisited in Chapter 11 (in the book), where operator overloading will make the problem much easier. For now we will use member functions add, sub, mul, div, and less that each carry out the operations +, -, *, /, and <. For example, a+b will be written a.add(b), and a<b will be written a.less(b).

Define a class for rational numbers. A rational number is a “ratio-nal” number, composed of two integers with division indicated. The division is not carried out, it is only indicated, as in ½, 2/3, 15/32, 65/4, 16/5. You should represent rational numbers by two int values, numerator and denominator.

We want to store rational numbers in canonical form, meaning the rational number 9/12 would be stored as ¾ and 25/5 would be stored as 5/1. This is discussed more below.

A principle of abstract data type construction is that constructors must be present to create objects with any legal values. You should provide constructors to make objects out of pairs of int values (i.e. a constructor with two int parameters). Since every int is also a rational number, as in 2/1 or 17/1, you should provide a constructor with a single int parameter, which just sets the numerator to the value of the parameter and the denominator to 1.

Provide member functions add, sub, mul, and div that return a rational value (each of these functions has a single rational parameter). Provide a function less that has a single rational parameter and returns a bool value. These functions should do the operation suggested by the name (e.g. num1.less(num2) returns true if the rational number num1 is less than the rational number num2). Provide a member function neg that has no parameters and returns a rational number that is the negative of the calling object.

Also provide a member function print that simply prints the rational number in a format like -9/13.

Each of these member functions should return a different instance of the class. So once you have an instance of the class, you cannot change its values (rationals will be “immutable”). For example, here is what the add function header looks like:

Rational add(Rational &other)
    int n, d;
    n = ...
    // ...
    return Rational(n, d);  // return a different rational number

The function above can be understood in the following way. The add function is a member function of class Rational (because it will be somewhere inside the class definition, which is not shown here), and it receives as its single parameter a reference to an instance of the same class (which we call other in the function). We make it a reference parameter (“call-by-reference”) to make the function call more efficient (the instance other need not be copied when the function is called).

To repeat, inside the add function, you’ll make an instance of the Rational class and set its values. Then you return that instance.

Always store and print the reduced form of the rational number; that is, always divide out the greatest common divisor (GCD) of the numerator and denominator. C++ code for finding the GCD is abundant on the internet; here is one example. I recommend you make a gcd function that’s not a member function, that only has two integers as its parameters, and that returns an integer.

Some advice: Use the GCD function in the constructor that has two inputs (numerator and denominator); only use the GCD function here. Then, like the code example above, every other function (e.g. add, div, etc.) should call the constructor. That way, every function returns a reduced form of the answer.

Provide a main function that thoroughly tests your class implementation (write a little test for each of the functions).

The following formulas will be useful in defining functions.

a/b + c/d = (a*d + b*c) / (b*d)
a/b - c/d = (a*d - b*c) / (b*d)
(a/b) * (c/d) = (a*c) / (b*d)
(a/b) / (c/d) = (a*d) / (c*b)
-(a/b) = (-a/b)
(a/b) < (c/d) means (a*d) < (c*b)
(a/b) == (c/d) means (a*d) == (c*b)

Keep any negative sign in the numerator; keep the denominator positive. (So 5/-2 should be saved as -5/2.)

Finally, you must split your code into three files (exactly these files):

Submit to me all three files (either in a ZIP or three email attachments).

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