CPSC 170 A

Lecture 4- Classes and Objects

As usual, create a directory to hold today's activities:

$ mkdir ~/cs170/labs/lab4 
$ cd ~/cs170/labs/lab4

Creating Classes (From Scratch)

Last class, we saw the simple version of how to create classes and objects. Today, we will explore more in depth how classes and objects work, as far as creating our own datatypes goes!

Lab Activity 1

Fractions

Today is the day that you create your first legitimate data type, and this time it is from scratch! One of the major complaints about the floating point data type is that it cannot represent every rational number. So, let's make a data type that can do that.

Details

Create a class called Fraction in a file called fractions.py. Your class should be able to represent arbitrary fractions. You should be able to add, subtract, multiply, and divide fractions. You should also be able to print fractions, so you can see the result of your work. Your code should only work for positive fractions.

Think about what attributes you need to represent a fraction. This should be decently straight forward, but if you need a refresher on fractions take a look at this web page.

Example

>>> fraction_1 = Fraction(1, 2)
>>> fraction_2 = Fraction(3, 4)
>>> result = fraction_1.add(fraction_2)
>>> print(fraction_1)
1/2
>>> print(fraction_2)
3/4
>>> print(result)
5/4
>>> result = fraction_2.multiply(fraction_1)
>>> print(result)
3/8

Note: Your methods for this class should return a new fraction. It should not modify any fraction in place.

Hint

You are definitely going to need two attributes, one for the numerator, and another for the denominator.
Your operators should behave just like the operators do for other data types: They should not modify either of the current fractions. Instead, they should return a new fraction, which is the result of the operation.
Remember, you need to override the __str__ method, so you can just use the print function to print out your fractions.
Multiplication is easy, just multiply the numerators together, and the denominators together.
Your add function is going to have to compute a common denominator. The easiest way to accomplish this is by multiplying the two denominators together.

This means you need to multiply the numerator of the current fraction by the other fractions denominator (and vice versa) to make sure the value of each fraction does not change. Then you just add the new numerators together.

If you have written your methods correctly, you should be able to override the built-in operators by simply changing the name of the methods to __add__ and __mul__:

      >>> result = fraction_1 + fraction_2
      >>> print(result)
      5/4
      >>> result = fraction_1 * fraction_2
      >>> print(result)
      3/8

Challenge

The way the fraction class is currently set up, you can easily get a fraction 2/4. This probably makes the math majors in the room cringe, but is technically a valid fraction. It just is not in its most reduced form.

Let's define the reduced form of a fraction as follows:

The GCD of the numerator and denominator is 1.
The denominator is always positive (so a negative fraction has a negative numerator).