1.12. ObjectOriented Programming in C++: Defining Classes¶
We stated earlier that C++ is an objectoriented programming language. Objectoriented programming is a programming technique based on real world things such as turtles, airplanes, customers, etc. Each object has its own characteristics or attributes as well as its own set of behaviors.
So far, we have used a number of builtin classes to show examples of data and control structures. One of the most powerful features in an objectoriented programming language is the ability to allow a programmer (problem solver) to create new classes that model data that is needed to solve the problem. Each object created with the class data type is called an instance of the class.
Remember that we use abstract data types to provide the logical description or blueprint for what a data object looks like (its state given by object attributes) and what it can do (its behaviors given by class methods). Defining a class creates the blueprint which defines the behaviors and attributes of objects of that new data type. By building a class that implements an abstract data type, a programmer can take advantage of the abstraction process and at the same time provide the details necessary to actually use the abstraction in a program. Hence, whenever we want to implement an abstract data type, we will do so with a new class which will provide the blueprint or template for all of the objects of that type.
 Four key principles are associated with objectoriented programming:
 abstraction
 encapsulation
 inheritance
 polymorphism
We will highlight each principle via examples.
1.12.1. A Fraction
Class¶
A very common example to show the details of implementing a userdefined
class is to construct a class to implement the abstract data type
Fraction
. We have already seen that C++ provides a number of
numeric data types for our use. There are times, however, that it would be
most appropriate to be able to create data objects that both look and act like
fractions.
A fraction such as \(\frac {3}{5}\) consists of two parts. The top value, known as the numerator, can be any integer. The bottom value, called the denominator, can be any integer greater than 0 (negative fractions have a negative numerator). Although it is possible to create a floating point approximation for any fraction, we would like to represent the fraction using exact values to avoid problems inherent in approximations.
Since defining a class makes a new data type, the operations for the
Fraction
type will allow a Fraction
data
object to behave like any other numeric type. We need to be able to
add, subtract, multiply, and divide fractions. We also want to be able
to print fractions using the standard “slash” form, for example 3/5. In
addition, all fraction methods should return results in their lowest
terms so that no matter what computation is performed, we always end up
with the most common form.
In C++, we define a new class by providing a name and a set of method definitions that are syntactically similar to function definitions. For this example:
class Fraction {
// The class methods and class variables go here
}; // The ";" is required by C++ to end a class definition
provides the framework for us to define the methods. The first method
that all classes should provide is the constructor.
The constructor
defines the way in which data objects are created.
It’s considered good practice to have a constructor completely setup a class object,
so that it’s impossible to create an object in an invalid state.
To create a
Fraction
object, we will need to initialize two pieces of data, the
numerator and the denominator. In C++, the constructor method is
always named with the same name as the class it creates
and is shown in Listing 2.
Listing 2
class Fraction {
public:
Fraction(int top, int bottom) {
/** Fraction contructor method */
num = top; // setting num's value
den = bottom; // setting den's value
}
private:
int num; // num atribute
int den; // den attribute
};
As described earlier, fractions require
two pieces of state data, the numerator and the denominator. The
notation int num
outside the constructor defines the fraction
object
to have an internal data object called num
as part of its state.
Likewise, int den
creates the denominator. The values of the two
formal parameters are initially assigned to the state, allowing the new
fraction
object to know its starting values.
To create an object or instance of the Fraction
class, we must invoke the
constructor. This happens by using the name of the class and passing
actual values for the necessary state after the variable name. For example,
Fraction myfraction(3, 5);
creates an object called myfraction
representing the fraction
\(\frac {3}{5}\) (threefifths). Figure 5 shows this
object as it is now implemented.
1.12.2. Abstraction and Encapsulation¶
Another way to think about fractions is as “parts of a whole” as shown in the following figure:
Since we are using classes to create abstract data types, we should probably discuss the meaning of the word “abstract” in this context. Abstraction in objectoriented programming requires you to focus only the desired properties and behaviors of the objects and discard what is unimportant or irrelevant. Hence, if we do not need to think about the “parts of a whole” metaphor, then we will not include it in the class. If that metaphor is important, then we will include it. For our purposes, we want to think of fractions as numbers, so we will not use the “parts of a whole” visual metaphor.
The objectoriented principle of encapsulation is the notion that we should
hide the contents of a class, except what is
absolutely necessary to expose.
Hence, we will restrict the access to our class as much
as we can, so that a user can change the class properties and behaviors only from methods
provided by the class. C++ allows us to control access with the access keywords public
and private
.
It is typical in C++ to make all data attributes private
and most methods public
.
All attribute variables under the private
keyword will only be able to be accessed by the object’s class methods, not by the user.
Only C++’s ‘public
methods can be accessed and used by the user. Because we
want our user to be able to call every constructor directly, we always place the
constructor under public
. A third access keyword, protected
will be discussed later.
1.12.3. Polymorphism¶
Polymorphism means the ability to appear in many forms. In objectoriented programming, polymorphism refers to the ability to process objects or methods differently depending on their data type, class, number of arguments, etc. For example, we can overload a constructor with different numbers and types of arguments to give us more optional ways to instantiate an object of the class in question. For example, we can add additional constructors to handle whole numbers and instances with no parameters given:
Fraction(int top, int bottom){
num = top;
den = bottom;
}
Fraction (int top){
num = top;
den = 1;
}
Fraction (){
num = 0;
den = 1;
}
Calling the constructor with two arguments will invoke the first method, calling it with a single argument will invoke the second method, and calling it with no arguments will invoke the third method.
Using optional parameters will accomplish the same task in this case. Since the class will behave the same no matter which implementation you use and the user will have no idea which implementation was chosen, this is an example of encapsulation.
Fraction(int top = 0, int bottom = 1){
num = top;
den = bottom;
}
The next thing we need to do is implement some behaviors that the abstract
data type requires. To begin, let’s consider what happens when we try to print
a Fraction
object.
int main() {
Fraction myfraction(3, 5);
// Throws an error
cout << myfraction << endl;
return 0;
}
The fraction
object, myfraction
, does not know how to respond to this
request to print to the console. The cout
function requires that the object
knows how to interact with the <<
operator so that the string can be sent to the
output stream. Without this, our class will throw an error, which is obviously not what we
want.
There are two ways we can solve this problem. One is to define a method
called something like show
that will allow the Fraction
object to print itself
as a string. We can implement this method as shown in
Listing 3. If we create a Fraction
object as before, we
can ask it to show itself, in other words, print itself in the proper
format by invoking the show method on our fractions.
The downside of this that it is not how we expect to print to the console.
In C++, there are many operators that are provided for atomic and STL data types
that may not work as expected with a user defined class until you overload them.
One of these, <<
, is the operator to
send data to the output stream.
It would be nicer to provide a “better” implementation for this method
via operator overloading.
Like function overloading, operator overloading allows us to make operators work for user defined classes by defining a special meaning for that operator when applied to objects of the class as operands.
In C++ this new operator needs to be implemented as a friend of the class in order to
define the operator’s behavior on objects of the class from a nonclass method <<
.
Operator overloading is yet another example
of polymorphism in objectoriented programming.
A friend function of a class is a function defined outside that class’ scope
but with the right to access
all private and protected members of the class.
In C++, we do operator overloading by declaring a friend
function with the name <<
give it a new implementation outside as shown in Listing 4.
Note that stream operators
need to return the address of the stream because of the fact that the
stream is changed by the stream operator.
Listing 4
We can override many other operators for our new Fraction
class. Some
of the most important of these are the basic arithmetic operations. We
would like to be able to create two Fraction
objects and then be able to add
them together using the standard “+” notation. At this point, if we try
to add two fractions using “+”, we get the following:
Fraction f1(1, 4);
Fraction f2(1, 2);
Fraction f3 = f1 + f2;
>>error: no match for ‘operator+’ (operand types are ‘Fraction’ and ‘Fraction’))
If you look closely at the error, you see that the problem is that the
“+” operator does not understand the Fraction
operands.
We can, of course create something like:
f1.add(f2)
which would ask the Fraction
object f1
to add the Fraction
object
f2
to itself. It would be much better to be written in the standard notation,
f1 + f2
. We can fix this by providing the Fraction
class with a friend that
overrides the +
operator.
As you know, two fractions must have the same denominator to be added. The easiest
way to make sure they have the same denominator is to simply use the
product of the two denominators as a common denominator so that
\(\frac {a}{b} + \frac {c}{d} = \frac {ad}{bd} + \frac {cb}{bd} = \frac{ad+cb}{bd}\)
The implementation is shown in Listing 5. The addition
function returns a new Fraction
object with the numerator and
denominator of the sum. We can use this method by writing a standard
arithmetic expression involving fractions, assigning the result of the
addition, and then printing our result.
Listing 5
Fraction operator +(const Fraction &otherFrac){
//Note the return type is a Fraction
int newnum = num*otherFrac.den + den*otherFrac.num;
int newden = den*otherFrac.den;
return Fraction(newnum, newden);
}
The addition method works as we desire, but a couple of things
can be improved. When we use a binary operator like +
we
like more symmetry.
Binary operators can either be members of their
lefthand argument’s class or friend functions.
Since the stream operators’ lefthand argument is a stream,
stream operators either have to be members of the stream class
or friend functions.
However, that is not true for +
.
Let’s rewrite the addition operator as a friend function.
Listing 6
Fraction operator +(const &Fraction otherFrac){
//Note the return type is a Fraction
int newnum = num*otherFrac.den + den*otherFrac.num;
int newden = den*otherFrac.den;
return Fraction(newnum, newden);
}
How you choose to overload operators like +
is a design choice
since both methods will work perfectly well. This is Another
example of encapsulation; your user does not need to
which you choose to use!
There is one more thing we can improve in our addition function. Note that \(6/8\) is the correct result (\(\frac {1}{4} + \frac {1}{2}\)) but that it is not in the “lowest terms” representation. The best representation would be \(3/4\). In order to be sure that our results are always in the lowest terms, we need a helper function that knows how to reduce fractions. This function will need to look for the greatest common divisor, or GCD. We can then divide the numerator and the denominator by the GCD and the result will be reduced to lowest terms.
The bestknown algorithm for finding a greatest common divisor is Euclid’s Algorithm, which will be discussed in detail in Chapter 8. Euclid’s Algorithm states that the greatest common divisor of two integers \(m\) and \(n\) is \(n\) if \(n\) divides \(m\) evenly. However, if \(n\) does not divide \(m\) evenly, then the answer is the greatest common divisor of \(n\) and the remainder of \(m\) divided by \(n\). We will simply provide an iterative implementation here (see ActiveCode 1). Note that this implementation of the GCD algorithm only works when the denominator is positive. This is acceptable for our fraction class because we have said that a negative fraction will be represented by a negative numerator.
Now we can use this function to help reduce any fraction. To put a fraction in lowest terms, we will divide the numerator and the denominator by their greatest common divisor. So, for the fraction \(6/8\), the greatest common divisor is 2. Dividing the top and the bottom by 2 creates a new fraction, \(3/4\) (see Listing 6).
Listing 6
Our Fraction
object now has two very useful methods and looks
like Figure 6. An additional group of methods that we need to
include in our example Fraction
class will allow two fractions to
compare themselves to one another using ==
.
We want the ==
operator to compare Fraction objects and to return
true
if they are equivalent in value, false
otherwise.
This is a design choice because we want \(\frac {1}{2}\) to be considered
equal to \(\frac {2}{4}\) as well as \(\frac {3}{6}\), etc.
Hence, in the Fraction
class, we can implement the ==
method by
crossmultiplying (see Listing 7) rather than
by just comparing numerators and denominators.
Of course there are other relational operators that can be overridden. For example, the
<=
operator could be overridden to provide the less than or equal functionality.
Listing 7
bool operator ==(Fraction &otherFrac) {
int firstnum = num*otherFrac.den;
int secondnum = otherFrac.num*den;
return firstnum==secondnum;
}
The complete Fraction
class, up to this point, is shown in
ActiveCode 6. We leave the remaining arithmetic and relational
methods as exercises.
1.12.4. Self Check¶
class Fraction { public: Fraction(int top, int bottom) { /** Fraction contructor method */ num = top; // setting num's value den = bottom; // setting den's value } private: int num; // num atribute int den; // den attribute }

Q2: Drag the word on the left to its corresponding definition
Review the elements of object oriented programming
 Encapsulation
 hiding the contents of a class except when absolutely necessary
 Abstraction
 focusing on desired behaviors and properties while disregarding what is irrelevant/unimportant
 Polymorphism
 processing objects or methods differently depending on their data type, class, number of arguments, etc.

Q3: Drag the word on the left to its corresponding definition
Review classes and their properties
 instance
 an occurrence
 constructor
 an special function to initialize
 access keywords
 private and public
 class
 a template for creating objects
 To make sure you understand how operators are implemented in C++ classes, and how to properly write methods, write some methods to implement
*, /,
and
. Also implement comparison operators > and <. 
Our the next section will introduce another important aspect of objectoriented programming, namely inheritance.