ObjectOrientedProgrammingDefiningClasses.ptx

<section xml:id="introduction_object-oriented-programming-in-c-defining-classes">
        <title>Object-Oriented Programming in C++: Defining Classes</title>
        <introduction>
        <p><idx>object-oriented programming</idx>We stated earlier that C++ is an <term>object-oriented programming
            language</term>. Object-oriented 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.</p>
        <p><idx>object</idx><idx>instance</idx>So far, we have used a number of built-in classes to show
            examples of data and control structures. One of the most powerful
            features in an object-oriented 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 <term>object</term> created with the class data type is called an <term>instance</term> of  the class.</p>
        <p><idx>object attributes</idx><idx>class methods</idx><idx>class</idx>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 <term>object attributes</term>)
            and what it can do (its behaviors given by <term>class methods</term>).
            Defining a class creates the blueprint which defines the behaviors and attributes
            of objects of that new data type.
            By building a <term>class</term> 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.</p>
        <p>Four key principles are associated with object-oriented programming:</p>
        <blockquote>
            <p><ol marker="1">
                <li>
                    <p>abstraction</p>
                </li>
                <li>
                    <p>encapsulation</p>
                </li>
                <li>
                    <p>inheritance</p>
                </li>
                <li>
                    <p>polymorphism</p>
                </li>
            </ol></p>
        </blockquote>
        <p>We will highlight each principle via examples.</p>
        </introduction>
        <subsection xml:id="introduction_a-fraction-class">
            <title>A <c>Fraction</c> Class</title>
            <p>A very common example to show the details of implementing a user-defined
                class is to construct a class to implement the abstract data type
                <c>Fraction</c>. 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.</p>
            <p>A fraction such as <m>\frac {3}{5}</m> 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.</p>
            <p>Since defining a class makes a new data type, the operations for the
                <c>Fraction</c> type will allow a <c>Fraction</c> 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 <q>slash</q> 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.</p>
            <p>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 example, see <xref ref="defn-classes"/>.</p>
            <exploration xml:id="defn-classes">
                <title>Defining Classes</title>
                <task xml:id="defn-classes-cpp" label="defn-classes-cpp">
                    <title>C++ Implementation</title>
                    <statement><program language="cpp" label="defn-classes-cpp-prog"><input>
class Fraction {
    // The class methods and class variables go here
};  // The ";" is required by C++ to end a class definition
                    </input></program></statement>
                </task>
                <task xml:id="defn-classes-py" label="defn-classes-py">
                    <title>Python Implementation</title>
                    <statement><program language="python" label="defn-classes-py-prog"><input>
class Fraction:

#the methods go here
                    </input></program></statement>
                </task>
            </exploration>
            <p><idx>constructor</idx>provides the framework for us to define the methods. The first method
                that all classes should provide is the <term>constructor</term>.
                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
                <c>Fraction</c> 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 <xref ref="introduction_lst-constructor-cpp"/>.</p>

            <exploration xml:id="introduction_lst-constructor">
                <title>Constructor for <c>Fraction</c> class</title>
                <task xml:id="introduction_lst-constructor-cpp" label="introduction_lst-constructor-cpp">
                    <title>C++</title>
                    <statement><program language="cpp" label="introduction_lst-constructor-cpp-prog"><input>
class Fraction {
    public:
      Fraction(int top, int bottom) {
         /** Fraction constructor method */
          num = top;     // setting num's value
          den = bottom;  // setting den's value
        }
     private:
       int num; // num attribute
       int den; // den attribute
};
                </input></program></statement></task>
                <task xml:id="introduction_lst-constructor-py" label="introduction_lst-constructor-py">
                    <title>Python</title>
                    <statement><program language="Python" label="introduction_lst-constructor-py-prog"><input>
class Fraction:

    def __init__(self,top,bottom):

        self.num = top
        self.den = bottom
            </input></program></statement></task></exploration>

            <p>As described earlier, fractions require
                two pieces of state data, the numerator and the denominator. The
                notation <c>int num</c> outside the constructor defines the <c>fraction</c> object
                to have an internal data object called <c>num</c> as part of its state.
                Likewise, <c>int den</c> creates the denominator. The values of the two
                formal parameters are initially assigned to the state, allowing the new
                <c>fraction</c> object to know its starting values.</p>
            <p>To create an object or instance of the <c>Fraction</c> 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, see <xref ref="invoking-constructor"/>.</p>
            <exploration xml:id="invoking-constructor">
                <title>Invoking Constructor</title>
                <task xml:id="invoking-constructor-cpp" label="invoking-constructor-cpp">
                    <title>C++ Implementation</title>
                    <statement><program language="cpp" label="invoking-constructor-cpp-prog"><input>
Fraction myfraction(3, 5);
                    </input></program></statement>
                </task>
                <task xml:id="invoking-constructor-py" label="invoking-constructor-py">
                    <title>Python Implementation</title>
                    <statement><program language="python" label="invoking-constructor-py-prog"><input>
myfraction = Fraction(3, 5)
                    </input></program></statement>
                </task>
            </exploration>
            <p>creates an object called <c>myfraction</c> representing the fraction
                <m>\frac {3}{5}</m> (three-fifths). <xref ref="fig-fraction1cpp"/> shows this
                object as it is now implemented.</p>
            
            <figure align="center" xml:id="fig-fraction1cpp">
                <caption>An instance of the <c>Fraction</c> Class</caption>
                    <image source="Introduction/fraction1cpp.png" width="50%">
                    <description><p>Diagram showing an instance of the Fraction class. The instance is named 'myfraction' and is depicted as a set of concentric circles. The innermost circle is labeled 'State' and contains two segments: 'num' with the number 3 above 'den' with the number 5, representing the numerator and denominator of a fraction. The middle circle is labeled 'Methods', indicating the functionality associated with the fraction instance.</p></description>
                    </image>
                </figure>

        </subsection>
        <subsection xml:id="introduction_abstraction-and-encapsulation">
            <title>Abstraction and Encapsulation</title>
            <p>Another way to think about fractions is as <q>parts of a whole</q> as shown in the
                following figure:</p>
            <blockquote>
                <image source="Introduction/fractions_partsofwhole.png" width="50%"> 
                    <description>
                    <p>
                        Image showing a visual representation of fractions as "parts of a whole." The diagram begins with a full circle labeled "1," 
                        followed by a circle divided into two equal parts labeled "1/2," then into four parts labeled "1/4," and finally into 
                        eight parts labeled "1/8." The sequence visually illustrates how a whole can be divided into progressively smaller fractions.
                    </p>
                    </description>
                </image>
            </blockquote>
            <p><idx>abstraction</idx>Because we are using classes to create abstract data types, we should probably
                define the term <q>abstract</q> in this context. In object-oriented programming,
                <term>abstraction</term> requires you to focus solely on the desired properties and behaviors of
                the objects, discarding everything else that is unimportant or irrelevant. As a result,
                if we don't need to consider the <q>parts of a whole</q> visual metaphor of a fraction, we won't include it in the
                <c>Fraction</c> class. If a given metaphor is important, we will include it. For our purposes, we want to
                think of fractions as numbers, so we will avoid using the <q>parts of a whole</q> visual
                metaphor.</p>
            <p><idx>access keywords</idx><idx>encapsulation</idx>The object-oriented principle of <term>encapsulation</term> 
                refers to the practice of grouping or encapsulating related data and the methods that operate on that data into a single unit, typically a class. Encapsulation also requires we hide most of the internal contents of that 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 <term>access keywords</term> <c>public</c> and <c>private</c>.
                It is typical in C++ to make all data attributes <c>private</c> and most methods <c>public</c>.
                All attribute variables under the <c>private</c>
                keyword will only be able to be accessed by the object's class methods, not by the user.
                Only C++<rsq/>s <c>public</c> 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 <c>public</c>. A third access keyword, <c>protected</c> will be discussed later.</p>

        </subsection>
        <subsection xml:id="introduction_polymorphism">
            <title>Polymorphism</title>
            <p><idx>polymorphism</idx><term>Polymorphism</term> means the ability to appear in many forms. In object-oriented programming,
                <term>polymorphism</term> refers to the ability to handle 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 multiple ways to instantiate an object of a class as shown in <xref ref="frac-poly"/> for
                the <c>Fraction</c> class.</p>
            <listing xml:id="frac-poly">
                <caption>Example of Polymorphism</caption>
                <program language="cpp" label="frac-poly-prog"><input>
Fraction(int top, int bottom){
    num = top;
    den = bottom;
}
Fraction (int top){
    num = top;
    den = 1;
}
Fraction (){
    num = 0;
    den = 1;
}
            </input></program></listing>

            <p>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.</p>
            <p>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.</p>
            <pre>Fraction(int top = 0, int bottom = 1){
    num = top;
    den = bottom;
}</pre>
            <p>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 <c>Fraction</c> object.</p>
            <program language="cpp" label="ObjectOrientedProgrammingDefiningClasses-prog">int main() {
    Fraction myfraction(3, 5);

    // Throws an error
    cout &lt;&lt; myfraction &lt;&lt; endl;

    return 0;
}</program>
            <p>The <c>fraction</c> object, <c>myfraction</c>, does not know how to respond to this
                request to print to the console. The <c>cout</c> function requires that the object
                knows how to interact with the <c>&lt;&lt;</c> 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.</p>
            <p>There are two ways we can solve this problem. One is to define a method
                called something like <c>show</c> that will allow the <c>Fraction</c> object to print itself
                as a string. We can implement this method as shown in
                <xref ref="showmethod-cpp"/>. If we create a <c>Fraction</c> 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.</p>

            <exploration>
                <title>Implementing a <c>show</c> method</title>
                <task xml:id="showmethod-cpp" label="showmethod-cpp">
                    <title>C++</title>
                    <statement><program interactive="activecode" language="cpp" label="showmethod-cpp-prog"><input>
//using functions to print fractions to the command line.
#include &lt;iostream&gt;
using namespace std;

class Fraction {
    public:
        Fraction(int top = 0, int bottom = 1){
            num = top;
            den = bottom;
        }

        void show(){
            cout &lt;&lt; num &lt;&lt; "/" &lt;&lt; den &lt;&lt; endl;
        }
    private:
        int num, den;
};

int main() {
    Fraction fraca(3, 5);
    Fraction fracb(3);
    Fraction fracc; //notice there are no parentheses here.
    // cout &lt;&lt; fraca &lt;&lt; endl; //uncomment to see error
    fraca.show();
    fracb.show();
    fracc.show();
    return 0;
}
                    </input></program></statement>
                </task>
                <task xml:id="showmethod-py" label="showmethod_py">
                    <title>Python</title>
                    <statement><program interactive="activecode" language="python" label="showmethod_py-prog"><input>
class Fraction:

    def __init__(self,top = 0,bottom = 1):

        self.num = top
        self.den = bottom
    def show(self):
        print(self.num,"/",self.den)
# main code below
fraca = Fraction(3,5)
fracb = Fraction(3)
fracc = Fraction()# notice no parameters are passed
# notice print(fraca) will give you an unexpected output
fraca.show()
fracb.show()
fracc.show()
                    </input></program></statement>
                </task>
            </exploration>

            <p>The downside of this approach is 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 <term>overload</term> them.
                One of these, <c>&lt;&lt;</c>, is the operator to
                send data to the output stream.
                It would be nicer to provide a <q>better</q> implementation for this method
                via operator overloading.</p>
            <p><idx>operator overloading</idx>Like function overloading, <term>operator overloading</term> 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.
                This is a form of polymorphism because it enables the same operator to have
                different behaviors depending on the class of the objects involved, demonstrating
                how the same operation can be adapted to various types.</p>
            <p><idx>friend</idx>In C++ this new operator needs to be implemented as a <term>friend</term> of the class in order to
                define the operator's behavior on objects of the class from a non-class method <c>&lt;&lt;</c>.
                Operator overloading is yet another example
                of polymorphism in object-oriented programming.</p>
            <p><idx>friend function</idx>A <term>friend function</term> 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 overload an operator by declaring it a <term>friend</term>
                function in the class definition and giving it a new implementation.
                <xref ref="expl-overload"/> shows an example of the <c>&lt;&lt;</c> operator being overloaded
                in the <c>Fraction</c> class.
                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.</p>
            <exploration xml:id="expl-overload">
                <title>Operator Overloading Example</title>
                <task xml:id="overloaded-cpp" label="overloaded-cpp">
                    <title>C++ Implementation</title>
                    <statement><program xml:id="overloaded_cpp" interactive="activecode" language="cpp" label="overloaded_cpp-prog"><input>
/*overloading functions to take in different
inputs and output the correct results*/
#include &lt;iostream&gt;
using namespace std;

class Fraction {
    public:
        Fraction(int top = 0, int bottom = 1){
            num = top;
            den = bottom;
        }

    //the following tells the compiler to look for this friend's definition outside the class
    friend ostream &amp;operator &lt;&lt; (ostream &amp;stream, const Fraction &amp;frac);

    private:
        int num, den;
};

ostream &amp;operator &lt;&lt; (ostream &amp;stream, const Fraction &amp;frac) {
    /** this is the definition. */
    stream &lt;&lt; frac.num &lt;&lt; "/" &lt;&lt; frac.den;
    return stream;
}

int main() {
    Fraction myfraction(3, 5);
    cout &lt;&lt; myfraction &lt;&lt; " is my fraction" &lt;&lt; endl;

    return 0;
}
                    </input></program></statement>
                </task>
                <task xml:id="overloaded-py" label="overloaded-py">
                    <title>Python Implementation</title>
                    <statement><program language="python" label="overloaded-py-prog"><input>
def __str__(self):
    return str(self.num)+"/"+str(self.den)

    myf = Fraction(3,5)
    print(myf)
    print("I ate", myf, "of the pizza")
                    </input></program></statement>
                </task>
            </exploration>
            <p>We can overload many other operators for our new <c>Fraction</c> class. Some
                of the most important of these are the basic arithmetic operations. We
                would like to be able to create two <c>Fraction</c> objects and then be able to add
                them together using the standard <q>+</q> notation. At this point, if we try
                to add two fractions using <q>+</q>, we get the following:</p>
            <exploration xml:id="expl-adderror">
                <title>Error Before Overloading Addition</title>
                <task xml:id="adderror-cpp" label="adderror-cpp">
                    <title>C++ Addition Error</title>
                    <statement><console><input prompt="">
Fraction f1(1, 4);
Fraction f2(1, 2);
Fraction f3 = f1 + f2;
                    </input><output>
&gt;&gt; error: no match for `operator+' (operand types are `Fraction' and `Fraction'))
                    </output></console></statement>
                </task>
                <task xml:id="adderror-py" label="adderror-py">
                    <title>Python Addition Error</title>
                    <statement><console><input prompt="">
f1 = Fraction(1,4)
f2 = Fraction(1,2)
f1+f2
                    </input><output>
Traceback (most recent call last):
File "&lt;pyshell#173&gt;", line 1, in -toplevel- f1+f2
TypeError: unsupported operand type(s) for +: 'instance' and 'instance'
                    </output></console></statement>
                </task>
            </exploration>
            <p>If you look closely at the error, you see that the problem is that the
                <q>+</q> operator does not understand the <c>Fraction</c> operands.</p>
            <p>We can, of course create something like <xref ref="expl-addmodel"/>.</p>
            <exploration xml:id="expl-addmodel">
                <title>Function for Addition</title>
                <task xml:id="addmodel-cpp" label="addmodel-cpp">
                    <title>C++</title>
                    <statement><program language="cpp" label="addmodel-cpp-prog"><input>
f1.add(f2)
                    </input></program></statement>
                </task>
                <task xml:id="addmodel-py" label="addmodel-py">
                    <title>Python</title>
                    <statement><program language="python" label="addmodel-py-prog"><input>
f1.__add__(f2)
                    </input></program></statement>
                </task>
            </exploration>
            <p>which would ask the <c>Fraction</c> object <c>f1</c> to add the <c>Fraction</c> object
                <c>f2</c> to itself. It would be much better to be written in the standard notation,
                <c>f1 + f2</c>. We can fix this by providing the <c>Fraction</c> class with a friend that
                overloads the <c>+</c>  operator.</p>
            <p>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
                <m>\frac {a}{b} + \frac {c}{d} = \frac {ad}{bd} + \frac {cb}{bd} = \frac{ad+cb}{bd}</m>
                The implementation is shown in <xref ref="introduction_lst-addmethod-cpp"/>. The addition
                function returns a new <c>Fraction</c> 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.</p>
            
            <exploration xml:id="expl-lst-addmethod">
                <title>Adding an addition method</title>
                <task xml:id="introduction_lst-addmethod-cpp" label="introduction_lst-addmethod-cpp">
                    <title>C++ Implementation</title>
                    <statement><program language="cpp" label="introduction_lst-addmethod-cpp-prog"><input>
Fraction operator +(const Fraction &amp;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);
}
                    </input></program></statement>
                </task>
                <task xml:id="introduction_lst-addmethod-py" label="introduction_lst-addmethod-py">
                    <title>Python Implementation</title>
                    <statement><program language="python" label="introduction_lst-addmethod-py-prog"><input>
def __add__(self, otherfraction):

  newnum = self.num*otherfraction.den + self.den*otherfraction.num
  newden = self.den * otherfraction.den

  return Fraction(newnum,newden)
                    </input></program></statement>
                </task>
                <task xml:id="introduction_lst-addmethod-cpp-usage" label="introduction_lst-addmethod-cpp-usage">
                    <title>C++ Usage Example</title>
                    <statement><program xml:id="addfrac_cpp" label="addfrac_cpp" language="cpp" interactive="activecode"><input>
//using functions to abstract the idea of a fraction
#include &lt;iostream&gt;
using namespace std;

class Fraction {
    public:
        Fraction(int top = 0, int bottom = 1) {
            num = top;
            den = bottom;
        }
        Fraction operator +(const Fraction &amp;otherFrac) {
            int newnum = otherFrac.num*den + otherFrac.den*num;
            int newden = den*otherFrac.den;
            return Fraction(newnum, newden);
        }

    friend ostream &amp;operator &lt;&lt; (ostream &amp;stream, const Fraction &amp;frac);

    private:
        int num, den;
};

ostream &amp;operator &lt;&lt; (ostream &amp;stream, const Fraction &amp;frac) {
    stream &lt;&lt; frac.num &lt;&lt; "/" &lt;&lt; frac.den;
    return stream;
}

int main(){
    Fraction f1(1, 4);
    Fraction f2(1, 2);
    Fraction f3 = f1 + f2;
    cout &lt;&lt; f3 &lt;&lt; " is "&lt;&lt; f1 &lt;&lt; " + " &lt;&lt; f2 &lt;&lt; endl;
    return 0;
}
                    </input></program></statement>
                </task>
                <task xml:id="introduction_lst-addmethod-py-usage" label="introduction_lst-addmethod-py-usage">
                    <title>Python Usage Example</title>
                    <statement><program xml:id="addfrac_py" label="addfrac_py" language="python" interactive="activecode"><input>
f1=Fraction(1,4)
f2=Fraction(1,2)
f3=f1+f2
print(f3)
                    </input></program></statement>
                </task>
            </exploration>
            <p>The addition method works as we desire, but a couple of things
                can be improved. When we use a binary operator like <c>+</c>, we
                like more symmetry.
                Binary operators can either be members of their
                left-hand argument's class or friend functions.
                Since the stream operators' left-hand argument is a stream,
                stream operators (such as <c>&lt;&lt;</c> and <c>&gt;&gt;</c>) must be either member functions of the stream class
                or friend functions of the class they are used with.
                However, that is not true for the <c>+</c> operator.
                Let's rewrite the addition operator as a friend function.</p>
            <exploration xml:id="expl-addoverload">
                <title>Overloading Addition</title>
                <task xml:id="addoverload-cpp" label="addoverload-cpp">
                    <title>C++ Implementation</title>
                    <statement><program language="cpp" label="addoverload-cpp-prog"><input>
Fraction operator +(const Fraction &amp;frac1, const Fraction &amp;frac2) {
    int newnum = frac1.num * frac2.den + frac1.den * frac2.num;
    int newden = frac1.den * frac2.den;
    return Fraction(newnum, newden);
}
                    </input></program></statement>
                </task>
                <task xml:id="addoverload-py" label="addoverload-py">
                    <title>Python Implementation</title>
                    <statement><program language="python" label="addoverload-py-prog"><input>
def __add__(self,otherfraction):
    newnum = self.num*otherfraction.den + self.den*otherfraction.num
    newden = self.den * otherfraction.den
    return Fraction(newnum,newden)
                    </input></program></statement>
                </task>
                <task xml:id="addoverload-usage" label="addoverload-usage">
                    <title>C++ Usage</title>
                    <statement><program interactive="activecode" language="cpp" label="addoverload-usage-prog"><input>
//overloading the addition operator to create clearer syntax
#include &lt;iostream&gt;
using namespace std;

class Fraction {
    public:
        Fraction(int top = 0, int bottom = 1) {
            num = top;
            den = bottom;
        }

    friend ostream &amp;operator &lt;&lt; (ostream &amp;stream, const Fraction &amp;frac);
    friend Fraction operator +(const Fraction &amp;frac1, const Fraction &amp;frac2);

    private:
        int num, den;
};

ostream &amp;operator &lt;&lt; (ostream &amp;stream, const Fraction &amp;frac) {
    stream &lt;&lt; frac.num &lt;&lt; "/" &lt;&lt; frac.den;
    return stream;
}

Fraction operator +(const Fraction &amp;frac1, const Fraction &amp;frac2) {
    int newnum = frac1.num * frac2.den + frac1.den * frac2.num;
    int newden = frac1.den * frac2.den;
    return Fraction(newnum, newden);
}


int main(){
    Fraction f1(1, 4);
    Fraction f2(1, 2);
    Fraction f3 = f1 + f2;
    cout &lt;&lt; f3 &lt;&lt; " is "&lt;&lt; f1 &lt;&lt; " + " &lt;&lt; f2 &lt;&lt; endl;
    return 0;
}
                    </input></program></statement>
                </task>
            </exploration>
            <p>How you choose to overload operators  like <c>+</c> is a design choice
                since both methods will work perfectly well. This is another
                example of encapsulation; your user does not need to know
                which you choose to use!</p>
            <p>There is one more thing we can improve in our addition function.
                Note that <m>6/8</m> is the correct result
                (<m>\frac {1}{4} + \frac {1}{2}</m>) but that it is not in the
                <q>lowest terms</q> representation. The best representation would be
                <m>3/4</m>. 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.</p>
            <p>The best-known algorithm for finding a greatest common divisor is
                Euclid's Algorithm, which will be discussed in detail in <xref ref="ch-trees"/>.
                Euclid's Algorithm states that the greatest common divisor of two
                integers <m>m</m> and <m>n</m> is <m>n</m> if <m>n</m>
                divides <m>m</m> evenly. However, if <m>n</m> does not divide
                <m>m</m> evenly, then the answer is the greatest common divisor of
                <m>n</m> and the remainder of <m>m</m> divided by <m>n</m>. We
                will simply provide an iterative implementation here (see
                <inline classes="xref std std-ref">ActiveCode 1</inline>). 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.</p>
            
            <exploration xml:id="gcdalg">
                <title>Greatest Common Divisor</title>
                <task xml:id="gcd-cpp" label="gcd-cpp">
                    <title>C++ Implementation</title>
                    <statement><program interactive="activecode" language="cpp" label="gcd-cpp-prog"><input>
#include &lt;iostream&gt;
using namespace std;

int gcd(int m, int n) {
    while (m%n != 0) {
        int oldm = m;
        int oldn = n;

        m = oldn;
        n = oldm%oldn;
    }

    return n;
}

int main() {
    cout &lt;&lt; gcd(20, 10) &lt;&lt; endl;
    return 0;
}
                    </input></program></statement>
                </task>
                <task xml:id="gcd-py" label="gcd-py">
                    <title>Python Implementation</title>
                    <statement><program interactive="activecode" language="python" label="gcd-py-prog"><input>
def gcd(m,n):
    while m%n != 0:
        oldm = m
        oldn = n

        m = oldn
        n = oldm%oldn
    return n

print(gcd(20,10))
                    </input></program></statement>
                </task>
            </exploration>
            <p>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
                <m>6/8</m>, the greatest common divisor is 2. Dividing the top and
                the bottom by 2 creates a new fraction, <m>3/4</m> (see
                <xref ref="introduction_lst-newaddmethod"/>).</p>
            
    <listing xml:id="introduction_lst-newaddmethod">
        <caption>New addition implementation using <c>gcd</c></caption>
        <program xml:id="gcdadd" label="gcdadd" interactive="activecode" language="cpp"><input>
#include &lt;iostream&gt;
using namespace std;

int gcd(int m, int n){
    /** gcd is a helper function, used by but not part of the Fraction class */
    while (m%n != 0) {
        int oldm = m;
        int oldn = n;

        m = oldn;
        n = oldm%oldn;
    }
    return n;
}

class Fraction {
    public:
        Fraction(int top, int bottom) {
            num = top;
            den = bottom;
        }
        Fraction(int top){
            num = top;
            den = 1;
        }
        Fraction(){
            num = 1;
            den = 1;
        }
        Fraction operator +(const Fraction &amp;otherFrac) {
            int newnum = num*otherFrac.den + den*otherFrac.num;
            int newden = den*otherFrac.den;
            int common = gcd(newnum, newden);
            return Fraction(newnum/common, newden/common);
        }

    friend ostream&amp; operator &lt;&lt; (ostream&amp; stream, const Fraction&amp; fraction);

    private:
        int num, den;
};

ostream &amp; operator &lt;&lt; (ostream&amp; stream, const Fraction&amp; fraction) {
    stream&lt;&lt;fraction.num&lt;&lt;"/"&lt;&lt;fraction.den;
    return stream;
}

int main(){
    Fraction f1(1, 4);
    Fraction f2(1, 2);
    Fraction f3 = f1 + f2;
    cout &lt;&lt; f3 &lt;&lt; " is "&lt;&lt; f1 &lt;&lt; " + " &lt;&lt; f2 &lt;&lt; endl;
    return 0;
}
        </input></program>
    </listing>
            <figure align="center" xml:id="fig-fraction2cpp">
                <caption>An Instance of the <c>Fraction</c> Class with Two Methods</caption>
                    <image source="Introduction/fraction2cpp.png" width="50%">
                    <description><p>Visual representation of a Fraction class instance called 'myfraction'. It features concentric circles with the innermost labeled 'State' showcasing 'num' with a value of 3 above 'den' with a value of 5, indicating the fraction's numerator and denominator. The outer circle is labeled 'Methods', suggesting the object's functionality. Two symbols, '&lt;&lt;' and '+', are shown outside the Methods circle, implying additional methods.</p></description>
                    </image>
                </figure>

            <p>Our <c>Fraction</c> object now has two very useful methods and looks
                like <xref ref="fig-fraction2cpp"/>. An additional group of methods that we need to
                include in our example <c>Fraction</c> class will allow two fractions to
                compare themselves to one another using <c>==</c>.</p>
            <p>We want the <c>==</c> operator to compare Fraction objects and to return
                <c>true</c> if they are equivalent in value, <c>false</c> otherwise.
                This is a design choice because we want <m>\frac {1}{2}</m> to be considered
                equal to <m>\frac {2}{4}</m> as well as <m>\frac {3}{6}</m>, etc.
                Hence, in the <c>Fraction</c> class, we can implement the <c>==</c> method by
                cross-multiplying (see <xref ref="introduction_lst-cmpmethod-cpp"/>) rather than
                by just comparing numerators and denominators.</p>
            <p>Of course there are other relational operators that can be overridden. For example, the
                <c>&lt;=</c> operator could be overridden to provide the less than or equal functionality.</p>
            
            <exploration xml:id="introduction_lst-cmpmethod">
                <title>Overloading the comparison operator</title>
                <task xml:id="introduction_lst-cmpmethod-cpp" label="introduction_lst-cmpmethod-cpp">
                    <title>C++</title>
                    <statement><program language="cpp" label="introduction_lst-cmpmethod-cpp-prog"><input>
bool operator ==(const Fraction &amp;otherFrac) {
    int firstnum = num*otherFrac.den;
    int secondnum = otherFrac.num*den;

    return firstnum==secondnum;
}
                    </input></program></statement>
                </task>
                <task label="introduction_lst-cmpmethod-py">
                    <title>Python</title>
                    <statement><program language="python" label="introduction_lst-cmpmethod-py-prog"><input>
def __eq__(self, other):
    firstnum = self.num * other.den
    secondnum = other.num * self.den

    return firstnum == secondnum
                    </input></program></statement>
                </task>
            </exploration>

            <p>The complete <c>Fraction</c> class, up to this point, is shown in
                <xref ref="fraction_class_cpp"/>. We leave the remaining arithmetic and relational
                methods as exercises.</p>


            <exploration xml:id="fraction_class">
                <title>Complete <c>Fraction</c> class</title>
                <task xml:id="fraction_class_cpp" label="fraction_class_cpp">
                    <title>C++</title>
                    <statement><program interactive="activecode" language="cpp" label="fraction_class_cpp-prog"><input>
#include &lt;iostream&gt;
using namespace std;

int gcd(int m, int n) {
    while (m%n != 0) {
        int oldm = m;
        int oldn = n;

        m = oldn;
        n = oldm%oldn;
    }
    return n;
}

class Fraction {
    public:
        Fraction(int top, int bottom) {
            num = top;
            den = bottom;
        }
        Fraction(int top){
            num = top;
            den = 1;
        }
        Fraction(){
            num = 1;
            den = 1;
        }
        Fraction operator +(const Fraction &amp;otherFrac) {
            int newnum = num*otherFrac.den + den*otherFrac.num;
            int newden = den*otherFrac.den;
            int common = gcd(newnum, newden);

            return Fraction(newnum/common,newden/common);
        }
        bool operator ==(const Fraction &amp;otherFrac) {
            int firstnum = num*otherFrac.den;
            int secondnum = otherFrac.num*den;
            return firstnum==secondnum;
        }


    friend ostream&amp; operator&lt;&lt;(ostream&amp; stream, const Fraction&amp; fraction);

    private:
        int num, den;
};

ostream&amp; operator &lt;&lt; (ostream&amp; stream, const Fraction&amp; fraction) {
    stream &lt;&lt; fraction.num &lt;&lt; "/" &lt;&lt; fraction.den;

    return stream;
}

int main(){
    Fraction x(1, 2);
    Fraction y(2, 4);
    cout &lt;&lt; x &lt;&lt; " + " &lt;&lt; y &lt;&lt; " = " &lt;&lt; x+y &lt;&lt; endl;
    if (x==y){
        cout &lt;&lt; "x is equal y" &lt;&lt; endl;
    }
    else{
        cout &lt;&lt; "x is not equal y" &lt;&lt; endl;
    }
    return 0;
}
                    </input></program></statement>
                </task>
            <task label="fraction_class_py">
                <title>Python</title>
                <statement><program xml:id="fraction_class_py" interactive="activecode" language="python" label="fraction_class_py-prog"><input>
def gcd(m,n):
    while m%n != 0:
        oldm = m
        oldn = n

        m = oldn
        n = oldm%oldn
    return n

class Fraction:
    def __init__(self,top,bottom):
        self.num = top
        self.den = bottom

    def __str__(self):
        return str(self.num)+"/"+str(self.den)

    def show(self):
        print(self.num,"/",self.den)

    def __add__(self,otherfraction):
        newnum = self.num*otherfraction.den + \
                    self.den*otherfraction.num
        newden = self.den * otherfraction.den
        common = gcd(newnum,newden)
        return Fraction(newnum//common,newden//common)

    def __eq__(self, other):
        firstnum = self.num * other.den
        secondnum = other.num * self.den

        return firstnum == secondnum

x = Fraction(1,2)
y = Fraction(2,3)
print(x + y)
print(x == y)
            </input></program></statement></task>
        </exploration>>
        </subsection>
        <subsection xml:id="introduction_self-check">
            <title>Self-Check</title>
            <p>To make sure you understand how operators are implemented in C++ classes, and how to properly write methods, write some methods to implement
                <c>*</c>, <c>/</c>, and <c>-</c>.  Also implement comparison operators <c>&gt;</c> and <c>&lt;</c>.</p>

    <program xml:id="self_check_4cpp" interactive="activecode" language="cpp" label="self_check_4cpp-prog">
        <input>
#include &lt;iostream&gt;
using namespace std;

int gcd(int m, int n) {
    while (m%n != 0) {
        int oldm = m;
        int oldn = n;

        m = oldn;
        n = oldm%oldn;
    }
    return n;
}

class Fraction {
    public:
        Fraction(int top, int bottom) {
            num = top;
            den = bottom;
        }
        Fraction(int top){
            num = top;
            den = 1;
        }
        Fraction(){
            num = 1;
            den = 1;
        }
        Fraction operator +(const Fraction &amp;otherFrac) {
            int newnum = num*otherFrac.den + den*otherFrac.num;
            int newden = den*otherFrac.den;
            int common = gcd(newnum, newden);

            return Fraction(newnum/common,newden/common);
        }
        bool operator ==(const Fraction &amp;otherFrac) {
            int firstnum = num*otherFrac.den;
            int secondnum = otherFrac.num*den;

            return firstnum==secondnum;
        }

    friend ostream&amp; operator&lt;&lt;(ostream&amp; stream, const Fraction&amp; fraction);

    private:
        int num, den;
};

ostream&amp; operator &lt;&lt; (ostream&amp; stream, const Fraction&amp; fraction) {
    stream &lt;&lt; fraction.num &lt;&lt; "/" &lt;&lt; fraction.den;

    return stream;
}

int main(){
    Fraction x(1, 2);
    Fraction y(2, 4);
    cout &lt;&lt; x &lt;&lt; " + " &lt;&lt; y &lt;&lt; " = " &lt;&lt; x+y &lt;&lt; endl;
    if (x==y){
        cout &lt;&lt; "x is equal y" &lt;&lt; endl;
    }
    else{
        cout &lt;&lt; "x is not equal y" &lt;&lt; endl;
    }
    return 0;
}
        </input>
    </program>
            <p>Our the next section will introduce another important aspect of
                object-oriented programming, namely <term>inheritance</term>.</p>
<reading-questions xml:id="rq-oop">
    <title>Reading Questions</title>
    <exercise label="aande">
        <statement><p>Match the corresponding key word to the appropriate scenario.</p></statement>
        <feedback><p>Review the definitions of the key words.</p></feedback>
    <matches><match order="1"><premise>Encapsulation</premise><response>A situation where bank software programmers want to protect users' personal information.</response></match><match order="2"><premise>Abstraction</premise><response>A situation where software programmers want to develop similar objects without having to redefine the most similar properties.</response></match></matches></exercise>
    
    <exercise label="class_syntax">
    <statement><p>Click on the line where there is a syntax error when defining the following class</p></statement>
    <feedback><p>C++ class definitions end with a certain symbol</p></feedback>
    <areas>
        <cline><area correct="no">class Fraction {</area></cline>
        <cline>  <area correct="no">public:</area></cline>
        <cline>      <area correct="no">Fraction(int top, int bottom) {</area></cline>
        <cline>          <area correct="no">/** Fraction constructor method */</area></cline>
        <cline>          <area correct="no">num = top;     // setting num's value</area></cline>
        <cline>          <area correct="no">den = bottom;  // setting den's value</area></cline>
        <cline>      <area correct="no">}</area></cline>
        <cline>  <area correct="no">private:</area></cline>
        <cline>      <area correct="no">int num; // num atribute</area></cline>
        <cline>      <area correct="no">int den; // den attribute</area></cline>
        <cline><area correct="yes">}</area></cline> <!-- line with syntax error-->
    </areas>
</exercise>


    

    <exercise label="elements_of_OOP">
        <statement><p>Drag the word on the left to its corresponding definition</p></statement>
        <feedback><p>Review the elements of object oriented programming</p></feedback>
    <matches><match order="1"><premise>Encapsulation</premise><response>hiding the contents of a class except when absolutely necessary</response></match><match order="2"><premise>Abstraction</premise><response>focusing on desired behaviors and properties while disregarding what is irrelevant/unimportant</response></match><match order="3"><premise>Polymorphism</premise><response>processing objects or methods differently depending on their data type, class, number of arguments, etc.</response></match></matches></exercise>
    <exercise label="elements_of_classses">
        <statement><p>Drag the word on the left to its corresponding definition</p></statement>
        <feedback><p>Review classes and their properties</p></feedback>
    <matches><match order="4"><premise>instance</premise><response>an object of a class</response></match><match order="5"><premise>constructor</premise><response>an special function to initialize</response></match><match order="6"><premise>access keywords</premise><response> private and public</response></match><match order="7"><premise>class</premise><response>a template for creating objects</response></match></matches></exercise>  
</reading-questions>


        </subsection>
        <conclusion><p>
            <!-- extra space before the progress bar -->
        </p></conclusion>
    </section>