Virtual functions allow functions in derived classes to override functions in base classes. When a base class pointer points to a derived class object, calling a virtual function through the pointer will call the derived class's version. This allows the same interface to behave differently based on the actual object. Virtual functions are useful for mathematical operations, where a base class defines an interface and derived classes perform specific calculations like addition, subtraction etc. depending on the object type pointed to by the base class pointer.

1. IMPORTANT POINTS RELATED TO VIRTUAL FUNCTIONS
VIRTUAL FUNCTIONS ARE USED IN CASE OF FUNCTION OVER RIDING.
FUNCTION OVERRIDING MEANS BASE CLASS AND DERIVED CLASS HAVING SAME FUNCTION NAME AND
ARGUMENTS, BUT PERFORM DIFFERENT OPERATIONS.
VIRTUAL FUNCTIONS ARE USED TO ACCESS BOTH BASE CLASS AND DERIVED CLASS FUNCTIONS.
VIRTUAL FUNCTIONS DECLARATION IS SAME AS OTHER FUNCTION BUT THE VIRTUAL KEYWORD IS
PRECEEDED WITH THE FUNCTIONS DECLARATION.
VIRTUAL FUNCTIONS ARE ACCESSED USING POINTERS:
(*ptr).functioname();
Or
ptr->functionname();
Where *ptr is a pointer to base class object.
When base class pointer, points to base class object’s address as ptr =&b1, where b1 is the object of
base class. We can access the base class function. And when It points to derived class object’s address,
we can access derived class functions.
SIMPLE PROGRAM SHOWING THE EFFECT OF VIRTUAL FUNCTION.
#include<iostream.h>
#include<conio.h>
class one //base class
{
public:
int a,b;
void get_data()
{
cout<<"enter a:";
cin>>a;
cout<<"enter b:";
cin>>b;
cout<<"n a is:"<<a;
cout<<"n b is:"<<b;
}
virtual void cal() //virtual function over rided in derived class
{
cout<<"sum is"<<a+b;
}
};
class two :public one //two class derived from one
{
void cal()
{
cout<<"sub is"<<a-b;
}
};
int main()
{
one o1,*ptr; //created object and pointer to base class object.

2. two t1; // created object of derived class.
clrscr();
cout<<"n PTR POINTS TO BASE CLASS..";
ptr=&o1;
ptr->get_data();
ptr->cal();
cout<<"n PTR POINTS TO DERIVED CLASS...";
ptr =&t1;
ptr->get_data();
ptr->cal();
getch();
return 0;
}
**OUTPUT**
PTR POINTS TO BASE CLASS.
Enter a: 45
Enter b: 12
Sum is: 57
PTR POINTS TO DERIVED CLASS.
Enter a: 12
Enter b: 5
Sub is: 7
VIRTUAL FUNCTION USED TO PERFORM VARIOUS MATHEMATICAL OPERATIONS.
#include<iostream.h>
#include<conio.h>
class add
{
public:
virtual int calculate(int num1, int num2)//virtual func overloaded in der classes...
{
return num1+num2;
}
};
class sub:public add
{
public:
int calculate (int num1, int num2)
{
return num1-num2;
}
};
class mul:public sub
{
public:
int calculate(int num1, int num2)

3. {
return num1*num2;
}
};
class div:public mul
{
public:
int calculate(int num1, int num2)
{
return num1/num2;
}
};
int main()
{
int a,b,ch;
clrscr();
cout<<"enter a:";
cin>>a;
cout<<"enter b:";
cin>>b;
cout<<"n(1)ADDITION n (2)SUBTRACTION n (3) MULTIPLICATION n (4) DIVISIONn Enter your choice";
cin>>ch;
add a1,*ptr;
sub s1;
mul m1;
div d1;
switch(ch)
{
case 1:
ptr =&a1;
cout<<"SUM IS:"<<ptr->calculate(a,b);
break;
case 2:
ptr =&s1;
cout<<"SUBTRACTION IS:"<<ptr->calculate(a,b);
break;
case 3:
ptr=&m1;
cout<<"MULTIPLICATION IS:"<<ptr->calculate(a,b);
break;
case 4:
ptr=&d1;
cout<<"DIVISION IS:"<<ptr->calculate(a,b);
break;
default:
cout<<"WRONG CHOICE......";
}

4. getch();
return 0;
}
** OUTPUT **
Enter a: 96
Enter b: 12
(1) ADDITION.
(2) SUBTRACTION.
(3) MULTIPLICATION.
(4) DIVISION.
Enter your choice: 4
Division is: 8