double-Dispatch

#include <iostream>
#include <string>
using namespace std;

class Number;       
class Integer;
class Rational;

class Number
{
public:
    int num, den;
    virtual Number* add(Number&) = 0;
    virtual Number* addInteger(Integer&) =0 ;
    virtual Number* addRational(Rational&) =0 ;
    virtual string toString() = 0;
};

class Rational : public Number
{
    Rational* addInteger(Integer& i);

    Rational* addRational(Rational &r);

public:

	string toString(){
        std::string s = to_string(this->num) + "/" + to_string(this->den);
		return s;
	}

    Number* add(Number& n)
    {
        Number *t = n.addRational(*this);

        return t;
    }

    Rational(int n, int d)
    {
        this->num = n;
        this->den = d;
    }
};

class Integer : public Number
{
    Integer* addInteger(Integer& i);

    Rational* addRational(Rational& r);

public:

	string toString(){
        std::string s = to_string(this->num) ;

		return s;
	}
    Number* add(Number& n)
    {
         Number* t = n.addInteger(*this);
         
         return t;
    }

    Integer(int n)
    {
        this->num = n;
        this->den = 1;
    }
};

Rational* Rational::addInteger(Integer& i)
{

    int num = this->num + i.num*this->den;
    int den = this->den;
    Rational *r = new Rational(num, den);
    return r;
}

Rational* Rational::addRational(Rational &r)
{
    int num = this->num*r.den + this->den*r.num;
    int den = this->den*r.den;
    Rational *rf = new Rational(num, den);
    return rf;
}

Integer* Integer::addInteger(Integer& i)
{
    int num = this-> num + i.num;
    int den = 1;
    Integer *is = new Integer(num);
    return is;

}

Rational* Integer::addRational(Rational& r)
{
    int num = this->num*r.den + r.num;
    int den = r.den;
    Rational *rf = new Rational(num, den);
    return rf; 

}

int main()
{
	Integer i1 = Integer(2);
    Integer i2 = Integer(3);
    Rational r1 = Rational(2 , 3); // numerator = 2 , denominator = 3.
    Rational r2 = Rational(4 , 5);
    Number *n1 = i1. add(i2);
    Number *n2 = i1. add(r1);
    Number *n3 = r1. add(r2);
    Number *n4 = r1. add(i1);
    cout << " n1 = " << n1 -> toString() << endl ;
    cout << " n2 = " << n2 -> toString() << endl ;
    cout << " n3 = " << n3 -> toString() << endl ;
    cout << " n4 = " << n4 -> toString() << endl ;
    return 0;
}

compile g++ -std=c++11