Question

c++

Write a rational number class. A rational number is a number that can be written as p/q where p and q are integers. The division is not carried out, only indicated. Thus you should represent rational numbers by two int values, numerator and denominator.

Constructors must be present to create objects with any legal values. You should provide constructors to make objects out of pairs of int values; that is, a constructor with two int parameters. Since very int is also a rational number, as in 2/1 or 17/1, you should provide a constructor with a single int parameter as well. You should take into account that if the user constructs a rational number that corresponds to a non-reduced fraction, you should automatically “reduce” the fraction in your constructor. For example, if the user constructs a rational number with numerator 4 and denominator 16, you should store it as numerator 1 and denominator 4. You should also take into account the storage of negative values. For simplicity’s sake, always store a negative in the numerator if need be. For example, if the user constructs a rational number with numerator 2 and denominator -4, it should be stored as -1, 2 respectively. In addition, if the user constructs a rational number with numerator -1 and denominator -3, it should be stored as 1, 3 respectively. Lastly, if the user happens to construct a rational number with zero as the denominator, simply change the denominator to 1.

Provide the following public member functions:

add – accepts a rational number parameter and returns a rational number

sub– accepts a rational number parameter and returns a rational number

mul– accepts a rational number parameter and returns a rational number

div– accepts a rational number parameter and returns a rational number

equals– accepts a rational number parameter and returns a bool

less_than– accepts a rational number parameter and returns a bool

greater_than– accepts a rational number parameter and returns a bool

input – accepts an istream parameter and gets input in the form numerator/denominator from the keyboard

output – accepts an ostream parameter and writes rational numbers in the form numerator/denominator or numerator if the denominator is 1, or 0 if the numerator is zero

Provide the following private member functions:

reduce – a void function that accepts no arguments and reduces the rational number

gcd – a function that returns an int and returns the greatest common divisor of its two int parameters num1 and num2 (body given below) – this uses Euclid’s algorithm

   while (num1 != num2)

        if (num1 > num2)

           num1 = num1 - num2;

        else

           num2 = num2 - num1;

     return num1;

using this main for testing:

int main()
{
        ofstream fout;
        fout.open("out.txt");
        RationalNumber op1 = RationalNumber(1, -4);
        op1.output(fout);

        RationalNumber op2 = RationalNumber(5);
        op2.output(fout);
        RationalNumber op3 = RationalNumber(-6, -9);
        op3.output(fout);

        RationalNumber sum = op1.add(op2);
        fout << "sum: ";
        sum.output(fout);


        RationalNumber difference = op2.sub(op3);
        fout << "difference: ";
        difference.output(fout);

        RationalNumber product = op1.mul(op3);
        fout << "product: ";
        product.output(fout);

        RationalNumber quotient = op3.div(op2);
        fout << "quotient: ";
        quotient.output(fout);

        bool lessThan = op1.less_than(op2), greaterThan = op1.greater_than(op3), equalTo = op1.equals(RationalNumber(2, -6)), equalTo2 = op1.equals(op2);

        fout << lessThan << endl;
        fout << greaterThan << endl;
        fout << equalTo << endl;
        fout << equalTo2 << endl;

}

Answer 1

Compilation command

g++ RationalNumber.cpp main.cpp -o RationalNumber

main.cpp is the one given in question.

CODE

RationalNumber.cpp

#include "RationalNumber.h"

// Constructor when denom is 1
RationalNumber::RationalNumber(int num) {
   // calling the constructor with numerator and denominator.
   RationalNumber x = RationalNumber(num,1);

   // initializing the member variables.
   numerator = x.numerator;
   denominator = x.denominator;
}
RationalNumber::RationalNumber(int num, int denom = 1) {

   // variable to keep track of negative fractions.
   bool neg = false;

   // if denom is 0 then make it 1
   denom = denom == 0? 1:denom;

  
   // if numerator less than zero then make neg to true.
   if(num < 0) {
       num = -num;
       neg = neg ^ true;
   }
   // if denominator less than zero then make neg to true.
   if(denom < 0) {
       denom = -denom;
       neg = neg ^ true;
   }

   // xor of neg will make it false if both are negative or both +ve

   numerator = num;
   denominator = denom;
   // to simplify we must call the gcd on numerator and denominator.
   int gcdNum = gcd();

   // divide the gcd with numerator and denominator
   if(gcdNum != 0) {
       numerator = numerator/gcdNum;
       denominator = denominator/gcdNum;
   }

   // if the number is negative make numerator negative.
   numerator = neg?-numerator:numerator;

}

int RationalNumber::gcd() {
   int a = numerator;
   int b = denominator;

   int t;

   // Euclidean method to compute gcd
   while(b) {
       t = b;
       b = a%b;
       a = t;
   }
   return a;
}

// adding of two rational numbers
RationalNumber RationalNumber::add(RationalNumber r) {

   // computing numerator.
   int num = numerator * r.denominator + denominator * r.numerator;
   // computing denominator.
   int denom = r.denominator * denominator;

   //constructing new object and returning it
   RationalNumber ans(num,denom);
   return ans;
}

void RationalNumber::output(ofstream out) {
   // if numerator is zero output 0
   if(numerator == 0) {
       out<<0<<endl;
   }
   // if denominator is 1 then just print numerator
   else if(denominator == 1) {
       out<<numerator<<endl;
   }
   // print the fraction.
   else {
       out<<numerator<<"/"<<denominator<<endl;
   }

}

// subtracts two fraction.
RationalNumber RationalNumber::sub(RationalNumber r) {

   // computing numerator.
   int num = numerator * r.denominator - denominator * r.numerator;

   // computing denominator.
   int denom = r.denominator * denominator;

   RationalNumber ans(num,denom);
   return ans;
}

// multiplication of two rational numbers
RationalNumber RationalNumber::mul(RationalNumber r) {

   cout<<r.numerator<< " "<<r.denominator<<endl;
   // computing numerator.
   int num = numerator * r.numerator;
   // computing denominator.
   int denom = r.denominator * denominator;

   RationalNumber ans(num,denom);
   return ans;
}

// division of two rational numbers
RationalNumber RationalNumber::div(RationalNumber r) {

   cout<<r.numerator<< " "<<r.denominator<<endl;
   // computing numerator.
   int num = numerator * r.denominator;
   // computing denominator.
   int denom = r.numerator * denominator;

   RationalNumber ans(num,denom);
   return ans;
}

// check for less than
bool RationalNumber::less_than(RationalNumber r) {
   return (numerator*r.denominator)<(denominator*r.numerator);
}

// check for greater than opposite of less than
bool RationalNumber::greater_than(RationalNumber r) {
   return (numerator*r.denominator)>(denominator*r.numerator);
}

// check for equals
bool RationalNumber::equals(RationalNumber r) {
   return (numerator==r.numerator)&&(denominator==r.denominator);
}

RationalNumber.h

#include <iostream>
#include <fstream>

using namespace std;

// Class declaration of RAtional Number;

class RationalNumber {
   public:
       int numerator;
       int denominator;

       RationalNumber(int num, int denom);
       RationalNumber(int num);
       int gcd();

       RationalNumber add(RationalNumber r);
       RationalNumber sub(RationalNumber r);
       RationalNumber mul(RationalNumber r);
       RationalNumber div(RationalNumber r);

       bool less_than(RationalNumber r);
       bool greater_than(RationalNumber r);
       bool equals(RationalNumber r);

      
       void output(ofstream &out);

  
};

OUTPUT

-1/4
5
2/3
sum: 19/4
difference: 13/3
product: -1/6
quotient: 2/15
1
0
0
0

Thanks,