Chapter 3, Problem 21E

Explanation of Solution

Code which supports unary negation and the four standard arithmetic operators:

//include the required header files

#include <cmath>

using std::abs;

using std::round;

#include <iostream>

using std::ostream;

using std::cout;

//definition of class "rational"

class rational

{

    //declare the required variables

    int num;

    int den;

    //definition of "gcd" function

    int gcd(int i, int j)

    {

        //set the absolute values

        i = abs(i);

        j = abs(j);

        //check "i" is not equal to "j"

        while (i != j)

        {

            //check "i" is greater than "j"

            if (i > j)

/*subtract the values and store the result in "i"*/

                i = i - j;

            //otherwise

            else

/*subtract the values and store the result in "j"*/

            j = j - i;

        }

        //return the "i" value

        return i;

    }

    //definition of "normalize" function

    void normalize()

    {

        //check "den" is less than 0

        if (den < 0)

        {

            //calculate numerator value

            num = -num;

            //calculate denominator value

            den = -den;

        }

        //call the "gcd" function with a parameters

        int g = gcd(num, den);

        //calculate numerator value

        num /= g;

        //calculate denominator value

        den /= g;

    }

    //access specifier

    public:

    //definition constructor

    rational(int n, int d)

    {

        //set the values

        num = n;

        den = d;

        //call the function

        normalize();

    }

    // definition of constructor

    rational(double r, double e)

    {

        //set the values

        num = (int) r;

        den = 1;

        //check the condition

while (abs(r - ((double)num)/((double)den)) > e)

        {

            //increment the value

            ++den;

            //calculate numerator value

            num = round(den*r);

        }

    }

    //definition of operator "-"

    rational operator-()

    {

        //calculate numerator value

        num = -num;

        //return the value

        return *this;

    }

    //definition of operator "+"

    rational operator+(const rational o)

    {

        //declare the variable and calculate the value

        int p = den * o.den;

        //calculate numerator value

        num = num * o.den + den * o.num;

        //set the value

        den = p;

        //call the function

        normalize();

        //return the value

        return *this;

    }

    //definition of operator "-"

    rational operator-(const rational o)

    {

        //declare the variable and calculate the value

        int p = den * o.den;

        //calculate numerator value

        num = num * o.den - den * o.num;

        //set the value

        den = p;

        //call the function

        normalize();

        //return the value

        return *this;

    }

    //definition of operator "*"

    rational operator*(const rational o)

    {

        //calculate numerator value

        num *= o.num;

        //calculate denominator value

        den *= o.den;

        //call the function

        normalize();

        //return the value

        return *this;

    }

    //definition of operator "/"

    rational operator/(const rational o)

    {

        //calculate numerator value

        num *= o.den;

        //calculate denominator value

        den *= o.num;

        //call the function

        normalize();

        //return the value

        return *this;

    }

};

Explanation:

• The header files are included in the beginning of the program.
• The “rational” class is defined. Inside the class,
  • The “num” and “den” variables are declared.
  • The “gcd” function is defined
    • Get the absolute values of “i” and “j” and store it in the corresponding variables.
    • The “while” loop is used to check “i” is not equal to “j”.
      • If the “i” value is greater than “j” value, then subtract the “i” and “j” value and store the result in the “i” variable.
      • Otherwise, subtract the “j” and “i” value and store the result in the “j” variable.
    • Return the “i” value.
  • The “normalize” function is defined.
    • If the “den” is less than 0, then calculate the “num” and “den” values.
    • Call the “gcd” function with the parameters.
    • Calculate the numerator and denominator values.
  • The constructor of “rational” is defined with two parameters.
    • Set the values
    • Call the “normalize” function.
  • Again, the constructor of “rational” is defined with another two parameters.
    • Set the values.
    • Check the “while” condition
      • Increment the denominator value
      • Calculate the numerator
  • The operator “-” is defined
    • Calculate the “num” value
    • Return the result
  • The operator “+” is defined with parameter
    • Calculate the “p” and “num” values
    • Set the value
    • Call the “normalize” function
    • Return the result
  • The operator “-” is defined with parameter
    • Calculate the “p” and “num” values
    • Set the value
    • Call the “normalize” function
    • Return the result
  • The operator “*” is defined with parameter
    • Calculate the “den” and “num” values
    • Call the “normalize” function
    • Return the result
  • The operator “/” is defined with parameter
    • Calculate the “den” and “num” values
    • Call the “normalize” function
    • Return the result