Rational Numbers Project (cs162)

//by Curtis Michels
//main.cpp

#include <iostream>
#include "Rationals.h"

using namespace std;

void test() {
    Rational x{-1,2};
    Rational y{5};


    cout << x.toString() << endl;
    cout << y.toString() << endl;

    Rational z{x+y};

    cout << "x + y = " << z.toString() << endl;
    cout << "x - y = " << (x-y).toString() << endl;
}

void test2() {
    cout << GCD(54,888);
}

void test3() {
    Rational x{2,4};
    Rational y{1,8};
    cout << "x + y = " << (x+y).toString() << endl;
    cout << "x * y = " << (x*y).toString() << endl;
    cout << "x / y = " << (x/y).toString() << endl;
}

void test4() {
    Rational x{2,4};
    Rational y{2,4};
    Rational z{2,6};
    Rational g{4,8};
    Rational h{1};
    cout << "x " << x << endl;
    cout << "y " << y << endl;
    cout << "z " << z << endl;
    cout << "g " << g << endl;
    cout <<endl;
    cout << (x == y) << endl;
    cout << (x == z) << endl;
    cout << endl;
    cout << (x == g) << endl;
    cout << (x != y) << endl;
    cout << (x != z) << endl;
    cout << (x != g) << endl;
    cout << endl;
    cout << (x<h) << endl;
    cout << (x>h) << endl;
    cout << (x>y) << endl;
    cout << (x<y) << endl;
    cout << endl;
    cout << (x<=h) << endl;
    cout << (x>=h) << endl;
    cout << (x>=y) << endl;
    cout << (x<=y) << endl;

}

int main()
{
    test();
    test2();
    test3();
    test4();
    return 0;
}


//by Curtis Michels
//Rationals.h

#ifndef RATIONALS_H
#define RATIONALS_H
#include <iostream>
#include <sstream>
#include <vector>
#include <math.h>
#include <stdexcept>

int GCD(const int, const int); //returns greatest common divisor between two numbers

class Rational {
    friend std::ostream& operator<<(std::ostream&,const Rational);
public:
    Rational(); //default constructor, defaults to a numerator of 0 and denominator of 1
    Rational(const int Numerator, const int Denominator); //constructor that takes ints for the num/denom
    Rational(const int Numerator); //constructor that only takes numerator, default denominator is 1

    int getNumerator(); //returns numerator
    int getDenominator(); //returns denominator

    void setNumerator(const int); //sets numerator, can be <= 0
    void setDenominator(const int); //sets denominator, must be > 0

    std::string toString(); //outputs the rational number as a string

    Rational reduce(); //reduces the fraction, keeping the correct sign

    Rational operator+(const Rational); //properly adds two rational numbers
    Rational operator-(const Rational); //properly subtracts two rational numbers
    Rational operator*(const Rational); //multiplies two rationals
    Rational operator/(const Rational); //divides two rationals
    bool operator==(const Rational); //checks if two rationals are the same
    bool operator!=(const Rational); //checks if two rationals are not the same
    bool operator<(const Rational); //checks if a rational is less than another
    bool operator>(const Rational); //checks if a rational is bigger than another
    bool operator<=(const Rational); //checks if a rational is less than or equal to another
    bool operator>=(const Rational); //checks if a rational is large than or equal to another

private:
    int numerator{}; //can be any integer
    int denominator{}; //cannot be <= 0
};




#endif // RATIONALS_H


//by Curtis Michels
//Rationals.cpp

#include "Rationals.h"

Rational::Rational():numerator{0}, denominator{1}{ //default constructor, initializes fraction to 0
}

Rational::Rational(int inNumerator, int inDenominator){ //constructor that takes in two ints
    setNumerator(inNumerator);
    setDenominator(inDenominator);
}

Rational::Rational(int inNumerator){ //constructor that takes in just the numerator
    setNumerator(inNumerator);
    setDenominator(1);
}

std::ostream& operator<<(std::ostream& oin,Rational in) { //overloads left shift operator to work with cout and similar, depends on toString function
    std::cout << in.toString();
    return oin;
}

int Rational::getNumerator() { //returns numerator
    return numerator;
}

int Rational::getDenominator() { //returns denominator
    return denominator;
}

void Rational::setNumerator(int in) { //sets numerator, can be anything including <= 0
    numerator = in;
}

void Rational::setDenominator(int in) { //sets denominator, must be > 0
    if (in > 0) {
            denominator = in;
    }
    else{
        throw std::invalid_argument("Denominator must be > 0");
    }
}

std::string Rational::toString() { //returns a string with numerator and denominator separated by a slash
    std::stringstream result;
    result << getNumerator() << "/" << getDenominator();
    return result.str();
}

Rational Rational::reduce() { //reduces fraction by finding and dividing both numerator and denominator by greatest common factor
    Rational result{};
    int gcd = GCD(getNumerator(),getDenominator());
    result.setNumerator(getNumerator()/gcd);
    result.setDenominator(getDenominator()/gcd);
    return result;
}

int GCD(int in1, int in2) { //finds greatest common factor via recursive Euclidian Algorithm, non-member function
    if (in1 < 0) { in1 = in1 * -1;} //this line ensures it always returns a positive number
    if (in1 == in2) {return in1;} //doesn't bother doing anything more if both inputs are equal
    int result{};
    int divisor{};
    int remainder{};
    if(in1 > in2) {
        divisor = in2;
        remainder = in1%in2;
    }
    else {
        divisor = in1;
        remainder = in2%in1;
    }
    if (remainder == 0) {result = divisor;}
    else {result = GCD(divisor,remainder);}
    return result;
}

Rational Rational::operator+(Rational in) { //adds and returns two rational numbers, reduces to most simplified form
    Rational result{};
    result.setNumerator(this->getNumerator() * in.getDenominator() + in.getNumerator() * this->getDenominator());
    result.setDenominator(this->getDenominator() * in.getDenominator());
    return result.reduce();
}

Rational Rational::operator-(Rational in) { //subtracts and returns two rational numbers (Depends on + overloaded operator), reduces to most simplified form
    Rational result{};
    result.setNumerator(-1 * in.getNumerator());
    result.setDenominator(in.getDenominator());
    return (*this+result);
}

Rational Rational::operator*(Rational in) { //multiplies two fractions, reduces to most simplified form
    Rational result{};
    result.setNumerator(this->getNumerator() * in.getNumerator());
    result.setDenominator(this->getDenominator() * in.getDenominator());
    return result.reduce();

}

Rational Rational::operator/(Rational in) { //divides two rational numbers, reduces to most simplified form, will throw an error if you try to divide by 0
    Rational result{};
    result.setNumerator(in.getDenominator()); //these two lines flip the numerator and denominator so we can multiply by the reciprocal
    result.setDenominator(in.getNumerator());
    result = result * *this;
}

bool Rational::operator==(Rational in) { //compares if two rational numbers are the same, (reduces both to most simplified form BEFORE comparing)
    bool result{false};
    if (this->reduce().getNumerator() == in.reduce().getNumerator() && this->reduce().getDenominator() == in.reduce().getDenominator()) {result = true;}
    return result;
}

bool Rational::operator!=(Rational in) {
    bool result{!(*this==in)};
    return result;
}

bool Rational::operator<(Rational in) { //checks if a rational is less than another
    bool result{false};
    double compare1{this->getNumerator()/this->getDenominator()};
    double compare2{in.getNumerator()/in.getDenominator()};
    if (compare1 < compare2) {result = true;}
    return result;

}

bool Rational::operator>(const Rational in) { //checks if a rational is bigger than another
    bool result{false};
    if (*this != in) { result = !(*this<in); }
    return result;
}

bool Rational::operator<=(Rational in) { //checks if a rational is less than or = to another
    bool result{false};
    double compare1{this->getNumerator()/this->getDenominator()};
    double compare2{in.getNumerator()/in.getDenominator()};
    if (compare1 <= compare2) {result = true;}
    return result;

}

bool Rational::operator>=(const Rational in) { //checks if a rational is bigger than or = to another
    bool result{false};
    result = !(*this<in);
    return result;
}