//Preprocessor Directives
#include<iostream>
#include <cstdlib>
using namespace std;


void normalize(int &n, int &d);

class Rational
{
public:
    Rational(int numerator, int denominator);
    Rational(int numerator);
    Rational();
    friend Rational operator+(const Rational&, const Rational&);
    friend Rational operator-(const Rational&, const Rational&);
    friend Rational operator*(const Rational&, const Rational&);
    friend Rational operator/(const Rational&, const Rational&);
    friend bool operator<(const Rational&, const Rational&);
    friend bool operator<=(const Rational&, const Rational&);
    friend bool operator>(const Rational&, const Rational&);
    friend bool operator>=(const Rational&, const Rational&);
    friend bool operator==(const Rational&, const Rational&);
    friend ostream& operator <<(ostream&, const Rational&);
    friend istream& operator >>(istream&, Rational&);
    int num() const { return n; };
    int den() const { return d; };
    void set_num(int sn) { n = sn; _normalize(); };
    void set_den(int sd) { d = sd; _normalize(); };
    void set(int sn, int sd) { n = sn; d = sd; _normalize(); };
    void _normalize() { normalize(n , d); }
private: int n;
         int d;
};

Rational::Rational(int numer, int denom)
{
    normalize(numer, denom);
    n = numer;
    d = denom;
}
Rational::Rational(int numer): n(numer), d(1)
{

}
Rational::Rational():n(0), d(1)
{

}
Rational operator +(const Rational& left, const Rational& right)
{
    int numer = left.num() * right.den() + left.den() * right.num();
    int denom = left.den() * right.den();
    normalize(numer, denom);
    Rational local(numer, denom);
    return local;
}
Rational operator -(const Rational& left, const Rational& right)
{
    int numer = left.num() * right.den() - left.den() * right.num();
    int denom = left.den() * right.den();
    normalize(numer, denom);
    Rational local(numer, denom);
    return local;
}
Rational operator *(const Rational& left, const Rational& right)
{
Rational product;

int numer = left.num() * right.num();
int denom = left.den() * right.den();
normalize(numer, denom);
product = Rational(numer, denom);
return product;
}
Rational operator/(const Rational& left, const Rational& right)
{
    Rational quotient;
    int numer = left.num() * right.den();
    int denom = left.den() * right.num();
    normalize(numer, denom);
    quotient = Rational(numer, denom);
    return quotient;
}
bool operator <(const Rational& left, const Rational& right)
{
    return left.num() * right.den() < right.num() * left.den();
}
bool operator >(const Rational& left, const Rational& right)
{
    return left.num() * right.den() > right.num() * left.den();
}
bool operator <=(const Rational& left, const Rational& right)
{
    return left.num() * right.den() <= right.num() * left.den();
}
bool operator>=(const Rational& left, const Rational& right)
{
    return left.num() * right.den() >= right.num() * left.den();
}
istream& operator>>(istream& in_str, Rational& right)
{
    char ch;
    int numer, denom;
    in_str >> numer >> ch >> denom;
    right.set(numer, denom);
    if (ch != '/')
    {
        cout << "bad input format for operator >>. Aborting!"
             << endl;
        exit (1);
    }
    right._normalize();
    return in_str;
}
ostream& operator << (ostream& out_str, const Rational& right)
{
    char ch;
    out_str << right.num() << '/' << right.den();
    return out_str;
}
int gcd(int m, int n)
{
    int t;
    m = abs (m);
    n = abs (n);
    if(n < m)
    {
        t = m;
        m = n;
        n = t;
    }
    int r;
    r = m % n;
    while(r != 0)
    {
        r = m % n;
        m = n;
        n = r;
    }
    return m;
}
void normalize (int& n, int& d)
{
    int g = gcd(n, d);
    n = n/g;
    d = d/g;
    if(n > 0 && d < 0 || n < 0 && d < 0)
    {
        n = -n;
        d = -d;
    }
}
//Main Function
int main()
{
    cout << "Testing declarations" << endl;
    cout << "Rational x, y (2), z(-5, -6), w(1,-3);" << endl;
    Rational x, y(2), z(-5, -6), w(1, -3);
    cout << "z = " << z << ", y = " << y << ", z = " << z << ", w = " << w << endl;
    cout << "Testing >> overloading: \nEnter " << "a fraction in the format "
        << "integer_numerator/integer_denominator"
        << endl;
    cin >> x;
    cout << "You entered the equivalent of: " << x << endl;
    cout << z << " - (" << w << ") = " << z - w << endl;
    cout << "Testing the constructor and normalization routines: " << endl;
    y = Rational (-128, -48); cout << "y = Rational(-128, -48) outputs as " << y << endl;
    y = Rational (-128, 48); cout << "y = Rational(-128, 48) outputs as " << y << endl;
    y = Rational (128, -48);
    cout << "y = Rational(128, -48) outputs as " << y << endl;
    Rational a(1,1);
    cout << "Rational a(1,1); a outputs as: " << a << endl;
    Rational ww = y*a;
    cout << y << " * " << a << " = " << ww << endl;
    w = Rational (25, 9);
    z = Rational (3, 5);
    cout << "Testing arithmetic and relational " << " operator overloading" << endl;
    cout << w << " * " << z << " = " << w * z << endl;
    cout << w << " + " << z << " = " << w + z << endl;
    cout << w << " - " << z << " = " << w - z << endl;
    cout << w << " / " << z << " = " << w / z << endl;
    cout << w << " < " << z << " = " << (w < z) << endl;
    cout << w << " < " << w << " = " << (w < z) << endl;
    cout << w << " <= " << z << " = " << (w <= z) << endl;
    cout << w << " <= " << w << " = " << (w <= z) << endl;
    cout << w << " > " << z << " = " << (w > z) << endl;
    cout << w << " > " << w << " = " << (w > z) << endl;
    cout << w << " >= " << z << " = " << (w >= z) << endl;
    cout << w << " >= " << w << " = " << (w >= z) << endl;
    w = Rational(-21, 9);
    z = Rational (3, 5);
    cout << w << " * " << z << " = " << w * z << endl;
    cout << w << " + " << z << " = " << w + z << endl;
    cout << w << " - " << z << " = " << w - z << endl;
    cout << w << " / " << z << " = " << w / z << endl;
    cout << w << " < " << z << " = " << (w < z) << endl;
    cout << w << " < " << w << " = " << (w < z) << endl;
    cout << w << " <= " << z << " = " << (w <= z) << endl;
    cout << w << " <= " << w << " = " << (w <= z) << endl;
    cout << w << " > " << z << " = " << (w > z) << endl;
    cout << w << " > " << w << " = " << (w > z) << endl;
    cout << w << " >= " << z << " = " << (w >= z) << endl;
    cout << w << " >= " << w << " = " << (w >= z) << endl;
    return 0;
}