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

bool Rational::gt(const Rational& other) const {
	// x   a       x*b   a*y
	// - ? -  <=>  --- ? ---  <=>  x*b ? a*y
	// y   b       y*b   y*b
	return numerator * other.denumerator > other.numerator * denumerator;
}

bool Rational::lt(const Rational& other) const {
	// x   a       x*b   a*y
	// - ? -  <=>  --- ? ---  <=>  x*b ? a*y
	// y   b       y*b   y*b
	return numerator * other.denumerator < other.numerator * denumerator;
}

int Rational::gcd() const {
	int a = numerator, b = denumerator;
	if (a < b) {
		int temp = a;
		a = b;
		b = temp;
	}

	while (b != 0) {
		int r = a % b;
		a = b;
		b = r;
	}
	return a;
}

Rational::Rational() : Rational(1, 1)
{}

Rational::Rational(int numerator, int denumerator) {
	if (denumerator == 0) numerator = denumerator = 1;

	set_numerator(numerator);
	set_denumerator(denumerator);
}

int Rational::get_numerator() const {
	return numerator;
}
void Rational::set_numerator(int numerator) {
	this->numerator = numerator;
}

int Rational::get_denumerator() const {
	return denumerator;
}
void Rational::set_denumerator(int denumerator) {
	if (denumerator == 0) denumerator = 1;

	this->denumerator = denumerator;
}

void Rational::canonize() {
	int gcdND = abs(gcd());
	set_numerator(numerator / gcdND);
	set_denumerator(denumerator / gcdND);
}

// Not needed, kept for fun
void Rational::canonizeRec() {
	if (denumerator == 1)
		return;

	int whole = numerator / denumerator, leftover = numerator % denumerator;
	if (leftover == 0) {
		numerator = whole;
		denumerator = 1;
		return;
	}

	Rational temp(denumerator, leftover);
	temp.canonize();
	numerator = whole * temp.numerator + temp.denumerator;
	denumerator = temp.numerator;
}

Rational Rational::operator+(const Rational& other) const {
	// x   a   x*b + a*y
	// - + - = ---------
	// y   b      y*b
	return Rational(numerator * other.denumerator + other.numerator * denumerator, denumerator * other.denumerator);
}

Rational Rational::operator-(const Rational& other) const {
	// x   a   x*b - a*y
	// - - - = ---------
	// y   b      y*b
	return Rational(numerator * other.denumerator - other.numerator * denumerator, denumerator * other.denumerator);
}

Rational Rational::operator*(const Rational& other) const {
	// x   a       x*b
	// - / -  <=>  ---
	// y   b       y*a
	return Rational(numerator * other.numerator, denumerator * other.denumerator);
}

Rational Rational::operator/(const Rational& other) const {
	// x   a       x   b
	// - / -  <=>  - * -
	// y   b       y   a
	return Rational(numerator * other.denumerator, denumerator * other.numerator);
}

int Rational::numcmp(const Rational& arg) const {
	return gt(arg) - lt(arg);
}

void Rational::print() const {
	std::cout << numerator << "/" << denumerator;
}