/**
 * Each Fraction object represents an immutable rational number with a numerator and denominator.
 * Fractions are always stored in reduced form such that the GCD of their
 * numerator and denominator is always 1.
 * 
 * @pre to all methods: valid arguments  (I know, I know...)
 * @author Marty Stepp
 */
public final class Fraction implements Comparable<Fraction> {
	private final int numerator;
	private final int denominator;
	
	public Fraction(int numerator) {
		this(numerator, 1);
	}
	
	public Fraction(int numerator, int denominator) {
		// reduce the fraction before storing it
		int g = gcd(numerator, denominator);
		numerator /= g;
		denominator /= g;
		if (denominator < 0) {
			numerator = -numerator;
			denominator = -denominator;
		}
		
		this.numerator = numerator;
		this.denominator = denominator;
	}
	
	public int getNumerator() {
		return numerator;
	}
	
	public int getDenominator() {
		return denominator;
	}
	
	public int compareTo(Fraction other) {
		// normalize to common denominator before comparing
		int myCommon = numerator * other.denominator;
		int otherCommon = other.numerator * denominator;
		return myCommon - otherCommon;
	}
	
	public boolean equals(Object o) {
		if (o != null && getClass() == o.getClass()) {
			Fraction other = (Fraction) o;
			return numerator == other.numerator && denominator == other.denominator;
		} else {
			return false;
		}
	}
	
	public Fraction add(Fraction other) {
		int n = numerator * other.denominator + other.numerator * denominator;
		int d = denominator * other.denominator;
		return new Fraction(n, d);
	}
	
	public Fraction subtract(Fraction other) {
		int n = numerator * other.denominator - other.numerator * denominator;
		int d = denominator * other.denominator;
		return new Fraction(n, d);
	}
	
	public Fraction multiply(Fraction other) {
		int n = numerator * other.numerator;
		int d = denominator * other.denominator;
		return new Fraction(n, d);
	}
	
	public Fraction divide(Fraction other) {
		int n = numerator * other.denominator;
		int d = denominator * other.numerator;
		return new Fraction(n, d);
	}
	
	public String toString() {
		if (denominator == 1) {
			return String.valueOf(numerator);
		} else {
			return numerator + "/" + denominator;
		}
	}
	
	private int gcd(int a, int b) {
		if (b == 0) {
			return Math.abs(a);
		} else {
			return gcd(b, a % b);
		}
	}
}