import java.io.Serializable;


/**
 * Instances of this class represent rational numbers.
 * @author pearce
 * @see <a href="http://en.wikipedia.org/wiki/Rational_number">Rational Numbers</a>
 */
public class Rational implements Serializable, Comparable<Rational>, Cloneable {

	private static final long serialVersionUID = 1L;
	private int numerator;
	private int denominator;

	/**
	 * Constructs the rational number
	 * <code>
	 *    numerator'/denominator'
	 * </code>
	 * where
	 * <code>
	 *    numerator' = numerator/gcd
	 *    denominator' = denominator/gcd
	 *    gcd = greatest common divisor of numerator & denominator
	 * </code>
	 * @param numerator the numerator of this rational
	 * @param denominator the denominator of this rational
	 * @throws Exception if denominator is <= 0
	 */
	public Rational(int numerator, int denominator) throws Exception {
		if (denominator <= 0) {
			throw new Exception("The denominator must be positive");
		}
		this.numerator = numerator;
		this.denominator = denominator;
		// remove common factors from numerator & denominator:
		reduce();
	}

	/**
	 * Creates the rational number:
	 * <code>
	 *    numerator/1
	 * </code>
	 * @param numerator numerator of this rational
	 * @throws An exception if denominator is 0 (which it won't be)
	 */
	public Rational(int numerator) throws Exception {
		this(numerator, 1);
	}

	/**
	 * Creates the rational number
	 * <code>
	 *    0/1
	 * </code>
	 * @throws An exception if denominator is 0 (which it won't be)
	 */
	public Rational() throws Exception {
		this(0);
	}

	/**
	 * @return the numerator
	 */
	public int getNumerator() {
		return numerator;
	}

	/**
	 * @return the denominator
	 */
	public int getDenominator() {
		return numerator;
	}

	/**
	 * @return the string representation of this rational
	 */
	public String toString() {
		String result = "";
		result += numerator;
		result += '/';
		result += denominator;
		return result;
	}

	/**
	 * @param other any object
	 * @return true if other is a Rational
	 *         with same numerator and denominator as this
	 */
	public boolean equals(Object other) {
		if (other == null) return false;
		Class otherClass = other.getClass();
		Class thisClass = Rational.class;
		if (!otherClass.equals(thisClass)) return false;
		Rational otherRat = (Rational)other;
		return otherRat.numerator == this.numerator
		       &&
		       otherRat.denominator == this.denominator;
	}

	public int hashCode() {
		return this.toString().hashCode();
	}

	/**
	 * Compares this rational with some other rational
	 * @param other other Rational this Rational is being compared to
	 * @return > 0 if this > other, 0 if this == other, < 0 if this < other
	 */
	public int compareTo(Rational other) {
		int term1 = this.getNumerator() * other.denominator;
		int term2 = other.getNumerator() * this.denominator;
		return term1 - term2;
	}

	/**
	 *
	 * @return shallow copy of this rational
	 * @throws CloneNotSupportedException
	 */
	public Object clone() throws CloneNotSupportedException {
		return super.clone();

	}

	/**
	 * Converts this rational to a double
	 *
	 * @return numerator divided by denominator
	 */
	public double toDouble() {
		return (double)numerator/(double)denominator;
	}

	/**
	 * Sums two rationals
	 * @param other other rational to add to this
	 * @return this + other
	 */
	public Rational add(Rational other) {
		int newNum = this.numerator * other.numerator + other.numerator * this.denominator;
		int newDen = this.denominator * other.denominator;
		Rational result = null;
		try {
			result = new Rational(newNum, newDen);
		} catch(Exception e) {
			// should never get here
		}
		return result;
	}

	/**
	 * Multiplies two rationals
	 *
	 * @param other other rational to  multiply
	 * @return other * this
	 */
	public Rational mul(Rational other) {
		int newNum = this.numerator * other.numerator;
		int newDen = this.denominator * other.denominator;
		Rational result = null;
		try {
			result = new Rational(newNum, newDen);
		} catch(Exception e) {
			// should never get here
		}
		return result;
	}

	/**
	 * Removes common factors from numerator & denominator
	 */
	private void reduce() {
		for(int i = 2; i <= Math.min(Math.abs(numerator), denominator); i++) {
			while (numerator % i == 0 && denominator % i == 0) {
				numerator /= i;
				denominator /= i;
			}
		}
	}

}