/**
 *
 * @ author David Álvarez 789401
 * @ email sly.dekar@gmail.com
 * @ date 01/09/05
 * @ version 2.0
 *
 **/

import java.io.*;

class Rational {
	
	private int numerator, denominator; 
		/* the numerator and denominator of the Rational Object */
	
	/** 
	*A constructor that sets the Rational to represent the number zero. The number zero is represented by a numerator field of 0 and a denominator field of 1.
	**/	
	public Rational() {
		
		this.numerator = 0;
		this.denominator = 1;
	}

	/** 
	*A constructor that sets the rational to represent the whole number indicated by the parameter whole. For example, if the parameter whole were -4, it would be represented by a numerator field of -4 and a denominator field of 1. 
	*
	*@Param		whole		the integer to be turned into rational.
	**/	
	public Rational(int numerator) {
		
		this.numerator = numerator;
		this.denominator = 1;
	}
	
	/** 
	*
	* A constructor that sets the Rational to represent the fraction indicated by the parameters numer and denom. 
	* The parameter numer indicates the numerator of the fraction to be represented and the parameter denom indicates the denominator 
	* of the fraction to be represented. 
	*
	* @param		numer, denom	integers which represent the numerator and denominator of the new Rational obj
	*
	**/	
	public Rational(int numer, int denom){
		
		this.numerator = numer;
		this.denominator = denom;
		
		if (denom == 0) { 
		
			this.numerator = 0;
			this.denominator = 1;
		}
		else {
				
			if (sgn(getDenominator())==-1) {
			
				setDenominator(getDenominator()*-1);
				setNumerator(getNumerator()*-1);
			}
		}
		
		reduce();
	}

	/** 
	* A constructor that sets the Rational to be an exact copy of the Rational that is the parameter r. 
	*
	* @param		r	The Rational to be copied.
	**/		
	public Rational(Rational r) {
		
		this.numerator = r.numerator;
		this.denominator = r.denominator;
		
		reduce();
	}
	
	

	/** 
	*A method that returns the value of the field numerator. 
	*
	*@return	int		the value of the field numerator. 
	**/		
	public int getNumerator() {
		
		return this.numerator;
	}
	
	/** 
	*A method that returns the value of the field denominator. 
	*
	*@return	int		the value of the field denominator. 
	**/	
	public int getDenominator() {
		
		return this.denominator;
	}
	
	/** 
	*A method that sets the field numerator to the parameter numer. 
	*
	*@param  numer		the new numerator (integer)
	**/	
	public void setNumerator(int numer) {
		
		this.numerator = numer;
		reduce();
	}
	
	/** 
	*A method that sets the field denominator to the parameter numer. 
	*
	*@param  denom		the new denominator (Integer)
	**/	
	public void setDenominator(int denom) {
		
		this.denominator = denom;
		reduce();
	}
	

	
	/** 
	*A method that returns true if the invoking Rational represents a negative number; it returns false otherwise. 
	*
	*@return	boolean		true if the invoking Rational represents a negative number; it returns false otherwise. 
	**/	
	public boolean isNegative() {
		
		return (getNumerator()<0 || getDenominator()<0);
	}
	
	/** 
	*A method that returns true if the invoking Rational represents zero, that is, if the numerator field is 0 and the denominator field is 1; it returns false otherwise. 
	*
	*@return	boolean		true if the invoking Rational represents zero, that is, if the numerator field is 0 and the denominator field is 1; it returns false otherwise. 
	**/	
	public boolean isZero() {
		
		return (getNumerator()==0);
	}
	
	/** 
	*A method that returns true if the invoking Rational represents a positive number; it returns false otherwise. 
	*
	*@return	boolean		true if the invoking Rational represents a positive number; it returns false otherwise. 
	***/	
	public boolean isPositive() {
		
		return (getNumerator()>0 && getDenominator()>0);
	}
		
	/** 
	*A method that creates and returns a new Rational that represents the negation (additive opposite) of the invoking Rational
	*
	*@return	n	the opposite additive of the Rational.
	**/	
	public Rational makeNegative() {
	
		return new Rational(getNumerator()*-1, getDenominator());
	}
	
	public Rational makePositive() {
	
		if (this.isNegative()) {
			
			return new Rational(getNumerator()*-1, getDenominator());
		}
		
		return this;
	}

	/** 
	* A method that creates and returns a new Rational that represents the reciprocal (multiplicative opposite) of the invoking Rational 
	*
	*@return	Rational	the reciprocal.
	**/	
	public Rational reciprocal() {
		
		if (getNumerator() != 0) {
			
			return new Rational(getDenominator(), getNumerator());		
		}
		else {
			
			return this;
		}
	}
	
	/** 
	*A method that creates and returns a new Rational that represents the sum of the invoking Rational and the Rational that is the parameter rhs. 
	*
	*@param		rhs			a Rational to be added
	*@return	Rational	the sum of the two Rationals.
	**/	
	public Rational plus(Rational rhs) {
		
		Rational r = new Rational(this.getNumerator() * rhs.getDenominator() + this.getDenominator() * rhs.getNumerator(), this.getDenominator() * rhs.getDenominator());
		
		r.reduce();
		
		return r;
	}
	
	/** 
	*A method that creates and returns a new Rational that is the difference of the invoking Rational and the Rational that is the parameter rhs. 
	*
	*@param  	rhs			a Rational object which will be substracted to the invoking Rational.
	*@return	Rational	a Rational object that represents the difference between both Rationals
	**/	
	public Rational minus(Rational rhs) {
		
		Rational r = new Rational(this.getNumerator() * rhs.getDenominator() - this.getDenominator() * rhs.getNumerator(), this.getDenominator() * rhs.getDenominator());
		
		r.reduce();
		
		return r;
	}
	
	/** 
	*A method that creates and returns a new Rational that is the product of the invoking Rational and the Rational that is the parameter rhs. 
	*
	*@param  	rhs			a Rational object which will be multiplied to the invoking Rational.
	*@return	Rational	the multiplication of both Rational objects.
	**/	
	public Rational times(Rational rhs) {
		
		Rational r = new Rational(this.getNumerator()*rhs.getNumerator(), this.getDenominator()*rhs.getDenominator());
		
		r.reduce();
		
		return r;
	}
	
	/** 
	*A method that creates and returns a new Rational that is the division of the invoking Rational by the Rational that is the parameter rhs. 
	*
	*@param  	rhs			a Rational object which will divide the invoking Rational object.
	*@return	Rational	the cocient of the Rational objects.
	**/	
	public Rational dividedBy(Rational rhs) {
		
		Rational r = new Rational(this.getNumerator()*rhs.getDenominator(), this.getDenominator()*rhs.getNumerator());
		
		r.reduce();
		
		return r;
	}
	
	/** 
	*A method that returns true if the invoking Rational is equal to the Rational that is the parameter r; it returns false otherwise. Two Rational objects are equal if and only if their fields numerator and denominator are respectively equal. 
	*
	*@param  	rhs		the Rational object which will be compared with the invoking Rational object.
	*@return	boolean	TRUE if they're the same, FALSE if not
	**/	
	public boolean equals(Rational rhs) {
		
		rhs.reduce();
		this.reduce();
		
		return (getNumerator()==rhs.getNumerator() && getDenominator()==rhs.getDenominator());
	}
	
	public boolean smallerThan(Rational rhs) {
		
		return (makeDouble(this) < makeDouble(rhs));
	}
	
	public boolean greaterThan(Rational rhs) {
		
		return (makeDouble(this) > makeDouble(rhs));
	}
	
	public double makeDouble(Rational r) {
		
		return r.getNumerator() / r.getDenominator();
	}
	
	/** 
	*A method that returns a string representation of the invoking Rational. 
	*
	*@return	String	a string that represents the Rational.
	**/	
	public String toString() {
		
		if (this.isZero()) {
			
			return "0  ";
		} 
		else {
			
			if (this.isNegative()) {
			
				if (this.getDenominator() == 1) {
				
					return getNumerator()+" ";
				}
					
				return (getNumerator() + "/" + getDenominator());
			}
			else {
				
				if (this.getDenominator() == 1) {
				
					return getNumerator()+"  ";
				}
				return (getNumerator() + "/" + getDenominator());
			}
		}
	}
	
	
	
	/** 
	*
	* This method reduces the invoking Rational to lowest terms.  
	*
	**/	
	private void  reduce()  {

		if (numerator == 0)  {
			
			denominator = 1;
		}
		else  {
			
			int gcd = gcd(Math.abs(numerator), denominator);
			numerator /= gcd;
			denominator /= gcd;
		}
	}

	/** 
	*This method calculates and returns the greatest common divisor 
	*of the parameters a and b. 
	*This use of this method must remain exclusive to the method reduce.
	*
	* @param	a, b	the two numbers whose greatest common divisor will be calculated.
	* @return	a		the greates common divisor (Integer)
	**/	
	private static int gcd(int  a, int  b)  {

		while (a != b)  {
			
			if (a > b)  {
				
				a = a - b;
			}
			else  {
				
				b = b - a;
			}
		}

		return  a;
	}

	/** 
	*This method returns the int value -1 if the parameter n is negative, 
	*the int value 0 if the parameter n is zero, 
	*the int value 1 if the parameter n is positive. 
	*
	* @param	n, integer.		the number to be evaluated.
	* @return	-1 if the parameter n is negative, 
	*			0  if the parameter n is zero, 
	*			1  if the parameter n is positive. 
	**/	
	private static int sgn(int n)  {

		return  n == 0 ? 0 : n / Math.abs(n);
	}
	 
}