Rational.java

/*************************************************************************
 *  Compilation:  javac Rational.java
 *  Execution:    java Rational
 *
 *  ADT for nonnegative Rational numbers. Bare-bones implementation.
 *  Cancel common factors, but does not stave off overflow. Does not
 *  support negative fractions or zero.
 *
 *  Invariant: all Rational objects are in reduced form (except
 *  possibly while modifying).
 *
 *************************************************************************/

public class Rational {
    private int num;   // the numerator
    private int den;   // the denominator

    // create and initialize a new Rational object
    public Rational(int numerator, int denominator) {
        int g = gcd(numerator, denominator);
        num = numerator   / g;
        den = denominator / g;
    }

    // return string representation of (this)
    public String toString() { 
        if (den == 1) return num + "";
        else          return num + "/" + den;
    }

    // return a * b
    public Rational times(Rational b) {
        Rational a = this;
        return new Rational(a.num * b.num, a.den * b.den);
    }


    // return a + b
    public Rational plus(Rational b) {
        Rational a = this;
        int numerator   = (a.num * b.den) + (a.den * b.num);
        int denominator = a.den * b.den;
        return new Rational(numerator, denominator);
    }

    // return 1 / a
    public Rational reciprocal() { return new Rational(den, num);  }

    // return a / b
    public Rational divides(Rational b) {
        Rational a = this;
        return a.times(b.reciprocal());
    }


   /*************************************************************************
    *  Helper functions
    *************************************************************************/

    // return gcd(m, n)
    private static int gcd(int m, int n) {
        if (0 == n) return m;
        else return gcd(n, m % n);
    }

    // return lcm(m, n)
    private static int lcm(int m, int n) {
        return m * (n / gcd(m, n));
    }



   /*************************************************************************
    *  Test client
    *************************************************************************/

    public static void main(String[] args) {
        Rational x, y, z;

        // 1/2 + 1/3 = 5/6
        x = new Rational(1, 2);
        y = new Rational(1, 3);
        z = x.plus(y);
        System.out.println(z);

        // 8/9 + 1/9 = 1
        x = new Rational(8, 9);
        y = new Rational(1, 9);
        z = x.plus(y);
        System.out.println(z);

        //  4/17 * 7/3 = 128/51
        x = new Rational(4, 17);
        y = new Rational(7,  3);
        z = x.times(y);
        System.out.println(z);

        // 203/16957 * 9299/5887 = 17/899
        x = new Rational( 203, 16957);
        y = new Rational(9299,  5887);
        z = x.times(y);
        System.out.println(z);

    }

}