public class Fraction {

    private int numerator;
    private int denominator;

    /**
     * Contruct a fraction numerator and denominator
     * <p>The fraction is reduced to it's minimum from if possible</p>
     * @param numerator Numerator
     * @param denominator Denominator
     */
    public Fraction(int numerator, int denominator){

        //This might get in recursive loop
        if (isReducible(numerator, denominator)){
            Fraction f = reduce(new Fraction(numerator, denominator));
            this.numerator = f.numerator;
            this.denominator = f.denominator;
        }
        else{
            this.numerator = numerator;
            this.denominator = denominator;
        }

    }

    /**
     * Default value of fraction is 1 (1/1)
     */
    public Fraction(){

        this.numerator = 1;
        this.denominator = 1;

    }

    /**
     * Reduces a fraction to it's minimum form
     * @param oldFraction The fraction to be reduced.
     * @return reduced fraction
     */
    private Fraction reduce(Fraction oldFraction) {

        if (isReducible(oldFraction)){
            int gcd = GCD(oldFraction.numerator, oldFraction.denominator);
            return new Fraction(oldFraction.numerator/gcd,
                    oldFraction.denominator/gcd);
        }
        else return oldFraction;

    }

    /**
     * Find the greatest common divisor of two numbers.
     * @param a First value
     * @param b Second value
     * @return Greatest common divisor as Integer.
     */
    private static int GCD(int a, int b){

        int gcd = 1;
        for (int i = 1; i <= b && i <= a; i++){
            if (b % i == 0 && a % i == 0) gcd = i; // i divides a and b
        }
        return gcd;
    }

    /**
     * Check if the fraction provided is equal in value
     * @param fraction The fraction to check
     * @return True if the fractions are equal, otherwise false.
     */
    public boolean equal(Fraction fraction){

        Fraction reducedFraction = reduce(fraction);
        if (this.numerator == reducedFraction.numerator &&
                this.denominator == reducedFraction.denominator) return true;
        return false;

    }

    /**
     * add two fractions
     * @param fraction1
     * @param fraction2
     * @return added fractions reduced to min form
     */
    public static Fraction add(Fraction fraction1, Fraction fraction2){

        //new denominator
        int mDenominatorResult = fraction1.denominator * fraction2.denominator;
        int mNumerator1 = fraction1.numerator * fraction2.denominator;
        int mNumerator2 = fraction2.numerator * fraction1.denominator;
        //new numerator
        int mNumeratorResult = mNumerator1 + mNumerator2;

        //
        return new Fraction(mNumeratorResult, mDenominatorResult);
    }

    /**
     * subtract two fractions
     * @param fraction1
     * @param fraction2
     * @return subtracted fractions reduced to min form
     */
    public static Fraction subtract(Fraction fraction1, Fraction fraction2){

        //new denominator
        int mDenominatorResult = fraction1.denominator * fraction2.denominator;
        int mNumerator1 = fraction1.numerator * fraction2.denominator;
        int mNumerator2 = fraction2.numerator * fraction1.denominator;
        //new num
        int mNumeratorResult = mNumerator1 - mNumerator2;

        return new Fraction(mNumeratorResult, mDenominatorResult);
    }

    /**
     * Multiply two fractions and reduce
     * @param fraction1
     * @param fraction2
     * @return fractions
     */
    public static Fraction multiply(Fraction fraction1, Fraction fraction2) {

        //The constructor already reduces.
        return new Fraction(fraction1.numerator * fraction2.numerator,
                fraction1.denominator * fraction2.denominator);

    }

    /**
     * Divide two fractions and reduce
     * @param fraction1
     * @param fraction2
     * @return fractions
     */
    public static Fraction divide(Fraction fraction1, Fraction fraction2){

        return new Fraction(fraction1.numerator * fraction2.denominator,
                fraction1.denominator * fraction2.numerator);

    }

    /**
     * string of the fraction in num/den form
     * overrides global toString()
     * @return fraction string
     */
    public String toString(){

        return String.format("%d/%d", this.numerator, this.denominator);

    }

    /**
     * returns a string with the decimal value of the fraction
     * @param digits precision
     * @return decimal string
     */
    public String decimal(int digits){

        return String.format("%."+digits, (double)this.numerator / this.denominator);

    }

    /**
     * Check if fraction is in simplest terms.
     * @param fraction Fraction object
     * @return  boolean
     */
    private boolean isReducible(Fraction fraction){

        int gcd = GCD(fraction.numerator, fraction.denominator);
        if (gcd == 1) return false;
        else return true;

    }

    /**
     * Check if fraction is in simplest terms.
     * @param numerator
     * @param denominator
     * @return boolean
     */
    private boolean isReducible(int numerator, int denominator){

        int gcd = GCD(numerator, denominator);
        if (gcd == 1) return false;
        else return true;

    }


}