Java语言程序设计 第13章

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设计一个Rational类，用于表示和处理有理数。
因为有理数共享了很多整数和浮点数的通用特征，而且Number是数值包装类的根类，所以讲Rational类定义为Number类的子类，因为有理数是可以比较的，所以Rational类也应该能够实现Comparable接口。
使用BigInteger实现数据类型。

import java.math.BigInteger;
import java.math.BigDecimal;

public class Rational extends Number implements Comparable
{
    private BigInteger numerator = new BigInteger("0");
    private BigInteger denominator = new BigInteger("1");

    public Rational()
    {
        this(new BigInteger("0"), new BigInteger("1"));
    }

    public Rational (BigInteger numerator, BigInteger denominator)
    {
        //System.out.println(numerator.toString() + " " + denominator.toString());
        BigInteger gcd = gcd(numerator, denominator);
        if (denominator.compareTo(new BigInteger("0")) > 0)
        {
            this.numerator = numerator.divide(gcd);
        }
        else
            numerator = numerator.multiply(new BigInteger("-1")).divide(gcd);
        this.denominator = denominator.abs().divide(gcd);
        //System.out.println(this.numerator.toString() + " " + this.denominator.toString());
    }

    private static BigInteger gcd (BigInteger n, BigInteger d)
    {
        BigInteger n1 = n.abs();
        BigInteger n2 = d.abs();
        BigInteger gcd = new BigInteger("1");

        BigInteger k2 = new BigInteger("1");
        for (int k = 1; k <= n1.intValue() && k <= n2.intValue(); k++)
        {
            if ((n1.remainder(k2).equals(new BigInteger("0"))) && 
                (n2.remainder(k2).equals(new BigInteger("0"))))
            {
                gcd = k2;
            }
            k2 = k2.add(new BigInteger("1"));
            //System.out.println(k2.toString() + " " + n1.toString() + " " + n2.toString());
        }

        return gcd;
    }

    public BigInteger getNumerator()
    {
        return numerator;
    }

    public BigInteger getDenominator()
    {
        return denominator;
    }

    public Rational add(Rational secondRational)
    {
        BigInteger n = numerator.multiply(secondRational.getDenominator()).add(denominator.multiply(secondRational.getNumerator()));
        BigInteger d = denominator.multiply(secondRational.getDenominator());

        return new Rational(n, d);
    }

    public Rational subtract(Rational secondRational)
    {
        BigInteger n = numerator.multiply(secondRational.getDenominator()).subtract(denominator.multiply(secondRational.getNumerator()));

        BigInteger d = denominator.multiply(secondRational.getDenominator());

        return new Rational(n, d);
    }

    public Rational multiply(Rational secondRational)
    {
        BigInteger n = numerator.multiply(secondRational.getNumerator());
        BigInteger d = denominator.multiply(secondRational.getDenominator());
        //System.out.println(numerator.toString() + " " + denominator.toString());
        return new Rational(n, d);
    }

    public Rational divide(Rational secondRational)
    {
        BigInteger n = numerator.multiply(secondRational.getDenominator());
        BigInteger d = denominator.multiply(secondRational.getNumerator());

        return new Rational(n, d);
    }

    @Override
    public String toString()
    {
        if (denominator.equals(new BigInteger("1")))
        {
            return numerator.toString();
        }
        else
            return numerator.toString() + "/" + denominator.toString();
    }

    @Override
    public boolean equals(Object other)
    {
        if (this.subtract((Rational)other).getNumerator().equals(new BigInteger("0")))
        {
            return true;
        }
        else
            return false;
    }

    @Override
    public int intValue()
    {
        return (int)doubleValue();
    }

    @Override
    public float floatValue()
    {
        return (float)doubleValue();
    }

    @Override
    public double doubleValue()
    {
        return numerator.divide(denominator).doubleValue();
    }

    @Override
    public long longValue()
    {
        return (long)doubleValue();
    }

    @Override
    public int compareTo(Rational o)
    {
        if (this.subtract(o).getNumerator().compareTo(new BigInteger("0")) > 0)
        {
            return 1;
        }
        else if (this.subtract(o).getNumerator().compareTo(new BigInteger("0")) < 0)
        {
            return -1;
        }
        else
            return 0;
    }
}

测试类

import java.math.BigInteger;

public class TestRational
{
    public static void main(String [] args)
    {
        BigInteger numerator = new BigInteger("1");
        BigInteger denominator = new BigInteger("123456789");
        Rational r1 = new Rational(numerator, denominator);
        Rational r2 = new Rational(numerator, denominator);
        Rational r3 = new Rational(numerator, denominator);

        System.out.println("r1 * r2 * r3 is " + r1.multiply(r2.multiply(r3)));
    }
}