第四届蓝桥杯Java B——有理数类

有理数就是可以表示为两个整数的比值的数字。一般情况下，我们用近似的小数表示。但有些时候，不允许出现误差，必须用两个整数来表示一个有理数。

这时，我们可以建立一个“有理数类”，下面的代码初步实现了这个目标。为了简明，它只提供了加法和乘法运算。

class Rational {
    private long ra;
    private long rb;
    
    private long gcd(long a, long b) {
        if(b == 0) return a;
        return gcd(b, a % b);
    }
    public Rational(long a, long b) {
        ra = a;
        rb = b;    
        long k = gcd(ra, rb);
        if(k > 1) { //需要约分
            ra /= k;  
            rb /= k;
        }
    }
    // 加法
    public Rational add(Rational x) {
        return ________________________________________;  //填空位置
    }
    // 乘法
    public Rational mul(Rational x) {
        return new Rational(ra*x.ra, rb*x.rb);
    }
    public String toString() {
        if(rb == 1) return "" + ra;
        return ra + "/" + rb;
    }
}

使用该类的示例：

Rational a = new Rational(1,3);
Rational b = new Rational(1,6);
Rational c = a.add(b);
System.out.println(a + "+" + b + "=" + c);

class Rational {
    private long ra;
    private long rb;

    private long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    public Rational(long a, long b) {
        ra = a;
        rb = b;
        long k = gcd(ra, rb);
        if (k > 1) { // 需要约分
            ra /= k;
            rb /= k;
        }
    }

    // 加法
    public Rational add(Rational x) {
        return new Rational(ra * x.rb + x.ra * rb, rb * x.rb); // 填空位置
    }

    // 乘法
    public Rational mul(Rational x) {
        return new Rational(ra * x.ra, rb * x.rb);
    }

    public String toString() {
        if (rb == 1)
            return "" + ra;
        return ra + "/" + rb;
    }
}

public class Main {

    public static void main(String[] args) {
        Rational a = new Rational(1, 3);
        Rational b = new Rational(1, 6);
        Rational c = a.add(b);
        System.out.println(a + "+" + b + "=" + c);
    }
}