11设计并实现一个有理数类Rational，要求:1用两个整数的比描述有理数; (2)能够进行加、减、乘、除等算术运算;(3)以分数形式输出有理数; (4)提供double类型到有理数的类型转换; (5)合理的初始化，注意检测分母和除数为0的错误，默认分子为0，分母为1。用c++编写

以下是实现有理数类Rational的代码：

#include <iostream>

using namespace std;

class Rational {
private:
    int numerator;  // 分子
    int denominator;  // 分母

public:
    // 构造函数
    Rational(int num = 0, int den = 1) {
        if (den == 0) {
            cout << "Error: the denominator can't be zero!" << endl;
            numerator = 0;
            denominator = 1;
        } else {
            numerator = num;
            denominator = den;
            reduce();  // 约分
        }
    }

    // 获取分子
    int getNumerator() const {
        return numerator;
    }

    // 获取分母
    int getDenominator() const {
        return denominator;
    }

    // 加法
    Rational operator+(const Rational& r) const {
        int num = numerator * r.denominator + r.numerator * denominator;
        int den = denominator * r.denominator;
        return Rational(num, den);
    }

    // 减法
    Rational operator-(const Rational& r) const {
        int num = numerator * r.denominator - r.numerator * denominator;
        int den = denominator * r.denominator;
        return Rational(num, den);
    }

    // 乘法
    Rational operator*(const Rational& r) const {
        int num = numerator * r.numerator;
        int den = denominator * r.denominator;
        return Rational(num, den);
    }

    // 除法
    Rational operator/(const Rational& r) const {
        int num = numerator * r.denominator;
        int den = denominator * r.numerator;
        return Rational(num, den);
    }

    // 转double类型
    operator double() const {
        return (double)numerator / denominator;
    }

    // 约分
    void reduce() {
        if (numerator == 0) {
            denominator = 1;
        } else {
            int gcd = getGCD(abs(numerator), denominator);
            numerator /= gcd;
            denominator /= gcd;
            if (denominator < 0) {
                numerator = -numerator;
                denominator = -denominator;
            }
        }
    }

    // 打印分数形式
    void print() const {
        cout << numerator << "/" << denominator << endl;
    }

private:
    // 求最大公约数
    int getGCD(int a, int b) {
        if (b == 0) {
            return a;
        } else {
            return getGCD(b, a % b);
        }
    }
};

用以下代码进行测试：

int main() {
    Rational r1(2, 3);
    Rational r2(3, 4);
    Rational r3;

    r3 = r1 + r2;
    r3.print();  // 打印结果为17/12

    r3 = r1 - r2;
    r3.print();  // 打印结果为-1/12

    r3 = r1 * r2;
    r3.print();  // 打印结果为1/2

    r3 = r1 / r2;
    r3.print();  // 打印结果为8/9

    double d = (double)r1;
    cout << d << endl;  // 输出结果为0.666667

    return 0;
}