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。

以下是实现了上述要求的Rational类的代码：

#include <iostream>
#include <cstdlib>

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

public:
    Rational(int num = 0, int den = 1) {
        if (den == 0) {
            std::cerr << "Error: denominator cannot be zero!" << std::endl;
            exit(EXIT_FAILURE);
        }
        numerator = num;
        denominator = den;
        simplify();
    }

    int getNumerator() const {
        return numerator;
    }

    int getDenominator() const {
        return denominator;
    }

    Rational operator+(const Rational& r) const {
        Rational result;
        result.numerator = numerator * r.denominator + r.numerator * denominator;
        result.denominator = denominator * r.denominator;
        result.simplify();
        return result;
    }

    Rational operator-(const Rational& r) const {
        Rational result;
        result.numerator = numerator * r.denominator - r.numerator * denominator;
        result.denominator = denominator * r.denominator;
        result.simplify();
        return result;
    }

    Rational operator*(const Rational& r) const {
        Rational result;
        result.numerator = numerator * r.numerator;
        result.denominator = denominator * r.denominator;
        result.simplify();
        return result;
    }

    Rational operator/(const Rational& r) const {
        if (r.numerator == 0) {
            std::cerr << "Error: division by zero!" << std::endl;
            exit(EXIT_FAILURE);
        }
        Rational result;
        result.numerator = numerator * r.denominator;
        result.denominator = denominator * r.numerator;
        result.simplify();
        return result;
    }

    double toDouble() const {
        return (double)numerator / (double)denominator;
    }

    void print() const {
        std::cout << numerator << "/" << denominator << std::endl;
    }

private:
    // 约分
    void simplify() {
        if (numerator == 0) {
            denominator = 1;
            return;
        }

        // 将分子、分母约分为最简形式
        int gcdValue = gcd(numerator, denominator);
        numerator /= gcdValue;
        denominator /= gcdValue;

        // 如果分母为负数，则将分子、分母都变为相反数
        if (denominator < 0) {
            numerator *= -1;
            denominator *= -1;
        }
    }

    // 计算最大公约数
    int gcd(int a, int b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }
};

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

    Rational sum = r1 + r2;
    Rational difference = r1 - r2;
    Rational product = r1 * r2;
    Rational quotient = r1 / r2;

    std::cout << "r1 = ";
    r1.print();
    std::cout << "r2 = ";
    r2.print();
    std::cout << "r1 + r2 = ";
    sum.print();
    std::cout << "r1 - r2 = ";
    difference.print();
    std::cout << "r1 * r2 = ";
    product.print();
    std::cout << "r1 / r2 = ";
    quotient.print();
    std::cout << "r1 as double: " << r1.toDouble() << std::endl;
    std::cout << "r2 as double: " << r2.toDouble() << std::endl;

    return 0;
}

输出结果如下：

r1 = 2/3
r2 = 3/4
r1 + r2 = 17/12
r1 - r2 = -1/12
r1 * r2 = 1/2
r1 / r2 = 8/9
r1 as double: 0.666667
r2 as double: 0.75