设计并实现一个有理数类Rational，要求：用两个整数的比描述有理数；能够进行加减除等算术运算；以分数形式输出有理数；提供double类型到有理数的类型转换；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Rational类的实现代码：

#include <iostream>

using namespace std;

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

public:
    Rational(int num = 0, int den = 1) {
        if (den == 0) {
            cout << "分母不能为0！" << endl;
            numerator = 0;
            denominator = 1;
        } else {
            numerator = num;
            denominator = den;
            reduce();
        }
    }

    Rational(const Rational& r) {
        numerator = r.numerator;
        denominator = r.denominator;
    }

    Rational& operator=(const Rational& r) {
        if (this != &r) {
            numerator = r.numerator;
            denominator = r.denominator;
        }
        return *this;
    }

    ~Rational() {}

    int getNumerator() const { return numerator; }

    int getDenominator() const { return denominator; }

    void setNumerator(int num) { numerator = num; }

    void setDenominator(int den) {
        if (den == 0) {
            cout << "分母不能为0！" << endl;
        } else {
            denominator = den;
            reduce();
        }
    }

    void reduce() {
        if (numerator == 0 || denominator == 1) {
            return;
        }

        int gcd = getGcd(numerator, denominator);
        numerator /= gcd;
        denominator /= gcd;

        if (denominator < 0) { // 分母为负数时，将分子和分母都变为负数
            numerator = -numerator;
            denominator = -denominator;
        }
    }

    int getGcd(int a, int b) {
        return b == 0 ? a : getGcd(b, a % b);
    }

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

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

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

    Rational operator/ (const Rational& r) const {
        if (r.numerator == 0) {
            cout << "除数不能为0！" << endl;
            return Rational();
        }
        int num = numerator * r.denominator;
        int den = denominator * r.numerator;
        return Rational(num, den);
    }

    bool operator== (const Rational& r) const {
        return numerator == r.numerator && denominator == r.denominator;
    }

    bool operator!= (const Rational& r) const {
        return !(*this == r);
    }

    bool operator> (const Rational& r) const {
        int num = numerator * r.denominator - r.numerator * denominator;
        return num > 0;
    }

    bool operator>= (const Rational& r) const {
        return (*this > r) || (*this == r);
    }

    bool operator< (const Rational& r) const {
        return !(*this >= r);
    }

    bool operator<= (const Rational& r) const {
        return !(*this > r);
    }

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

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

int main() {
    Rational r1(2, 3);
    Rational r2(1, 4);

    Rational r3 = r1 + r2;
    r3.print(); // 输出 11/12

    Rational r4 = r1 - r2;
    r4.print(); // 输出 5/12

    Rational r5 = r1 * r2;
    r5.print(); // 输出 1/6

    Rational r6 = r1 / r2;
    r6.print(); // 输出 8/3

    if (r1 == r2) {
        cout << "r1 == r2" << endl;
    } else {
        cout << "r1 != r2" << endl;
    }

    if (r1 > r2) {
        cout << "r1 > r2" << endl;
    } else {
        cout << "r1 <= r2" << endl;
    }

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

    return 0;
}

运行结果如下：

11/12
5/12
1/6
8/3
r1 != r2
r1 > r2
0.666667