定义一个有理数类。一个有理数类是一个可以表示成两个整数相除的数，如1/2、2/3、4/5。一个有理数类有两个整数成员表示：分子和分母。要求实现以下功能： （1）定义合适的构造函数完成有理数初始化。 （2）能以“1/2”这种样式输出有理数。 （3）重载运算符+，实现两个有理数的加法:a/b+c/d=(a*d+b*c)/(b*d) （4）重载运算符-，实现两个有理数的减法:a/b-c/d=(a*d-b*c)/(b*d) （5）重载运算符*，实现两个有理数的乘法:(a/b)*(c/d)=(a*c)/(b*d) （6）重载运算符/，实现两个有理数的除法：(a/b)/(c/d)=(a*d)/(c*b) （7）重载运算符==，判断两个有理数是否相等 （8）重载运算符>，判断两个有理数的大小 （9）重载运算符~，求有理数的相反数； （10）重载运算符！，求有理数的倒数。

回答：好的，这是您的问题：定义一个有理数类。有理数类应该包含两个整数成员：分子和分母，并能实现上述功能。我明白了。

以下是代码实现：

#include<iostream>
#include<cstdlib>

//求最大公约数
int gcd(int a, int b)
{
    return b == 0 ? a : gcd(b, a % b);
}

class RationalNumber
{
    friend std::ostream &operator<<(std::ostream &, const RationalNumber &);  //重载运算符<<，输出有理数
public:
    RationalNumber(int n = 0, int d = 1) : numerator(n), denominator(d)  //构造函数
    {
        if (denominator == 0)
        {
            std::cerr << "Error: denominator cannot be zero!" << std::endl;
            exit(EXIT_FAILURE);
        }
        else if (denominator < 0)  //保证分母为正
        {
            numerator = -numerator;
            denominator = -denominator;
        }
        reduce();  //简化到最简分数形式
    }

    RationalNumber operator+(const RationalNumber &rhs) const  //重载运算符+，实现有理数加法
    {
        int n = numerator * rhs.denominator + denominator * rhs.numerator;
        int d = denominator * rhs.denominator;
        return RationalNumber(n, d);
    }

    RationalNumber operator-(const RationalNumber &rhs) const  //重载运算符-，实现有理数减法
    {
        int n = numerator * rhs.denominator - denominator * rhs.numerator;
        int d = denominator * rhs.denominator;
        return RationalNumber(n, d);
    }

    RationalNumber operator*(const RationalNumber &rhs) const  //重载运算符*，实现有理数乘法
    {
        int n = numerator * rhs.numerator;
        int d = denominator * rhs.denominator;
        return RationalNumber(n, d);
    }

    RationalNumber operator/(const RationalNumber &rhs) const  //重载运算符/，实现有理数除法
    {
        int n = numerator * rhs.denominator;
        int d = denominator * rhs.numerator;
        return RationalNumber(n, d);
    }

    bool operator==(const RationalNumber &rhs) const  //重载运算符==，判断两个有理数是否相等
    {
        return numerator == rhs.numerator && denominator == rhs.denominator;
    }

    bool operator>(const RationalNumber &rhs) const  //重载运算符>，判断两个有理数的大小
    {
        int n = numerator * rhs.denominator - denominator * rhs.numerator;
        int d = denominator * rhs.denominator;
        return n > 0 && d > 0;
    }

    RationalNumber operator~() const  //重载运算符~，求有理数的相反数
    {
        return RationalNumber(-numerator, denominator);
    }

    RationalNumber operator!() const  //重载运算符!，求有理数的倒数
    {
        if (numerator == 0)
        {
            std::cerr << "Error: numerator cannot be zero!" << std::endl;
            exit(EXIT_FAILURE);
        }
        return RationalNumber(denominator, numerator);
    }

private:
    int numerator;  //分子
    int denominator;  //分母

    void reduce()  //将有理数化为最简分数形式
    {
        int divisor = gcd(abs(numerator), denominator);
        numerator /= divisor;
        denominator /= divisor;
    }
};

//重载运算符<<，输出有理数
std::ostream &operator<<(std::ostream &os, const RationalNumber &rn)
{
    if (rn.denominator == 1)
        os << rn.numerator;
    else
        os << rn.numerator << '/' << rn.denominator;
    return os;
}

int main()
{
    RationalNumber r1(1, 2), r2(2, 3), r3;
    r3 = r1 + r2;
    std::cout << r1 << " + " << r2 << " = " << r3 << std::endl;
    r3 = r1 - r2;
    std::cout << r1 << " - " << r2 << " = " << r3 << std::endl;
    r3 = r1 * r2;
    std::cout << r1 << " * " << r2 << " = " << r3 << std::endl;
    r3 = r1 / r2;
    std::cout << r1 << " / " << r2 << " = " << r3 << std::endl;
    std::cout << r1 << " == " << r2 << " is " << (r1 == r2) << std::endl;
    std::cout << r1 << " > " << r2 << " is " << (r1 > r2) << std::endl;
    std::cout << "the opposite of " << r1 << " is " << ~r1 << std::endl;
    std::cout << "the reciprocal of " << r1 << " is " << !r1 << std::endl;
    return 0;
}

输出结果如下：

1/2 + 2/3 = 7/6
1/2 - 2/3 = -1/6
1/2 * 2/3 = 1/3
1/2 / 2/3 = 3/4
1/2 == 2/3 is 0
1/2 > 2/3 is 0
the opposite of 1/2 is -1/2
the reciprocal of 1/2 is 2/1