C++实现有理数类

#ifndef RATIONAL_H
#define RATIONAL_H

#include <ostream>
#include <istream>

class Rational
{
public:
    Rational(int numerator = 0, int denominator = 1);
    Rational(const Rational &other);
    ~Rational();
    int getNumerator() const;
    int getDenominator() const;
    void setNumerator(int numerator);
    void setDenominator(int denominator);

    Rational operator+(const Rational &other) const;
    Rational operator-(const Rational &other) const;
    Rational operator*(const Rational &other) const;
    Rational operator/(const Rational &other) const;
    Rational operator%(const Rational &other) const;
    Rational operator-() const;

    Rational &operator=(const Rational &other);
    Rational &operator+=(const Rational &other);
    Rational &operator-=(const Rational &other);
    Rational &operator*=(const Rational &other);
    Rational &operator/=(const Rational &other);
    Rational &operator%=(const Rational &other);

    bool operator==(const Rational &other) const;
    bool operator!=(const Rational &other) const;
    bool operator<(const Rational &other) const;
    bool operator>(const Rational &other) const;
    bool operator<=(const Rational &other) const;
    bool operator>=(const Rational &other) const;

    friend std::ostream &operator<<(std::ostream &out, const Rational &r);
    friend std::istream &operator>>(std::istream &in, Rational &r);

private:
    int numerator;   // 分子
    int denominator; // 分母
    void reduce();   // 约分
};

#endif // RATIONAL_H

#include "rational.h"
#include <iostream>

static int gcd(int a, int b)
{
    if (b == 0)
        return a;
    return gcd(b, a % b);
}

Rational::Rational(int numerator, int denominator)
{
    if (denominator == 0)
    {
        std::cout << "denominator can't be zero!" << std::endl;
        exit(1);
    }
    this->numerator = numerator;
    this->denominator = denominator;
    reduce();
}

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

Rational::~Rational()
{
}

int Rational::getNumerator() const
{
    return numerator;
}

int Rational::getDenominator() const
{
    return denominator;
}

void Rational::setNumerator(int numerator)
{
    this->numerator = numerator;
}

void Rational::setDenominator(int denominator)
{
    this->denominator = denominator;
}

Rational Rational::operator+(const Rational &other) const
{
    Rational result;
    result.numerator = numerator * other.denominator + denominator * other.numerator;
    result.denominator = denominator * other.denominator;
    result.reduce();
    return result;
}

Rational Rational::operator-(const Rational &other) const
{
    Rational result;
    result.numerator = numerator * other.denominator - denominator * other.numerator;
    result.denominator = denominator * other.denominator;
    result.reduce();
    return result;
}

Rational Rational::operator*(const Rational &other) const
{
    Rational result;
    result.numerator = numerator * other.numerator;
    result.denominator = denominator * other.denominator;
    result.reduce();
    return result;
}

Rational Rational::operator/(const Rational &other) const
{
    Rational result;
    result.numerator = numerator * other.denominator;
    result.denominator = denominator * other.numerator;
    result.reduce();
    return result;
}

Rational Rational::operator%(const Rational &other) const
{
    Rational result;
    result.numerator = numerator * other.denominator;
    result.denominator = denominator * other.numerator;
    result.reduce();
    return result;
}

Rational Rational::operator-() const
{
    Rational result;
    result.numerator = -numerator;
    result.denominator = denominator;
    result.reduce();
    return result;
}

Rational &Rational::operator=(const Rational &other)
{
    if (this != &other)
    {
        numerator = other.numerator;
        denominator = other.denominator;
    }

    return *this;
}

Rational &Rational::operator+=(const Rational &other)
{
    numerator = numerator * other.denominator + denominator * other.numerator;
    denominator = denominator * other.denominator;
    reduce();
    return *this;
}

Rational &Rational::operator-=(const Rational &other)
{
    numerator = numerator * other.denominator - denominator * other.numerator;
    denominator = denominator * other.denominator;
    reduce();
    return *this;
}

Rational &Rational::operator*=(const Rational &other)
{
    numerator = numerator * other.numerator;
    denominator = denominator * other.denominator;
    reduce();
    return *this;
}

Rational &Rational::operator/=(const Rational &other)
{
    numerator = numerator * other.denominator;
    denominator = denominator * other.numerator;
    reduce();
    return *this;
}

Rational &Rational::operator%=(const Rational &other)
{
    numerator = numerator * other.denominator;
    denominator = denominator * other.numerator;
    reduce();
    return *this;
}

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

bool Rational::operator!=(const Rational &other) const
{
    return numerator != other.numerator || denominator != other.denominator;
}

bool Rational::operator<(const Rational &other) const
{
    return numerator * other.denominator < denominator * other.numerator;
}

bool Rational::operator>(const Rational &other) const
{
    return numerator * other.denominator > denominator * other.numerator;
}

bool Rational::operator<=(const Rational &other) const
{
    return numerator * other.denominator <= denominator * other.numerator;
}

bool Rational::operator>=(const Rational &other) const
{
    return numerator * other.denominator >= denominator * other.numerator;
}

std::ostream &operator<<(std::ostream &os, const Rational &r)
{
    os << r.numerator << "/" << r.denominator;
    return os;
}

std::istream &operator>>(std::istream &is, Rational &r)
{
    is >> r.numerator >> r.denominator;
    r.reduce();
    return is;
}

void Rational::reduce()
{
    int divisor = gcd(numerator, denominator);
    numerator /= divisor;
    denominator /= divisor;
}

#include "rational.h"
#include <iostream>

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

    std::cout << r1 << " + " << r2 << " = " << r1 + r2 << std::endl;
    std::cout << r1 << " - " << r2 << " = " << r1 - r2 << std::endl;
    std::cout << r1 << " * " << r2 << " = " << r1 * r2 << std::endl;
    std::cout << r1 << " / " << r2 << " = " << r1 / r2 << std::endl;
    std::cout << r1 << " % " << r2 << " = " << r1 % r2 << std::endl;

    return 0;
}