运用成员函数和友元函数运算符进行运算

Question

分别用成员函数和友元函数重载运算符，使对整型的运算符=、+、-、*、/适用于分数运算。要求：（1）输出结果是最简分数（可以是带分数）；（2）分母为1，只输出分子。

Answer 1

// g++ -Wall -std=c++17 main.cpp

#include <iostream>
#include <numeric>

class RationalNumber
{
public:
    typedef int value_type;

    constexpr RationalNumber(value_type a, value_type b) : _a(a), _b(b)
    {
        simplify();
    }

    constexpr RationalNumber &operator=(const RationalNumber &other)
    {
        _a = other._a;
        _b = other._b;
        return *this;
    }

    constexpr RationalNumber &operator+=(const RationalNumber &other)
    {
        auto a = _a * other._b + other._a * _b;
        auto b = _b * other._b;
        _a = a;
        _b = b;
        simplify();
        return *this;
    }

    constexpr RationalNumber &operator-=(const RationalNumber &other)
    {
        auto a = _a * other._b - other._a * _b;
        auto b = _b * other._b;
        _a = a;
        _b = b;
        simplify();
        return *this;
    }

    constexpr RationalNumber &operator*=(const RationalNumber &other)
    {
        _a *= other._a;
        _b *= other._b;
        simplify();
        return *this;
    }

    constexpr RationalNumber &operator/=(const RationalNumber &other)
    {
        _a *= other._b;
        _b *= other._a;
        simplify();
        return *this;
    }

    constexpr void simplify()
    {
        auto c = std::gcd(_a, _b);
        if (c != 0)
        {
            _a /= c;
            _b /= c;
        }
    }

private:
    value_type _a;
    value_type _b;

    friend constexpr RationalNumber operator+(const RationalNumber &lhs, const RationalNumber &rhs);
    friend constexpr RationalNumber operator-(const RationalNumber &lhs, const RationalNumber &rhs);
    friend constexpr RationalNumber operator*(const RationalNumber &lhs, const RationalNumber &rhs);
    friend constexpr RationalNumber operator/(const RationalNumber &lhs, const RationalNumber &rhs);
    template <typename CharT, typename Traits>
    friend std::basic_ostream<CharT, Traits> &operator<<(std::basic_ostream<CharT, Traits> &os, const RationalNumber &number);
};

constexpr RationalNumber operator+(const RationalNumber &lhs, const RationalNumber &rhs)
{
    RationalNumber tmp = lhs;
    tmp += rhs;
    return tmp;
}

constexpr RationalNumber operator-(const RationalNumber &lhs, const RationalNumber &rhs)
{
    RationalNumber tmp = lhs;
    tmp -= rhs;
    return tmp;
}

constexpr RationalNumber operator*(const RationalNumber &lhs, const RationalNumber &rhs)
{
    RationalNumber tmp = lhs;
    tmp *= rhs;
    return tmp;
}

constexpr RationalNumber operator/(const RationalNumber &lhs, const RationalNumber &rhs)
{
    RationalNumber tmp = lhs;
    tmp /= rhs;
    return tmp;
}

template <typename CharT, typename Traits>
std::basic_ostream<CharT, Traits> &operator<<(std::basic_ostream<CharT, Traits> &os, const RationalNumber &r)
{
    if (r._b == 0)
    {
        os << "INF";
    }
    else if (r._b == 1)
    {
        os << r._a;
    }
    else
    {
        auto c = r._a / r._b;
        if (c == 0)
        {
            os << r._a << '/' << r._b;
        }
        else
        {
            auto a = r._a % r._b;
            os << c << '+' << a << '/' << r._b;
        }
    }
    return os;
}

int main()
{
    char ch;
    int a1, b1, a2, b2;
    std::cout << "Input Fraction 1 (Format: a/b): ";
    std::cin >> a1 >> ch >> b1;
    std::cout << "Input Fraction 2 (Format: a/b): ";
    std::cin >> a2 >> ch >> b2;
    RationalNumber r1(a1, b1);
    RationalNumber r2(a2, b2);
    std::cout << r1 << " + " << r2 << " = " << r1 + r2 << '\n';
    std::cout << r1 << " - " << r2 << " = " << r1 - r2 << '\n';
    std::cout << r1 << " * " << r2 << " = " << r1 * r2 << '\n';
    std::cout << r1 << " / " << r2 << " = " << r1 / r2 << '\n';
    return 0;
}