c++实现分数类fraction

下面是一个简单的 C++ 分数类 `fraction` 的实现，它包含了分数的四则运算和比较运算。

#include <iostream>

using namespace std;

class fraction {
private:
    int num;  // 分子
    int den;  // 分母

public:
    fraction(int n = 0, int d = 1) {
        if (d == 0) {
            cout << "分母不能为0！" << endl;
            exit(1);
        }
        if (d < 0) {
            n = -n;
            d = -d;
        }
        num = n;
        den = d;
        reduce();
    }

    int getNum() const { return num; }
    int getDen() const { return den; }

    fraction operator-() const { return fraction(-num, den); }
    friend fraction operator+(const fraction& f1, const fraction& f2);
    friend fraction operator-(const fraction& f1, const fraction& f2);
    friend fraction operator*(const fraction& f1, const fraction& f2);
    friend fraction operator/(const fraction& f1, const fraction& f2);

    friend bool operator==(const fraction& f1, const fraction& f2);
    friend bool operator!=(const fraction& f1, const fraction& f2);
    friend bool operator<(const fraction& f1, const fraction& f2);
    friend bool operator>(const fraction& f1, const fraction& f2);
    friend bool operator<=(const fraction& f1, const fraction& f2);
    friend bool operator>=(const fraction& f1, const fraction& f2);

    friend istream& operator>>(istream& in, fraction& f);
    friend ostream& operator<<(ostream& out, const fraction& f);

private:
    void reduce() {
        int gcd = getGCD(num, den);
        num /= gcd;
        den /= gcd;
    }

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

fraction operator+(const fraction& f1, const fraction& f2) {
    return fraction(f1.getNum() * f2.getDen() + f2.getNum() * f1.getDen(),
                    f1.getDen() * f2.getDen());
}

fraction operator-(const fraction& f1, const fraction& f2) {
    return f1 + (-f2);
}

fraction operator*(const fraction& f1, const fraction& f2) {
    return fraction(f1.getNum() * f2.getNum(), f1.getDen() * f2.getDen());
}

fraction operator/(const fraction& f1, const fraction& f2) {
    return fraction(f1.getNum() * f2.getDen(), f1.getDen() * f2.getNum());
}

bool operator==(const fraction& f1, const fraction& f2) {
    return f1.getNum() == f2.getNum() && f1.getDen() == f2.getDen();
}

bool operator!=(const fraction& f1, const fraction& f2) {
    return !(f1 == f2);
}

bool operator<(const fraction& f1, const fraction& f2) {
    return f1.getNum() * f2.getDen() < f2.getNum() * f1.getDen();
}

bool operator>(const fraction& f1, const fraction& f2) {
    return f2 < f1;
}

bool operator<=(const fraction& f1, const fraction& f2) {
    return !(f2 < f1);
}

bool operator>=(const fraction& f1, const fraction& f2) {
    return !(f1 < f2);
}

istream& operator>>(istream& in, fraction& f) {
    char slash;
    in >> f.num >> slash >> f.den;
    f.reduce();
    return in;
}

ostream& operator<<(ostream& out, const fraction& f) {
    out << f.getNum() << '/' << f.getDen();
    return out;
}

int main() {
    fraction f1(1, 2), f2(3, 4), f3;
    cout << "f1 = " << f1 << endl;
    cout << "f2 = " << f2 << endl;
    cout << "f3 = " << f3 << endl;

    cout << "请输入一个分数：";
    cin >> f3;
    cout << "f3 = " << f3 << endl;

    cout << "f1 + f2 = " << f1 + f2 << endl;
    cout << "f1 - f2 = " << f1 - f2 << endl;
    cout << "f1 * f2 = " << f1 * f2 << endl;
    cout << "f1 / f2 = " << f1 / f2 << endl;

    cout << "f1 == f2 ? " << (f1 == f2) << endl;
    cout << "f1 != f2 ? " << (f1 != f2) << endl;
    cout << "f1 < f2 ? " << (f1 < f2) << endl;
    cout << "f1 > f2 ? " << (f1 > f2) << endl;
    cout << "f1 <= f2 ? " << (f1 <= f2) << endl;
    cout << "f1 >= f2 ? " << (f1 >= f2) << endl;

    return 0;
}

上述实现中，分数类 `fraction` 的成员变量包括分子 `num` 和分母 `den`，它们在构造函数中被初始化。构造函数中还进行了分母为零的判断和分数的约分处理。`fraction` 类重载了一些运算符，包括一元负号运算符、二元加减乘除运算符和比较运算符。此外，还重载了输入输出流运算符，方便用户输入和输出分数。在主函数中，演示了如何使用这些运算符进行分数的运算和比较。