C++重载运算符实现分数的加减乘除

#include<iostream>

using namespace std;

int abs(int x) {
    return x < 0 ? -x : x;
}

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

int lcm(int a, int b) {
    return a / gcd(a, b) * b;
}

struct Fraction{
    int up, down;
    friend Fraction operator+(Fraction f1, Fraction f2);
    friend Fraction operator-(Fraction f1, Fraction f2);
    friend Fraction operator*(Fraction f1, Fraction f2);
    friend Fraction operator/(Fraction f1, Fraction f2);
};

void reduction(Fraction &f) {
    if (f.down < 0) {
        f.up = -f.up;
        f.down = -f.down;
    }
    if (f.up == 0) f.down = 1;
    else {
        int gd = gcd(abs(f.up), abs(f.down));
        f.up /= gd;
        f.down /= gd;
    }
}

Fraction operator+(Fraction f1, Fraction f2) {
    Fraction res;
    // 通分算法
    // int lm = lcm(abs(f1.down), abs(f2.down));
    // f1.up *= (lm / f1.down);
    // f2.up *= (lm / f2.down);
    // f1.down = f2.down = lm;
    // res.up = f1.up + f2.up;
    // res.down = lm;

    // 不通分，简洁算法：
    res.up = f1.up * f2.down + f2.up * f1.down;
    res.down = f1.down * f2.down;
    reduction(res);
    return res;
}

Fraction operator-(Fraction f1, Fraction f2) {
    Fraction res;
    res.up = f1.up * f2.down - f2.up * f1.down;
    res.down = f1.down * f2.down;
    reduction(res);
    return res;
}

Fraction operator*(Fraction f1, Fraction f2) {
    Fraction res;
    res.up = f1.up * f2.up;
    res.down = f1.down * f2.down;
    reduction(res);
    return res;
}

Fraction operator/(Fraction f1, Fraction f2) {
    Fraction res;
    res.up = f1.up * f2.down;
    res.down = f1.down * f2.up;
    reduction(res);
    return res;
}

int main() {
    int a, b, c, d;
    cin >> a >> b >> c >> d;
    // 在没有定义重载函数，结构体按顺序初始化时要用大括号{} 
    Fraction f1{a, b}, f2{c, d};
    Fraction res = f1 / f2;

    if (res.down == 0) cout << "undefined" << endl;
    else if (res.down == 1) cout << res.up << endl;
    else cout << res.up << " " << res.down << endl;
    return 0;
}