这两天比赛遇到了一个分数的题，回想起来上课写的分数类，当时写的用上去以后漏洞百出，于是用闲暇时间又重写了一个作为模板。

#include<iostream>
#include<algorithm>
#include<cmath>
using namespace std;
int gcd(int x, int y)  //最大公因数（能整除x y 两数的最大整数）
{
    x = abs(x);
    y = abs(y);
    return y == 0 ? x : gcd(y, x%y);
}
int lcm(int a, int b)  //最小公倍数（能将a b 整除的最小整数）
{
    a = abs(a);
    b = abs(b);
    int m;
    a>b?1:m=a,a=b,b=m;
    return a*b / gcd(a, b);
}
class Fractions
{
public:
    int numerator;//分子  缩写 nmrtr
    int denominator;//分母  缩写 dnmtr

    Fractions(int nmrtr = 0,int dnmtr = 1):numerator(nmrtr),denominator(dnmtr)  //无参则为0
    {
        denominator = denominator == 0 ? denominator = 1 : denominator;//分母不为0，弱输入0，自动转换为1 变为整数
    }
    Fractions friend operator + (Fractions a,Fractions b)
    {
        Fractions c;
        if (a.numerator == 0) c = b;
        else
        {
            int deno_lcm = lcm(a.denominator,b.denominator);
            int nmrtr = a.numerator * (deno_lcm/a.denominator) + b.numerator * (deno_lcm / b.denominator);
            int dnmtr = deno_lcm;
            int c_gcd = gcd(nmrtr,dnmtr);
            c.numerator = nmrtr / c_gcd;
            c.denominator = dnmtr / c_gcd;
        }
        return c;
    }
    Fractions friend operator +  (Fractions a, int b)
    {
        Fractions c;
        if (a.numerator == 0)
        {
            c.numerator = b;
            c.denominator = 1;
        }
        else
        {
            int nmrtr = a.numerator + b * a.denominator;
            int dnmtr = a.denominator;
            int c_gcd = gcd(nmrtr, dnmtr);
            c.numerator = nmrtr / c_gcd;
            c.denominator = dnmtr / c_gcd;
        }
        return c;
    }
    Fractions friend operator - (Fractions a, Fractions b)
    {
        Fractions c;
        if (a.numerator == 0)
        {
            c = b;
            c.numerator = 0-c.numerator;
        }
        else
        {
            int deno_lcm = lcm(a.denominator, b.denominator);
            int nmrtr = a.numerator * (deno_lcm / a.denominator) - b.numerator * (deno_lcm / b.denominator);
            int dnmtr = deno_lcm;
            int c_gcd = gcd(nmrtr, dnmtr);
            c.numerator = nmrtr / c_gcd;
            c.denominator = dnmtr / c_gcd;
        }
        return c;
    }
    Fractions friend operator - (Fractions a, int b)
    {
        Fractions c;
        if (a.numerator == 0)
        {
            c.numerator = 0-b;
            c.denominator = 1;
        }
        else
        {
            int nmrtr = a.numerator - b * a.denominator;
            int dnmtr = a.denominator;
            int c_gcd = gcd(nmrtr, dnmtr);
            c.numerator = nmrtr / c_gcd;
            c.denominator = dnmtr / c_gcd;
        }
        return c;
    }
    istream friend &operator >> (istream &input, Fractions &a)
    {
        input >> a.numerator;
        input.get();
        input >> a.denominator;
        return input;
    }
    ostream friend &operator << (ostream &output,Fractions &a)
    {
        if (a.numerator == 0) output << 0;
        else if (a.denominator == 1) output << a.numerator;
        else output << a.numerator << "/" << a.denominator;
        return output;
    }
};
int main()
{
    Fractions a;
    Fractions b;
    Fractions x;
    char c;
    while (cin >> a >> c >> b)
    {
        if (c == '+')
        {
            x=a+b;
            cout<< x << endl;
        }
        else
        {
            x=a-b;
            cout << x << endl;
        }
    }
    return 0;
}

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