//實現一個有理數類，包括大小比較，有理數的加減乘除。測試你的類。
#include <iostream>
#include <stdlib.h>

class Rational
{
public:
    Rational(int num,int denom);                   //實現有理數的形式"num/denom"

    Rational operator+(Rational rhs);              //加法過載
    Rational operator-(Rational rhs);              //減法過載
    Rational operator
 
*(Rational rhs);              //乘法過載
    Rational operator/(Rational rhs);              //除法過載

    void print();                                  //列印結果輸出

private:
    void normalize();      //對分數的簡化處理

    int numerator;         //分子
    int denominator;       //分母
};

Rational::Rational(int num,int denom)
{
    numerator = num;
    denominator = denom;

    normalize();
}

void
 
 Rational::normalize()
{
    //確保分母為正
    if(denominator < 0)
    {
        numerator = -numerator;
        denominator = -denominator;
    }

    //歐幾里得演算法
    int a = abs(numerator);
    int b = abs(denominator);

    while(b>0)
    {
        int t = a%b;
        a = b;
        b = t;
    }

    numerator/=a;
    denominator/=a;
}


Rational Rational::operator
 
+(Rational rhs)
{
    int a = numerator;
    int b = denominator;
    int c = rhs.numerator;
    int d = rhs.denominator;

    int e = a*b +c*d;
    int f = b*d;

    return Rational(e,f);
}

Rational Rational::operator-(Rational rhs)
{
    rhs.numerator = -rhs.numerator;

    return operator+(rhs);
}

Rational Rational::operator*(Rational rhs)
{
    int a = numerator;
    int b = denominator;
    int c = rhs.numerator;
    int d = rhs.denominator;

    int e = a*c;
    int f = b*d;

    return Rational(e,f);
}

Rational Rational::operator/(Rational rhs)
{
    int t = rhs.numerator;
    rhs.numerator = rhs.denominator;
    rhs.denominator = t;

    return operator*(rhs);
}

void Rational::print()
{
    if(numerator%denominator == 0)
       std::cout<<numerator / denominator;
    else
       std::cout<<numerator <<"/"<<denominator;
}

int main()
{
    Rational f1(2,16);
    Rational f2(7,8);

    Rational res = f1+f2;
    f1.print();
    std::cout<<" + ";
    f2.print();
    std::cout<<" = ";
    res.print();
    std::cout<<"\n";


    res = f1 - f2;
    f1.print();
    std::cout<<" - ";
    f2.print();
    std::cout<<" = ";
    res.print();
    std::cout<<"\n";

    res = f1 * f2;
    f1.print();
    std::cout<<" * ";
    f2.print();
    std::cout<<" = ";
    res.print();
    std::cout<<"\n";

    res = f1 / f2;
    f1.print();
    std::cout<<" / ";
    f2.print();
    std::cout<<" = ";
    res.print();
    std::cout<<"\n";

    return 0;
}