/*
*Copyright (c)2014,煙臺大學計算機與控制工程學院
*All rights reserved.
*檔名稱：test.cpp
*作    者：徐洪祥
*完成日期：2015年5月9日
*版 本 號：v1.0
*
* 問題描述：實現分數類中的物件和整型數的四則運算，且運算符合交換律。
* 輸入描述：
* 程式輸出：
*/
#include <iostream>
#include <cmath>
using namespace std;
class CFraction
{
private:
    int nume;
    int deno;
public:
    CFraction(int nu=0,int de=1):nume(nu),deno(de) {}
    void simplify();
    void display();
    friend CFraction operator+(const CFraction &c1,const CFraction &c2);
    friend CFraction operator+(int c1,const CFraction &c2);
    friend CFraction operator+(const CFraction &c1,int c2);
    friend CFraction operator-(const CFraction &c1,const CFraction &c2);
    friend CFraction operator-(int c1,const CFraction &c2);
    friend CFraction operator-(const CFraction &c1,int c2);
    friend CFraction operator*(const CFraction &c1,const CFraction &c2);
    friend CFraction operator*(int c1,const CFraction &c2);
    friend CFraction operator*(const CFraction &c1,int c2);
    friend CFraction operator/(const CFraction &c1,const CFraction &c2);
    friend CFraction operator/(int c1,const CFraction &c2);
    friend CFraction operator/(const CFraction &c1,int c2);
    CFraction operator+();
    CFraction operator-();
    friend bool operator >(const CFraction &c1,const CFraction &c2);
    friend bool operator >(int c1,const CFraction &c2);
    friend bool operator >(const CFraction &c1,int c2);
    friend bool operator <(const CFraction &c1,const CFraction &c2);
    friend bool operator <(int c1,const CFraction &c2);
    friend bool operator <(const CFraction &c1,int c2);
    friend bool operator==(const CFraction &c1,const CFraction &c2);
    friend bool operator==(int c1,const CFraction &c2);
    friend bool operator==(const CFraction &c1,int c2);
    friend bool operator>=(const CFraction &c1,const CFraction &c2);
    friend bool operator>=(int c1,const CFraction &c2);
    friend bool operator>=(const CFraction &c1,int c2);
    friend bool operator<=(const CFraction &c1,const CFraction &c2);
    friend bool operator<=(int c1,const CFraction &c2);
    friend bool operator<=(const CFraction &c1,int c2);
    friend bool operator!=(const CFraction &c1,const CFraction &c2);
    friend bool operator!=(int c1,const CFraction &c2);
    friend bool operator!=(const CFraction &c1,int c2);
};
void CFraction::simplify()
{
    int m,n,r;
    m=fabs(deno);
    n=fabs(nume);
    while(r=m%n)
    {
        m=n;
        n=r;
    }
    deno/=n;
    nume/=n;
    if(deno<0)
    {
        deno=-deno;
        nume=-nume;
    }
}
void CFraction::display()
{
    cout<<nume<<"/"<<deno<<endl;
}
CFraction operator+(const CFraction &c1,const CFraction &c2)
{
    CFraction t;
    t.nume=c1.nume*c2.deno+c1.deno*c2.nume;
    t.deno=c1.deno*c2.deno;
    t.simplify();
    return t;
}
CFraction operator+(int c1,const CFraction &c2)
{
    CFraction c(c1*c2.deno+c2.nume,c2.deno);
    c.simplify();
    return c;
}
CFraction operator+(const CFraction &c1,int c2)
{
    CFraction c(c2*c1.deno+c1.nume,c1.deno);
    c.simplify();
    return c;
}
CFraction operator-(const CFraction &c1,const CFraction &c2)
{
    CFraction t;
    t.nume=c1.nume*c2.deno-c1.deno*c2.nume;
    t.deno=c1.deno*c2.deno;
    t.simplify();
    return t;
}
CFraction operator-(int c1,const CFraction &c2)
{
    CFraction c(c1*c2.deno-c2.nume,c2.deno);
    c.simplify();
    return c;
}
CFraction operator-(const CFraction &c1,int c2)
{
    CFraction c(c1.nume-c2*c1.deno,c1.deno);
    c.simplify();
    return c;
}
CFraction operator*(const CFraction &c1,const CFraction &c2)
{
    CFraction t;
    t.nume=c1.nume*c2.nume;
    t.deno=c1.deno*c2.deno;
    t.simplify();
    return t;
}
CFraction operator*(int c1,const CFraction &c2)
{
    CFraction c(c1*c2.nume,c2.deno);
    c.simplify();
    return c;
}
CFraction operator*(const CFraction &c1,int c2)
{
    CFraction c(c2*c1.nume,c1.deno);
    c.simplify();
    return c;
}
CFraction operator/(const CFraction &c1,const CFraction &c2)
{
    CFraction t;
    t.nume=c1.nume*c2.deno;
    t.deno=c1.deno*c2.nume;
    t.simplify();
    return t;
}
CFraction operator/(int c1,const CFraction &c2)
{
    CFraction c(c1*c2.deno,c2.nume);
    c.simplify();
    return c;
}
CFraction operator/(const CFraction &c1,int c2)
{
    CFraction c(c1.nume,c1.deno*c2);
    c.simplify();
    return c;
}
CFraction CFraction:: operator+()
{
    return *this;
}
CFraction CFraction:: operator-()
{
    CFraction c;
    c.nume=-nume;
    c.deno=-deno;
    return c;
}
bool operator>(const CFraction &c1, const CFraction &c2)
{
    int c1_nume,c2_nume,common_deno;
    c1_nume=c1.nume*c2.deno;
    c2_nume=c1.deno*c2.nume;
    common_deno=c1.deno*c2.deno;
    if((c1_nume-c2_nume)*common_deno>0)
        return true;
    else
        return false;
}
bool operator>(const CFraction &c1, int c2)
{
    if(c1.deno>0)
        return c1.nume>(c2*c1.deno);
    else
        return c1.nume<(c2*c1.deno);
}

bool operator>(int c1, const CFraction &c2)
{
    if(c2.deno>0)
        return (c1*c2.deno)>c2.nume;
    else
        return (c1*c2.deno)<c2.nume;
}
bool operator<(const CFraction &c1, const CFraction &c2)
{
    int c1_nume,c2_nume,common_deno;
    c1_nume=c1.nume*c2.deno;
    c2_nume=c2.nume*c1.deno;
    common_deno=c1.deno*c2.deno;
    if ((c1_nume-c2_nume)*common_deno<0)
        return true;
    else
        return false;
}
bool operator<(const CFraction &c1, int c2)
{
    if(c1.deno>0)
        return c1.nume<(c2*c1.deno);
    else
        return c1.nume>(c2*c1.deno);
}
bool operator<(int c1, const CFraction &c2)
{
    if(c2.deno>0)
        return (c1*c2.deno)<c2.nume;
    else
        return (c1*c2.deno)>c2.nume;
}
bool operator==(const CFraction &c1,const CFraction &c2)
{
    if(c1-c2!=0)
        return false;
    else
        return true;
}
bool operator==(const CFraction &c1, int c2)
{
    return c1.nume==(c2*c1.deno);
}
bool operator==(int c1, const CFraction &c2)
{
    return c2.nume==(c1*c2.deno);
}
bool operator>=(const CFraction &c1,const CFraction &c2)
{
    if(c1<c2)
        return false;
    else
        return true;
}
bool operator>=(const CFraction &c1, int c2)
{
    return !(c1<c2);
}
bool operator>=(int c1, const CFraction &c2)
{
    return !(c1<c2);
}
bool operator<=(const CFraction &c1,const CFraction &c2)
{
    if(c1>c2)
        return false;
    else
        return true;
}
bool operator<=(const CFraction &c1, int c2)
{
    return !(c1>c2);
}
bool operator<=(int c1, const CFraction &c2)
{
    return !(c1>c2);
}
bool operator!=(const CFraction &c1,const CFraction &c2)
{
    if(c1>c2||c1<c2)
        return true;
    else
        return false;
}
bool operator!=(const CFraction &c1, int c2)
{
    return c1.nume!=(c2*c1.deno);
}
bool operator!=(int c1, const CFraction &c2)
{
    return c2.nume!=(c1*c2.deno);
}
int main()
{
    CFraction x(2,5),y(-2,3),z;
    cout<<"x=2/5,y=-2/3"<<endl;
    z=x+y;
    cout<<"x+y=";
    z.display();
    z=x-y;
    cout<<"x-y=";
    z.display();
    z=x*y;
    cout<<"x*y=";
    z.display();
    z=x/y;
    cout<<"x/y=";
    z.display();
    if(x>y)
        cout<<"x>y"<<endl;
    if(x<y)
        cout<<"x<y"<<endl;
    if(x==y)
        cout<<"x=y"<<endl;
    cout<<endl;
    CFraction c1(5,3),c2;
    cout<<"c1=5/3"<<endl;
    c2=c1+5;
    cout<<"c1+5=";
    c2.display();
    c2=5+c1;
    cout<<"5+c1=";
    c2.display();
    c2=c1-5;
    cout<<"c1-5=";
    c2.display();
    c2=5-c1;
    cout<<"5-c1=";
    c2.display();
    c2=c1*5;
    cout<<"c1*5=";
    c2.display();
    c2=5*c1;
    cout<<"5*c1=";
    c2.display();
    c2=c1/5;
    cout<<"c1/5=";
    c2.display();
    c2=5/c1;
    cout<<"5/c1=";
    c2.display();
    return 0;
}
 

總結：注意友員函式跟成員函式的區別，取正一目運算、取反一目運算還沒搞懂有啥作用，剛開始做漏洞百出，還有好多地方只是參考老師的答案，沒有真正弄懂，友員函式比成員函式多出好多行程式碼啊。