第八周项目三（2）：分数类中的运算符重载：升级版

/*
*Copyright (c)2014,烟台大学计算机与控制工程学院
*All rights reserved.
*文件名称： 分数类中的运算符重载  .cpp
*作    者：白云飞
*完成日期：2015年4月25日
*版 本 号：v1.0
*
*问题描述：实现分数类中的运算符重载，在分数类中可以完成分数的加减乘除（运算后再化简）、比较（6种关系）的运算。实现分数类中的对象和整型数的四则运算。分数类中的对象可以和整型数进行四则运算，且运算符合交换律。
*程序输入：分子和分母
*程序输出：分数的各个形式
*/
#include <iostream>
#include<cmath>
#include<cstdlib>
using namespace std;
int gcd(int m, int n);
class CFraction
{
private:
    int nume;  // 分子
    int deno;  // 分母
public:
    CFraction(int nu=0,int de=1);   //构造函数，初始化用
    CFraction operator+( CFraction &c);
    CFraction operator-( CFraction &c);
    CFraction operator*( CFraction &c);
    CFraction operator/( CFraction &c);
    friend CFraction operator+(const CFraction &c, int i);
    friend CFraction operator+(int i, const CFraction &c );
    friend CFraction operator-(const CFraction &c, int i);
    friend CFraction operator-(int i, const CFraction &c );
    friend CFraction operator*(const CFraction &c, int i);
    friend CFraction operator*(int i, const CFraction &c );
    friend CFraction operator/(const CFraction &c, int i);
    friend CFraction operator/(int i, const CFraction &c );
    bool operator>(CFraction &c);
    bool operator<(CFraction &c);
    bool operator>=(CFraction &c);
    bool operator<=(CFraction &c);
    bool operator==(CFraction &c);
    bool operator!=(CFraction &c);
    friend bool operator>(const CFraction &c, int i);
    friend bool operator>(int i, const CFraction &c);
    friend bool operator<(const CFraction &c, int i);
    friend bool operator<(int i, const CFraction &c);
    friend bool operator==(const CFraction &c, int i);
    friend bool operator==(int i, const CFraction &c);
    friend bool operator!=(const CFraction &c, int i);
    friend bool operator!=(int i, const CFraction &c);
    friend bool operator>=(const CFraction &c, int i);
    friend bool operator>=(int i, const CFraction &c);
    friend bool operator<=(const CFraction &c, int i);
    friend bool operator<=(int i, const CFraction &c);
    void input();               //按照"nu/de"的格式，如"5/2"的形式输入
    void simplify();            //化简（使分子分母没有公因子）
    void output();
};
CFraction::CFraction(int nu,int de)
{
    if(de!=0)
    {
        nume=nu;
        deno=de;
    }
    else
    {
        cerr<<"输入错误！";
        exit(0);
    }
}
CFraction CFraction::operator+( CFraction &c)
{
    CFraction t;
    t.nume=nume*c.deno+c.nume*deno;
    t.deno=deno*c.deno;
    t.simplify();
    return t;
}
CFraction CFraction::operator-( CFraction &c)
{
    CFraction t;
    t.nume=nume*c.deno-c.nume*deno;
    t.deno=deno*c.deno;
    t.simplify();
    return t;
}
CFraction CFraction::operator*( CFraction &c)
{
    CFraction t;
    t.nume=nume*c.nume;
    t.deno=deno*c.deno;
    t.simplify();
    return t;
}
CFraction CFraction::operator/( CFraction &c)
{
    CFraction t;
    t.nume=nume*c.deno;
    t.deno=deno*c.nume;
    t.simplify();
    return t;

}
CFraction operator+(const CFraction &c, int i)
{
    CFraction t;
    t.nume=i*c.deno+c.nume;
    t.deno=c.deno;
    t.simplify();
    return t;
}
CFraction operator+(int i, const CFraction &c )
{
    CFraction t;
    t.nume=i*c.deno+c.nume;
    t.deno=c.deno;
    t.simplify();
    return t;
}
CFraction operator-(const CFraction &c, int i)
{
    CFraction t;
    t.nume=c.nume-i*c.deno;
    t.deno=c.deno;
    t.simplify();
    return t;
}
CFraction operator-(int i, const CFraction &c )
{
    CFraction t;
    t.nume=i*c.deno-c.nume;
    t.deno=c.deno;
    t.simplify();
    return t;
}
CFraction operator*(const CFraction &c, int i)
{
    CFraction t;
    t.nume=i*c.nume;
    t.deno=c.deno;
    t.simplify();
    return t;
}
CFraction operator*(int i, const CFraction &c )
{
    CFraction t;
    t.nume=i*c.nume;
    t.deno=c.deno;
    t.simplify();
    return t;
}
CFraction operator/(const CFraction &c, int i)
{
    CFraction t;
    t.nume=c.nume;
    t.deno=i*c.deno;
    t.simplify();
    return t;
}
CFraction operator/(int i, const CFraction &c )
{
    CFraction t;
    t.nume=i*c.deno;
    t.deno=c.nume;
    t.simplify();
    return t;
}
bool CFraction::operator>(CFraction &c)
{
    int nume1,nume2;
    nume1=nume*c.deno;
    nume2=c.nume*deno;
    if(nume1-nume2>0) return true;
    else return false;
}
bool CFraction::operator<(CFraction &c)
{
    int nume1,nume2;
    nume1=nume*c.deno;
    nume2=c.nume*deno;
    if(nume1-nume2<0) return true;
    else return false;
}
bool CFraction::operator>=(CFraction &c)
{
    return !(*this<c);
}
bool CFraction::operator<=(CFraction &c)
{
    return !(*this>c);
}
bool CFraction::operator==(CFraction &c)
{
    if(*this!=c) return false;
    else return true;
}
bool CFraction::operator!=(CFraction &c)
{
    if(*this>c||*this<c) return true;
    else return false;
}
bool operator>(const CFraction &c, int i)
{
    if(c.nume>i*c.deno)return true;
    else return false;
}
bool operator>(int i, const CFraction &c)
{
    if(i*c.deno>c.nume)return true;
    else return false;
}
bool operator<(const CFraction &c, int i)
{
    if(c.nume<i*c.deno)return true;
    else return false;
}
bool operator<(int i, const CFraction &c)
{
    if(i*c.deno<c.nume)return true;
    else return false;
}
bool operator==(const CFraction &c, int i)
{
    return c.nume==(i*c.deno);
}
bool operator==(int i, const CFraction &c)
{
    return c.nume==(i*c.deno);
}
bool operator!=(const CFraction &c, int i)
{
    return c.nume!=(i*c.deno);
}
bool operator!=(int i, const CFraction &c)
{
    return c.nume!=(i*c.deno);
}
bool operator>=(const CFraction &c, int i)
{
    return !(c<i);
}
bool operator>=(int i, const CFraction &c)
{
    return !(c>i);
}
bool operator<=(const CFraction &c, int i)
{
    return !(c>i);
}
bool operator<=(int i, const CFraction &c)
{
    return !(c<i);
}
void CFraction::input()
{
    int nu,de;
    char m;
    cout<<"请输入b分数（分子/分母）:";
    cin>>nu>>m>>de;
    if(m!='/')
        cout<<"输入格式错误";
    else if(de==0)
        cout<<"分母为零，输入错误.";
    else
    {
        nume=nu;
        deno=de;
    }
}
void CFraction::simplify()
{
    int n=gcd(deno, nume);
    deno/=n;     // 化简
    nume/=n;
}
int gcd(int m, int n) //这个函数可以定义为类的成员函数，也可以为一般函数
{
    int r;
    if (m<n)
    {
        r=m;
        m=n;
        n=r;
    }
    while(r=m%n)  // 求m，n的最大公约数
    {
        m=n;
        n=r;
    }
    return n;
}
void CFraction::output()
{
    cout<<"("<<nume<<"/"<<deno<<")"<<endl;
}
int main()
{
    CFraction a(10,12),b,c;
    cout<<"a=10/12 "<<endl;
    b.input();
    if (a>b) cout<<"a>b"<<endl;
    if (a<b) cout<<"a<b"<<endl;
    if (a>=b) cout<<"a>=b"<<endl;
    if (a<=b) cout<<"a<=b"<<endl;
    if (a==b) cout<<"a=b"<<endl;
    if (a!=b) cout<<"a!=b"<<endl;
    c=a+b;
    cout<<"a+b=";
    c.output();
    c=a-b;
    cout<<"a-b=";
    c.output();
    c=a*b;
    cout<<"a*b=";
    c.output();
    c=a/b;
    cout<<"a/b=";
    c.output();
    c=a+1;
    cout<<"a+1=";
    c.output();
    c=1+a;
    cout<<"1+a=";
    c.output();
    c=a-1;
    cout<<"a-1=";
    c.output();
    c=1-a;
    cout<<"1-a=";
    c.output();
    c=a*2;
    cout<<"a*2=";
    c.output();
    c=2*a;
    cout<<"2*a=";
    c.output();
    c=a/2;
    cout<<"a/2=";
    c.output();
    c=2/a;
    cout<<"2/a=";
    c.output();
    if (a>2) cout<<"a>2"<<endl;
    if (a<2) cout<<"a<2"<<endl;
    if (a>=2) cout<<"a>=2"<<endl;
    if (a<=2) cout<<"a<=2"<<endl;
    if (a==2) cout<<"a=2"<<endl;
    if (a!=2) cout<<"a!=2"<<endl;
    return 0;
}