7.1设计并实现有理数库，使用整数表示分子和分母，完成有理数的加减乘除与化简运算

//class_head.h
class Complex
{
public:
       Complex()
       {molecules=0;denominator=0;}
       Complex(int n,int m);
//对运算符的重载，c3默认会传第二个操作数的值，所以只要写一个参数
//也可以这样的写法 Complex operator+(Complex &c2);
       Complex operator+(Complex c3);
       Complex operator-(Complex c3);
       Complex operator*(Complex c3);
       Complex operator/(Complex c3);
       Complex input(Complex &c);//实现对私有成员的赋值操作
       void output();
private:
        int molecules;
        int denominator;
        void simplification();//化简
};

//class_yuan.cpp
#include<iostream>
using namespace std;
#include "class_head.h"
#include<cmath>
Complex::Complex(int n,int m)
{
molecules=n,denominator=m;
simplification();
}
//使用了欧几里得算法（辗转相除法）利用两个数的公约数对于较小数与两数之间的余数的公约数
void Complex::simplification()
{
if(denominator<0)
{
molecules=-molecules;
denominator=-denominator;
}
int a=abs(molecules);//abs（）是取绝对值，包含在头文件<cmath>里面
int b=abs(denominator);
while(b>0)
{
int t=a%b;
a=b;
b=t;
}
molecules=molecules/a;
denominator=denominator/a;
}
Complex Complex::operator+(Complex c3)
{
int a=molecules;
int b=denominator;
int c=c3.molecules;
int d=c3.denominator;
int e=a*d+b*c;
int f=b*d;
return Complex(e,f);
}
Complex Complex::operator-(Complex c3)
{
c3.molecules=-c3.molecules;
return operator+(c3);
}
Complex Complex::operator*(Complex c3)
{
int a=molecules;
int b=denominator;
int c=c3.molecules;
int d=c3.denominator;
int e=a*c;
int f=b*d;
return Complex(e,f);
}
Complex Complex::operator/(Complex c3)
{
int t=c3.molecules;
c3.molecules=c3.denominator;
c3.denominator=t;
return operator*(c3);
}
Complex Complex::input(Complex &c)
{
int a,b;
cout<<"输入分子 ";
cin>>a;
cout<<"输入分母 ";
cin>>b;
molecules=a;
denominator=b;
return c;
}
void Complex::output()
{
if(molecules%denominator==0)
cout<<molecules/denominator;
else
cout<<molecules<<"/"<<denominator;
}

　　

//main()
#include<iostream>
using namespace std;
#include "class_head.h"
int main()
{
int i;
Complex c1,c2,c3;
cout<<"￥￥输入第一个操作数￥￥"<<endl;
c1.input(c1);
cout<<"￥￥输入第二个操作数￥￥"<<endl;
c2.input(c2);
cout<<"请选择要进行的操作"<<endl;
cout<<"1表示+法"<<endl;
cout<<"2表示-法"<<endl;
cout<<"3表示*法"<<endl;
cout<<"4表示/法"<<endl;
cin>>i;
switch(i)
{
case 1:
c3=c1+c2;
cout<<"进行加法之后的结果为："<<endl;
cout<<"结果等于：";
c3.output();
cout<<endl;
break;
case 2:
c3=c1-c2;
cout<<"进行减法之后的结果为："<<endl;
cout<<"结果等于：";
c3.output();
cout<<endl;
break;
case 3:
c3=c1*c2;
cout<<"进行乘法之后的结果为："<<endl;
cout<<"结果等于：";
c3.output();
cout<<endl;
break;
case 4:
c3=c1/c2;
cout<<"进行除法之后的结果为："<<endl;
cout<<"结果等于：";
c3.output();
cout<<endl;
break;
}
return 0;
}

　　

 如果要使用友元函数

在vc中要将

#include<iostream>

改为

#include<iostream.h>

去掉using namespace std;

#include<iostream.h>
//using namespace std;
#include<cmath>
class Complex
{
public:
       Complex()
	   {molecules=0;denominator=0;}
	   Complex(int n,int m);
//修改处
	   friend Complex operator+(Complex &c1,Complex&c2);
	   friend Complex operator-(Complex &c1,Complex&c2);
	   Complex operator*(Complex c3);
	   Complex operator/(Complex c3);
	   Complex input(Complex &c);
	   void output();
private:
        int molecules;
		int denominator;
		void simplification();
};

Complex::Complex(int n,int m)
{
molecules=n,denominator=m;
simplification();
}
void Complex::simplification()
{
if(denominator<0)
{
molecules=-molecules;
denominator=-denominator;
}
int a=abs(molecules);
int b=abs(denominator);
while(b>0)
{
int t=a%b;
a=b;
b=t;
}
molecules=molecules/a;
denominator=denominator/a;
}
Complex operator+(Complex &c1,Complex &c2)
{
int a=c1.molecules;
int b=c1.denominator;
int c=c2.molecules;
int d=c2.denominator;
int e=a*d+b*c;
int f=b*d;
return Complex(e,f);
}
Complex operator-(Complex &c1,Complex &c2)
{
c2.molecules=-c2.molecules;
return operator+(c1,c2);
}
Complex Complex::operator*(Complex c3)
{
int a=molecules;
int b=denominator;
int c=c3.molecules;
int d=c3.denominator;
int e=a*c;
int f=b*d;
return Complex(e,f);
}
Complex Complex::operator/(Complex c3)
{
int t=c3.molecules;
c3.molecules=c3.denominator;
c3.denominator=t;
return operator*(c3);
}
Complex Complex::input(Complex &c)
{
int a,b;
cout<<"输入分子 ";
cin>>a;
cout<<"输入分母 ";
cin>>b;
molecules=a;
denominator=b;
return c;
}
void Complex::output()
{
if(molecules%denominator==0)
cout<<molecules/denominator;
else
cout<<molecules<<"/"<<denominator;
}
int main()
{
int i;
Complex c1,c2,c3;
cout<<"￥￥输入第一个操作数￥￥"<<endl;
c1.input(c1);
cout<<"￥￥输入第二个操作数￥￥"<<endl;
c2.input(c2);
cout<<"请选择要进行的操作"<<endl;
cout<<"1表示+法"<<endl;
cout<<"2表示-法"<<endl;
cout<<"3表示*法"<<endl;
cout<<"4表示/法"<<endl;
cin>>i;
switch(i)
{
case 1:
c3=c1+c2;
cout<<"进行加法之后的结果为："<<endl;
cout<<"结果等于：";
c3.output();
cout<<endl;
break;
case 2:
c3=c1-c2;
cout<<"进行减法之后的结果为："<<endl;
cout<<"结果等于：";
c3.output();
cout<<endl;
break;
case 3:
c3=c1*c2;
cout<<"进行乘法之后的结果为："<<endl;
cout<<"结果等于：";
c3.output();
cout<<endl;
break;
case 4:
c3=c1/c2;
cout<<"进行除法之后的结果为："<<endl;
cout<<"结果等于：";
c3.output();
cout<<endl;
break;
}
return 0;
}