【题目】在任务3的基础上拓展。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。例如：CFraction a(1,3),b; int i=2; 可以完成b=a+i;。同样，可以完成i+a, 45+a, a*27, 5/a等各种运算。

参考：第8周-任务3-实现分数类中的运算符重载

【参考解答】——逐一写出来，需要的是耐心

#include <iostream>
using namespace std;
class CFraction
{
private:
	int nume;  // 分子
	int deno;  // 分母
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);  //两个分数相加，结果要化简
	friend CFraction operator-(const CFraction &c1, const CFraction &c2);  //两个分数相减，结果要化简
	friend CFraction operator*(const CFraction &c1, const CFraction &c2);  //两个分数相乘，结果要化简
	friend CFraction operator/(const CFraction &c1, const CFraction &c2);  //两个分数相除，结果要化简

	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 );  

	CFraction operator+();  //取正一目运算
	CFraction operator-();  //取反一目运算

	friend bool operator>(const CFraction &c1, const CFraction &c2);
	friend bool operator<(const CFraction &c1, const CFraction &c2);
	friend bool operator==(const CFraction &c1, const CFraction &c2);
	friend bool operator!=(const CFraction &c1, const CFraction &c2);
	friend bool operator>=(const CFraction &c1, const CFraction &c2);
	friend bool operator<=(const CFraction &c1, const CFraction &c2);

	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);
};

// 分数化简
void CFraction::simplify()
{
	int m,n,r;
	m=abs(deno);
	n=abs(nume);
	while(r=m%n)  // 求m，n的最大公约数
	{
		m=n;
		n=r;
	}
	deno/=n;     // 化简
	nume/=n;
	if (deno<0)  // 将分母转化为正数
	{
		deno=-deno;
		nume=-nume;
	}
}

//显示分数
void CFraction::display()
{
	cout<<"("<<nume<<"/"<<deno<<")"<<endl;
}

// 分数相加
CFraction operator+(const CFraction &c1, const CFraction &c2)
{
	CFraction t;
	t.nume=c1.nume*c2.deno+c2.nume*c1.deno;
	t.deno=c1.deno*c2.deno;
	t.simplify();
	return t;
}

// 分数相减
CFraction operator-(const CFraction &c1, const CFraction &c2)
{
	CFraction t;
	t.nume=c1.nume*c2.deno-c2.nume*c1.deno;
	t.deno=c1.deno*c2.deno;
	t.simplify();
	return t;
}

// 分数相乘
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;
}

// 分数相除
CFraction operator/(const CFraction &c1, const CFraction &c2)
{
	CFraction t;
	if (!c2.nume) return c1;
	t.nume=c1.nume*c2.deno;
	t.deno=c1.deno*c2.nume;
	t.simplify();
	return t;
}

CFraction operator+(const CFraction &c, int i)
{
	CFraction c1(c.nume+i*c.deno,c.deno);
	c1.simplify();
	return c1;
}

CFraction operator+(int i, const CFraction &c )
{
	CFraction c1(c.nume+i*c.deno,c.deno);
	c1.simplify();
	return c1;
}

CFraction operator-(const CFraction &c, int i)  
{
	CFraction c1(c.nume-i*c.deno,c.deno);
	c1.simplify();
	return c1;
}

CFraction operator-(int i, const CFraction &c )
{
	CFraction c1(i*c.deno-c.nume,c.deno);
	c1.simplify();
	return c1;
}
CFraction operator*(const CFraction &c, int i)
{
	CFraction c1(c.nume*i,c.deno);
	c1.simplify();
	return c1;
}

CFraction operator*(int i, const CFraction &c )
{
	CFraction c1(c.nume*i,c.deno);
	c1.simplify();
	return c1;
}

CFraction operator/(const CFraction &c, int i)
{
	CFraction c1(c.nume,c.deno*i);
	c1.simplify();
	return c1;
}

CFraction operator/(int i, const CFraction &c )
{
	CFraction c1(i*c.deno,c.nume);
	c1.simplify();
	return c1;
}

// 分数取正号
CFraction CFraction:: operator+()
{
	return *this;
}

// 分数取负号
CFraction CFraction:: operator-()
{
	CFraction c;
	c.nume=-nume;
	c.deno=-deno;
	return c;     
}

// 分数比较大小
bool operator>(const CFraction &c1, const CFraction &c2)
{
	int c1_nume,c2_nume,common_deno;
	c1_nume=c1.nume*c2.deno;        // 计算分数通分后的分子，同分母为c1.deno*c2.deno
	c2_nume=c2.nume*c1.deno; 
	common_deno=c1.deno*c2.deno;
	//if (c1_nume>c2_nume) return true; 无法应对common_deno<0的情形
	//下面的语句更简练的一种写法if ((c1_nume-c2_nume)*common_deno>0) return true;
	if (c1_nume>c2_nume&&common_deno>0||c1_nume<c2_nume&&common_deno<0) return true; // 将通分后的分子比较大小
	return false;
}

// 分数比较大小
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; 
	return false;
}

// 分数比较大小
bool operator==(const CFraction &c1, const CFraction &c2)
{
	if (c1!=c2) return false;
	return true;
}

// 分数比较大小
bool operator!=(const CFraction &c1, const CFraction &c2)
{
	if (c1>c2 || c1<c2) return true;
	return false;
}

// 分数比较大小
bool operator>=(const CFraction &c1, const CFraction &c2)
{
	if (c1<c2) return false;
	return true;
}

// 分数比较大小
bool operator<=(const CFraction &c1, const CFraction &c2)
{
	if (c1>c2) return false;
	return true;
}

bool operator>(const CFraction &c, int i)
{
	if(c.deno>0) 
		return c.nume>(i*c.deno);
	else 
		return c.nume<(i*c.deno);
}

bool operator>(int i, const CFraction &c)
{
	if(c.deno>0) 
		return (i*c.deno)>c.nume;
	else 
		return (i*c.deno)<c.nume;
}

bool operator<(const CFraction &c, int i)
{
	if(c.deno>0) 
		return c.nume<(i*c.deno);
	else 
		return c.nume>(i*c.deno);
}

bool operator<(int i, const CFraction &c)
{
	if(c.deno>0) 
		return (i*c.deno)<c.nume;
	else 
		return (i*c.deno)>c.nume;
}

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 !(i<c);
}

bool operator<=(const CFraction &c, int i)
{
	return !(c>i);
}

bool operator<=(int i, const CFraction &c)
{
	return !(i>c);
}

int main()
{
	CFraction x(1,3),y(-5,10),s;
	cout<<"分数x=1/3      y=-5/10"<<endl;
	s=+x+y;
	cout<<"+x+y=";
	s.display();
	s=x-y;
	cout<<"x-y=";
	s.display();
	s=x*y;
	cout<<"x*y=";
	s.display();
	s=x/y;
	cout<<"x/y=";
	s.display();
	s=-x+y;
	cout<<"-x+y=";
	s.display();

	x.display();
	if (x>y) cout<<"大于"<<endl;
	if (x<y) cout<<"小于"<<endl;
	if (x==y) cout<<"等于"<<endl;
	y.display();
	cout<<endl;

	CFraction c1(5,3),c2;
	//以下建议在调试环境中完成测试，
	c2=c1+5;
	c2=5+c1;

	c2=c1-5;
	c2=5-c1;

	c2=c1*5;
	c2=5*c1;

	c2=c1/5;
	c2=5/c1;

	bool b;

	b=(c1>2);
	b=(2>c1);

	system("pause");
	return 0;
}