C++分数类（有理数类）重载四则运算、比较逻辑运算

任何有理数都可以表示为“分子/分母”的方式，其中分子、分母都是整数。

现实现一个有理数类，为这个有理数类重载四则运算（+、-、*、/）和所有的比较逻辑运算符（==、！=、>=、>、<=、<）

class Rational
{
private:
    int numerator;  // 分子
    int denominator;  // 分母
public:
    //构造函数及运算符重载的函数声明
};
//重载函数的实现及用于测试的main()函数

重载四则运算（+、-、*、/）和所有的比较逻辑运算符（==、！=、>=、>、<=、<）

---

方法一：所有重载均以类的成员函数的方式实现。

#include 
#include 
using namespace std;

class Rational{
public:
	Rational(int num=1,int denomi=1){ //构造函数，带默认参数 
		numerator = num;
		denominator = denomi;
		normalize();
	}
	Rational operator + (Rational &s); //重载加法运算 
	Rational operator - (Rational &s); //重载减法运算 
	Rational operator * (Rational &s); //重载乘法运算 
	Rational operator / (Rational &s); //重载除法运算

	bool operator > (Rational &s); //重载">"运算符 
	bool operator < (Rational &s); //重载"<"运算符 
	bool operator >= (Rational &s); //重载">="运算符 
	bool operator <= (Rational &s); //重载"<="运算符 
	bool operator == (Rational &s); //重载"=="运算符
	
	friend istream& operator >>(istream&,Rational&);
	friend ostream& operator <<(ostream&,Rational &); //重载输出运算符 
	 
	int gcd(int a,int b){
		return b?gcd(b,a%b):a;
	} 
	void normalize(); //将分数化为最简式函数 
private:
	int numerator; //分子
	int denominator; //分母 
};


void Rational::normalize(){ 
	if(denominator<0){ //保证分母大于0 
		numerator *= -1;
		denominator *= -1;
	}
	int a = abs(numerator);
	int b = abs(denominator);
	int gcd_ab = gcd(a,b); //求分子、分母的最大公约数 
	
	//分子、分母分别除以最大公约数，得到最简式 
	numerator /= gcd_ab;  
	denominator /=gcd_ab; 
} 

Rational Rational:: operator + (Rational &s){
	Rational t;
	t.numerator = numerator*s.denominator+denominator*s.numerator;
	t.denominator = denominator*s.denominator;
	return Rational(t.numerator,t.denominator);
}

Rational Rational::operator - (Rational &s){
	Rational t;
	t.numerator = numerator*s.denominator-denominator*s.numerator;
	t.denominator = denominator*s.denominator;
	return Rational(t.numerator,t.denominator);
}

Rational Rational::operator * (Rational &s){
	Rational t;
	t.numerator = numerator*s.numerator;
	t.denominator = denominator*s.denominator; 
	return Rational(t.numerator,t.denominator);
}

Rational Rational::operator / (Rational &s){
	Rational t;
	t.numerator = numerator*s.denominator;
	t.denominator = denominator*s.numerator; 
	return Rational(t.numerator,t.denominator);
} 

bool Rational::operator > (Rational &s){
	if(numerator*s.denominator-denominator*s.numerator>0)
		return true;
	else
		return false;
}

bool Rational::operator < (Rational &s){
	if(numerator*s.denominator-denominator*s.numerator<0)
		return true;
	else
		return false;
}

bool Rational::operator >= (Rational &s){
	if(numerator*s.denominator-denominator*s.numerator>=0)
		return true;
	else
		return false;
}

bool Rational::operator <= (Rational &s){
	if(numerator*s.denominator-denominator*s.numerator<=0)
		return true;
	else
		return false;
}

bool Rational::operator == (Rational &s){
	if(numerator*s.denominator-denominator*s.numerator==0)
		return true;
	else
		return false;
}

bool Rational::operator == (Rational &s){
	if(numerator*s.denominator-denominator*s.numerator!=0)
		return true;
	else
		return false;
}

istream& operator >> (istream& in,Rational &obj){
	cout << "输入分子：";
	in >> obj.numerator;
	cout << "输入分母："; 
	in >> obj.denominator;
	return in;
}
ostream& operator << (ostream& out,Rational &obj){
	if(obj.numerator==0)
		out << obj.numerator;
	if(obj.denominator==1)
		out << obj.numerator;
	else
		out << obj.numerator << '/' << obj.denominator;
	return out; 
}

int main(){
	Rational r1,r2;
	cout << "输入r1：" << endl;
	cin >> r1;
	cout << "r1 = " << r1 << endl; 
	cout << "输入r2：" << endl;
	cin >> r2;
	cout << "r2 = " << r2 << endl; 
	
	//测试四则运算运算符 
	Rational r3 = r1+r2;
	Rational r4 = r1-r2;
	Rational r5 = r1*r2;
	Rational r6 = r1/r2;	
	cout << "r1 + r2 = " << r3 << endl;
	cout << "r1 - r2 = " << r4 << endl;
	cout << "r1 * r2 = " << r5 << endl;
	cout << "r1 / r2 = " << r6 << endl;
	
	//测试比较运算符 
	if(r1>r2) cout << "r1大于r2" << endl;
	if(r1<r2) cout << "r1小于r2" << endl;
	if(r1==r2) cout << "r1等于r2" << endl;
	if(r1<=r2) cout << "r1小于等于r2" << endl;
	if(r1>=r2) cout << "r1大于等于r2" << endl;
	return 0;
}

测试1

输入：
1
3
2
3

测试2

输入：
8
9
5
7

---

**方法2：使用友元函数实现 **

#include 
#include 
using namespace std;

class Rational{
public:
	Rational(int num=1,int denomi=1){ //构造函数，带默认参数 
		numerator = num;
		denominator = denomi;
		normalize();
	}
	friend Rational operator + (Rational &,Rational &); //重载加法运算 
	friend Rational operator - (Rational &,Rational &); //重载减法运算 
	friend Rational operator * (Rational &,Rational &); //重载乘法运算 
	friend Rational operator / (Rational &,Rational &); //重载除法运算

	friend bool operator > (Rational &,Rational &); //重载">"运算符 
	friend bool operator < (Rational &,Rational &); //重载"<"运算符 
	friend bool operator >= (Rational &,Rational &); //重载">="运算符 
	friend bool operator <= (Rational &,Rational &); //重载"<="运算符 
	friend bool operator == (Rational &,Rational &); //重载"=="运算符
	
	friend istream& operator >>(istream&,Rational&);
	friend ostream& operator <<(ostream&,Rational &); //重载输出运算符 
	 
	int gcd(int a,int b){
		return b?gcd(b,a%b):a;
	} 
	void normalize(); //将分数化为最简式函数 
private:
	int numerator; //分子
	int denominator; //分母 
};


void Rational::normalize(){ 
	if(denominator<0){ //保证分母大于0 
		numerator *= -1;
		denominator *= -1;
	}
	int a = abs(numerator);
	int b = abs(denominator);
	int gcd_ab = gcd(a,b); //求分子、分母的最大公约数 
	
	//分子、分母分别除以最大公约数，得到最简式 
	numerator /= gcd_ab;  
	denominator /=gcd_ab; 
} 

Rational operator + (Rational &x,Rational &y){
	int a = x.numerator;
	int b = x.denominator;
	int c = y.numerator;
	int d = y.denominator;

	int e = a*d+c*b;
	int f = b*d;
	return Rational(e,f);
}

Rational operator - (Rational &x,Rational &y){
	int a = x.numerator;
	int b = x.denominator;
	int c = y.numerator;
	int d = y.denominator;

	int e = a*d-c*b;
	int f = b*d;
	return Rational(e,f);
}

Rational operator * (Rational &x,Rational &y){
	int a = x.numerator;
	int b = x.denominator;
	int c = y.numerator;
	int d = y.denominator;
	int e = a*c;
	int f = b*d;
	return Rational(e,f);
}

Rational operator / (Rational &x,Rational &y){
	int a = x.numerator;
	int b = x.denominator;
	int c = y.numerator;
	int d = y.denominator;
	int e = a*d;
	int f = b*c;
	return Rational(e,f);
} 

bool operator > (Rational &x,Rational &y){
	Rational p = x-y;
	return p.numerator > 0;
}

bool operator < (Rational &x,Rational &y){
	Rational p = x-y;
	return p.numerator < 0;
}

bool operator >= (Rational &x,Rational &y){
	Rational p = x-y;
	return p.numerator >= 0;
}

bool operator <= (Rational &x,Rational &y){
	Rational p = x-y;
	return p.numerator <= 0;
}

bool operator != (Rational &x,Rational &y){
	Rational p = x-y;
	return p.numerator <= 0;
	
bool operator == (Rational &x,Rational &y){
	Rational p = x-y;
	return p.numerator == 0;
}

istream& operator >> (istream& in,Rational &obj){
	cout << "输入分子：";
	in >> obj.numerator;
	cout << "输入分母："; 
	in >> obj.denominator;
	return in;
}
ostream& operator << (ostream& out,Rational &obj){
	if(obj.numerator==0)
		out << obj.numerator;
	if(obj.denominator==1)
		out << obj.numerator;
	else
		out << obj.numerator << '/' << obj.denominator;
	return out; 
}

int main(){
	Rational r1(3,5),r2(2,5);
	cout << "输入r1：" << endl;
	cin >> r1;
	cout << "r1 = " << r1 << endl; 
	cout << "输入r2：" << endl;
	cin >> r2;
	cout << "r2 = " << r2 << endl; 
	Rational r3 = r1+r2;
	Rational r4 = r1-r2;
	Rational r5 = r1*r2;
	Rational r6 = r1/r2;	
	cout << "r1 + r2 = " << r3 << endl;
	cout << "r1 - r2 = " << r4 << endl;
	cout << "r1 * r2 = " << r5 << endl;
	cout << "r1 / r2 = " << r6 << endl;
	
	return 0;
}