[C++知识库]C++运算符重载（有理数+-*/）

#include <iostream>
#include <string>
#include <stdlib.h>

class Rational
{
public:
	Rational(int num,int denom); //num == 分子，denom == 分母

	Rational operator+(Rational rhs); // rhs == right hand side
	Rational operator-(Rational rhs);
	Rational operator*(Rational rhs);
	Rational operator/(Rational rhs);

	void print();

private:
	void normalize(); //负责对分数的简化处理

	int numerator;		// 分子
	int denominator;   //  分母
};

Rational::Rational(int num,int denom)
{
	numerator = num;
	denominator = denom;

	normalize();
}
/*
normalize()对分数进行简化操作包括：
	1.只允许分子为负数，如果分母为负数则把负数挪到分子部分，如 1/-2 = -1/2
	2.利用欧几里得算法(辗转求余原理)将分数进行简化，如 2/8 = 1/4
*/
void Rational::normalize()
{
	//确保分母为正
	if(denominator < 0){
		numerator = -numerator;
		denominator = -denominator;
	}

	//欧几里得算法
	int a = abs(numerator);
	int b = abs(denominator);

	//求出最大公约数
	while(b > 0 ){
		int t = a % b;
		a = b;
		b = t;
	}

	// 分子、分母分别除以最大公约数得到最简化分数
	numerator /= a;
	denominator /= a;

}
/********加法*************************
 a    c     a*d    c*b     a*d  +  c*b
 -  + -  =  ---  + ---  =  -----------
 b    d     b*d    b*d        b*d
 */
Rational Rational::operator+(Rational rhs)
{
	int a = numerator;
	int b = denominator;
	int c = rhs.numerator;
	int d = rhs.denominator;

	int e = a*b + c*d;
	int f = b*d;

	return Rational(e,f);
}
/********减法*************************
 a    c     a    -c     
 -  - -  =  -  + -- 
 b    d     b    d 
 */
Rational Rational::operator-(Rational rhs)
{
	rhs.numerator = -rhs.numerator;

	return operator+(rhs);
}
/********乘法*************************
 a    c        a*d  +  c*b
 -  * -  =     -----------
 b    d            b*d
 */
Rational Rational::operator*(Rational rhs)
{
	int a = numerator;
	int b = denominator;
	int c = rhs.numerator;
	int d = rhs.denominator;

	int e = a*c;
	int f = b*d;

	return Rational(e,f);
}
/********除法*************************
 a    c        a  d   
 -  / -  =     - * -
 b    d        b  c
 */
Rational Rational::operator/(Rational rhs)
{
	int t = rhs.numerator;
	rhs.numerator = rhs.denominator;
	rhs.denominator = t;

	return operator*(rhs);
}
void Rational::print() // 1/4
{
	if( numerator % denominator == 0)
		std::cout << numerator / denominator;
	else
		std::cout << numerator << "/" << denominator;
}
int main(int argc, char const *argv[])
{
	Rational f1(2 ,8);
	Rational f2(8 ,3);

	//测试有理数加法运算
	Rational res = f1 + f2;
	f1.print();
	std::cout << " + ";
	f2.print();
	std::cout << " = ";
	res.print();
	std::cout << "\n";
	return 0;
}