类（运算符重载）实现有理数的加减乘除

喜欢ヅ旅行 2023-06-24 12:28 4阅读 0赞

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**补充概念：有理数 = 可以用分数表达的数**

**代码如下：**

#include <iostream>
    #include <cmath>
    int gcd(int a,int b)
    { 
        return b==0?a:gcd(b,a%b);
    }
    class Rational
    { 
    	public:
    		Rational(int num,int denom); // num =分子，denom =分母
    		Rational operator +(Rational rhs);
    		Rational operator -(Rational rhs);
    		Rational operator *(Rational rhs);
    		Rational operator /(Rational rhs);
    		void print();
    	private:
    		void hj(); //负责对分数的简化处理
    		int fz; // 分子
    		int fm; // 分母
    };
    Rational::Rational(int num,int denom )
    { 
    	fz = num;
    	fm = denom;
    	hj();
    }
    // hj()对分数进行简化的操作包括:
    // 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.表示最简分数：A / B = (A/gcd(A,B)) / (B/gcd(A,B))，只要把 A,B最大公约数去除掉就可以了
    void Rational::hj()
    { 
    	//确保分母为正
    	if(fm<0)
    	{ 
    	fz = -fz;
    	fm = -fm;
    	}
    	//欧几里德算法
    	int a = abs (fz);
    	int b = abs (fm);
    	//求出最大公约数
    	int gcd_max = gcd(a,b);
    	//分子、分母分别除以最大公约数得到最简化分数
    	fz /= gcd_max;
    	fm /= gcd_max;
    }
    //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 = fz ;
    	int b = fm;
    	int c = rhs.fz;
    	int d = rhs.fm;
    	int e = a*b + c*d;
    	int f = b*d;
    	return Rational(e,f);
    }
    //a c a -c
    //- - - = - + --
    //b d b d
    Rational Rational::operator -(Rational rhs) //分子变成负数，再使用加法函数
    { 
    	rhs.fz = -rhs.fz;
    	return operator +(rhs);
    }
    //a c a*c
    //- * - = ---
    //b d b*d
    Rational Rational:: operator *(Rational rhs)
    { 
    	int a = fz;
    	int b = fm;
    	int c = rhs.fz;
    	int d = rhs.fm;
    	
    	int e = a*c;
    	int f = b*d;
    	return Rational(e,f);
    }
    //a c a d
    //- / - = - * -
    //b d b c
    Rational Rational:: operator /(Rational rhs) //分子分母倒过来，再使用乘法函数
    { 
    	int t = rhs.fz;
    	rhs.fz = rhs.fm;
    	rhs.fm = t;
    	return operator*(rhs) ;
    }
    void Rational::print() //判断输入整数还是分数
    { 
    	if( fz % fm == 0 )
    	std::cout << fz / fm;
    	else
    	std::cout << fz << "/" << fm;
    }
    int main()
    { 
    	Rational f1(2,16);
    	Rational f2(7,8);
    	//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";
    	// 测试有理数减法运算
    	res=f1-f2;
    	f1.print();
    	std::cout <<" - ";
    	f2.print();
    	std::cout <<" = ";
    	res.print();
    	return 0;
    }

纯手打…不容易

output:
    1/8 + 7/8 = 1
    1/8 - 7/8 = -3/4

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