C++分数类（有理数类）重载四则运算、比较逻辑运算

以你之姓@ 2022-12-20 09:05 257阅读 0赞

**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 <iostream>
    #include <cmath>
    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1结果][1]  
**测试2**

输入：
    8
    9
    5
    7

![测试2结果][2]

--------------------

\*\*方法2：使用友元函数实现 \*\*

#include <iostream>
    #include <cmath>
    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;
    }

[1]: /images/20221120/4bff38d1e27f466b9fc9e4829a4b98b9.png
[2]: https://img-blog.csdnimg.cn/20201111192020971.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L01hcms3NzU4,size_16,color_FFFFFF,t_70#pic_center