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C++第8周项目1 - 实现复数类中的运算符重载 - 迂者-贺利坚的专栏

[日期:2013-04-20] 来源:  作者: [字体: ]

课程首页地址:http://blog.csdn.net/sxhelijian/article/details/7910565,本周题目链接:http://blog.csdn.net/sxhelijian/article/details/8806111
【项目1-实现复数类中的运算符重载】定义一个复数类重载运算符+、-、*、/,使之能用于复数的加减乘除。
(1)任务一:请用类的成员函数完成运算符的重载;

class Complex
{public:
	Complex(){real=0;imag=0;}
	Complex(double r,double i){real=r;imag=i;}
	Complex operator+(Complex &c2);
	Complex operator-(Complex &c2);
	Complex operator*(Complex &c2);
	Complex operator/(Complex &c2);
	void display();
 private:
	double real;
	double imag;
};
//下面定义成员函数

//下面定义用于测试的main()函数
int main()
{
	Complex c1(3,4),c2(5,-10),c3;
	cout<<"c1=";
	c1.display();
	cout<<"c2=";
	c2.display();
	c3=c1+c2;
	cout<<"c1+c2=";
	c3.display();
	c3=c1-c2;
	cout<<"c1-c2=";
	c3.display();
	c3=c1*c2;
	cout<<"c1*c2=";
	c3.display();
	c3=c1/c2;
	cout<<"c1/c2=";
	c3.display();
	return 0;
}

参考解答:

#include <iostream>
using namespace std;
class Complex
{
public:
	Complex(){real=0;imag=0;}
	Complex(double r,double i){real=r;imag=i;}
	Complex operator+(Complex &c2);
	Complex operator-(Complex &c2);
	Complex operator*(Complex &c2);
	Complex operator/(Complex &c2);
	void display();
private:
	double real;
	double imag;
};
//复数相加: (a+bi)+(c+di)=(a+c)+(b+d)i. 
Complex Complex::operator+(Complex &c2)
{
	Complex c;
	c.real=real+c2.real;
	c.imag=imag+c2.imag;
	return c;
}
//复数相减:(a+bi)-(c+di)=(a-c)+(b-d)i.
Complex Complex::operator-(Complex &c2)
{
	Complex c;
	c.real=real-c2.real;
	c.imag=imag-c2.imag;
	return c;
}
//复数相乘:(a+bi)(c+di)=(ac-bd)+(bc+ad)i.
Complex Complex::operator*(Complex &c2)
{
	Complex c;
	c.real=real*c2.real-imag*c2.imag;
	c.imag=imag*c2.real+real*c2.imag;
	return c;
}

//复数相除:(a+bi)/(c+di)=(ac+bd)/(c^2+d^2) +(bc-ad)/(c^2+d^2)i 
Complex Complex::operator/(Complex &c2)
{
	Complex c;
	c.real=(real*c2.real+imag*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag);
	c.imag=(imag*c2.real-real*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag);
	return c;
}

void Complex::display()
{
	cout<<"("<<real<<","<<imag<<"i)"<<endl;
}

int main()
{
	Complex c1(3,4),c2(5,-10),c3;
	cout<<"c1=";
	c1.display();
	cout<<"c2=";
	c2.display();
	c3=c1+c2;
	cout<<"c1+c2=";
	c3.display();
	c3=c1-c2;
	cout<<"c1-c2=";
	c3.display();
	c3=c1*c2;
	cout<<"c1*c2=";
	c3.display();
	c3=c1/c2;
	cout<<"c1/c2=";
	c3.display();
	return 0;
}

(2)任务二:请用类的友元函数,而不是成员函数,完成上面提及的运算符的重载;

参考解答:

#include <iostream>
using namespace std;
class Complex
{
public:
    Complex()
    {
        real=0;
        imag=0;
    }
    Complex(double r,double i)
    {
        real=r;
        imag=i;
    }
    friend Complex operator+(Complex &c1, Complex &c2);
    friend Complex operator-(Complex &c1, Complex &c2);
    friend Complex operator*(Complex &c1, Complex &c2);
    friend Complex operator/(Complex &c1, Complex &c2);
    void display();
private:
    double real;
    double imag;
};

//复数相加:(a+bi)+(c+di)=(a+c)+(b+d)i.
Complex operator+(Complex &c1, Complex &c2)
{
    Complex c;
    c.real=c1.real+c2.real;
    c.imag=c1.imag+c2.imag;
    return c;
}

//复数相减:(a+bi)-(c+di)=(a-c)+(b-d)i.
Complex operator-(Complex &c1, Complex &c2)
{
    Complex c;
    c.real=c1.real-c2.real;
    c.imag=c1.imag-c2.imag;
    return c;
}

//复数相乘:(a+bi)(c+di)=(ac-bd)+(bc+ad)i.
Complex operator*(Complex &c1, Complex &c2)
{
    Complex c;
    c.real=c1.real*c2.real-c1.imag*c2.imag;
    c.imag=c1.imag*c2.real+c1.real*c2.imag;
    return c;
}

//复数相除:(a+bi)/(c+di)=(ac+bd)/(c^2+d^2) +(bc-ad)/(c^2+d^2)i
Complex operator/(Complex &c1, Complex &c2)
{
    Complex c;
    c.real=(c1.real*c2.real+c1.imag*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag);
    c.imag=(c1.imag*c2.real-c1.real*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag);
    return c;
}

void Complex::display()
{
    cout<<"("<<real<<","<<imag<<"i)"<<endl;
}

int main()
{
    Complex c1(3,4),c2(5,-10),c3;
    cout<<"c1=";
    c1.display();
    cout<<"c2=";
    c2.display();
    c3=c1+c2;
    cout<<"c1+c2=";
    c3.display();
    c3=c1-c2;
    cout<<"c1-c2=";
    c3.display();
    c3=c1*c2;
    cout<<"c1*c2=";
    c3.display();
    c3=c1/c2;
    cout<<"c1/c2=";
    c3.display();
    return 0;
}

事实上,运算符重载的函数还可以定义成一般函数,只不过这种做法并不好。下面给出使用一般函数完成运算符重载的程序。其中,加了序号的3处注释值得关注。

#include <iostream>
using namespace std;
class Complex
{
public:
	Complex(){real=0;imag=0;}
	Complex(double r,double i){real=r;imag=i;}
	double getReal() const {return real;}  //(1)定义公用的数据接口,可以为const成员函数
	double getImag() const {return imag;}
	void setReal(double r){real=r;}        //(1)定义公用的数据接口
	void setImag(double i){imag=i;}


	void display();
private:
	double real;
	double imag;
};

//复数相加:(a+bi)+(c+di)=(a+c)+(b+d)i.
Complex operator+(const Complex &c1, const Complex &c2) //(3)将参数处理为const更符合需求
{
	Complex c;
	c.setReal(c1.getReal()+c2.getReal());   //(2)调用公用数据接口读取和修改私有数据成员
	c.setImag(c1.getImag()+c2.getImag());
	return c;
}

//复数相减:(a+bi)-(c+di)=(a-c)+(b-d)i.
Complex operator-(const Complex &c1, const Complex &c2)
{
	Complex c;
	c.setReal(c1.getReal()-c2.getReal());
	c.setImag(c1.getImag()-c2.getImag());
	return c;
}

//复数相乘:(a+bi)(c+di)=(ac-bd)+(bc+ad)i.
Complex operator*(const Complex &c1, const Complex &c2)
{
	Complex c;
	c.setReal(c1.getReal()*c2.getReal()-c1.getImag()*c2.getImag());
	c.setImag(c1.getImag()*c2.getReal()+c1.getReal()*c2.getImag());
	return c;
}

//复数相除:(a+bi)/(c+di)=(ac+bd)/(c^2+d^2) +(bc-ad)/(c^2+d^2)i
Complex operator/(const Complex &c1, const Complex &c2)
{
	Complex c;
	double d= (c2.getReal()*c2.getReal()+c2.getImag()*c2.getImag());
	c.setReal((c1.getReal()*c2.getReal()+c1.getImag()*c2.getImag())/d);
	c.setImag((c1.getImag()*c2.getReal()-c1.getReal()*c2.getImag())/d);
	return c;
}

void Complex::display()
{
	cout<<"("<<real<<","<<imag<<"i)"<<endl;
}

int main()
{
	Complex c1(3,4),c2(5,-10),c3;
	cout<<"c1=";
	c1.display();
	cout<<"c2=";
	c2.display();
	c3=c1+c2;
	cout<<"c1+c2=";
	c3.display();
	c3=c1-c2;
	cout<<"c1-c2=";
	c3.display();
	c3=c1*c2;
	cout<<"c1*c2=";
	c3.display();
	c3=c1/c2;
	cout<<"c1/c2=";
	c3.display();
	return 0;
}

(3)任务三:在任务二的基础上,扩展+、-、*、/运算符的功能,使之能与double型数据进行运算。设Complex c; double d; c?d和d?c的结果为“将d视为实部为d的复数同c运算”的结果(其中?为+、-、*、/之一)。另外,再定义一目运算符 -,-c相当于0-c。

#include <iostream>
using namespace std;
class Complex
{
public:
	Complex(){real=0;imag=0;}
	Complex(double r,double i){real=r;imag=i;}
	Complex operator-();
	friend Complex operator+(Complex &c1, Complex &c2);
	friend Complex operator+(double d1, Complex &c2);
	friend Complex operator+(Complex &c1, double d2);
	friend Complex operator-(Complex &c1, Complex &c2);
	friend Complex operator-(double d1, Complex &c2);
	friend Complex operator-(Complex &c1, double d2);
	friend Complex operator*(Complex &c1, Complex &c2);
	friend Complex operator*(double d1, Complex &c2);
	friend Complex operator*(Complex &c1, double d2);
	friend Complex operator/(Complex &c1, Complex &c2);
	friend Complex operator/(double d1, Complex &c2);
	friend Complex operator/(Complex &c1, double d2);
	void display();
private:
	double real;
	double imag;
};

Complex Complex::operator-()
{
	return(0-*this);
}

//复数相加:(a+bi)+(c+di)=(a+c)+(b+d)i. 
Complex operator+(Complex &c1, Complex &c2)
{
	Complex c;
	c.real=c1.real+c2.real;
	c.imag=c1.imag+c2.imag;
	return c;
}
Complex operator+(double d1, Complex &c2)
{
	Complex c(d1,0);
	return c+c2; //按运算法则计算的确可以,但充分利用已经定义好的代码,既省人力,也避免引入新的错误,但可能机器的效率会不佳
}
Complex operator+(Complex &c1, double d2)
{
	Complex c(d2,0);
	return c1+c;
}
//复数相减:(a+bi)-(c+di)=(a-c)+(b-d)i.
Complex operator-(Complex &c1, Complex &c2)
{
	Complex c;
	c.real=c1.real-c2.real;
	c.imag=c1.imag-c2.imag;
	return c;
}
Complex operator-(double d1, Complex &c2)
{
	Complex c(d1,0);
	return c-c2;  
}
Complex operator-(Complex &c1, double d2)
{
	Complex c(d2,0);
	return c1-c;
}

//复数相乘:(a+bi)(c+di)=(ac-bd)+(bc+ad)i.
Complex operator*(Complex &c1, Complex &c2)
{
	Complex c;
	c.real=c1.real*c2.real-c1.imag*c2.imag;
	c.imag=c1.imag*c2.real+c1.real*c2.imag;
	return c;
}
Complex operator*(double d1, Complex &c2)
{
	Complex c(d1,0);
	return c*c2;
}
Complex operator*(Complex &c1, double d2)
{
	Complex c(d2,0);
	return c1*c;
}

//复数相除:(a+bi)/(c+di)=(ac+bd)/(c^2+d^2) +(bc-ad)/(c^2+d^2)i 
Complex operator/(Complex &c1, Complex &c2)
{
	Complex c;
	c.real=(c1.real*c2.real+c1.imag*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag);
	c.imag=(c1.imag*c2.real-c1.real*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag);
	return c;
}
Complex operator/(double d1, Complex &c2)
{
	Complex c(d1,0);
	return c/c2;
}
Complex operator/(Complex &c1, double d2)
{
	Complex c(d2,0);
	return c1/c;
}

void Complex::display()
{
	cout<<"("<<real<<","<<imag<<"i)"<<endl;
}

int main()
{
	Complex c1(3,4),c2(5,-10),c3;
	double d=11;
	cout<<"c1="; c1.display();
	cout<<"c2="; c2.display();
	cout<<"d="<<d<<endl;
	cout<<"-c1=";(-c1).display();
	c3=c1+c2;
	cout<<"c1+c2="; c3.display();
	cout<<"c1+d=";	(c1+d).display();
	cout<<"d+c1=";	(d+c1).display();
	c3=c1-c2;
	cout<<"c1-c2="; c3.display();
	cout<<"c1-d=";	(c1-d).display();
	cout<<"d-c1=";	(d-c1).display();
	c3=c1*c2;
	cout<<"c1*c2="; c3.display();
	cout<<"c1*d=";	(c1*d).display();
	cout<<"d*c1=";	(d*c1).display();
	c3=c1/c2;
	cout<<"c1/c2=";	c3.display();
	cout<<"c1/d=";	(c1/d).display();
	cout<<"d/c1=";	(d/c1).display();

	system("pause");
	return 0;
}






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