C++实践参考——复数类中的运算符重载

【项目-实现复数类中的运算符重载】
（1）请用类的成员函数，定义复数类重载运算符+、-、*、/，使之能用于复数的加减乘除
class Complex
{
public:
Complex(){real=0;imag=0;}
Complex(double r,double i){real=r; imag=i;}
Complex operator+(const Complex &c2);
Complex operator-(const Complex &c2);
Complex operator*(const Complex &c2);
Complex operator/(const 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+(const Complex &c2);
Complex operator-(const Complex &c2);
Complex operator*(const Complex &c2);
Complex operator/(const Complex &c2);
void display();
private:
double real;
double imag;
};
//下面定义成员函数
//复数相加： (a+bi)+(c+di)=(a+c)+(b+d)i.
Complex Complex::operator+(const 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-(const Complex &c2)
{
Complex c;
c.real=real-c2.real;
c.imag=imag-c2.imag;
return c;
}
Complex Complex::operator*(const Complex &c2)
{
Complex c;
c.real=real*c2.real-imag*c2.imag;
c.imag=imag*c2.real+real*c2.imag;
return c;
}

Complex Complex::operator/(const 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;
}
//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;
}

（2）请用类的友元函数，而不是成员函数，再次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;
}

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/(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，加了序号的几处注释值得关注。

#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;
}

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;
}

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）定义一个定义完整的类（是可以当作独立的产品发布，成为众多项目中的“基础工程”）。这样的类在(2)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相加”，其他-、*、/运算符类似。
[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+(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;
};

//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;
}

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;
}

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<<endl;
cout<<"下面是重载运算符的计算结果: "<<endl;
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();
return 0;
}

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