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;
}
