第八周【项目1-实现复数类中的运算符重载】

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本文详细介绍了如何使用类的成员函数和友元函数重载复数的加、减、乘、除运算符，并通过代码示例展示了实现过程。

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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

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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;

}

代码如下：

#include<iostream>
using namespace std;
class Complex
{
private:
    double real;
    double imag;
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();
};
//下面定义成员函数
void Complex::display()
{
    cout<<"("<<real<<";"<<imag<<")"<<endl;
}
Complex Complex::operator/(const Complex &c2)
{
    Complex x;
    x.real=(real*c2.real+imag*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag);
    x.imag=(imag*c2.real-real*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag);
    return x;
}
Complex Complex::operator*(const Complex &c2)
{
    Complex x;
    x.real=(real*c2.real-imag*c2.imag);
    x.imag=(imag*c2.real+real*c2.imag);
    return x;
}
Complex Complex::operator-(const Complex &c2)
{
    Complex x;
    x.real=real-c2.real;
    x.imag=imag-c2.imag;
    return x;
}
Complex Complex::operator+(const Complex &c2)
{
    Complex x;
    x.real=real+c2.real;
    x.imag=imag+c2.imag;
    return x;
}

//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）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

#include<iostream>
using namespace std;
class Complex
{
private:
    double real;
    double imag;
public:
    Complex()
    {
        real=0;
        imag=0;
    }
    Complex(double r,double i)
    {
        real=r;
        imag=i;
    }
    friend Complex operator+(const Complex &c1,const Complex &c2);
    friend Complex operator-(const Complex &c1,const Complex &c2);
    friend Complex operator*(const Complex &c1,const Complex &c2);
    friend Complex operator/(const Complex &c1,const Complex &c2);
    void display();
};
//下面定义成员函数
void Complex::display()
{
    cout<<"("<<real<<";"<<imag<<")"<<endl;
}
Complex operator/(const Complex &c1,const Complex &c2)
{
    Complex x;
    x.real=(c1.real*c2.real+c1.imag*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag);
    x.imag=(c1.imag*c2.real-c1.real*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag);
    return x;
}
Complex operator*(const Complex &c1,const Complex &c2)
{
    Complex x;
    x.real=(c1.real*c2.real-c1.imag*c2.imag);
    x.imag=(c1.imag*c2.real+c1.real*c2.imag);
    return x;
}
Complex operator-(const Complex &c1,const Complex &c2)
{
    Complex x;
    x.real=c1.real-c2.real;
    x.imag=c1.imag-c2.imag;
    return x;
}
Complex operator+(const Complex &c1,const Complex &c2)
{
    Complex x;
    x.real=c1.real+c2.real;
    x.imag=c1.imag+c2.imag;
    return x;
}

//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;
}

（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。

<pre name="code" class="cpp">#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);
    Complex operator+(double n);
    Complex operator -(double n);
    Complex operator*(double n);
    Complex operator/(double n);
    friend Complex operator+(double n,const Complex &c2 );
    friend Complex operator-(double n,const Complex &c2);
    friend Complex operator*(double n,const Complex &c2);
    friend Complex operator/(double n,const Complex &c2);
    void display();
private:
    double real;
    double imag;
};
//下面定义成员函数
Complex operator/(double n,const Complex &c2)
{
    return Complex(c2.real*n,c2.real*n);
}
Complex operator*(double n,const Complex &c2)
{
    return Complex(c2.real*n,c2.imag*n);
}
Complex operator-(double n,const Complex &c2)
{
    return Complex(n-c2.real,-c2.imag);
}
Complex operator+(double n,const Complex &c2 )
{
    return Complex(c2.real+n,c2.imag);
}
Complex Complex::operator-(double n)
{
    Complex x;
    x.real=real-n;
    x.imag=imag;
    return x;
}
Complex Complex::operator/(double n)
{
    Complex x;
    x.real=real/n;
    x.imag=imag/n;
    return x;
}
Complex Complex::operator*(double n)
{
    Complex x;
    x.real=real*n;
    x.imag=imag*n;
    return x;
}
Complex Complex::operator+(double n)
{
    Complex x;
    x.real=real+n;
    x.imag=imag;
    return(x);
}
void Complex::display()
{
    cout<<"("<<real<<";"<<imag<<")"<<endl;
}
Complex Complex::operator/(const Complex &c2)
{
    Complex x;
    x.real=(real*c2.real+imag*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag);
    x.imag=(imag*c2.real-real*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag);
    return x;
}
Complex Complex::operator*(const Complex &c2)
{
    Complex x;
    x.real=(real*c2.real-imag*c2.imag);
    x.imag=(imag*c2.real+real*c2.imag);
    return x;
}
Complex Complex::operator-(const Complex &c2)
{
    Complex x;
    x.real=real-c2.real;
    x.imag=imag-c2.imag;
    return x;
}
Complex Complex::operator+(const Complex &c2)
{
    Complex x;
    x.real=real+c2.real;
    x.imag=imag+c2.imag;
    return x;
}

//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();
    c3=c1+2;
    cout<<"c1+2=";
    c3.display();
    c3=3+c2;
    cout<<"3+c2=";
    c3.display();
    return 0;
}

类就是解决一类问题，运算符的重载方便了人们解救相似问题的方法。