第八週上級項目1 實現複數類中的運算符重載

（1）請用類的成員函數，定義複數類重載運算符+、-、*、/，使之能用於複數的加減乘除

/*
* Copyright (c) 2015,煙臺大學計算機學院
* All right reserved.
* 作者：曹莉萍
* 文件：Demo.cpp
* 完成時間：2015年05月16日
* 版本號：v1.0
*/
#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;
};
//下面定義成員函數
//複數相加： (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;
}
//複數相減：(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;
}
//複數相乘：(a+bi)(c+di)=(ac－bd)+(bc+ad)i.
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;
}

//複數相除：(a+bi)/(c+di)=(ac+bd)/(c^2+d^2) +(bc-ad)/(c^2+d^2)i
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;
}
//下面定義用於測試的main()函數
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）請用類的友元函數，而不是成員函數，再次完成上面提及的運算符的重載；

/*
* Copyright (c) 2015,煙臺大學計算機學院
* All right reserved.
* 作者：曹莉萍
* 文件：Demo.cpp
* 完成時間：2015年05月16日
* 版本號：v1.0
*/
#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;
};

//複數相加：(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;
}

//複數相減：(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;
}

//複數相乘：(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;
}

//複數相除：(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;
}

（3）定義一個定義完整的類（是可以當作獨立的產品發佈，成爲衆多項目中的“基礎工程”）。這樣的類在(2)的基礎上，擴展+、-、*、/運算符的功能，使之能與double型數據進行運算。設Complex c; double d; c+d和d+c的結果爲“將d視爲實部爲d的複數同c相加”，其他-、*、/運算符類似。

/*
* Copyright (c) 2015,煙臺大學計算機學院
* All right reserved.
* 作者：曹莉萍
* 文件：Demo.cpp
* 完成時間：2015年05月16日
* 版本號：v1.0
*/
#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;
};

//複數相加：(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; //按運算法則計算的確可以，但充分利用已經定義好的代碼，既省人力，也避免引入新的錯誤，但可能機器的效率會不佳
}
Complex operator+(Complex &c1, double d2)
{    Complex c(d2,0);
    return c1+c;
}
//複數相減：(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;
}

//複數相乘：(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;
}

//複數相除：(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<<endl;
    cout<<"下面是重載運算符的計算結果: "<<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;
}