运算符重载(复杂的相关计算)

       运算符重载实际上是一种特殊的函数重载，你必须定义一个函数。并告诉C++翻译器，当遇到重载运算符调用该函数。该功能称为运算符重载函数，通常类的成员函数。
　    定义运算符重载函数的一般格式：
返回值类型 类名::operator重载的运算符(參数表)
{……}

operator是keyword。它与重载的运算符一起构成函数名。

因函数名的特殊性。C++编译器能够将这类函数识别出来。

详细的加减乘除等代码运算例如以下：

<span style="font-size:18px;">#include<iostream>
#include<string>
using namespace std;

class Complex;                                       //提前声明
Complex operator+(int x, Complex &c);                //整数和对象的运算   
ostream& operator<<(ostream &out, const Complex &c); //输出流
istream& operator>>(istream &in, Complex &c);        //输入流

class Complex                                        //定义Complex类
{
	friend istream& operator>>(istream &in, Complex &c);//定义友元，能够訪问私有成员
	friend ostream& operator<<(ostream &out, const Complex &c);
	friend Complex operator+(int x, Complex &c);
public:
	Complex(const double real=0,const double imag=0):m_real(real),m_imag(imag)//构造函数（初始化）
	{}
	~Complex()                                       //析构函数
	{}
	void Show()const                                 //显示
	{
		cout<<"("<<m_real<<","<<m_imag<<")"<<endl;
	}
	Complex operator+(int x)                         //整型加
	{
		return Complex(m_real+x,m_imag);
	}
	Complex operator+(Complex &c)                    //对象加
	{
		return Complex(m_real+c.m_real,m_imag+c.m_imag);
	}
	Complex operator-(Complex &c)                    //对象减
	{
		return Complex(m_real-c.m_real,m_imag-c.m_imag);
	}
	Complex operator*(Complex &c)                    //对象乘
	{
		return Complex(m_real*c.m_real-m_imag*c.m_imag,
			   m_real*c.m_imag+m_imag*c.m_real);
	}
	Complex operator/(Complex &c)                    //对象除
	{
		double t = c.m_real*c.m_real+ c.m_imag * c.m_imag;//分母
		return Complex((m_real *c.m_real+ m_imag * c.m_imag)/t,
			   (m_imag *c.m_real - m_real * c.m_imag)/t);
	}
	Complex operator+=(Complex &c)                    //对象加等于
	{ 
		return Complex(m_real+m_real+c.m_real,m_imag+m_imag+c.m_imag);
	}
	Complex operator-=(Complex &c)                    //对象减等于
	{
		return Complex(c.m_real,c.m_imag);
	}
	Complex operator*=(Complex &c)                    //对象乘等于
	{
		return Complex(m_real*m_real*c.m_real-m_real*m_imag*
			c.m_imag-m_imag*m_real*c.m_imag-m_imag*m_imag*c.m_real ,
			m_real*m_real*c.m_imag+m_real*m_imag*c.m_real+
			m_imag*m_real*c.m_real-m_imag*m_imag*c.m_imag);
	}
	Complex operator/=(Complex &c)                    //对象除等于
	{
		double t = c.m_real*c.m_real+ c.m_imag * c.m_imag;//分母的分母
		double m = (((m_real *c.m_real+ m_imag * c.m_imag)/t)*//分母
			((m_real *c.m_real+ m_imag * c.m_imag)/t)
			+((m_imag *c.m_real - m_real * c.m_imag)/t)*
			((m_imag *c.m_real - m_real * c.m_imag)/t));
		double a = (m_real *c.m_real+ m_imag * c.m_imag)/t;//后值的实部
		double b = (m_imag *c.m_real - m_real * c.m_imag)/t;//后值的虚部
		return Complex((m_real*a-m_imag*b)/m,(m_imag*a+m_real*b)/m);
	}
private:
	double m_real;                                           //私有成员
	double m_imag;                                           //私有成员
};

Complex operator+(int x, Complex &c)                         //类外定义
{
	return Complex(x+c.m_real,c.m_imag);
}

ostream& operator<<(ostream &out, const Complex &c)
{
	out<<"("<<c.m_real<<","<<c.m_imag<<")";
	return out;
}

istream& operator>>(istream &in, Complex &c)
{
	in>>c.m_real>>c.m_imag;
	return in;
}

void main()                                                  //函数測试
{
	Complex c1(1,2);
	Complex c2(2,3);

	Complex n;
	int s;
	cin >> s; 
	n = s;
	cout<<n<<endl;

	Complex a;
	a = c1 + c2;
	cout<<a<<endl;

	Complex b;
	b = c1 - c2;
	cout<<b<<endl;

	Complex c;
	c = c1 * c2;
	cout<<c<<endl;

	Complex d;
	d = c1 / c2;
	cout<<d<<endl;

	Complex e;
	e = c1 += c2;
	cout<<e<<endl;

	Complex f;
	f = c1 -= c2;
	cout<<f<<endl;

	Complex g;
	g = c1 *= c2;
	cout<<g<<endl;

	Complex k;
	k = c1 /= c2;
	cout<<k<<endl;

	Complex l;
	int x;
	cin >> x;
	l = x + c1;
	cout<<l<<endl;
}</span>

假设有不完好的地方希望大家能够指出，谢谢~

在后期的学习中。我发现对于+=、-=、*=、/=的理解有错误。改正例如以下：

<span style="font-size:18px;">Complex operator+=(Complex &c)                    //对象加等于
	{ 
		m_real = m_real+c.m_real;
		m_imag = m_imag+c.m_imag;
		return *this;
	}
	Complex operator-=(Complex &c)                    //对象减等于
	{
		m_real = m_real-c.m_real;
		m_imag = m_imag-c.m_imag;
		return *this;
	}
	Complex operator*=(Complex &c)                    //对象乘等于
	{
		int new_m_real = m_real;
		m_real = m_real*c.m_real-m_imag*c.m_imag;
		m_imag = new_m_real*c.m_imag+m_imag*c.m_real;
		return *this;
	}
	Complex operator/=(Complex &c)                        //对象除等于
	{
		double t = c.m_real*c.m_real+ c.m_imag * c.m_imag;//分母
		int new_m_real = m_real;
		m_real = (m_real *c.m_real+ m_imag * c.m_imag)/t;
		m_imag = (m_imag *c.m_real - new_m_real * c.m_imag)/t;
		return *this;
	}</span>

注：在进行測试时。因为+=、-=、*=、/=它会改变原来值，无需单独测试。

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