1.特性

• 复数类应该具有的操作
  • 运算：+，-，*，/
  • 比较：==，！=
  • 赋值：=
  • 求模：modulus
• 利用操作符重载
  • 统一复数与实数的运算方式
  • 统一复数与实数的比较方式

Complex operator+(const Complex& c);   
Complex operator-(const Complex& c);   
Complex operator*(const Complex& c);   
Complex operator/(const Complex& c);   
  
bool operator==(const Complex& c);   
bool operator!=(const Complex& c);   
  
Complex& operator=(const Complex& c);   
//在对象需要使用这些操作符时，会使用这些操作符

2、编程实验

• 复数类的实现   
• Complex.h

#include "Complex.h"
#include "math.h"

Complex::Complex(double a, double b)
{
	this->a = a;
	this->b = b;
}

double Complex::getA()
{
	return a;
}

double Complex::getB() 
{
	return b;
}

double Complex::getModulus() 
{
	return sqrt(a*a + b * b);
}

Complex Complex::operator+(const Complex &c) 
{
	double na = a + c.a;
	double nb = b + c.b;
	Complex ret(na, nb);
	
	return ret;
}

Complex Complex::operator-(const Complex& c) 
{
	double na = a - c.a;
	double nb = b - c.b;
	Complex ret(na, nb);
	
	return ret;
}

Complex Complex::operator*(const Complex &c) 
{
	double na = a * c.a - b * c.b;
	double nb = a * c.b + b * c.a;
	Complex ret(na, nb);
	
	return ret;
}

Complex Complex::operator/(const Complex& c) 
{
	double cm = c.a*c.a + c.b*c.b;
	double na = (a*c.a + b * c.b) / cm;
	double nb = (b*c.a - a * c.b) / cm;
	Complex ret(na, nb);
	
	return ret;
}

bool Complex::operator==(const Complex &c) 
{
	return (a == c.a) && (b == c.b);
}

bool Complex::operator!=(const Complex &c) 
{
	return !(*this == c);
}

Complex& Complex::operator=(const Complex &c) 
{
	if (this != &c) 
	{
		a = c.a;
		b = c.b;
	}
	
	return *this;
}

• Complex.c

#include "Complex.h"
#include "math.h"

Complex::Complex(double a, double b)
{
	this->a = a;
	this->b = b;
}

double Complex::getA()
{
	return a;
}

double Complex::getB() 
{
	return b;
}

double Complex::getModulus() 
{
	return sqrt(a*a + b * b);
}

Complex Complex::operator+(const Complex &c) 
{
	double na = a + c.a;
	double nb = b + c.b;
	Complex ret(na, nb);
	
	return ret;
}

Complex Complex::operator-(const Complex& c) 
{
	double na = a - c.a;
	double nb = b - c.b;
	Complex ret(na, nb);
	
	return ret;
}

Complex Complex::operator*(const Complex &c) 
{
	double na = a * c.a - b * c.b;
	double nb = a * c.b + b * c.a;
	Complex ret(na, nb);
	
	return ret;
}

Complex Complex::operator/(const Complex& c) 
{
	double cm = c.a*c.a + c.b*c.b;
	double na = (a*c.a + b * c.b) / cm;
	double nb = (b*c.a - a * c.b) / cm;
	Complex ret(na, nb);
	
	return ret;
}

bool Complex::operator==(const Complex &c) 
{
	return (a == c.a) && (b == c.b);
}

bool Complex::operator!=(const Complex &c) 
{
	return !(*this == c);
}

Complex& Complex::operator=(const Complex &c) 
{
	if (this != &c) 
	{
		a = c.a;
		b = c.b;
	}
	
	return *this;
}

• main.cpp

#include <stdio.h>
#include "Complex.h"

int main() 
{
	Complex c1(1, 2);
	Complex c2(3, 6);
	Complex c3 = c2 - c1;
	Complex c4 = c1 * c3;
	Complex c5 = c2 / c1;

	printf("c3.a = %f, c3.b = %f\n", c3.getA(), c3.getB());
	printf("c4.a = %f, c4.b = %f\n", c4.getA(), c4.getB());
	printf("c5.a = %f, c5.b = %f\n", c5.getA(), c5.getB());

	Complex c6(2, 4);

	printf("c3 == c6 : %d\n", c3 == c6);
	printf("c3 != c4 : %d\n", c3 != c4);

	(c3 = c2) = c1;

	printf("c1.a = %f, c1.b = %f\n", c1.getA(), c1.getB());
	printf("c2.a = %f, c2.b = %f\n", c2.getA(), c2.getB());
	printf("c3.a = %f, c3.b = %f\n", c3.getA(), c3.getB());

	return 0;
}

• 运行结果

• 仔细观察this指针的灵活使用

3.注意事项

• C++规定赋值操作符（=）只能重载为成员函数
• 操作符重载不能改变原操作符的优先级
• 操作符重载不能改变操作数的个数
• 操作符重载不应改变操作符的原有语义

4.总结

• 复数的概念可以通过自定义类实现
• 复数中的运算操作可以通过操作符重载实现
• 赋值操作符只能通过成员函数实现
• 操作符重载的本质为函数定义