C++中采用操作符重载完善复数类

1，复数类应该具有的操作：

    1，运算：+，-，*，/；

    2，比较：==，!=；

    3，赋值：=；

    4，求模：modulus；

 （5），完善的复数类操作符重载必不可少；

   

2，利用操作符重载：

    1，统一复数与实数的运算方式；

       1，Complex operator + (const Complex& c);

       2，Complex operator - (const Complex& c);

       3，Complex operator * (const Complex& c);

       4，Complex operator / (const Complex& c);

    2，统一复数域实数的比较方式；

       1，bool operator == (const Complex& c);

       2，bool operator != (const Complex& c);

    3，赋值操作符：

       1，Complex& operator = (const Complex& c);

       2，特殊在只能将赋值操作符作为成员函数来实现；

    4，这些成员函数是普通的函数，只不过使用了 operator 作为函数名的一部分，   因此就成为了操作符重载函数；

   

3，复数类的实现编程实验：

    1，Complex.h 文件： 

#ifndef _COMPLEX_H_
#define _COMPLEX_H_

class Complex
{
    double a;
    double b;
public:
    Complex(double a = 0, double b = 0);
    double getA();
    double getB();
    double getModulus();
    
    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);  
};

#endif

　2，Complex.cpp 文件：

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

Complex::Complex(double a, double b)// 默认值只能在函数声明的地方指定；
{
    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);  // 将实部和虚部指定进去；
    
    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;  // 赋值操作可以连续，所以要返回左操作数；
}

　3，main.cpp 文件：

#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
", c3.getA(), c3.getB());
    printf("c4.a = %f, c4.b = %f
", c4.getA(), c4.getB());
    printf("c5.a = %f, c5.b = %f
", c5.getA(), c5.getB());
    
    Complex c6(2, 4);
    
    printf("c3 == c6 : %d
", c3 == c6);
    printf("c3 != c4 : %d
", c3 != c4);
    
    (c3 = c2) = c1;
    
    printf("c1.a = %f, c1.b = %f
", c1.getA(), c1.getB());
    printf("c2.a = %f, c2.b = %f
", c2.getA(), c2.getB());
    printf("c3.a = %f, c3.b = %f
", c3.getA(), c3.getB());
    
    return 0;
}

　4，输出结果：

c3.a = 2.000000, c3.b = 4.000000
c4.a = -6.000000, c4.b = 8.000000
c5.a = 3.000000, c5.b = 0.000000
c3 == c6 : 1
c3 != c4 : 1
c1.a = 1.000000, c1.b = 2.000000
c2.a = 3.000000, c2.b = 6.000000
c3.a = 1.000000, c3.b = 2.000000

   

4，注意事项：

    1，C++ 规定赋值操作符（=）只能重载为成员函数；

    2，操作符重载不能改变原操作符的优先级；

    3，操作符重载不能改变操作数的个数；

    4，操作符重载不应改变操作符的原有语义；

   

5，小结：

    1，复数的概念可以通过自定义类实现；

    2，复数中的运算操作可以通过操作符重载实现；

    3，赋值操作符只能通过成员函数实现；

    4，操作符重载的本质为函数定义；

       1，定义新的函数扩展已有功能；