第31课 完善的复数类

1. 复数类应具有的操作

（1）运算：+、-、*、/

（2）比较：==、!=

（3）赋值：=

（4）求模：modulus

2. 利用操作符重载

（1）统一复数与实数的运算方式

• Complex operator + (const Complex& c);

• Complex operator - (const Complex& c);

• Complex operator * (const Complex& c);

• Complex operator / (const Complex& c);

• Complex& operator = (const Complex& c);//赋值

（2）统一复数与实数的比较方式

• bool operator == (const Complex& c);

• bool operator != (const Complex& c);

【编程实验】复数类的实现   Complex.cpp

//Complex.h

#ifndef _COMPLEX_H_

#define _COMPLEX_H_

 

class Complex

{

private:

    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

//Complex.cpp

#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;

 

    return Complex(na, nb);

}

 

Complex Complex::operator - (const Complex& c)

{

    double na = a - c.a;

    double nb = b - c.b;

 

    return Complex(na, nb);

}

 

Complex Complex::operator * (const Complex& c)

{

    double na = a * c.a - b * c.b;

    double nb = a * c.b - b * c.a;

 

    return Complex(na, nb);

}

 

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;

 

    return  Complex(na, nb);

}

   

bool Complex::operator == (const Complex& c)

{

    return (a == c.a) && (b == c.b);

}

 

bool Complex::operator != (const Complex& c)

{

    //整个复数对象就两个成员，如果这个2个对象的

    //内存完全相等时，则两个复数相等

    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("
");

   
    printf("c3.a = %f, c3.b = %f
",c3.getA(), c3.getB());//2, 4

    printf("c4.a = %f, c4.b = %f
",c4.getA(), c4.getB());//-6, 0

    printf("c5.a = %f, c5.b = %f
",c5.getA(), c5.getB());//3, 0  

 

    printf("
");

   

    Complex c6(2, 4);

    printf("c3 == c6: %d
", c3 == c6); //1

    printf("c3 != c4: %d
", c3 != c4); //1

 

    printf("
");

   

    (c3 = c2) = c1;//赋值操作赋返回值是引用，可以连续赋值

   

    printf("c1.a = %f, c1.b = %f
",c1.getA(), c1.getB());//1, 2

    printf("c2.a = %f, c2.b = %f
",c2.getA(), c2.getB());//3, 6

    printf("c3.a = %f, c3.b = %f
",c3.getA(), c3.getB());//1, 2    

 

    return 0;

}

运行结果：

　　

3. 注意事项

（1）C++规定赋值操作符（=）只能重载为成员函数（而不能是全局函数）

（2）操作符重载改变不了原操作符的优先级

（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

4. 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