数学运算符重载
运算符重载其实就是定义一个函数，在函数体内实现想要的功能，当用到该运算符时，编译器会自动调用这个函数。也就是说，运算符重载是通过函数实现的，它本质上是函数重载。
运算符重载的格式为：
返回值类型 operator 运算符名称 (形参表列){
//TODO:
}
operator是关键字，专门用于定义重载运算符的函数。我们可以将operator 运算符名称这一部分看做函数名，对于上面的代码，函数名就是operator+。
运算符重载函数不仅可以作为类的成员函数，还可以作为全局函数
能够重载的运算符有: + - * / % ^ & | ~ ! = < > += -= = /= %= ^= &= |= << >> <<= >>= == != <= >= && || ++ -- , -> -> () [] new new[] delete delete[] 其中[]是下标运算符，()是函数调用运算符。自增自减运算符的前置和后置形式都可以重载。长度运算符sizeof、条件运算符: ?、成员选择符.和域解析运算符::不能被重载。
重载不能改变运算符的优先级和结合性。重载不会改变运算符的用法，原有有几个操作数、操作数在左边还是在右边，这些都不会改变。例如~号右边只有一个操作数，+号总是出现在两个操作数之间，重载后也必须如此。运算符重载函数不能有默认的参数，否则就改变了运算符操作数的个数，这显然是错误的。运算符重载函数既可以作为类的成员函数，也可以作为全局函数。
将运算符重载函数作为类的成员函数时，二元运算符的参数只有一个，一元运算符不需要参数。之所以少一个参数，是因为这个参数是隐含的。
将运算符重载函数作为全局函数时，二元操作符就需要两个参数，一元操作符需要一个参数，而且其中必须有一个参数是对象，好让编译器区分这是程序员自定义的运算符，防止程序员修改用于内置类型的运算符的性质。如果有两个参数，这两个参数可以都是对象，也可以一个是对象..另外，将运算符重载函数作为全局函数时，一般都需要在类中将该函数声明为友元函数。原因很简单，该函数大部分情况下都需要使用类的 private 成员。
箭头运算符->、下标运算符[ ]、函数调用运算符( )、赋值运算符=只能以成员函数的形式重载。
#include <iostream>
#include <cmath>
using namespace std;
//复数类
class Complex{
public: //构造函数
Complex(double real = 0.0, double imag = 0.0): m_real(real), m_imag(imag){ }
public: //运算符重载
//以全局函数的形式重载
friend Complex operator+(const Complex &c1, const Complex &c2);
friend Complex operator-(const Complex &c1, const Complex &c2);
friend Complex operator*(const Complex &c1, const Complex &c2);
friend Complex operator/(const Complex &c1, const Complex &c2);
friend bool operator==(const Complex &c1, const Complex &c2);
friend bool operator!=(const Complex &c1, const Complex &c2);
//以成员函数的形式重载
Complex & operator+=(const Complex &c);
Complex & operator-=(const Complex &c);
Complex & operator*=(const Complex &c);
Complex & operator/=(const Complex &c);
public: //成员函数
double real() const{ return m_real; }
double imag() const{ return m_imag; }
private:
double m_real; //实部
double m_imag; //虚部
};
//重载+运算符
Complex operator+(const Complex &c1, const Complex &c2){
Complex c;
c.m_real = c1.m_real + c2.m_real;
c.m_imag = c1.m_imag + c2.m_imag;
return c;
}
//重载-运算符
Complex operator-(const Complex &c1, const Complex &c2){
Complex c;
c.m_real = c1.m_real - c2.m_real;
c.m_imag = c1.m_imag - c2.m_imag;
return c;
}
//重载*运算符 (a+bi) * (c+di) = (ac-bd) + (bc+ad)i
Complex operator*(const Complex &c1, const Complex &c2){
Complex c;
c.m_real = c1.m_real * c2.m_real - c1.m_imag * c2.m_imag;
c.m_imag = c1.m_imag * c2.m_real + c1.m_real * c2.m_imag;
return c;
}
//重载/运算符 (a+bi) / (c+di) = [(ac+bd) / (c²+d²)] + [(bc-ad) / (c²+d²)]i
Complex operator/(const Complex &c1, const Complex &c2){
Complex c;
c.m_real = (c1.m_real*c2.m_real + c1.m_imag*c2.m_imag) / (pow(c2.m_real, 2) + pow(c2.m_imag, 2));
c.m_imag = (c1.m_imag*c2.m_real - c1.m_real*c2.m_imag) / (pow(c2.m_real, 2) + pow(c2.m_imag, 2));
return c;
}
//重载==运算符
bool operator==(const Complex &c1, const Complex &c2){
if( c1.m_real == c2.m_real && c1.m_imag == c2.m_imag ){
return true;
}else{
return false;
}
}
//重载!=运算符
bool operator!=(const Complex &c1, const Complex &c2){
if( c1.m_real != c2.m_real || c1.m_imag != c2.m_imag ){
return true;
}else{
return false;
}
}
//重载+=运算符
Complex & Complex::operator+=(const Complex &c){
this->m_real += c.m_real;
this->m_imag += c.m_imag;
return *this;
}
//重载-=运算符
Complex & Complex::operator-=(const Complex &c){
this->m_real -= c.m_real;
this->m_imag -= c.m_imag;
return *this;
}
//重载*=运算符
Complex & Complex::operator*=(const Complex &c){
this->m_real = this->m_real * c.m_real - this->m_imag * c.m_imag;
this->m_imag = this->m_imag * c.m_real + this->m_real * c.m_imag;
return *this;
}
//重载/=运算符
Complex & Complex::operator/=(const Complex &c){
this->m_real = (this->m_real*c.m_real + this->m_imag*c.m_imag) / (pow(c.m_real, 2) + pow(c.m_imag, 2));
this->m_imag = (this->m_imag*c.m_real - this->m_real*c.m_imag) / (pow(c.m_real, 2) + pow(c.m_imag, 2));
return *this;
}
int main(){
Complex c1(25, 35);
Complex c2(10, 20);
Complex c3(1, 2);
Complex c4(4, 9);
Complex c5(34, 6);
Complex c6(80, 90);
Complex c7 = c1 + c2;
Complex c8 = c1 - c2;
Complex c9 = c1 * c2;
Complex c10 = c1 / c2;
cout<<"c7 = "<<c7.real()<<" + "<<c7.imag()<<"i"<<endl;
cout<<"c8 = "<<c8.real()<<" + "<<c8.imag()<<"i"<<endl;
cout<<"c9 = "<<c9.real()<<" + "<<c9.imag()<<"i"<<endl;
cout<<"c10 = "<<c10.real()<<" + "<<c10.imag()<<"i"<<endl;
c3 += c1;
c4 -= c2;
c5 *= c2;
c6 /= c2;
cout<<"c3 = "<<c3.real()<<" + "<<c3.imag()<<"i"<<endl;
cout<<"c4 = "<<c4.real()<<" + "<<c4.imag()<<"i"<<endl;
cout<<"c5 = "<<c5.real()<<" + "<<c5.imag()<<"i"<<endl;
cout<<"c6 = "<<c6.real()<<" + "<<c6.imag()<<"i"<<endl;
if(c1 == c2){
cout<<"c1 == c2"<<endl;
}
if(c1 != c2){
cout<<"c1 != c2"<<endl;
}
return 0;
}
