C++第8周(春)项目1 实现复数类中的运算符重载
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【项目1】实现复数类中的运算符重载
(1)请用类的成员函数,定义复数类重载运算符+、-、*、/,使之能用于复数的加减乘除
class Complex { public: Complex(){real=0;imag=0;} Complex(double r,double i){real=r; imag=i;} Complex operator+(Complex &c2); Complex operator-(Complex &c2); Complex operator*(Complex &c2); Complex operator/(Complex &c2); void display(); private: double real; double imag; }; //下面定义成员函数 //下面定义用于测试的main()函数 int main() { Complex c1(3,4),c2(5,-10),c3; cout<<"c1="; c1.display(); cout<<"c2="; c2.display(); c3=c1+c2; cout<<"c1+c2="; c3.display(); c3=c1-c2; cout<<"c1-c2="; c3.display(); c3=c1*c2; cout<<"c1*c2="; c3.display(); c3=c1/c2; cout<<"c1/c2="; c3.display(); return 0; }(2)请用类的友元函数,而不是成员函数,完成上面提及的运算符的重载;
(3)一个定义完整的类,是可以当作独立的产品发布,成为众多项目中的“基础工程”,这样的类在方案二的基础上,扩展+、-、*、/运算符的功能,使之能与double型数据进行运算。设Complex c; double d; c+d和d+c的结果为“将d视为实部为d的复数同c相加”,其他-、*、/运算符类似。
(1)请用类的成员函数,定义复数类重载运算符+、-、*、/,使之能用于复数的加减乘除
参考解答
#include <iostream> using namespace std; class Complex { public: Complex() { real=0; imag=0; } Complex(double r,double i) { real=r; imag=i; } Complex operator+(Complex &c2); Complex operator-(Complex &c2); Complex operator*(Complex &c2); Complex operator/(Complex &c2); void display(); private: double real; double imag; }; //复数相加: (a+bi)+(c+di)=(a+c)+(b+d)i. Complex Complex::operator+(Complex &c2) { Complex c; c.real=real+c2.real; c.imag=imag+c2.imag; return c; } //复数相减:(a+bi)-(c+di)=(a-c)+(b-d)i. Complex Complex::operator-(Complex &c2) { Complex c; c.real=real-c2.real; c.imag=imag-c2.imag; return c; } //复数相乘:(a+bi)(c+di)=(ac-bd)+(bc+ad)i. Complex Complex::operator*(Complex &c2) { Complex c; c.real=real*c2.real-imag*c2.imag; c.imag=imag*c2.real+real*c2.imag; return c; } //复数相除:(a+bi)/(c+di)=(ac+bd)/(c^2+d^2) +(bc-ad)/(c^2+d^2)i Complex Complex::operator/(Complex &c2) { Complex c; c.real=(real*c2.real+imag*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag); c.imag=(imag*c2.real-real*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag); return c; } void Complex::display() { cout<<"("<<real<<","<<imag<<"i)"<<endl; } int main() { Complex c1(3,4),c2(5,-10),c3; cout<<"c1="; c1.display(); cout<<"c2="; c2.display(); c3=c1+c2; cout<<"c1+c2="; c3.display(); c3=c1-c2; cout<<"c1-c2="; c3.display(); c3=c1*c2; cout<<"c1*c2="; c3.display(); c3=c1/c2; cout<<"c1/c2="; c3.display(); return 0; }
(2)请用类的友元函数,而不是成员函数,完成上面提及的运算符的重载;
参考解答
#include <iostream> using namespace std; class Complex { public: Complex() { real=0; imag=0; } Complex(double r,double i) { real=r; imag=i; } friend Complex operator+(Complex &c1, Complex &c2); friend Complex operator-(Complex &c1, Complex &c2); friend Complex operator*(Complex &c1, Complex &c2); friend Complex operator/(Complex &c1, Complex &c2); void display(); private: double real; double imag; }; //复数相加:(a+bi)+(c+di)=(a+c)+(b+d)i. Complex operator+(Complex &c1, Complex &c2) { Complex c; c.real=c1.real+c2.real; c.imag=c1.imag+c2.imag; return c; } //复数相减:(a+bi)-(c+di)=(a-c)+(b-d)i. Complex operator-(Complex &c1, Complex &c2) { Complex c; c.real=c1.real-c2.real; c.imag=c1.imag-c2.imag; return c; } //复数相乘:(a+bi)(c+di)=(ac-bd)+(bc+ad)i. Complex operator*(Complex &c1, Complex &c2) { Complex c; c.real=c1.real*c2.real-c1.imag*c2.imag; c.imag=c1.imag*c2.real+c1.real*c2.imag; return c; } //复数相除:(a+bi)/(c+di)=(ac+bd)/(c^2+d^2) +(bc-ad)/(c^2+d^2)i Complex operator/(Complex &c1, Complex &c2) { Complex c; c.real=(c1.real*c2.real+c1.imag*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag); c.imag=(c1.imag*c2.real-c1.real*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag); return c; } void Complex::display() { cout<<"("<<real<<","<<imag<<"i)"<<endl; } int main() { Complex c1(3,4),c2(5,-10),c3; cout<<"c1="; c1.display(); cout<<"c2="; c2.display(); c3=c1+c2; cout<<"c1+c2="; c3.display(); c3=c1-c2; cout<<"c1-c2="; c3.display(); c3=c1*c2; cout<<"c1*c2="; c3.display(); c3=c1/c2; cout<<"c1/c2="; c3.display(); return 0; }
事实上,运算符重载的函数还可以定义成一般函数,只不过这种做法并不好。下面给出使用一般函数完成运算符重载的程序。其中,加了序号的3处注释值得关注。
#include <iostream> using namespace std; class Complex { public: Complex() { real=0; imag=0; } Complex(double r,double i) { real=r; imag=i; } double getReal() const { return real; //(1)定义公用的数据接口,可以为const成员函数 } double getImag() const { return imag; } void setReal(double r) { real=r; //(1)定义公用的数据接口 } void setImag(double i) { imag=i; } void display(); private: double real; double imag; }; //复数相加:(a+bi)+(c+di)=(a+c)+(b+d)i. Complex operator+(const Complex &c1, const Complex &c2) //(3)将参数处理为const更符合需求 { Complex c; c.setReal(c1.getReal()+c2.getReal()); //(2)调用公用数据接口读取和修改私有数据成员 c.setImag(c1.getImag()+c2.getImag()); return c; } //复数相减:(a+bi)-(c+di)=(a-c)+(b-d)i. Complex operator-(const Complex &c1, const Complex &c2) { Complex c; c.setReal(c1.getReal()-c2.getReal()); c.setImag(c1.getImag()-c2.getImag()); return c; } //复数相乘:(a+bi)(c+di)=(ac-bd)+(bc+ad)i. Complex operator*(const Complex &c1, const Complex &c2) { Complex c; c.setReal(c1.getReal()*c2.getReal()-c1.getImag()*c2.getImag()); c.setImag(c1.getImag()*c2.getReal()+c1.getReal()*c2.getImag()); return c; } //复数相除:(a+bi)/(c+di)=(ac+bd)/(c^2+d^2) +(bc-ad)/(c^2+d^2)i Complex operator/(const Complex &c1, const Complex &c2) { Complex c; double d= (c2.getReal()*c2.getReal()+c2.getImag()*c2.getImag()); c.setReal((c1.getReal()*c2.getReal()+c1.getImag()*c2.getImag())/d); c.setImag((c1.getImag()*c2.getReal()-c1.getReal()*c2.getImag())/d); return c; } void Complex::display() { cout<<"("<<real<<","<<imag<<"i)"<<endl; } int main() { Complex c1(3,4),c2(5,-10),c3; cout<<"c1="; c1.display(); cout<<"c2="; c2.display(); c3=c1+c2; cout<<"c1+c2="; c3.display(); c3=c1-c2; cout<<"c1-c2="; c3.display(); c3=c1*c2; cout<<"c1*c2="; c3.display(); c3=c1/c2; cout<<"c1/c2="; c3.display(); return 0; }
(3)一个定义完整的类,是可以当作独立的产品发布,成为众多项目中的“基础工程”,这样的类在方案二的基础上,扩展+、-、*、/运算符的功能,使之能与double型数据进行运算。设Complex c; double d; c+d和d+c的结果为“将d视为实部为d的复数同c相加”,其他-、*、/运算符类似。
参考解答
#include <iostream> using namespace std; class Complex { public: Complex() { real=0; imag=0; } Complex(double r,double i) { real=r; imag=i; } friend Complex operator+(Complex &c1, Complex &c2); friend Complex operator+(double d1, Complex &c2); friend Complex operator+(Complex &c1, double d2); friend Complex operator-(Complex &c1, Complex &c2); friend Complex operator-(double d1, Complex &c2); friend Complex operator-(Complex &c1, double d2); friend Complex operator*(Complex &c1, Complex &c2); friend Complex operator*(double d1, Complex &c2); friend Complex operator*(Complex &c1, double d2); friend Complex operator/(Complex &c1, Complex &c2); friend Complex operator/(double d1, Complex &c2); friend Complex operator/(Complex &c1, double d2); void display(); private: double real; double imag; }; //复数相加:(a+bi)+(c+di)=(a+c)+(b+d)i. Complex operator+(Complex &c1, Complex &c2) { Complex c; c.real=c1.real+c2.real; c.imag=c1.imag+c2.imag; return c; } Complex operator+(double d1, Complex &c2) { Complex c(d1,0); return c+c2; //按运算法则计算的确可以,但充分利用已经定义好的代码,既省人力,也避免引入新的错误,但可能机器的效率会不佳 } Complex operator+(Complex &c1, double d2) { Complex c(d2,0); return c1+c; } //复数相减:(a+bi)-(c+di)=(a-c)+(b-d)i. Complex operator-(Complex &c1, Complex &c2) { Complex c; c.real=c1.real-c2.real; c.imag=c1.imag-c2.imag; return c; } Complex operator-(double d1, Complex &c2) { Complex c(d1,0); return c-c2; } Complex operator-(Complex &c1, double d2) { Complex c(d2,0); return c1-c; } //复数相乘:(a+bi)(c+di)=(ac-bd)+(bc+ad)i. Complex operator*(Complex &c1, Complex &c2) { Complex c; c.real=c1.real*c2.real-c1.imag*c2.imag; c.imag=c1.imag*c2.real+c1.real*c2.imag; return c; } Complex operator*(double d1, Complex &c2) { Complex c(d1,0); return c*c2; } Complex operator*(Complex &c1, double d2) { Complex c(d2,0); return c1*c; } //复数相除:(a+bi)/(c+di)=(ac+bd)/(c^2+d^2) +(bc-ad)/(c^2+d^2)i Complex operator/(Complex &c1, Complex &c2) { Complex c; c.real=(c1.real*c2.real+c1.imag*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag); c.imag=(c1.imag*c2.real-c1.real*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag); return c; } Complex operator/(double d1, Complex &c2) { Complex c(d1,0); return c/c2; } Complex operator/(Complex &c1, double d2) { Complex c(d2,0); return c1/c; } void Complex::display() { cout<<"("<<real<<","<<imag<<"i)"<<endl; } int main() { Complex c1(3,4),c2(5,-10),c3; double d=11; cout<<"c1="; c1.display(); cout<<"c2="; c2.display(); cout<<"d="<<d<<endl<<endl; cout<<"下面是重载运算符的计算结果: "<<endl; c3=c1+c2; cout<<"c1+c2="; c3.display(); cout<<"c1+d="; (c1+d).display(); cout<<"d+c1="; (d+c1).display(); c3=c1-c2; cout<<"c1-c2="; c3.display(); cout<<"c1-d="; (c1-d).display(); cout<<"d-c1="; (d-c1).display(); c3=c1*c2; cout<<"c1*c2="; c3.display(); cout<<"c1*d="; (c1*d).display(); cout<<"d*c1="; (d*c1).display(); c3=c1/c2; cout<<"c1/c2="; c3.display(); cout<<"c1/d="; (c1/d).display(); cout<<"d/c1="; (d/c1).display(); return 0; }
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