updating lec 14 readme

lectures/14_operators/README.md

@@ -16,3 +16,82 @@ called the imaginary part.
 a
 2 + b
 2
+
+## 14.2 Complex Class declaration (complex.h)
+
+```cpp
+class Complex {
+public:
+Complex(double x=0, double y=0) : real_(x), imag_(y) {} // default constructor
+Complex(Complex const& old) : real_(old.real_), imag_(old.imag_) {} // copy constructor
+Complex& operator= (Complex const& rhs); // Assignment operator
+double Real() const { return real_; }
+void SetReal(double x) { real_ = x; }
+double Imaginary() const { return imag_; }
+void SetImaginary(double y) { imag_ = y; }
+double Magnitude() const { return sqrt(real_*real_ + imag_*imag_); }
+Complex operator+ (Complex const& rhs) const;
+Complex operator- () const; // unary operator- negates a complex number
+friend istream& operator>> (istream& istr, Complex& c);
+private:
+double real_, imag_;
+};
+Complex operator- (Complex const& left, Complex const& right); // non-member function
+ostream& operator<< (ostream& ostr, Complex const& c); // non-member function
+```
+
+## 14.3 Implementation of Complex Class (complex.cpp)
+
+```cpp
+// Assignment operator
+Complex& Complex::operator= (Complex const& rhs) {
+real_ = rhs.real_;
+imag_ = rhs.imag_;
+return *this;
+}
+// Addition operator as a member function.
+Complex Complex::operator+ (Complex const& rhs) const {
+double re = real_ + rhs.real_;
+double im = imag_ + rhs.imag_;
+return Complex(re, im);
+}
+// Subtraction operator as a non-member function.
+Complex operator- (Complex const& lhs, Complex const& rhs) {
+return Complex(lhs.Real()-rhs.Real(), lhs.Imaginary()-rhs.Imaginary());
+}
+// Unary negation operator. Note that there are no arguments.
+Complex Complex::operator- () const {
+return Complex(-real_, -imag_);
+}
+// Input stream operator as a friend function
+istream& operator>> (istream & istr, Complex & c) {
+istr >> c.real_ >> c.imag_;
+return istr;
+}
+// Output stream operator as an ordinary non-member function
+ostream& operator<< (ostream & ostr, Complex const& c) {
+if (c.Imaginary() < 0) ostr << c.Real() << " - " << -c.Imaginary() << " i ";
+else ostr << c.Real() << " + " << c.Imaginary() << " i ";
+return ostr;
+}
+```
+
+## 14.4 Operators as Non-Member Functions and as Member Functions
+
+- We have already written our own operators, especially operator<, to sort objects stored in STL containers
+and to create our own keys for maps.
+- We can write them as non-member functions (e.g., operator-). When implemented as a non-member function,
+the expression: z - w is translated by the compiler into the function call: operator- (z, w)
+- We can also write them as member functions (e.g., operator+). When implemented as a member function, the
+expression: z + w is translated into: z.operator+ (w)
+This shows that operator+ is a member function of z, since z appears on the left-hand side of the operator.
+Observe that the function has only one argument!
+There are several important properties of the implementation of an operator as a member function:
+  – It is within the scope of class Complex, so private member variables can be accessed directly.
+  – The member variables of z, whose member function is actually called, are referenced by directly by name.
+  – The member variables of w are accessed through the parameter rhs.
+  – The member function is const, which means that z will not (and can not) be changed by the function.
+- Also, since w will not be changed since the argument is also marked const.
+- Both operator+ and operator- return Complex objects, so both must call Complex constructors to create these
+objects. Calling constructors for Complex objects inside functions, especially member functions that work on
+Complex objects, seems somewhat counter-intuitive at first, but it is common practice!