Finally, consider the class Pair:

    1   class Pair
    2   {
    3     int x;
    4     int y;
    5   public:
    6     Pair() : x(0), y(0)
    7       { }
    8   
    9     Pair(int x, int y) : x(x), y(y)
   10     { }
   11   
   12     int getX() const;
   13     int getY() const;
   14     string toString() const;
   15   
   16     friend ostream& operator<<(ostream& os, const Pair& pr);
   17   
   18   };

We really don't need to make this operator<< be a friend, since it will use the public method toString().

A friend function may be declared inside a class definition, even though it is not a member function of the class.

If a non-member function is not a friend, it must be declared outside the class.