How can it be useful to overload the "function call" operator?

Question

I recently discovered that in C++ you can overload the "function call" operator, in a strange way in which you have to write two pair of parenthesis to do so:

class A { 
  int n;
public: 
  void operator ()() const; 
};

And then use it this way:

A a;
a();

When is this useful?

Answer 1

This can be used to create "functors", objects that act like functions:

class Multiplier {
public:
    Multiplier(int m): multiplier(m) {}
    int operator()(int x) { return multiplier * x; }
private:
    int multiplier;
};

Multiplier m(5);
cout << m(4) << endl;

The above prints 20. The Wikipedia article linked above gives more substantial examples.