// Definition of four different template classes.
// Each defining static member template functions less_than and distance_to.
// Notice that we just assume that getx and gety are public members in C!
// Other designs may be possible - and preferable!

#include <cmath>

struct FixedNorm{
  template<typename C> static bool less_than(const C& a, const C& b){
    return false;
  }

  template<typename C> static double distance_to(const C& a, const C& b){
    return 7.0;
  }
};



struct HorizontalNorm{
  template<typename C> static bool less_than(const C& a, const C& b){
    return a.getx() < b.getx();
  }

  template<typename C> static double distance_to(const C& a, const C& b){
    return fabs(a.getx() - b.getx());
  }
};



struct VerticalNorm{
  template<typename C> static bool less_than(const C& a, const C& b){
    return a.gety() < b.gety();
  }

  template<typename C> static double distance_to(const C& a, const C& b){
    return fabs(a.gety() - b.gety());
  }
};



template<typename T>double square(T a){
  return a*a;
}

struct Norm{
  template<typename C> static bool less_than(const C& a, const C& b){
    return (a.getx() < b.getx()) && (a.gety() < b.gety());
  }

  template<typename C> static double distance_to(const C& a, const C& b){
    return sqrt(square(a.getx() - b.getx()) + square(a.gety() - b.gety()));
  }
};