/**
2 dimensional vector (plainvector) implementation

*/
#ifndef HUGO_XY_H
#define HUGO_XY_H

#include <iostream>

using namespace std;
template<typename T>
class xy {
  T _x,_y;

public:

  ///Default constructor: both coordinates become 0
  xy() { _x=_y=0; }

  ///Constructing from coordinates
  xy(T a, T b) { _x=a; _y=b; }

  ///Gives back the x coordinate
  T x(){
    return _x;
  };

  ///Gives back the y coordinate
  T y(){
    return _y;
  };

  ///Gives back the square of the norm of the vector
  T normSquare(){
    return _x*_x+_y*_y;
  };
  
  ///Increments the left hand side by u
  xy<T>& operator +=(const xy<T>& u){
    _x += u._x;
    _y += u._y;
    return *this;
  };
  
  ///Decrements the left hand side by u
  xy<T>& operator -=(const xy<T>& u){
    _x -= u._x;
    _y -= u._y;
    return *this;
  };

  ///Multiplying the left hand side with a scalar
  xy<T>& operator *=(const T &u){
    _x *= u;
    _y *= u;
    return *this;
  };
  
  ///Returns the scalar product of two vectors
  T operator *(const xy<T>& u){
    return _x*u._x+_y*u._y;
  };
  
  ///Returns the sum of two vectors
  xy<T> operator+(const xy<T> &u) const {
    xy<T> b=*this;
    return b+=u;
  };

  ///Returns the difference of two vectors
  xy<T> operator-(const xy<T> &u) const {
    xy<T> b=*this;
    return b-=u;
  };

  ///Returns a vector multiplied by a scalar
  xy<T> operator*(const T &u) const {
    xy<T> b=*this;
    return b*=u;
  };

  ///Testing equality
  bool operator==(const xy<T> &u){
    return (_x==u._x) && (_y==u._y);
  };

  ///Testing inequality
  bool operator!=(xy u){
    return  (_x!=u._x) || (_y!=u._y);
  };

};
///Reading a plainvector from a stream
template<typename T>
inline
istream& operator>>(istream &is, xy<T> &z)
{
  ///This is not the best solution here: I didn't know how to solve this with friend functions
  T a,b;
  is >> a >> b;
  xy<T> buf(a,b);
  z=buf;
  return is;
}

///Outputting a plainvector to a stream
template<typename T>
inline
ostream& operator<<(ostream &os, xy<T> z)
{
	os << "(" << z.x() << ", " << z.y() << ")";
	return os;
}



#endif //HUGO_XY_H