/* -*- C++ -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2003-2006

 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_XY_H

#define LEMON_XY_H

#include <iostream>

#include <lemon/bits/utility.h>

///\ingroup misc

///\file

///\brief A simple two dimensional vector and a bounding box implementation 

///

/// The class \ref lemon::xy "xy" implements

///a two dimensional vector with the usual

/// operations.

///

/// The class \ref lemon::BoundingBox "BoundingBox" can be used to determine

/// the rectangular bounding box of a set of \ref lemon::xy "xy"'s.

///

///\author Attila Bernath

namespace lemon {

  /// \addtogroup misc

  /// @{

  /// A simple two dimensional vector (plainvector) implementation

  /// A simple two dimensional vector (plainvector) implementation

  ///with the usual vector

  /// operators.

  ///

  ///\author Attila Bernath

  template<typename T>

    class xy {

    public:

      typedef T Value;

      ///First co-ordinate

      T x;

      ///Second co-ordinate

      T y;     

      ///Default constructor

      xy() {}

      ///Constructing the instance from coordinates

      xy(T a, T b) : x(a), y(b) { }

      ///Conversion constructor

      template<class TT> xy(const xy<TT> &p) : x(p.x), y(p.y) {}

      ///Gives back the square of the norm of the vector

      T normSquare() const {

        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;

      }

      ///Dividing the left hand side by 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) const {

        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 neg of the vectors

      xy<T> operator-() const {

        xy<T> b=*this;

        b.x=-b.x; b.y=-b.y;

        return b;

      }

      ///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;

      }

      ///Returns a vector divided 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) const {

        return (x==u.x) && (y==u.y);

      }

      ///Testing inequality

      bool operator!=(xy u) const {

        return  (x!=u.x) || (y!=u.y);

      }

    };

  ///Returns an xy 

  ///Returns an xy

  ///\relates xy

  template <typename T>

  inline xy<T> make_xy(const T& x, const T& y) {

    return xy<T>(x, y);

  }

  ///Returns a vector multiplied by a scalar

  ///Returns a vector multiplied by a scalar

  ///\relates xy

  template<typename T> xy<T> operator*(const T &u,const xy<T> &x) {

    return x*u;

  }

  ///Read a plainvector from a stream

  ///Read a plainvector from a stream

  ///\relates xy

  ///

  template<typename T>

  inline std::istream& operator>>(std::istream &is, xy<T> &z) {

    char c;

    if (is >> c) {

      if (c != '(') is.putback(c);

    } else {

      is.clear();

    }

    if (!(is >> z.x)) return is;

    if (is >> c) {

      if (c != ',') is.putback(c);

    } else {

      is.clear();

    }

    if (!(is >> z.y)) return is;

    if (is >> c) {

      if (c != ')') is.putback(c);

    } else {

      is.clear();

    }

    return is;

  }

  ///Write a plainvector to a stream

  ///Write a plainvector to a stream

  ///\relates xy

  ///

  template<typename T>

  inline std::ostream& operator<<(std::ostream &os, const xy<T>& z)

  {

    os << "(" << z.x << ", " << z.y << ")";

    return os;

  }

  ///Rotate by 90 degrees

  ///Returns its parameter rotated by 90 degrees in positive direction.

  ///\relates xy

  ///

  template<typename T>

  inline xy<T> rot90(const xy<T> &z)

  {

    return xy<T>(-z.y,z.x);

  }

  ///Rotate by 270 degrees

  ///Returns its parameter rotated by 90 degrees in negative direction.

  ///\relates xy

  ///

  template<typename T>

  inline xy<T> rot270(const xy<T> &z)

  {

    return xy<T>(z.y,-z.x);

  }

  /// A class to calculate or store the bounding box of plainvectors.

  /// A class to calculate or store the bounding box of plainvectors.

  ///

  ///\author Attila Bernath

  template<typename T>

    class BoundingBox {

      xy<T> bottom_left, top_right;

      bool _empty;

    public:

      ///Default constructor: creates an empty bounding box

      BoundingBox() { _empty = true; }

      ///Constructing the instance from one point

      BoundingBox(xy<T> a) { bottom_left=top_right=a; _empty = false; }

      ///Were any points added?

      bool empty() const {

        return _empty;

      }

      ///Makes the BoundingBox empty

      void clear() {

        _empty=1;

      }

      ///\brief Gives back the bottom left corner

      ///(if the bounding box is empty, then the return value is not defined) 

      xy<T> bottomLeft() const {

        return bottom_left;

      }

      ///\brief Sets the bottom left corner

      ///(should only bee used for non-empty box) 

      void bottomLeft(xy<T> p) {

	bottom_left = p;

      }

      ///\brief Gives back the top right corner

      ///(if the bounding box is empty, then the return value is not defined) 

      xy<T> topRight() const {

        return top_right;

      }

      ///\brief Sets the top right corner

      ///(should only bee used for non-empty box) 

      void topRight(xy<T> p) {

	top_right = p;

      }

      ///\brief Gives back the bottom right corner

      ///(if the bounding box is empty, then the return value is not defined) 

      xy<T> bottomRight() const {

        return xy<T>(top_right.x,bottom_left.y);

      }

      ///\brief Sets the bottom right corner

      ///(should only bee used for non-empty box) 

      void bottomRight(xy<T> p) {

	top_right.x = p.x;

	bottom_left.y = p.y;

      }

      ///\brief Gives back the top left corner

      ///(if the bounding box is empty, then the return value is not defined) 

      xy<T> topLeft() const {

        return xy<T>(bottom_left.x,top_right.y);

      }

      ///\brief Sets the top left corner

      ///(should only bee used for non-empty box) 

      void topLeft(xy<T> p) {

	top_right.y = p.y;

	bottom_left.x = p.x;

      }

      ///\brief Gives back the bottom of the box

      ///(if the bounding box is empty, then the return value is not defined) 

      T bottom() const {

        return bottom_left.y;

      }

      ///\brief Sets the bottom of the box

      ///(should only bee used for non-empty box) 

      void bottom(T t) {

	bottom_left.y = t;

      }

      ///\brief Gives back the top of the box

      ///(if the bounding box is empty, then the return value is not defined) 

      T top() const {

        return top_right.y;

      }

      ///\brief Sets the top of the box

      ///(should only bee used for non-empty box) 

      void top(T t) {

	top_right.y = t;

      }

      ///\brief Gives back the left side of the box

      ///(if the bounding box is empty, then the return value is not defined) 

      T left() const {

        return bottom_left.x;

      }

      ///\brief Sets the left side of the box

      ///(should only bee used for non-empty box) 

      void left(T t) {

	bottom_left.x = t;

      }

      ///\brief Gives back the right side of the box

      ///(if the bounding box is empty, then the return value is not defined) 

      T right() const {

        return top_right.x;

      }

      ///\brief Sets the right side of the box

      ///(should only bee used for non-empty box) 

      void right(T t) {

	top_right.x = t;

      }

      ///\brief Gives back the height of the box

      ///(if the bounding box is empty, then the return value is not defined) 

      T height() const {

        return top_right.y-bottom_left.y;

      }

      ///\brief Gives back the width of the box

      ///(if the bounding box is empty, then the return value is not defined) 

      T width() const {

        return top_right.x-bottom_left.x;

      }

      ///Checks whether a point is inside a bounding box

      bool inside(const xy<T>& u){

        if (_empty)

          return false;

        else{

          return ((u.x-bottom_left.x)*(top_right.x-u.x) >= 0 &&

              (u.y-bottom_left.y)*(top_right.y-u.y) >= 0 );

        }

      }

      ///Increments a bounding box with a point

      BoundingBox& add(const xy<T>& u){

        if (_empty){

          bottom_left=top_right=u;

          _empty = false;

        }

        else{

          if (bottom_left.x > u.x) bottom_left.x = u.x;

          if (bottom_left.y > u.y) bottom_left.y = u.y;

          if (top_right.x < u.x) top_right.x = u.x;

          if (top_right.y < u.y) top_right.y = u.y;

        }

        return *this;

      }

//       ///Sums a bounding box and a point

//       BoundingBox operator +(const xy<T>& u){

//         BoundingBox b = *this;

//         return b += u;

//       }

      ///Increments a bounding box with another bounding box

      BoundingBox& add(const BoundingBox &u){

        if ( !u.empty() ){

          this->add(u.bottomLeft());

	  this->add(u.topRight());

        }

        return *this;

      }

      ///Sums two bounding boxes

      BoundingBox operator +(const BoundingBox& u){

        BoundingBox b = *this;

        return b.add(u);

      }

      ///Intersection of two bounding boxes

      BoundingBox operator &(const BoundingBox& u){

        BoundingBox b;

	b.bottom_left.x=std::max(this->bottom_left.x,u.bottom_left.x);

	b.bottom_left.y=std::max(this->bottom_left.y,u.bottom_left.y);

	b.top_right.x=std::min(this->top_right.x,u.top_right.x);

	b.top_right.y=std::min(this->top_right.y,u.top_right.y);

	b._empty = this->_empty || u._empty ||

	  b.bottom_left.x>top_right.x && b.bottom_left.y>top_right.y;

        return b;

      }

    };//class Boundingbox

  ///Map of x-coordinates of an xy<>-map

  ///\ingroup maps

  ///

  template<class M>

  class XMap 

  {

    M& _map;

  public:

    typedef typename M::Value::Value Value;

    typedef typename M::Key Key;

    ///\e

    XMap(M& map) : _map(map) {}

    Value operator[](Key k) const {return _map[k].x;}

    void set(Key k,Value v) {_map.set(k,typename M::Value(v,_map[k].y));}

  };

  ///Returns an \ref XMap class

  ///This function just returns an \ref XMap class.

  ///

  ///\ingroup maps

  ///\relates XMap

  template<class M> 

  inline XMap<M> xMap(M &m) 

  {

    return XMap<M>(m);

  }

  template<class M> 

  inline XMap<M> xMap(const M &m) 

  {

    return XMap<M>(m);

  }

  ///Constant (read only) version of \ref XMap

  ///\ingroup maps

  ///

  template<class M>

  class ConstXMap 

  {

    const M& _map;

  public:

    typedef typename M::Value::Value Value;

    typedef typename M::Key Key;

    ///\e

    ConstXMap(const M &map) : _map(map) {}

    Value operator[](Key k) const {return _map[k].x;}

  };

  ///Returns a \ref ConstXMap class

  ///This function just returns an \ref ConstXMap class.

  ///

  ///\ingroup maps

  ///\relates ConstXMap

  template<class M> 

  inline ConstXMap<M> xMap(const M &m) 

  {

    return ConstXMap<M>(m);

  }

  ///Map of y-coordinates of an xy<>-map

  ///\ingroup maps

  ///

  template<class M>

  class YMap 

  {

    M& _map;

  public:

    typedef typename M::Value::Value Value;

    typedef typename M::Key Key;

    ///\e

    YMap(M& map) : _map(map) {}

    Value operator[](Key k) const {return _map[k].y;}

    void set(Key k,Value v) {_map.set(k,typename M::Value(_map[k].x,v));}

  };

  ///Returns an \ref YMap class

  ///This function just returns an \ref YMap class.

  ///

  ///\ingroup maps

  ///\relates YMap

  template<class M> 

  inline YMap<M> yMap(M &m) 

  {

    return YMap<M>(m);

  }

  template<class M> 

  inline YMap<M> yMap(const M &m) 

  {

    return YMap<M>(m);

  }

  ///Constant (read only) version of \ref YMap

  ///\ingroup maps

  ///

  template<class M>

  class ConstYMap 

  {

    const M& _map;

  public:

    typedef typename M::Value::Value Value;

    typedef typename M::Key Key;

    ///\e

    ConstYMap(const M &map) : _map(map) {}

    Value operator[](Key k) const {return _map[k].y;}

  };

  ///Returns a \ref ConstYMap class

  ///This function just returns an \ref ConstYMap class.

  ///

  ///\ingroup maps

  ///\relates ConstYMap

  template<class M> 

  inline ConstYMap<M> yMap(const M &m) 

  {

    return ConstYMap<M>(m);

  }

  ///Map of the \ref xy::normSquare() "normSquare()" of an \ref xy "xy"-map

  ///Map of the \ref xy::normSquare() "normSquare()" of an \ref xy "xy"-map

  ///\ingroup maps

  ///

  template<class M>

  class NormSquareMap 

  {

    const M& _map;

  public:

    typedef typename M::Value::Value Value;

    typedef typename M::Key Key;

    ///\e

    NormSquareMap(const M &map) : _map(map) {}

    Value operator[](Key k) const {return _map[k].normSquare();}

  };

  ///Returns a \ref NormSquareMap class

  ///This function just returns an \ref NormSquareMap class.

  ///

  ///\ingroup maps

  ///\relates NormSquareMap

  template<class M> 

  inline NormSquareMap<M> normSquareMap(const M &m) 

  {

    return NormSquareMap<M>(m);

  }

  /// @}

} //namespace lemon

#endif //LEMON_XY_H