/* -*- 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/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 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 an other 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