/* -*- C++ -*-

  *

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

  *

  * Copyright (C) 2003-2008

  * 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_DIM2_H

 #define LEMON_DIM2_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::dim2::Point "dim2::Point" implements

 ///a two dimensional vector with the usual

 /// operations.

 ///

 /// The class \ref lemon::dim2::BoundingBox "dim2::BoundingBox"

 /// can be used to determine

 /// the rectangular bounding box of a set of

 /// \ref lemon::dim2::Point "dim2::Point"'s.

 namespace lemon {

   ///Tools for handling two dimensional coordinates

   ///This namespace is a storage of several

   ///tools for handling two dimensional coordinates

   namespace dim2 {

   /// \addtogroup misc

   /// @{

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

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

   ///with the usual vector

   /// operators.

   ///

   template<typename T>

     class Point {

     public:

       typedef T Value;

       ///First coordinate

       T x;

       ///Second coordinate

       T y;     

       ///Default constructor

       Point() {}

       ///Construct an instance from coordinates

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

       ///The dimension of the vector.

       ///The dimension of the vector.

       ///This function always returns 2. 

       int size() const { return 2; }

       ///Subscripting operator

       ///\c p[0] is \c p.x and \c p[1] is \c p.y

       ///

       T& operator[](int idx) { return idx == 0 ? x : y; }

       ///Const subscripting operator

       ///\c p[0] is \c p.x and \c p[1] is \c p.y

       ///

       const T& operator[](int idx) const { return idx == 0 ? x : y; }

       ///Conversion constructor

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

       ///Give back the square of the norm of the vector

       T normSquare() const {

         return x*x+y*y;

       }

       ///Increment the left hand side by u

       Point<T>& operator +=(const Point<T>& u) {

         x += u.x;

         y += u.y;

         return *this;

       }

       ///Decrement the left hand side by u

       Point<T>& operator -=(const Point<T>& u) {

         x -= u.x;

         y -= u.y;

         return *this;

       }

       ///Multiply the left hand side with a scalar

       Point<T>& operator *=(const T &u) {

         x *= u;

         y *= u;

         return *this;

       }

       ///Divide the left hand side by a scalar

       Point<T>& operator /=(const T &u) {

         x /= u;

         y /= u;

         return *this;

       }

       ///Return the scalar product of two vectors

       T operator *(const Point<T>& u) const {

         return x*u.x+y*u.y;

       }

       ///Return the sum of two vectors

       Point<T> operator+(const Point<T> &u) const {

         Point<T> b=*this;

         return b+=u;

       }

       ///Return the negative of the vector

       Point<T> operator-() const {

         Point<T> b=*this;

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

         return b;

       }

       ///Return the difference of two vectors

       Point<T> operator-(const Point<T> &u) const {

         Point<T> b=*this;

         return b-=u;

       }

       ///Return a vector multiplied by a scalar

       Point<T> operator*(const T &u) const {

         Point<T> b=*this;

         return b*=u;

       }

       ///Return a vector divided by a scalar

       Point<T> operator/(const T &u) const {

         Point<T> b=*this;

         return b/=u;

       }

       ///Test equality

       bool operator==(const Point<T> &u) const {

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

       }

       ///Test inequality

       bool operator!=(Point u) const {

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

       }

     };

   ///Return a Point 

   ///Return a Point.

   ///\relates Point

   template <typename T>

   inline Point<T> makePoint(const T& x, const T& y) {

     return Point<T>(x, y);

   }

   ///Return a vector multiplied by a scalar

   ///Return a vector multiplied by a scalar.

   ///\relates Point

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

     return x*u;

   }

   ///Read a plainvector from a stream

   ///Read a plainvector from a stream.

   ///\relates Point

   ///

   template<typename T>

   inline std::istream& operator>>(std::istream &is, Point<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 Point

   ///

   template<typename T>

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

   {

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

     return os;

   }

   ///Rotate by 90 degrees

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

   ///\relates Point

   ///

   template<typename T>

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

   {

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

   }

   ///Rotate by 180 degrees

   ///Returns the parameter rotated by 180 degrees.

   ///\relates Point

   ///

   template<typename T>

   inline Point<T> rot180(const Point<T> &z)

   {

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

   }

   ///Rotate by 270 degrees

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

   ///\relates Point

   ///

   template<typename T>

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

   {

     return Point<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.

   ///

     template<typename T>

     class BoundingBox {

       Point<T> bottom_left, top_right;

       bool _empty;

     public:

       ///Default constructor: creates an empty bounding box

       BoundingBox() { _empty = true; }

       ///Construct an instance from one point

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

       ///Construct an instance from two points

       ///Construct an instance from two points.

       ///\param a The bottom left corner.

       ///\param b The top right corner.

       ///\warning The coordinates of the bottom left corner must be no more

       ///than those of the top right one.

       BoundingBox(Point<T> a,Point<T> b)

       {

 	bottom_left=a;

 	top_right=b;

 	_empty = false;

       }

       ///Construct an instance from four numbers

       ///Construct an instance from four numbers.

       ///\param l The left side of the box.

       ///\param b The bottom of the box.

       ///\param r The right side of the box.

       ///\param t The top of the box.

       ///\warning The left side must be no more than the right side and

       ///bottom must be no more than the top. 

       BoundingBox(T l,T b,T r,T t)

       {

 	bottom_left=Point<T>(l,b);

 	top_right=Point<T>(r,t);

 	_empty = false;

       }

       ///Return \c true if the bounding box is empty.

       ///Return \c true if the bounding box is empty (i.e. return \c false

       ///if at least one point was added to the box or the coordinates of

       ///the box were set).

       ///The coordinates of an empty bounding box are not defined. 

       bool empty() const {

         return _empty;

       }

       ///Make the BoundingBox empty

       void clear() {

         _empty=1;

       }

       ///Give back the bottom left corner

       ///Give back the bottom left corner.

       ///If the bounding box is empty, then the return value is not defined.

       Point<T> bottomLeft() const {

         return bottom_left;

       }

       ///Set the bottom left corner

       ///Set the bottom left corner.

       ///It should only be used for non-empty box.

       void bottomLeft(Point<T> p) {

 	bottom_left = p;

       }

       ///Give back the top right corner

       ///Give back the top right corner.

       ///If the bounding box is empty, then the return value is not defined.

       Point<T> topRight() const {

         return top_right;

       }

       ///Set the top right corner

       ///Set the top right corner.

       ///It should only be used for non-empty box.

       void topRight(Point<T> p) {

 	top_right = p;

       }

       ///Give back the bottom right corner

       ///Give back the bottom right corner.

       ///If the bounding box is empty, then the return value is not defined.

       Point<T> bottomRight() const {

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

       }

       ///Set the bottom right corner

       ///Set the bottom right corner.

       ///It should only be used for non-empty box.

       void bottomRight(Point<T> p) {

 	top_right.x = p.x;

 	bottom_left.y = p.y;

       }

       ///Give back the top left corner

       ///Give back the top left corner.

       ///If the bounding box is empty, then the return value is not defined.

       Point<T> topLeft() const {

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

       }

       ///Set the top left corner

       ///Set the top left corner.

       ///It should only be used for non-empty box.

       void topLeft(Point<T> p) {

 	top_right.y = p.y;

 	bottom_left.x = p.x;

       }

       ///Give back the bottom of the box

       ///Give 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;

       }

       ///Set the bottom of the box

       ///Set the bottom of the box.

       ///It should only be used for non-empty box.

       void bottom(T t) {

 	bottom_left.y = t;

       }

       ///Give back the top of the box

       ///Give 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;

       }

       ///Set the top of the box

       ///Set the top of the box.

       ///It should only be used for non-empty box.

       void top(T t) {

 	top_right.y = t;

       }

       ///Give back the left side of the box

       ///Give 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;

       }

       ///Set the left side of the box

       ///Set the left side of the box.

       ///It should only be used for non-empty box.

       void left(T t) {

 	bottom_left.x = t;

       }

       /// Give back the right side of the box

       /// Give 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;

       }

       ///Set the right side of the box

       ///Set the right side of the box.

       ///It should only be used for non-empty box.

       void right(T t) {

 	top_right.x = t;

       }

       ///Give back the height of the box

       ///Give 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;

       }

       ///Give back the width of the box

       ///Give 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 Point<T>& u) const {

         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

       ///Increments a bounding box with a point.

       ///

       BoundingBox& add(const Point<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;

       }

       ///Increments a bounding box to contain another bounding box

       ///Increments a bounding box to contain another bounding box.

       ///

       BoundingBox& add(const BoundingBox &u){

         if ( !u.empty() ){

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

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

         }

         return *this;

       }

       ///Intersection of two bounding boxes

       ///Intersection of two bounding boxes.

       ///

       BoundingBox operator&(const BoundingBox& u) const {

         BoundingBox b;

         if (this->_empty || u._empty) {

 	  b._empty = true;

 	} else {

 	  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 = b.bottom_left.x > b.top_right.x ||

 	             b.bottom_left.y > b.top_right.y;

 	} 

         return b;

       }

     };//class Boundingbox

   ///Map of x-coordinates of a \ref Point "Point"-map

   ///\ingroup maps

   ///Map of x-coordinates of a \ref Point "Point"-map.

   ///

   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

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

   ///

   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 a \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 a \ref Point "Point"-map

   ///\ingroup maps

   ///Map of y-coordinates of a \ref Point "Point"-map.

   ///

   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 a \ref YMap class

   ///This function just returns a \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

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

   ///

   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 a \ref ConstYMap class.

   ///

   ///\ingroup maps

   ///\relates ConstYMap

   template<class M> 

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

   {

     return ConstYMap<M>(m);

   }

     ///\brief Map of the \ref Point::normSquare() "normSquare()"

     ///of a \ref Point "Point"-map

     ///

     ///Map of the \ref Point::normSquare() "normSquare()"

     ///of a \ref Point "Point"-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 a \ref NormSquareMap class.

   ///

   ///\ingroup maps

   ///\relates NormSquareMap

   template<class M> 

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

   {

     return NormSquareMap<M>(m);

   }

   /// @}

   } //namespce dim2

 } //namespace lemon

 #endif //LEMON_DIM2_H