/* -*- 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 Point map

  ///\ingroup maps

  ///Map of x-coordinates of a \ref dim2::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 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 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 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 normSquare()

    ///of a 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