/* -*- mode: C++; indent-tabs-mode: nil; -*-

  *

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

  *

  * Copyright (C) 2003-2009

  * 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 GRID_GRAPH_H

 #define GRID_GRAPH_H

 #include <lemon/core.h>

 #include <lemon/bits/graph_extender.h>

 #include <lemon/dim2.h>

 #include <lemon/assert.h>

 ///\ingroup graphs

 ///\file

 ///\brief GridGraph class.

 namespace lemon {

   class GridGraphBase {

   public:

     typedef GridGraphBase Graph;

     class Node;

     class Edge;

     class Arc;

   public:

     GridGraphBase() {}

   protected:

     void construct(int width, int height) {

        _width = width; _height = height;

       _node_num = width * height;

       _edge_num = 2 * _node_num - width - height;

       _edge_limit = _node_num - _width;

     }

   public:

     Node operator()(int i, int j) const {

       LEMON_DEBUG(0 <= i && i < _width &&

                   0 <= j  && j < _height, "Index out of range");

       return Node(i + j * _width);

     }

     int col(Node n) const {

       return n._id % _width;

     }

     int row(Node n) const {

       return n._id / _width;

     }

     dim2::Point<int> pos(Node n) const {

       return dim2::Point<int>(col(n), row(n));

     }

     int width() const {

       return _width;

     }

     int height() const {

       return _height;

     }

     typedef True NodeNumTag;

     typedef True EdgeNumTag;

     typedef True ArcNumTag;

     int nodeNum() const { return _node_num; }

     int edgeNum() const { return _edge_num; }

     int arcNum() const { return 2 * _edge_num; }

     Node u(Edge edge) const {

       if (edge._id < _edge_limit) {

         return edge._id;

       } else {

         return (edge._id - _edge_limit) % (_width - 1) +

           (edge._id - _edge_limit) / (_width - 1) * _width;

       }

     }

     Node v(Edge edge) const {

       if (edge._id < _edge_limit) {

         return edge._id + _width;

       } else {

         return (edge._id - _edge_limit) % (_width - 1) +

           (edge._id - _edge_limit) / (_width - 1) * _width + 1;

       }

     }

     Node source(Arc arc) const {

       return (arc._id & 1) == 1 ? u(arc) : v(arc);

     }

     Node target(Arc arc) const {

       return (arc._id & 1) == 1 ? v(arc) : u(arc);

     }

     static int id(Node node) { return node._id; }

     static int id(Edge edge) { return edge._id; }

     static int id(Arc arc) { return arc._id; }

     int maxNodeId() const { return _node_num - 1; }

     int maxEdgeId() const { return _edge_num - 1; }

     int maxArcId() const { return 2 * _edge_num - 1; }

     static Node nodeFromId(int id) { return Node(id);}

     static Edge edgeFromId(int id) { return Edge(id);}

     static Arc arcFromId(int id) { return Arc(id);}

     typedef True FindEdgeTag;

     typedef True FindArcTag;

     Edge findEdge(Node u, Node v, Edge prev = INVALID) const {

       if (prev != INVALID) return INVALID;

       if (v._id > u._id) {

         if (v._id - u._id == _width)

           return Edge(u._id);

         if (v._id - u._id == 1 && u._id % _width < _width - 1) {

           return Edge(u._id / _width * (_width - 1) +

                       u._id % _width + _edge_limit);

         }

       } else {

         if (u._id - v._id == _width)

           return Edge(v._id);

         if (u._id - v._id == 1 && v._id % _width < _width - 1) {

           return Edge(v._id / _width * (_width - 1) +

                       v._id % _width + _edge_limit);

         }

       }

       return INVALID;

     }

     Arc findArc(Node u, Node v, Arc prev = INVALID) const {

       if (prev != INVALID) return INVALID;

       if (v._id > u._id) {

         if (v._id - u._id == _width)

           return Arc((u._id << 1) | 1);

         if (v._id - u._id == 1 && u._id % _width < _width - 1) {

           return Arc(((u._id / _width * (_width - 1) +

                        u._id % _width + _edge_limit) << 1) | 1);

         }

       } else {

         if (u._id - v._id == _width)

           return Arc(v._id << 1);

         if (u._id - v._id == 1 && v._id % _width < _width - 1) {

           return Arc((v._id / _width * (_width - 1) +

                        v._id % _width + _edge_limit) << 1);

         }

       }

       return INVALID;

     }

     class Node {

       friend class GridGraphBase;

     protected:

       int _id;

       Node(int id) : _id(id) {}

     public:

       Node() {}

       Node (Invalid) : _id(-1) {}

       bool operator==(const Node node) const {return _id == node._id;}

       bool operator!=(const Node node) const {return _id != node._id;}

       bool operator<(const Node node) const {return _id < node._id;}

     };

     class Edge {

       friend class GridGraphBase;

       friend class Arc;

     protected:

       int _id;

       Edge(int id) : _id(id) {}

     public:

       Edge() {}

       Edge (Invalid) : _id(-1) {}

       bool operator==(const Edge edge) const {return _id == edge._id;}

       bool operator!=(const Edge edge) const {return _id != edge._id;}

       bool operator<(const Edge edge) const {return _id < edge._id;}

     };

     class Arc {

       friend class GridGraphBase;

     protected:

       int _id;

       Arc(int id) : _id(id) {}

     public:

       Arc() {}

       Arc (Invalid) : _id(-1) {}

       operator Edge() const { return _id != -1 ? Edge(_id >> 1) : INVALID; }

       bool operator==(const Arc arc) const {return _id == arc._id;}

       bool operator!=(const Arc arc) const {return _id != arc._id;}

       bool operator<(const Arc arc) const {return _id < arc._id;}

     };

     static bool direction(Arc arc) {

       return (arc._id & 1) == 1;

     }

     static Arc direct(Edge edge, bool dir) {

       return Arc((edge._id << 1) | (dir ? 1 : 0));

     }

     void first(Node& node) const {

       node._id = _node_num - 1;

     }

     static void next(Node& node) {

       --node._id;

     }

     void first(Edge& edge) const {

       edge._id = _edge_num - 1;

     }

     static void next(Edge& edge) {

       --edge._id;

     }

     void first(Arc& arc) const {

       arc._id = 2 * _edge_num - 1;

     }

     static void next(Arc& arc) {

       --arc._id;

     }

     void firstOut(Arc& arc, const Node& node) const {

       if (node._id % _width < _width - 1) {

         arc._id = (_edge_limit + node._id % _width +

                    (node._id / _width) * (_width - 1)) << 1 | 1;

         return;

       }

       if (node._id < _node_num - _width) {

         arc._id = node._id << 1 | 1;

         return;

       }

       if (node._id % _width > 0) {

         arc._id = (_edge_limit + node._id % _width +

                    (node._id / _width) * (_width - 1) - 1) << 1;

         return;

       }

       if (node._id >= _width) {

         arc._id = (node._id - _width) << 1;

         return;

       }

       arc._id = -1;

     }

     void nextOut(Arc& arc) const {

       int nid = arc._id >> 1;

       if ((arc._id & 1) == 1) {

         if (nid >= _edge_limit) {

           nid = (nid - _edge_limit) % (_width - 1) +

             (nid - _edge_limit) / (_width - 1) * _width;

           if (nid < _node_num - _width) {

             arc._id = nid << 1 | 1;

             return;

           }

         }

         if (nid % _width > 0) {

           arc._id = (_edge_limit + nid % _width +

                      (nid / _width) * (_width - 1) - 1) << 1;

           return;

         }

         if (nid >= _width) {

           arc._id = (nid - _width) << 1;

           return;

         }

       } else {

         if (nid >= _edge_limit) {

           nid = (nid - _edge_limit) % (_width - 1) +

             (nid - _edge_limit) / (_width - 1) * _width + 1;

           if (nid >= _width) {

             arc._id = (nid - _width) << 1;

             return;

           }

         }

       }

       arc._id = -1;

     }

     void firstIn(Arc& arc, const Node& node) const {

       if (node._id % _width < _width - 1) {

         arc._id = (_edge_limit + node._id % _width +

                    (node._id / _width) * (_width - 1)) << 1;

         return;

       }

       if (node._id < _node_num - _width) {

         arc._id = node._id << 1;

         return;

       }

       if (node._id % _width > 0) {

         arc._id = (_edge_limit + node._id % _width +

                    (node._id / _width) * (_width - 1) - 1) << 1 | 1;

         return;

       }

       if (node._id >= _width) {

         arc._id = (node._id - _width) << 1 | 1;

         return;

       }

       arc._id = -1;

     }

     void nextIn(Arc& arc) const {

       int nid = arc._id >> 1;

       if ((arc._id & 1) == 0) {

         if (nid >= _edge_limit) {

           nid = (nid - _edge_limit) % (_width - 1) +

             (nid - _edge_limit) / (_width - 1) * _width;

           if (nid < _node_num - _width) {

             arc._id = nid << 1;

             return;

           }

         }

         if (nid % _width > 0) {

           arc._id = (_edge_limit + nid % _width +

                      (nid / _width) * (_width - 1) - 1) << 1 | 1;

           return;

         }

         if (nid >= _width) {

           arc._id = (nid - _width) << 1 | 1;

           return;

         }

       } else {

         if (nid >= _edge_limit) {

           nid = (nid - _edge_limit) % (_width - 1) +

             (nid - _edge_limit) / (_width - 1) * _width + 1;

           if (nid >= _width) {

             arc._id = (nid - _width) << 1 | 1;

             return;

           }

         }

       }

       arc._id = -1;

     }

     void firstInc(Edge& edge, bool& dir, const Node& node) const {

       if (node._id % _width < _width - 1) {

         edge._id = _edge_limit + node._id % _width +

           (node._id / _width) * (_width - 1);

         dir = true;

         return;

       }

       if (node._id < _node_num - _width) {

         edge._id = node._id;

         dir = true;

         return;

       }

       if (node._id % _width > 0) {

         edge._id = _edge_limit + node._id % _width +

           (node._id / _width) * (_width - 1) - 1;

         dir = false;

         return;

       }

       if (node._id >= _width) {

         edge._id = node._id - _width;

         dir = false;

         return;

       }

       edge._id = -1;

       dir = true;

     }

     void nextInc(Edge& edge, bool& dir) const {

       int nid = edge._id;

       if (dir) {

         if (nid >= _edge_limit) {

           nid = (nid - _edge_limit) % (_width - 1) +

             (nid - _edge_limit) / (_width - 1) * _width;

           if (nid < _node_num - _width) {

             edge._id = nid;

             return;

           }

         }

         if (nid % _width > 0) {

           edge._id = _edge_limit + nid % _width +

             (nid / _width) * (_width - 1) - 1;

           dir = false;

           return;

         }

         if (nid >= _width) {

           edge._id = nid - _width;

           dir = false;

           return;

         }

       } else {

         if (nid >= _edge_limit) {

           nid = (nid - _edge_limit) % (_width - 1) +

             (nid - _edge_limit) / (_width - 1) * _width + 1;

           if (nid >= _width) {

             edge._id = nid - _width;

             return;

           }

         }

       }

       edge._id = -1;

       dir = true;

     }

     Arc right(Node n) const {

       if (n._id % _width < _width - 1) {

         return Arc(((_edge_limit + n._id % _width +

                     (n._id / _width) * (_width - 1)) << 1) | 1);

       } else {

         return INVALID;

       }

     }

     Arc left(Node n) const {

       if (n._id % _width > 0) {

         return Arc((_edge_limit + n._id % _width +

                      (n._id / _width) * (_width - 1) - 1) << 1);

       } else {

         return INVALID;

       }

     }

     Arc up(Node n) const {

       if (n._id < _edge_limit) {

         return Arc((n._id << 1) | 1);

       } else {

         return INVALID;

       }

     }

     Arc down(Node n) const {

       if (n._id >= _width) {

         return Arc((n._id - _width) << 1);

       } else {

         return INVALID;

       }

     }

   private:

     int _width, _height;

     int _node_num, _edge_num;

     int _edge_limit;

   };

   typedef GraphExtender<GridGraphBase> ExtendedGridGraphBase;

   /// \ingroup graphs

   ///

   /// \brief Grid graph class

   ///

   /// GridGraph implements a special graph type. The nodes of the

   /// graph can be indexed by two integer values \c (i,j) where \c i is

   /// in the range <tt>[0..width()-1]</tt> and j is in the range

   /// <tt>[0..height()-1]</tt>. Two nodes are connected in the graph if

   /// the indices differ exactly on one position and the difference is

   /// also exactly one. The nodes of the graph can be obtained by position

   /// using the \c operator()() function and the indices of the nodes can

   /// be obtained using \c pos(), \c col() and \c row() members. The outgoing

   /// arcs can be retrieved with the \c right(), \c up(), \c left()

   /// and \c down() functions, where the bottom-left corner is the

   /// origin.

   ///

   /// This class is completely static and it needs constant memory space.

   /// Thus you can neither add nor delete nodes or edges, however

   /// the structure can be resized using resize().

   ///

   /// \image html grid_graph.png

   /// \image latex grid_graph.eps "Grid graph" width=\textwidth

   ///

   /// A short example about the basic usage:

   ///\code

   /// GridGraph graph(rows, cols);

   /// GridGraph::NodeMap<int> val(graph);

   /// for (int i = 0; i < graph.width(); ++i) {

   ///   for (int j = 0; j < graph.height(); ++j) {

   ///     val[graph(i, j)] = i + j;

   ///   }

   /// }

   ///\endcode

   ///

   /// This type fully conforms to the \ref concepts::Graph "Graph concept".

   /// Most of its member functions and nested classes are documented

   /// only in the concept class.

   ///

   /// This class provides constant time counting for nodes, edges and arcs.

   class GridGraph : public ExtendedGridGraphBase {

     typedef ExtendedGridGraphBase Parent;

   public:

     /// \brief Map to get the indices of the nodes as \ref dim2::Point

     /// "dim2::Point<int>".

     ///

     /// Map to get the indices of the nodes as \ref dim2::Point

     /// "dim2::Point<int>".

     class IndexMap {

     public:

       /// \brief The key type of the map

       typedef GridGraph::Node Key;

       /// \brief The value type of the map

       typedef dim2::Point<int> Value;

       /// \brief Constructor

       IndexMap(const GridGraph& graph) : _graph(graph) {}

       /// \brief The subscript operator

       Value operator[](Key key) const {

         return _graph.pos(key);

       }

     private:

       const GridGraph& _graph;

     };

     /// \brief Map to get the column of the nodes.

     ///

     /// Map to get the column of the nodes.

     class ColMap {

     public:

       /// \brief The key type of the map

       typedef GridGraph::Node Key;

       /// \brief The value type of the map

       typedef int Value;

       /// \brief Constructor

       ColMap(const GridGraph& graph) : _graph(graph) {}

       /// \brief The subscript operator

       Value operator[](Key key) const {

         return _graph.col(key);

       }

     private:

       const GridGraph& _graph;

     };

     /// \brief Map to get the row of the nodes.

     ///

     /// Map to get the row of the nodes.

     class RowMap {

     public:

       /// \brief The key type of the map

       typedef GridGraph::Node Key;

       /// \brief The value type of the map

       typedef int Value;

       /// \brief Constructor

       RowMap(const GridGraph& graph) : _graph(graph) {}

       /// \brief The subscript operator

       Value operator[](Key key) const {

         return _graph.row(key);

       }

     private:

       const GridGraph& _graph;

     };

     /// \brief Constructor

     ///

     /// Construct a grid graph with the given size.

     GridGraph(int width, int height) { construct(width, height); }

     /// \brief Resizes the graph

     ///

     /// This function resizes the graph. It fully destroys and

     /// rebuilds the structure, therefore the maps of the graph will be

     /// reallocated automatically and the previous values will be lost.

     void resize(int width, int height) {

       Parent::notifier(Arc()).clear();

       Parent::notifier(Edge()).clear();

       Parent::notifier(Node()).clear();

       construct(width, height);

       Parent::notifier(Node()).build();

       Parent::notifier(Edge()).build();

       Parent::notifier(Arc()).build();

     }

     /// \brief The node on the given position.

     ///

     /// Gives back the node on the given position.

     Node operator()(int i, int j) const {

       return Parent::operator()(i, j);

     }

     /// \brief The column index of the node.

     ///

     /// Gives back the column index of the node.

     int col(Node n) const {

       return Parent::col(n);

     }

     /// \brief The row index of the node.

     ///

     /// Gives back the row index of the node.

     int row(Node n) const {

       return Parent::row(n);

     }

     /// \brief The position of the node.

     ///

     /// Gives back the position of the node, ie. the <tt>(col,row)</tt> pair.

     dim2::Point<int> pos(Node n) const {

       return Parent::pos(n);

     }

     /// \brief The number of the columns.

     ///

     /// Gives back the number of the columns.

     int width() const {

       return Parent::width();

     }

     /// \brief The number of the rows.

     ///

     /// Gives back the number of the rows.

     int height() const {

       return Parent::height();

     }

     /// \brief The arc goes right from the node.

     ///

     /// Gives back the arc goes right from the node. If there is not

     /// outgoing arc then it gives back INVALID.

     Arc right(Node n) const {

       return Parent::right(n);

     }

     /// \brief The arc goes left from the node.

     ///

     /// Gives back the arc goes left from the node. If there is not

     /// outgoing arc then it gives back INVALID.

     Arc left(Node n) const {

       return Parent::left(n);

     }

     /// \brief The arc goes up from the node.

     ///

     /// Gives back the arc goes up from the node. If there is not

     /// outgoing arc then it gives back INVALID.

     Arc up(Node n) const {

       return Parent::up(n);

     }

     /// \brief The arc goes down from the node.

     ///

     /// Gives back the arc goes down from the node. If there is not

     /// outgoing arc then it gives back INVALID.

     Arc down(Node n) const {

       return Parent::down(n);

     }

     /// \brief Index map of the grid graph

     ///

     /// Just returns an IndexMap for the grid graph.

     IndexMap indexMap() const {

       return IndexMap(*this);

     }

     /// \brief Row map of the grid graph

     ///

     /// Just returns a RowMap for the grid graph.

     RowMap rowMap() const {

       return RowMap(*this);

     }

     /// \brief Column map of the grid graph

     ///

     /// Just returns a ColMap for the grid graph.

     ColMap colMap() const {

       return ColMap(*this);

     }

   };

 }

 #endif