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

  *

  * 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 GRID_GRAPH_H

 #define GRID_GRAPH_H

 #include <iostream>

 #include <lemon/core.h>

 #include <lemon/assert.h>

 #include <lemon/bits/base_extender.h>

 #include <lemon/bits/graph_extender.h>

 #include <lemon/dim2.h>

 ///\ingroup graphs

 ///\file

 ///\brief GridGraph class.

 namespace lemon {

   class GridGraphBase {

   public:

     typedef GridGraphBase Graph;

     class Node;

     class Arc;

   public:

     GridGraphBase() {}

   protected:

     void construct(int w, int h) {

       _height = h; _width = w;

       _nodeNum = h * w; _arcNum = 2 * _nodeNum - w - h;

       _arcLimit = _nodeNum - w;

     }

     Arc _down(Node n) const {

       if (n.id < _nodeNum - _width) {

         return Arc(n.id);

       } else {

         return INVALID;

       }

     }

     Arc _up(Node n) const {

       if (n.id >= _width) {

         return Arc(n.id - _width);

       } else {

         return INVALID;

       }

     }

     Arc _right(Node n) const {

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

         return _arcLimit + n.id % _width + (n.id / _width) * (_width - 1);

       } else {

         return INVALID;

       }

     }

     Arc _left(Node n) const {

       if (n.id % _width > 0) {

         return _arcLimit + n.id % _width + (n.id / _width) * (_width - 1) - 1;

       } else {

         return INVALID;

       }

     }

   public:

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

       LEMON_ASSERT(0 <= i && i < width() &&

                    0 <= j && j < height(), "lemon::GridGraph::IndexError");

       return Node(i + j * _width);

     }

     int row(Node n) const {

       return n.id / _width;

     }

     int col(Node n) const {

       return n.id % _width;

     }

     int width() const {

       return _width;

     }

     int height() const {

       return _height;

     }

     typedef True NodeNumTag;

     typedef True ArcNumTag;

     int nodeNum() const { return _nodeNum; }

     int arcNum() const { return _arcNum; }

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

     int maxArcId() const { return arcNum() - 1; }

     Node source(Arc e) const {

       if (e.id < _arcLimit) {

         return e.id;

       } else {

         return (e.id - _arcLimit) % (_width - 1) +

           (e.id - _arcLimit) / (_width - 1) * _width;

       }

     }

     Node target(Arc e) const {

       if (e.id < _arcLimit) {

         return e.id + _width;

       } else {

         return (e.id - _arcLimit) % (_width - 1) +

           (e.id - _arcLimit) / (_width - 1) * _width + 1;

       }

     }

     static int id(Node v) { return v.id; }

     static int id(Arc e) { return e.id; }

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

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

     typedef True FindArcTag;

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

       if (prev != INVALID) return INVALID;

       if (v.id - u.id == _width) return Arc(u.id);

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

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

                    u.id % _width + _arcLimit);

       }

       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 Arc {

       friend class GridGraphBase;

     protected:

       int id;

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

     public:

       Arc() {}

       Arc (Invalid) { id = -1; }

       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; }

     };

     void first(Node& node) const {

       node.id = nodeNum() - 1;

     }

     static void next(Node& node) {

       --node.id;

     }

     void first(Arc& arc) const {

       arc.id = arcNum() - 1;

     }

     static void next(Arc& arc) {

       --arc.id;

     }

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

       if (node.id < _nodeNum - _width) {

         arc.id = node.id;

       } else if (node.id % _width < _width - 1) {

         arc.id = _arcLimit + node.id % _width +

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

       } else {

         arc.id = -1;

       }

     }

     void nextOut(Arc& arc) const {

       if (arc.id >= _arcLimit) {

         arc.id = -1;

       } else if (arc.id % _width < _width - 1) {

         arc.id = _arcLimit + arc.id % _width +

           (arc.id / _width) * (_width - 1);

       } else {

         arc.id = -1;

       }

     }

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

       if (node.id >= _width) {

         arc.id = node.id - _width;

       } else if (node.id % _width > 0) {

         arc.id = _arcLimit + node.id % _width +

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

       } else {

         arc.id = -1;

       }

     }

     void nextIn(Arc& arc) const {

       if (arc.id >= _arcLimit) {

         arc.id = -1;

       } else if (arc.id % _width > 0) {

         arc.id = _arcLimit + arc.id % _width +

           (arc.id / _width + 1) * (_width - 1) - 1;

       } else {

         arc.id = -1;

       }

     }

   private:

     int _width, _height;

     int _nodeNum, _arcNum;

     int _arcLimit;

   };

   typedef GraphExtender<UndirDigraphExtender<GridGraphBase> >

     ExtendedGridGraphBase;

   /// \ingroup graphs

   ///

   /// \brief Grid graph class

   ///

   /// This class implements a special graph type. The nodes of the

   /// graph can be indiced by two integer \c (i,j) value where \c i

   /// is in the \c [0,width) range and j is in the [0, height) range.

   /// Two nodes are connected in the graph if the indices differ only

   /// on one position and only one is the difference.

   ///

   /// \image html grid_graph.png

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

   ///

   /// The graph can be indiced in the following way:

   ///\code

   /// GridGraph gr(w, h);

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

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

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

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

   ///   }

   /// }

   ///\endcode

   ///

   /// This graph type is fully conform to the \ref concepts::Graph

   /// "Undirected Graph" concept, and it also has an important extra

   /// feature that its maps are real \ref concepts::ReferenceMap

   /// "reference map"s.

   class GridGraph : public ExtendedGridGraphBase {

   public:

     typedef ExtendedGridGraphBase Parent;

     /// \brief Map to get the indices of the nodes as dim2::Point<int>.

     ///

     /// Map to get the indices of the nodes as dim2::Point<int>.

     class IndexMap {

     public:

       /// The key type of the map

       typedef GridGraph::Node Key;

       /// The value type of the map

       typedef dim2::Point<int> Value;

       /// Constructor

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

       /// The subscript operator

       Value operator[](const Key& key) const {

         return dim2::Point<int>(_graph.row(key), _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:

       /// The key type of the map

       typedef GridGraph::Node Key;

       /// The value type of the map

       typedef int Value;

       /// Constructor

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

       /// The subscript operator

       Value operator[](const Key& key) const {

         return _graph.row(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:

       /// The key type of the map

       typedef GridGraph::Node Key;

       /// The value type of the map

       typedef int Value;

       /// Constructor

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

       /// The subscript operator

       Value operator[](const Key& key) const {

         return _graph.col(key);

       }

     private:

       const GridGraph& _graph;

     };

     /// \brief Constructor

     ///

     /// Constructor.

     /// \param width The width of the grid.

     /// \param height The height of the grid.

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

     /// \brief Resize the graph

     ///

     /// Resize the grid.

     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 Gives back the row index of the node.

     ///

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

     int row(Node n) const {

       return Parent::row(n);

     }

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

     ///

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

     int col(Node n) const {

       return Parent::col(n);

     }

     /// \brief Gives back the width of the grid.

     ///

     /// Gives back the width of the grid.

     int width() const {

       return Parent::width();

     }

     /// \brief Gives back the height of the grid.

     ///

     /// Gives back the height of the grid.

     int height() const {

       return Parent::height();

     }

     /// \brief Gives back 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 \c INVALID.

     Arc down(Node n) const {

       Edge e = _down(n);

       return e != INVALID ? direct(e, true) : INVALID;

     }

     /// \brief Gives back 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 \c INVALID.

     Arc up(Node n) const {

       Edge e = _up(n);

       return e != INVALID ? direct(e, false) : INVALID;

     }

     /// \brief Gives back 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 \c INVALID.

     Arc right(Node n) const {

       Edge e = _right(n);

       return e != INVALID ? direct(e, true) : INVALID;

     }

     /// \brief Gives back 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 \c INVALID.

     Arc left(Node n) const {

       Edge e = _left(n);

       return e != INVALID ? direct(e, false) : INVALID;

     }

   }; // class GridGraph

   /// \brief Index map of the grid graph

   ///

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

   inline GridGraph::IndexMap indexMap(const GridGraph& graph) {

     return GridGraph::IndexMap(graph);

   }

   /// \brief Row map of the grid graph

   ///

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

   inline GridGraph::RowMap rowMap(const GridGraph& graph) {

     return GridGraph::RowMap(graph);

   }

   /// \brief Column map of the grid graph

   ///

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

   inline GridGraph::ColMap colMap(const GridGraph& graph) {

     return GridGraph::ColMap(graph);

   }

 }

 #endif // GRID_GRAPH_H