/* -*- 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