/* -*- 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