/* -*- C++ -*-

 * lemon/grid_graph.h - Part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2005 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/invalid.h>

#include <lemon/utility.h>

#include <lemon/bits/iterable_graph_extender.h>

#include <lemon/bits/alteration_notifier.h>

#include <lemon/bits/static_map.h>

#include <lemon/bits/undir_graph_extender.h>

#include <lemon/xy.h>

///\ingroup graphs

///\file

///\brief GridGraph class.

namespace lemon {

  /// \brief Base graph for GridGraph.

  ///

  /// Base graph for grid graph. It describes some member functions

  /// which can be used in the GridGraph.

  ///

  /// \warning Always use the GridGraph instead of this.

  /// \see GridGraph

  class GridGraphBase {

  public:

    typedef GridGraphBase Graph;

    class Node;

    class Edge;

  public:

    GridGraphBase() {}

  protected:

    /// \brief Creates a grid graph with the given size.

    ///

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

    void construct(int width, int height) {

      _height = height; _width = width;

      _nodeNum = height * width; _edgeNum = 2 * _nodeNum - width - height;

      _edgeLimit = _nodeNum - width;

    }

    /// \brief Gives back the edge goes down from the node.

    ///

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

    /// outgoing edge then it gives back INVALID.

    Edge _down(Node n) const {

      if (n.id < _nodeNum - _width) {

	return Edge(n.id);

      } else {

	return INVALID;

      }

    }

    /// \brief Gives back the edge comes from up into the node.

    ///

    /// Gives back the edge comes from up into the node. If there is not

    /// incoming edge then it gives back INVALID.

    Edge _up(Node n) const {

      if (n.id >= _width) {

	return Edge(n.id - _width);

      } else {

	return INVALID;

      }

    }

    /// \brief Gives back the edge goes right from the node.

    ///

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

    /// outgoing edge then it gives back INVALID.

    Edge _right(Node n) const {

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

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

      } else {

	return INVALID;

      }

    }

    /// \brief Gives back the edge comes from left into the node.

    ///

    /// Gives back the edge comes left up into the node. If there is not

    /// incoming edge then it gives back INVALID.

    Edge _left(Node n) const {

      if (n.id % _width > 0) {

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

      } else {

	return INVALID;

      }

    }

  public:

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

    /// 

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

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

      return Node(i + j * _width);

    }

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

    ///

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

    int row(Node n) const {

      return n.id / _width;

    }

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

    ///

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

    int col(Node n) const {

      return n.id % _width;    

    }

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

    ///

    /// Gives back the width of the graph.

    int width() const {

      return _width;

    }

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

    ///

    /// Gives back the height of the graph.

    int height() const {

      return _height;

    }

    typedef True NodeNumTag;

    typedef True EdgeNumTag;

    ///Number of nodes.

    int nodeNum() const { return _nodeNum; }

    ///Number of edges.

    int edgeNum() const { return _edgeNum; }

    /// Maximum node ID.

    /// Maximum node ID.

    ///\sa id(Node)

    int maxId(Node = INVALID) const { return nodeNum() - 1; }

    /// Maximum edge ID.

    /// Maximum edge ID.

    ///\sa id(Edge)

    int maxId(Edge = INVALID) const { return edgeNum() - 1; }

    /// \brief Gives back the source node of an edge.

    ///    

    /// Gives back the source node of an edge.

    Node source(Edge e) const {

      if (e.id < _edgeLimit) {

	return e.id;

      } else {

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

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

      }

    }

    /// \brief Gives back the target node of an edge.

    ///    

    /// Gives back the target node of an edge.

    Node target(Edge e) const {

      if (e.id < _edgeLimit) {

	return e.id + _width;

      } else {

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

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

      }

    }

    /// Node ID.

    /// The ID of a valid Node is a nonnegative integer not greater than

    /// \ref maxNodeId(). The range of the ID's is not surely continuous

    /// and the greatest node ID can be actually less then \ref maxNodeId().

    ///

    /// The ID of the \ref INVALID node is -1.

    ///\return The ID of the node \c v. 

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

    /// Edge ID.

    /// The ID of a valid Edge is a nonnegative integer not greater than

    /// \ref maxEdgeId(). The range of the ID's is not surely continuous

    /// and the greatest edge ID can be actually less then \ref maxEdgeId().

    ///

    /// The ID of the \ref INVALID edge is -1.

    ///\return The ID of the edge \c e. 

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

    static Node fromId(int id, Node) { return Node(id);}

    static Edge fromId(int id, Edge) { return Edge(id);}

    typedef True FindEdgeTag;

    /// Finds an edge between two nodes.

    /// Finds an edge from node \c u to node \c v.

    ///

    /// If \c prev is \ref INVALID (this is the default value), then

    /// It finds the first edge from \c u to \c v. Otherwise it looks for

    /// the next edge from \c u to \c v after \c prev.

    /// \return The found edge or INVALID if there is no such an edge.

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

      if (prev != INVALID) return INVALID;

      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 + _edgeLimit);

      }

      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;

    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;}

    };

    void first(Node& node) const {

      node.id = nodeNum() - 1;

    }

    static void next(Node& node) {

      --node.id;

    }

    void first(Edge& edge) const {

      edge.id = edgeNum() - 1;

    }

    static void next(Edge& edge) {

      --edge.id;

    }

    void firstOut(Edge& edge, const Node& node) const {

      if (node.id < _nodeNum - _width) {

	edge.id = node.id;

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

	edge.id = _edgeLimit + node.id % _width +

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

      } else {

	edge.id = -1;

      }

    }

    void nextOut(Edge& edge) const {

      if (edge.id >= _edgeLimit) {

	edge.id = -1;

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

	edge.id = _edgeLimit + edge.id % _width +

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

      } else {

	edge.id = -1;

      }

    }

    void firstIn(Edge& edge, const Node& node) const {

      if (node.id >= _width) {

	edge.id = node.id - _width;

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

	edge.id = _edgeLimit + node.id % _width +

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

      } else {

	edge.id = -1;

      }

    }

    void nextIn(Edge& edge) const {

      if (edge.id >= _edgeLimit) {

	edge.id = -1;

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

	edge.id = _edgeLimit + edge.id % _width +

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

      } else {

	edge.id = -1;

      }

    }

  private:

    int _width, _height;

    int _nodeNum, _edgeNum;

    int _edgeLimit;

  };

  typedef StaticMappableUndirGraphExtender<

    IterableUndirGraphExtender<

    AlterableUndirGraphExtender<

    UndirGraphExtender<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,height) range and j is in the [0, width) range.

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

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

  ///

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

  /// \code

  /// GridGraph graph(h, w);

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

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

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

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

  ///   }

  /// }

  /// \endcode

  ///

  /// The graph type is fully conform to the \ref concept::UndirGraph

  /// "Undirected Graph" concept.

  ///

  /// \author Balazs Dezso

  /// \see GridGraphBase

  class GridGraph : public ExtendedGridGraphBase {

  public:

    /// \brief Map to get the indices of the nodes as xy<int>.

    ///

    /// Map to get the indices of the nodes as xy<int>.

    class IndexMap {

    public:

      typedef True NeedCopy;

      /// \brief The key type of the map

      typedef GridGraph::Node Key;

      /// \brief The value type of the map

      typedef xy<int> Value;

      /// \brief Constructor

      ///

      /// Constructor

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

      /// \brief The subscript operator

      ///

      /// The subscript operator.

      Value operator[](Key key) const {

	return xy<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:

      typedef True NeedCopy;

      /// \brief The key type of the map

      typedef GridGraph::Node Key;

      /// \brief The value type of the map

      typedef int Value;

      /// \brief Constructor

      ///

      /// Constructor

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

      /// \brief The subscript operator

      ///

      /// The subscript operator.

      Value operator[](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:

      typedef True NeedCopy;

      /// \brief The key type of the map

      typedef GridGraph::Node Key;

      /// \brief The value type of the map

      typedef int Value;

      /// \brief Constructor

      ///

      /// Constructor

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

      /// \brief The subscript operator

      ///

      /// The subscript operator.

      Value operator[](Key key) const {

	return graph.col(key);

      }

    private:

      const GridGraph& graph;

    };

    GridGraph(int n, int m) { construct(n, m); }

    /// \brief Gives back the edge goes down from the node.

    ///

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

    /// outgoing edge then it gives back INVALID.

    Edge down(Node n) const {

      UndirEdge ue = _down(n);

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

    }

    /// \brief Gives back the edge goes up from the node.

    ///

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

    /// outgoing edge then it gives back INVALID.

    Edge up(Node n) const {

      UndirEdge ue = _up(n);

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

    }

    /// \brief Gives back the edge goes right from the node.

    ///

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

    /// outgoing edge then it gives back INVALID.

    Edge right(Node n) const {

      UndirEdge ue = _right(n);

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

    }

    /// \brief Gives back the edge goes left from the node.

    ///

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

    /// outgoing edge then it gives back INVALID.

    Edge left(Node n) const {

      UndirEdge ue = _left(n);

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

    }

  };

  /// \brief Index map of the grid graph

  ///

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

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

    return GridGraph::IndexMap(graph);

  }

  /// \brief Row map of the grid graph

  ///

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

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

    return GridGraph::RowMap(graph);

  }

  /// \brief Coloumn map of the grid graph

  ///

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

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

    return GridGraph::ColMap(graph);

  }

}

#endif