/* -*- 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/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 maxNodeId() const { return nodeNum() - 1; }
    /// Maximum edge ID.
    
    /// Maximum edge ID.
    ///\sa id(Edge)
    int maxEdgeId() 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 nodeFromId(int id) { return Node(id);}
    
    static Edge edgeFromId(int id) { 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.width(); ++i) {
  ///   for (int j = 0; j < graph.height(); ++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 a RowMap for the grid graph.
  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.
  GridGraph::ColMap colMap(const GridGraph& graph) {
    return GridGraph::ColMap(graph);
  }
}
#endif