/* -*- 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