/* -*- C++ -*-

  *

  * 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_UGRAPH_H

 #define GRID_UGRAPH_H

 #include <iostream>

 #include <lemon/bits/invalid.h>

 #include <lemon/bits/utility.h>

 #include <lemon/bits/base_extender.h>

 #include <lemon/bits/graph_extender.h>

 #include <lemon/dim2.h>

 ///\ingroup graphs

 ///\file

 ///\brief GridUGraph class.

 namespace lemon {

   class GridUGraphBase {

   public:

     typedef GridUGraphBase UGraph;

     class Node;

     class Edge;

   public:

     GridUGraphBase() {}

   protected:

     void construct(int w, int h) {

       _height = h; _width = w;

       _nodeNum = h * w; _edgeNum = 2 * _nodeNum - w - h;

       _edgeLimit = _nodeNum - w;

     }

     Edge _down(Node n) const {

       if (n.id < _nodeNum - _width) {

 	return Edge(n.id);

       } else {

 	return INVALID;

       }

     }

     Edge _up(Node n) const {

       if (n.id >= _width) {

 	return Edge(n.id - _width);

       } else {

 	return 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;

       }

     }

     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:

     class IndexError : public RuntimeError {

     public:

       virtual const char* what() const throw() {

         return "lemon::GridUGraph::IndexError";

       }  

     };

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

       LEMON_ASSERT(0 <= i && i < width() && 0 <= j  && 

                    j < height(), 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 EdgeNumTag;

     int nodeNum() const { return _nodeNum; }

     int edgeNum() const { return _edgeNum; }

     int maxNodeId() const { return nodeNum() - 1; }

     int maxEdgeId() const { return edgeNum() - 1; }

     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;

       }

     }

     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;

       }

     }

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

     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;

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

       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 GridUGraphBase;

     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 GridUGraphBase;

     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 UGraphExtender<UndirGraphExtender<GridUGraphBase> > 

   ExtendedGridUGraphBase;

   /// \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_ugraph.png

   /// \image latex grid_ugraph.eps "Grid graph" width=\textwidth

   ///

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

   ///\code

   /// GridUGraph graph(w, h);

   /// GridUGraph::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 concepts::UGraph

   /// "Undirected Graph" concept,  and it also has an

   ///important extra feature that

   ///its maps are real \ref concepts::ReferenceMap "reference map"s.

   ///

   ///

   /// \author Balazs Dezso

   class GridUGraph : public ExtendedGridUGraphBase {

   public:

     typedef ExtendedGridUGraphBase 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:

       /// \brief The key type of the map

       typedef GridUGraph::Node Key;

       /// \brief The value type of the map

       typedef dim2::Point<int> Value;

       /// \brief Constructor

       ///

       /// Constructor

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

       /// \brief The subscript operator

       ///

       /// The subscript operator.

       Value operator[](Key key) const {

 	return dim2::Point<int>(graph.row(key), graph.col(key));

       }

     private:

       const GridUGraph& 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 GridUGraph::Node Key;

       /// \brief The value type of the map

       typedef int Value;

       /// \brief Constructor

       ///

       /// Constructor

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

       /// \brief The subscript operator

       ///

       /// The subscript operator.

       Value operator[](Key key) const {

 	return graph.row(key);

       }

     private:

       const GridUGraph& 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 GridUGraph::Node Key;

       /// \brief The value type of the map

       typedef int Value;

       /// \brief Constructor

       ///

       /// Constructor

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

       /// \brief The subscript operator

       ///

       /// The subscript operator.

       Value operator[](Key key) const {

 	return graph.col(key);

       }

     private:

       const GridUGraph& graph;

     };

     /// \brief Constructor

     ///

     /// 

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

     /// \brief Resize the graph

     ///

     void resize(int n, int m) {

       Parent::notifier(Edge()).clear();

       Parent::notifier(UEdge()).clear();

       Parent::notifier(Node()).clear();

       construct(n, m);

       Parent::notifier(Node()).build();

       Parent::notifier(UEdge()).build();

       Parent::notifier(Edge()).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 coloumn index of the node.

     ///

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

     int col(Node n) const {

       return Parent::col(n);

     }

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

     ///

     /// Gives back the width of the graph.

     int width() const {

       return Parent::width();

     }

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

     ///

     /// Gives back the height of the graph.

     int height() const {

       return Parent::height();

     }

     /// \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 {

       UEdge 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 {

       UEdge 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 {

       UEdge 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 {

       UEdge 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.

   inline GridUGraph::IndexMap indexMap(const GridUGraph& graph) {

     return GridUGraph::IndexMap(graph);

   }

   /// \brief Row map of the grid graph

   ///

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

   inline GridUGraph::RowMap rowMap(const GridUGraph& graph) {

     return GridUGraph::RowMap(graph);

   }

   /// \brief Column map of the grid graph

   ///

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

   inline GridUGraph::ColMap colMap(const GridUGraph& graph) {

     return GridUGraph::ColMap(graph);

   }

 }

 #endif