/* -*- C++ -*-

  * lemon/graph_utils.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 LEMON_GRAPH_UTILS_H

 #define LEMON_GRAPH_UTILS_H

 #include <iterator>

 #include <vector>

 #include <map>

 #include <cmath>

 #include <lemon/invalid.h>

 #include <lemon/utility.h>

 #include <lemon/maps.h>

 #include <lemon/bits/alteration_notifier.h>

 ///\ingroup gutils

 ///\file

 ///\brief Graph utilities.

 ///

 ///

 namespace lemon {

   /// \addtogroup gutils

   /// @{

   /// \brief Function to count the items in the graph.

   ///

   /// This function counts the items (nodes, edges etc) in the graph.

   /// The complexity of the function is O(n) because

   /// it iterates on all of the items.

   template <typename Graph, typename ItemIt>

   inline int countItems(const Graph& g) {

     int num = 0;

     for (ItemIt it(g); it != INVALID; ++it) {

       ++num;

     }

     return num;

   }

   // Node counting:

   template <typename Graph>

   inline

   typename enable_if<typename Graph::NodeNumTag, int>::type

   _countNodes(const Graph &g) {

     return g.nodeNum();

   }

   template <typename Graph>

   inline int _countNodes(Wrap<Graph> w) {

     return countItems<Graph, typename Graph::NodeIt>(w.value);

   }

   /// \brief Function to count the nodes in the graph.

   ///

   /// This function counts the nodes in the graph.

   /// The complexity of the function is O(n) but for some

   /// graph structures it is specialized to run in O(1).

   ///

   /// \todo refer how to specialize it

   template <typename Graph>

   inline int countNodes(const Graph& g) {

     return _countNodes<Graph>(g);

   }

   // Edge counting:

   template <typename Graph>

   inline

   typename enable_if<typename Graph::EdgeNumTag, int>::type

   _countEdges(const Graph &g) {

     return g.edgeNum();

   }

   template <typename Graph>

   inline int _countEdges(Wrap<Graph> w) {

     return countItems<Graph, typename Graph::EdgeIt>(w.value);

   }

   /// \brief Function to count the edges in the graph.

   ///

   /// This function counts the edges in the graph.

   /// The complexity of the function is O(e) but for some

   /// graph structures it is specialized to run in O(1).

   template <typename Graph>

   inline int countEdges(const Graph& g) {

     return _countEdges<Graph>(g);

   }

   // Undirected edge counting:

   template <typename Graph>

   inline

   typename enable_if<typename Graph::EdgeNumTag, int>::type

   _countUndirEdges(const Graph &g) {

     return g.undirEdgeNum();

   }

   template <typename Graph>

   inline int _countUndirEdges(Wrap<Graph> w) {

     return countItems<Graph, typename Graph::UndirEdgeIt>(w.value);

   }

   /// \brief Function to count the undirected edges in the graph.

   ///

   /// This function counts the undirected edges in the graph.

   /// The complexity of the function is O(e) but for some

   /// graph structures it is specialized to run in O(1).

   template <typename Graph>

   inline int countUndirEdges(const Graph& g) {

     return _countUndirEdges<Graph>(g);

   }

   template <typename Graph, typename DegIt>

   inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {

     int num = 0;

     for (DegIt it(_g, _n); it != INVALID; ++it) {

       ++num;

     }

     return num;

   }

   /// \brief Function to count the number of the out-edges from node \c n.

   ///

   /// This function counts the number of the out-edges from node \c n

   /// in the graph.  

   template <typename Graph>

   inline int countOutEdges(const Graph& _g,  const typename Graph::Node& _n) {

     return countNodeDegree<Graph, typename Graph::OutEdgeIt>(_g, _n);

   }

   /// \brief Function to count the number of the in-edges to node \c n.

   ///

   /// This function counts the number of the in-edges to node \c n

   /// in the graph.  

   template <typename Graph>

   inline int countInEdges(const Graph& _g,  const typename Graph::Node& _n) {

     return countNodeDegree<Graph, typename Graph::InEdgeIt>(_g, _n);

   }

   /// \brief Function to count the number of the inc-edges to node \c n.

   ///

   /// This function counts the number of the inc-edges to node \c n

   /// in the graph.  

   template <typename Graph>

   inline int countIncEdges(const Graph& _g,  const typename Graph::Node& _n) {

     return countNodeDegree<Graph, typename Graph::IncEdgeIt>(_g, _n);

   }

   template <typename Graph>

   inline

   typename enable_if<typename Graph::FindEdgeTag, typename Graph::Edge>::type 

   _findEdge(const Graph &g,

 	    typename Graph::Node u, typename Graph::Node v,

 	    typename Graph::Edge prev = INVALID) {

     return g.findEdge(u, v, prev);

   }

   template <typename Graph>

   inline typename Graph::Edge 

   _findEdge(Wrap<Graph> w,

 	    typename Graph::Node u, 

 	    typename Graph::Node v,

 	    typename Graph::Edge prev = INVALID) {

     const Graph& g = w.value;

     if (prev == INVALID) {

       typename Graph::OutEdgeIt e(g, u);

       while (e != INVALID && g.target(e) != v) ++e;

       return e;

     } else {

       typename Graph::OutEdgeIt e(g, prev); ++e;

       while (e != INVALID && g.target(e) != v) ++e;

       return e;

     }

   }

   /// \brief Finds an edge between two nodes of a graph.

   ///

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

   ///

   /// 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 \ref INVALID if there is no such an edge.

   ///

   /// Thus you can iterate through each edge from \c u to \c v as it follows.

   /// \code

   /// for(Edge e=findEdge(g,u,v);e!=INVALID;e=findEdge(g,u,v,e)) {

   ///   ...

   /// }

   /// \endcode

   // /// \todo We may want to use the "GraphBase" 

   // /// interface here...

   template <typename Graph>

   inline typename Graph::Edge findEdge(const Graph &g,

 				       typename Graph::Node u, 

 				       typename Graph::Node v,

 				       typename Graph::Edge prev = INVALID) {

     return _findEdge<Graph>(g, u, v, prev);

   }

   /// \brief Iterator for iterating on edges connected the same nodes.

   ///

   /// Iterator for iterating on edges connected the same nodes. It is 

   /// higher level interface for the findEdge() function. You can

   /// use it the following way:

   /// \code

   /// for (ConEdgeIt<Graph> it(g, src, trg); it != INVALID; ++it) {

   ///   ...

   /// }

   /// \endcode

   ///

   /// \author Balazs Dezso 

   template <typename _Graph>

   class ConEdgeIt : public _Graph::Edge {

   public:

     typedef _Graph Graph;

     typedef typename Graph::Edge Parent;

     typedef typename Graph::Edge Edge;

     typedef typename Graph::Node Node;

     /// \brief Constructor.

     ///

     /// Construct a new ConEdgeIt iterating on the edges which

     /// connects the \c u and \c v node.

     ConEdgeIt(const Graph& g, Node u, Node v) : graph(g) {

       Parent::operator=(findEdge(graph, u, v));

     }

     /// \brief Constructor.

     ///

     /// Construct a new ConEdgeIt which continues the iterating from 

     /// the \c e edge.

     ConEdgeIt(const Graph& g, Edge e) : Parent(e), graph(g) {}

     /// \brief Increment operator.

     ///

     /// It increments the iterator and gives back the next edge.

     ConEdgeIt& operator++() {

       Parent::operator=(findEdge(graph, graph.source(*this), 

 				 graph.target(*this), *this));

       return *this;

     }

   private:

     const Graph& graph;

   };

   template <typename Graph>

   inline

   typename enable_if<

     typename Graph::FindEdgeTag, 

     typename Graph::UndirEdge>::type 

   _findUndirEdge(const Graph &g,

 	    typename Graph::Node u, typename Graph::Node v,

 	    typename Graph::UndirEdge prev = INVALID) {

     return g.findUndirEdge(u, v, prev);

   }

   template <typename Graph>

   inline typename Graph::UndirEdge 

   _findUndirEdge(Wrap<Graph> w,

 	    typename Graph::Node u, 

 	    typename Graph::Node v,

 	    typename Graph::UndirEdge prev = INVALID) {

     const Graph& g = w.value;

     if (prev == INVALID) {

       typename Graph::OutEdgeIt e(g, u);

       while (e != INVALID && g.target(e) != v) ++e;

       return e;

     } else {

       typename Graph::OutEdgeIt e(g, g.direct(prev, u)); ++e;

       while (e != INVALID && g.target(e) != v) ++e;

       return e;

     }

   }

   /// \brief Finds an undir edge between two nodes of a graph.

   ///

   /// Finds an undir edge from node \c u to node \c v in graph \c g.

   ///

   /// 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 \ref INVALID if there is no such an edge.

   ///

   /// Thus you can iterate through each edge from \c u to \c v as it follows.

   /// \code

   /// for(UndirEdge e = findUndirEdge(g,u,v); e != INVALID; 

   ///     e = findUndirEdge(g,u,v,e)) {

   ///   ...

   /// }

   /// \endcode

   // /// \todo We may want to use the "GraphBase" 

   // /// interface here...

   template <typename Graph>

   inline typename Graph::UndirEdge 

   findUndirEdge(const Graph &g,

 		typename Graph::Node u, 

 		typename Graph::Node v,

 		typename Graph::UndirEdge prev = INVALID) {

     return _findUndirEdge<Graph>(g, u, v, prev);

   }

   /// \brief Iterator for iterating on undir edges connected the same nodes.

   ///

   /// Iterator for iterating on undir edges connected the same nodes. It is 

   /// higher level interface for the findUndirEdge() function. You can

   /// use it the following way:

   /// \code

   /// for (ConUndirEdgeIt<Graph> it(g, src, trg); it != INVALID; ++it) {

   ///   ...

   /// }

   /// \endcode

   ///

   /// \author Balazs Dezso 

   template <typename _Graph>

   class ConUndirEdgeIt : public _Graph::UndirEdge {

   public:

     typedef _Graph Graph;

     typedef typename Graph::UndirEdge Parent;

     typedef typename Graph::UndirEdge UndirEdge;

     typedef typename Graph::Node Node;

     /// \brief Constructor.

     ///

     /// Construct a new ConUndirEdgeIt iterating on the edges which

     /// connects the \c u and \c v node.

     ConUndirEdgeIt(const Graph& g, Node u, Node v) : graph(g) {

       Parent::operator=(findUndirEdge(graph, u, v));

     }

     /// \brief Constructor.

     ///

     /// Construct a new ConUndirEdgeIt which continues the iterating from 

     /// the \c e edge.

     ConUndirEdgeIt(const Graph& g, UndirEdge e) : Parent(e), graph(g) {}

     /// \brief Increment operator.

     ///

     /// It increments the iterator and gives back the next edge.

     ConUndirEdgeIt& operator++() {

       Parent::operator=(findUndirEdge(graph, graph.source(*this), 

 				 graph.target(*this), *this));

       return *this;

     }

   private:

     const Graph& graph;

   };

   /// \brief Copy a map.

   ///

   /// This function copies the \c source map to the \c target map. It uses the

   /// given iterator to iterate on the data structure and it uses the \c ref

   /// mapping to convert the source's keys to the target's keys.

   template <typename Target, typename Source, 

 	    typename ItemIt, typename Ref>	    

   void copyMap(Target& target, const Source& source, 

 	       ItemIt it, const Ref& ref) {

     for (; it != INVALID; ++it) {

       target[ref[it]] = source[it];

     }

   }

   /// \brief Copy the source map to the target map.

   ///

   /// Copy the \c source map to the \c target map. It uses the given iterator

   /// to iterate on the data structure.

   template <typename Target, typename Source, 

 	    typename ItemIt>	    

   void copyMap(Target& target, const Source& source, ItemIt it) {

     for (; it != INVALID; ++it) {

       target[it] = source[it];

     }

   }

   /// \brief Class to copy a graph.

   ///

   /// Class to copy a graph to an other graph (duplicate a graph). The

   /// simplest way of using it is through the \c copyGraph() function.

   template <typename Target, typename Source>

   class GraphCopy {

   public: 

     typedef typename Source::Node Node;

     typedef typename Source::NodeIt NodeIt;

     typedef typename Source::Edge Edge;

     typedef typename Source::EdgeIt EdgeIt;

     typedef typename Source::template NodeMap<typename Target::Node>NodeRefMap;

     typedef typename Source::template EdgeMap<typename Target::Edge>EdgeRefMap;

     /// \brief Constructor for the GraphCopy.

     ///

     /// It copies the content of the \c _source graph into the

     /// \c _target graph. It creates also two references, one beetween

     /// the two nodeset and one beetween the two edgesets.

     GraphCopy(Target& _target, const Source& _source) 

       : source(_source), target(_target), 

 	nodeRefMap(_source), edgeRefMap(_source) {

       for (NodeIt it(source); it != INVALID; ++it) {

 	nodeRefMap[it] = target.addNode();

       }

       for (EdgeIt it(source); it != INVALID; ++it) {

 	edgeRefMap[it] = target.addEdge(nodeRefMap[source.source(it)], 

 					nodeRefMap[source.target(it)]);

       }

     }

     /// \brief Copies the node references into the given map.

     ///

     /// Copies the node references into the given map.

     template <typename NodeRef>

     const GraphCopy& nodeRef(NodeRef& map) const {

       for (NodeIt it(source); it != INVALID; ++it) {

 	map.set(it, nodeRefMap[it]);

       }

       return *this;

     }

     /// \brief Reverse and copies the node references into the given map.

     ///

     /// Reverse and copies the node references into the given map.

     template <typename NodeRef>

     const GraphCopy& nodeCrossRef(NodeRef& map) const {

       for (NodeIt it(source); it != INVALID; ++it) {

 	map.set(nodeRefMap[it], it);

       }

       return *this;

     }

     /// \brief Copies the edge references into the given map.

     ///

     /// Copies the edge references into the given map.

     template <typename EdgeRef>

     const GraphCopy& edgeRef(EdgeRef& map) const {

       for (EdgeIt it(source); it != INVALID; ++it) {

 	map.set(it, edgeRefMap[it]);

       }

       return *this;

     }

     /// \brief Reverse and copies the edge references into the given map.

     ///

     /// Reverse and copies the edge references into the given map.

     template <typename EdgeRef>

     const GraphCopy& edgeCrossRef(EdgeRef& map) const {

       for (EdgeIt it(source); it != INVALID; ++it) {

 	map.set(edgeRefMap[it], it);

       }

       return *this;

     }

     /// \brief Make copy of the given map.

     ///

     /// Makes copy of the given map for the newly created graph. 

     /// The new map's key type is the target graph's node type,

     /// and the copied map's key type is the source graph's node

     /// type.  

     template <typename TargetMap, typename SourceMap>

     const GraphCopy& nodeMap(TargetMap& tMap, const SourceMap& sMap) const {

       copyMap(tMap, sMap, NodeIt(source), nodeRefMap);

       return *this;

     }

     /// \brief Make copy of the given map.

     ///

     /// Makes copy of the given map for the newly created graph. 

     /// The new map's key type is the target graph's edge type,

     /// and the copied map's key type is the source graph's edge

     /// type.  

     template <typename TargetMap, typename SourceMap>

     const GraphCopy& edgeMap(TargetMap& tMap, const SourceMap& sMap) const {

       copyMap(tMap, sMap, EdgeIt(source), edgeRefMap);

       return *this;

     }

     /// \brief Gives back the stored node references.

     ///

     /// Gives back the stored node references.

     const NodeRefMap& nodeRef() const {

       return nodeRefMap;

     }

     /// \brief Gives back the stored edge references.

     ///

     /// Gives back the stored edge references.

     const EdgeRefMap& edgeRef() const {

       return edgeRefMap;

     }

   private:

     const Source& source;

     Target& target;

     NodeRefMap nodeRefMap;

     EdgeRefMap edgeRefMap;

   };

   /// \brief Copy a graph to an other graph.

   ///

   /// Copy a graph to an other graph.

   /// The usage of the function:

   /// 

   /// \code

   /// copyGraph(trg, src).nodeRef(nr).edgeCrossRef(ecr);

   /// \endcode

   /// 

   /// After the copy the \c nr map will contain the mapping from the

   /// source graph's nodes to the target graph's nodes and the \c ecr will

   /// contain the mapping from the target graph's edges to the source's

   /// edges.

   template <typename Target, typename Source>

   GraphCopy<Target, Source> copyGraph(Target& target, const Source& source) {

     return GraphCopy<Target, Source>(target, source);

   }

   template <typename _Graph, typename _Item>

   class ItemSetTraits {};

   template <typename _Graph>

   class ItemSetTraits<_Graph, typename _Graph::Node> {

   public:

     typedef _Graph Graph;

     typedef typename Graph::Node Item;

     typedef typename Graph::NodeIt ItemIt;

     template <typename _Value>

     class Map : public Graph::template NodeMap<_Value> {

     public:

       typedef typename Graph::template NodeMap<_Value> Parent; 

       typedef typename Parent::Value Value;

       Map(const Graph& _graph) : Parent(_graph) {}

       Map(const Graph& _graph, const Value& _value) 

 	: Parent(_graph, _value) {}

     };

   };

   template <typename _Graph>

   class ItemSetTraits<_Graph, typename _Graph::Edge> {

   public:

     typedef _Graph Graph;

     typedef typename Graph::Edge Item;

     typedef typename Graph::EdgeIt ItemIt;

     template <typename _Value>

     class Map : public Graph::template EdgeMap<_Value> {

     public:

       typedef typename Graph::template EdgeMap<_Value> Parent; 

       typedef typename Parent::Value Value;

       Map(const Graph& _graph) : Parent(_graph) {}

       Map(const Graph& _graph, const Value& _value) 

 	: Parent(_graph, _value) {}

     };

   };

   template <typename _Graph>

   class ItemSetTraits<_Graph, typename _Graph::UndirEdge> {

   public:

     typedef _Graph Graph;

     typedef typename Graph::UndirEdge Item;

     typedef typename Graph::UndirEdgeIt ItemIt;

     template <typename _Value>

     class Map : public Graph::template UndirEdgeMap<_Value> {

     public:

       typedef typename Graph::template UndirEdgeMap<_Value> Parent; 

       typedef typename Parent::Value Value;

       Map(const Graph& _graph) : Parent(_graph) {}

       Map(const Graph& _graph, const Value& _value) 

 	: Parent(_graph, _value) {}

     };

   };

   /// @}

   /// \addtogroup graph_maps

   /// @{

   template <typename Map, typename Enable = void>

   struct ReferenceMapTraits {

     typedef typename Map::Value Value;

     typedef typename Map::Value& Reference;

     typedef const typename Map::Value& ConstReference;

     typedef typename Map::Value* Pointer;

     typedef const typename Map::Value* ConstPointer;

   };

   template <typename Map>

   struct ReferenceMapTraits<

     Map, 

     typename enable_if<typename Map::FullTypeTag, void>::type

   > {

     typedef typename Map::Value Value;

     typedef typename Map::Reference Reference;

     typedef typename Map::ConstReference ConstReference;

     typedef typename Map::Pointer Pointer;

     typedef typename Map::ConstPointer ConstPointer;

   };

   /// Provides an immutable and unique id for each item in the graph.

   /// The IdMap class provides a unique and immutable id for each item of the

   /// same type (e.g. node) in the graph. This id is <ul><li>\b unique:

   /// different items (nodes) get different ids <li>\b immutable: the id of an

   /// item (node) does not change (even if you delete other nodes).  </ul>

   /// Through this map you get access (i.e. can read) the inner id values of

   /// the items stored in the graph. This map can be inverted with its member

   /// class \c InverseMap.

   ///

   template <typename _Graph, typename _Item>

   class IdMap {

   public:

     typedef _Graph Graph;

     typedef int Value;

     typedef _Item Item;

     typedef _Item Key;

     /// \brief Constructor.

     ///

     /// Constructor for creating id map.

     IdMap(const Graph& _graph) : graph(&_graph) {}

     /// \brief Gives back the \e id of the item.

     ///

     /// Gives back the immutable and unique \e id of the map.

     int operator[](const Item& item) const { return graph->id(item);}

   private:

     const Graph* graph;

   public:

     /// \brief The class represents the inverse of its owner (IdMap).

     ///

     /// The class represents the inverse of its owner (IdMap).

     /// \see inverse()

     class InverseMap {

     public:

       /// \brief Constructor.

       ///

       /// Constructor for creating an id-to-item map.

       InverseMap(const Graph& _graph) : graph(&_graph) {}

       /// \brief Constructor.

       ///

       /// Constructor for creating an id-to-item map.

       InverseMap(const IdMap& idMap) : graph(idMap.graph) {}

       /// \brief Gives back the given item from its id.

       ///

       /// Gives back the given item from its id.

       /// 

       Item operator[](int id) const { return graph->fromId(id, Item());}

     private:

       const Graph* graph;

     };

     /// \brief Gives back the inverse of the map.

     ///

     /// Gives back the inverse of the IdMap.

     InverseMap inverse() const { return InverseMap(*graph);} 

   };

   /// \brief General invertable graph-map type.

   /// This type provides simple invertable graph-maps. 

   /// The InvertableMap wraps an arbitrary ReadWriteMap 

   /// and if a key is set to a new value then store it

   /// in the inverse map.

   /// \param _Graph The graph type.

   /// \param _Map The map to extend with invertable functionality. 

   template <

     typename _Graph,

     typename _Item, 

     typename _Value,

     typename _Map 

     = typename ItemSetTraits<_Graph, _Item>::template Map<_Value>::Parent 

   >

   class InvertableMap : protected _Map {

   public:

     typedef _Map Map;

     typedef _Graph Graph;

     /// The key type of InvertableMap (Node, Edge, UndirEdge).

     typedef typename _Map::Key Key;

     /// The value type of the InvertableMap.

     typedef typename _Map::Value Value;

     /// \brief Constructor.

     ///

     /// Construct a new InvertableMap for the graph.

     ///

     InvertableMap(const Graph& graph) : Map(graph) {} 

     /// \brief The setter function of the map.

     ///

     /// Sets the mapped value.

     void set(const Key& key, const Value& val) {

       Value oldval = Map::operator[](key);

       typename Container::iterator it = invMap.find(oldval);

       if (it != invMap.end() && it->second == key) {

 	invMap.erase(it);

       }      

       invMap.insert(make_pair(val, key));

       Map::set(key, val);

     }

     /// \brief The getter function of the map.

     ///

     /// It gives back the value associated with the key.

     const Value operator[](const Key& key) const {

       return Map::operator[](key);

     }

   protected:

     /// \brief Add a new key to the map.

     ///

     /// Add a new key to the map. It is called by the

     /// \c AlterationNotifier.

     virtual void add(const Key& key) {

       Map::add(key);

     }

     /// \brief Erase the key from the map.

     ///

     /// Erase the key to the map. It is called by the

     /// \c AlterationNotifier.

     virtual void erase(const Key& key) {

       Value val = Map::operator[](key);

       typename Container::iterator it = invMap.find(val);

       if (it != invMap.end() && it->second == key) {

 	invMap.erase(it);

       }

       Map::erase(key);

     }

     /// \brief Clear the keys from the map and inverse map.

     ///

     /// Clear the keys from the map and inverse map. It is called by the

     /// \c AlterationNotifier.

     virtual void clear() {

       invMap.clear();

       Map::clear();

     }

   private:

     typedef std::map<Value, Key> Container;

     Container invMap;    

   public:

     /// \brief The inverse map type.

     ///

     /// The inverse of this map. The subscript operator of the map

     /// gives back always the item what was last assigned to the value. 

     class InverseMap {

     public:

       /// \brief Constructor of the InverseMap.

       ///

       /// Constructor of the InverseMap.

       InverseMap(const InvertableMap& _inverted) : inverted(_inverted) {}

       /// The value type of the InverseMap.

       typedef typename InvertableMap::Key Value;

       /// The key type of the InverseMap.

       typedef typename InvertableMap::Value Key; 

       /// \brief Subscript operator. 

       ///

       /// Subscript operator. It gives back always the item 

       /// what was last assigned to the value.

       Value operator[](const Key& key) const {

 	typename Container::const_iterator it = inverted.invMap.find(key);

 	return it->second;

       }

     private:

       const InvertableMap& inverted;

     };

     /// \brief It gives back the just readeable inverse map.

     ///

     /// It gives back the just readeable inverse map.

     InverseMap inverse() const {

       return InverseMap(*this);

     } 

   };

   /// \brief Provides a mutable, continuous and unique descriptor for each 

   /// item in the graph.

   ///

   /// The DescriptorMap class provides a unique and continuous (but mutable)

   /// descriptor (id) for each item of the same type (e.g. node) in the

   /// graph. This id is <ul><li>\b unique: different items (nodes) get

   /// different ids <li>\b continuous: the range of the ids is the set of

   /// integers between 0 and \c n-1, where \c n is the number of the items of

   /// this type (e.g. nodes) (so the id of a node can change if you delete an

   /// other node, i.e. this id is mutable).  </ul> This map can be inverted

   /// with its member class \c InverseMap.

   ///

   /// \param _Graph The graph class the \c DescriptorMap belongs to.

   /// \param _Item The Item is the Key of the Map. It may be Node, Edge or 

   /// UndirEdge.

   /// \param _Map A ReadWriteMap mapping from the item type to integer.

   template <

     typename _Graph,   

     typename _Item,

     typename _Map 

     = typename ItemSetTraits<_Graph, _Item>::template Map<int>::Parent

   >

   class DescriptorMap : protected _Map {

     typedef _Item Item;

     typedef _Map Map;

   public:

     /// The graph class of DescriptorMap.

     typedef _Graph Graph;

     /// The key type of DescriptorMap (Node, Edge, UndirEdge).

     typedef typename _Map::Key Key;

     /// The value type of DescriptorMap.

     typedef typename _Map::Value Value;

     /// \brief Constructor.

     ///

     /// Constructor for descriptor map.

     DescriptorMap(const Graph& _graph) : Map(_graph) {

       build();

     }

   protected:

     /// \brief Add a new key to the map.

     ///

     /// Add a new key to the map. It is called by the

     /// \c AlterationNotifier.

     virtual void add(const Item& item) {

       Map::add(item);

       Map::set(item, invMap.size());

       invMap.push_back(item);

     }

     /// \brief Erase the key from the map.

     ///

     /// Erase the key to the map. It is called by the

     /// \c AlterationNotifier.

     virtual void erase(const Item& item) {

       Map::set(invMap.back(), Map::operator[](item));

       invMap[Map::operator[](item)] = invMap.back();

       invMap.pop_back();

       Map::erase(item);

     }

     /// \brief Build the unique map.

     ///

     /// Build the unique map. It is called by the

     /// \c AlterationNotifier.

     virtual void build() {

       Map::build();

       Item it;

       const typename Map::Graph* graph = Map::getGraph(); 

       for (graph->first(it); it != INVALID; graph->next(it)) {

 	Map::set(it, invMap.size());

 	invMap.push_back(it);	

       }      

     }

     /// \brief Clear the keys from the map.

     ///

     /// Clear the keys from the map. It is called by the

     /// \c AlterationNotifier.

     virtual void clear() {

       invMap.clear();

       Map::clear();

     }

   public:

     /// \brief Swaps the position of the two items in the map.

     ///

     /// Swaps the position of the two items in the map.

     void swap(const Item& p, const Item& q) {

       int pi = Map::operator[](p);

       int qi = Map::operator[](q);

       Map::set(p, qi);

       invMap[qi] = p;

       Map::set(q, pi);

       invMap[pi] = q;

     }

     /// \brief Gives back the \e descriptor of the item.

     ///

     /// Gives back the mutable and unique \e descriptor of the map.

     int operator[](const Item& item) const {

       return Map::operator[](item);

     }

   private:

     typedef std::vector<Item> Container;

     Container invMap;

   public:

     /// \brief The inverse map type of DescriptorMap.

     ///

     /// The inverse map type of DescriptorMap.

     class InverseMap {

     public:

       /// \brief Constructor of the InverseMap.

       ///

       /// Constructor of the InverseMap.

       InverseMap(const DescriptorMap& _inverted) 

 	: inverted(_inverted) {}

       /// The value type of the InverseMap.

       typedef typename DescriptorMap::Key Value;

       /// The key type of the InverseMap.

       typedef typename DescriptorMap::Value Key; 

       /// \brief Subscript operator. 

       ///

       /// Subscript operator. It gives back the item 

       /// that the descriptor belongs to currently.

       Value operator[](const Key& key) const {

 	return inverted.invMap[key];

       }

       /// \brief Size of the map.

       ///

       /// Returns the size of the map.

       int size() const {

 	return inverted.invMap.size();

       }

     private:

       const DescriptorMap& inverted;

     };

     /// \brief Gives back the inverse of the map.

     ///

     /// Gives back the inverse of the map.

     const InverseMap inverse() const {

       return InverseMap(*this);

     }

   };

   /// \brief Returns the source of the given edge.

   ///

   /// The SourceMap gives back the source Node of the given edge. 

   /// \author Balazs Dezso

   template <typename Graph>

   class SourceMap {

   public:

     typedef typename Graph::Node Value;

     typedef typename Graph::Edge Key;

     /// \brief Constructor

     ///

     /// Constructor

     /// \param _graph The graph that the map belongs to.

     SourceMap(const Graph& _graph) : graph(_graph) {}

     /// \brief The subscript operator.

     ///

     /// The subscript operator.

     /// \param edge The edge 

     /// \return The source of the edge 

     Value operator[](const Key& edge) const {

       return graph.source(edge);

     }

   private:

     const Graph& graph;

   };

   /// \brief Returns a \ref SourceMap class

   ///

   /// This function just returns an \ref SourceMap class.

   /// \relates SourceMap

   template <typename Graph>

   inline SourceMap<Graph> sourceMap(const Graph& graph) {

     return SourceMap<Graph>(graph);

   } 

   /// \brief Returns the target of the given edge.

   ///

   /// The TargetMap gives back the target Node of the given edge. 

   /// \author Balazs Dezso

   template <typename Graph>

   class TargetMap {

   public:

     typedef typename Graph::Node Value;

     typedef typename Graph::Edge Key;

     /// \brief Constructor

     ///

     /// Constructor

     /// \param _graph The graph that the map belongs to.

     TargetMap(const Graph& _graph) : graph(_graph) {}

     /// \brief The subscript operator.

     ///

     /// The subscript operator.

     /// \param e The edge 

     /// \return The target of the edge 

     Value operator[](const Key& e) const {

       return graph.target(e);

     }

   private:

     const Graph& graph;

   };

   /// \brief Returns a \ref TargetMap class

   ///

   /// This function just returns a \ref TargetMap class.

   /// \relates TargetMap

   template <typename Graph>

   inline TargetMap<Graph> targetMap(const Graph& graph) {

     return TargetMap<Graph>(graph);

   }

   /// \brief Returns the "forward" directed edge view of an undirected edge.

   ///

   /// Returns the "forward" directed edge view of an undirected edge.

   /// \author Balazs Dezso

   template <typename Graph>

   class ForwardMap {

   public:

     typedef typename Graph::Edge Value;

     typedef typename Graph::UndirEdge Key;

     /// \brief Constructor

     ///

     /// Constructor

     /// \param _graph The graph that the map belongs to.

     ForwardMap(const Graph& _graph) : graph(_graph) {}

     /// \brief The subscript operator.

     ///

     /// The subscript operator.

     /// \param key An undirected edge 

     /// \return The "forward" directed edge view of undirected edge 

     Value operator[](const Key& key) const {

       return graph.direct(key, true);

     }

   private:

     const Graph& graph;

   };

   /// \brief Returns a \ref ForwardMap class

   ///

   /// This function just returns an \ref ForwardMap class.

   /// \relates ForwardMap

   template <typename Graph>

   inline ForwardMap<Graph> forwardMap(const Graph& graph) {

     return ForwardMap<Graph>(graph);

   }

   /// \brief Returns the "backward" directed edge view of an undirected edge.

   ///

   /// Returns the "backward" directed edge view of an undirected edge.

   /// \author Balazs Dezso

   template <typename Graph>

   class BackwardMap {

   public:

     typedef typename Graph::Edge Value;

     typedef typename Graph::UndirEdge Key;

     /// \brief Constructor

     ///

     /// Constructor

     /// \param _graph The graph that the map belongs to.

     BackwardMap(const Graph& _graph) : graph(_graph) {}

     /// \brief The subscript operator.

     ///

     /// The subscript operator.

     /// \param key An undirected edge 

     /// \return The "backward" directed edge view of undirected edge 

     Value operator[](const Key& key) const {

       return graph.direct(key, false);

     }

   private:

     const Graph& graph;

   };

   /// \brief Returns a \ref BackwardMap class

   /// This function just returns a \ref BackwardMap class.

   /// \relates BackwardMap

   template <typename Graph>

   inline BackwardMap<Graph> backwardMap(const Graph& graph) {

     return BackwardMap<Graph>(graph);

   }

   /// \brief Potential difference map

   ///

   /// If there is an potential map on the nodes then we

   /// can get an edge map as we get the substraction of the

   /// values of the target and source.

   template <typename Graph, typename NodeMap>

   class PotentialDifferenceMap {

   public:

     typedef typename Graph::Edge Key;

     typedef typename NodeMap::Value Value;

     /// \brief Constructor

     ///

     /// Contructor of the map

     PotentialDifferenceMap(const Graph& _graph, const NodeMap& _potential) 

       : graph(_graph), potential(_potential) {}

     /// \brief Const subscription operator

     ///

     /// Const subscription operator

     Value operator[](const Key& edge) const {

       return potential[graph.target(edge)] - potential[graph.source(edge)];

     }

   private:

     const Graph& graph;

     const NodeMap& potential;

   };

   /// \brief Just returns a PotentialDifferenceMap

   ///

   /// Just returns a PotentialDifferenceMap

   /// \relates PotentialDifferenceMap

   template <typename Graph, typename NodeMap>

   PotentialDifferenceMap<Graph, NodeMap> 

   potentialDifferenceMap(const Graph& graph, const NodeMap& potential) {

     return PotentialDifferenceMap<Graph, NodeMap>(graph, potential);

   }

   /// \brief Container for store values for each ordered pair of nodes

   ///

   /// Container for store values for each ordered pair of nodes.

   template <typename _Graph, typename _Value>

   class NodeMatrixMap 

     : protected AlterationNotifier<typename _Graph::Node>::ObserverBase {

   public:

     typedef _Graph Graph;

     typedef typename Graph::Node Node;

     typedef Node Key;

     typedef _Value Value;

     /// \brief Creates a node matrix for the given graph

     ///

     /// Creates a node matrix for the given graph.

     NodeMatrixMap(const Graph& _graph) 

       : graph(_graph), values(size(_graph.maxId(Node()) + 1)) {}

     /// \brief Creates a node matrix for the given graph

     ///

     /// Creates a node matrix for the given graph and assigns each

     /// initial value to the given parameter.

     NodeMatrixMap(const Graph& _graph, const Value& _val) 

       : graph(_graph), values(size(_graph.maxId(Node()) + 1), _val) {}

     /// \brief Gives back the value assigned to the \c left - \c right

     /// ordered pair.

     ///

     /// Gives back the value assigned to the \c left - \c right ordered pair.

     const Value& operator()(const Node& left, const Node& right) const {

       return values[index(graph.id(left), graph.id(right))];

     }

     /// \brief Gives back the value assigned to the \c left - \c right

     /// ordered pair.

     ///

     /// Gives back the value assigned to the \c left - \c right ordered pair.

     Value& operator()(const Node& left, const Node& right) {

       return values[index(graph.id(left), graph.id(right))];

     }

     /// \brief Setter function for the matrix map.

     ///

     /// Setter function for the matrix map.

     void set(const Node& left, const Node& right, const Value& val) {

       values[index(graph.id(left), graph.id(right))] = val;

     }

     /// \brief Map for the coloumn view of the matrix

     ///

     /// Map for the coloumn view of the matrix.

     class ColMap : public MapBase<Node, Value> {

       friend class NodeMatrixMap;

     private:

       ColMap(NodeMatrixMap& _matrix, Node _col) 

 	: matrix(_matrix), col(_col) {}

     public:

       /// \brief Subscription operator

       ///

       /// Subscription operator.

       Value& operator[](Node row) {

 	return matrix(col, row);

       }

       /// \brief Setter function

       ///

       /// Setter function.

       void set(Node row, const Value& val) {

 	matrix.set(col, row, val);

       }

       /// \brief Subscription operator

       ///

       /// Subscription operator.

       const Value& operator[](Node row) const {

 	return matrix(col, row);

       }

     private:

       NodeMatrixMap& matrix;

       Node col;

     };

     /// \brief Map for the const coloumn view of the matrix

     ///

     /// Map for the const coloumn view of the matrix.

     class ConstColMap : public MapBase<Node, Value> {

       friend class NodeMatrixMap;

     private:

       ConstColMap(const NodeMatrixMap& _matrix, Node _col) 

 	: matrix(_matrix), col(_col) {}

     public:

       /// \brief Subscription operator

       ///

       /// Subscription operator.

       const Value& operator[](Node row) const {

 	return matrix(col, row);

       }

     private:

       const NodeMatrixMap& matrix;

       Node col;

     };

     /// \brief Map for the row view of the matrix

     ///

     /// Map for the row view of the matrix.

     class RowMap : public MapBase<Node, Value> {

     public:

       friend class NodeMatrixMap;

     private:

       RowMap(NodeMatrixMap& _matrix, Node _row) 

 	: matrix(_matrix), row(_row) {}

     public:

       /// \brief Subscription operator

       ///

       /// Subscription operator.

       Value& operator[](Node col) {

 	return matrix(col, row);

       }

       /// \brief Setter function

       ///

       /// Setter function.

       void set(Node col, const Value& val) {

 	matrix.set(col, row, val);

       }

       /// \brief Subscription operator

       ///

       /// Subscription operator.

       const Value& operator[](Node col) const {

 	return matrix(col, row);

       }

     private:

       NodeMatrixMap& matrix;

       Node row;

     };

     /// \brief Map for the const row view of the matrix

     ///

     /// Map for the row const view of the matrix.

     class ConstRowMap : public MapBase<Node, Value> {

     public:

       friend class NodeMatrixMap;

     private:

       ConstRowMap(const NodeMatrixMap& _matrix, Node _row) 

 	: matrix(_matrix), row(_row) {}

     public:

       /// \brief Subscription operator

       ///

       /// Subscription operator.

       const Value& operator[](Node col) const {

 	return matrix(col, row);

       }

     private:

       const NodeMatrixMap& matrix;

       Node row;

     };

     /// \brief Gives back the column view for the given node

     ///

     /// Gives back the column view for the given node

     ConstColMap operator[](Node col) const { return ConstColMap(*this, col); }

     /// \brief Gives back the column view for the given node

     ///

     /// Gives back the column view for the given node

     ColMap operator[](Node col) { return ColMap(*this, col); }

     /// \brief Gives back the column view for the given node

     ///

     /// Gives back the column view for the given node

     ConstColMap colMap(Node col) const { return ConstColMap(*this, col); }

     /// \brief Gives back the column view for the given node

     ///

     /// Gives back the column view for the given node

     ColMap colMap(Node col) { return ColMap(*this, col); }

     /// \brief Gives back the row view for the given node

     ///

     /// Gives back the row view for the given node

     ConstRowMap rowMap(Node row) const { return ConstRowMap(*this, row); }

     /// \brief Gives back the row view for the given node

     ///

     /// Gives back the row view for the given node

     RowMap rowMap(Node row) { return RowMap(*this, row); }

   protected:

     static int index(int i, int j) {

       if (i < j) {

 	return j * j + i;

       } else {

 	return i * i + i + j;

       }

     }

     static int size(int s) {

       return s * s;

     }

     void add(const Node& node) {

       if (size(graph.id(node) + 1) >= (int)values.size()) {

 	values.resize(size(graph.id(node) + 1));	

       }

     }

     void erase(const Node&) {}

     void build() {

       values.resize(size(graph.maxId(Node()) + 1));

     }

     void clear() {

       values.clear();

     }   

   private:

     const Graph& graph;

     std::vector<Value> values;

   };

   /// \brief Map of the node in-degrees.

   ///

   /// This map returns the in-degree of a node. Once it is constructed,

   /// the degrees are stored in a standard NodeMap, so each query is done

   /// in constant time. On the other hand, the values are updated automatically

   /// whenever the graph changes.

   ///

   /// \warning Besides addNode() and addEdge(), a graph structure may provide

   /// alternative ways to mogify the graph. The correct behavior of InDegMap

   /// is not guarantied if these additional featureas are used. For example

   /// the funstions \ref ListGraph::changeSource() "changeSource()",

   /// \ref ListGraph::changeTarget() "changeTarget()" and

   /// \ref ListGraph::reverseEdge() "reverseEdge()"

   /// of \ref ListGraph will \e not update the degree values correctly.

   ///

   /// \sa OutDegMap

   template <typename _Graph>

   class InDegMap  

     : protected AlterationNotifier<typename _Graph::Edge>::ObserverBase {

   public:

     typedef _Graph Graph;

     typedef int Value;

     typedef typename Graph::Node Key;

   private:

     class AutoNodeMap : public Graph::template NodeMap<int> {

     public:

       typedef typename Graph::template NodeMap<int> Parent;

       typedef typename Parent::Key Key;

       typedef typename Parent::Value Value;

       AutoNodeMap(const Graph& graph) : Parent(graph, 0) {}

       void add(const Key& key) {

 	Parent::add(key);

 	Parent::set(key, 0);

       }

     };

   public:

     /// \brief Constructor.

     ///

     /// Constructor for creating in-degree map.

     InDegMap(const Graph& _graph) : graph(_graph), deg(_graph) {

       AlterationNotifier<typename _Graph::Edge>

 	::ObserverBase::attach(graph.getNotifier(typename _Graph::Edge()));

       for(typename _Graph::NodeIt it(graph); it != INVALID; ++it) {

 	deg[it] = countInEdges(graph, it);

       }

     }

     virtual ~InDegMap() {

       AlterationNotifier<typename _Graph::Edge>::

 	ObserverBase::detach();

     }

     /// Gives back the in-degree of a Node.

     int operator[](const Key& key) const {

       return deg[key];

     }

   protected:

     typedef typename Graph::Edge Edge;

     virtual void add(const Edge& edge) {

       ++deg[graph.target(edge)];

     }

     virtual void erase(const Edge& edge) {

       --deg[graph.target(edge)];

     }

     virtual void build() {

       for(typename _Graph::NodeIt it(graph); it != INVALID; ++it) {

 	deg[it] = countInEdges(graph, it);

       }      

     }

     virtual void clear() {

       for(typename _Graph::NodeIt it(graph); it != INVALID; ++it) {

 	deg[it] = 0;

       }

     }

   private:

     const _Graph& graph;

     AutoNodeMap deg;

   };

   /// \brief Map of the node out-degrees.

   ///

   /// This map returns the out-degree of a node. Once it is constructed,

   /// the degrees are stored in a standard NodeMap, so each query is done

   /// in constant time. On the other hand, the values are updated automatically

   /// whenever the graph changes.

   ///

   /// \warning Besides addNode() and addEdge(), a graph structure may provide

   /// alternative ways to mogify the graph. The correct behavior of OutDegMap

   /// is not guarantied if these additional featureas are used. For example

   /// the funstions \ref ListGraph::changeSource() "changeSource()",

   /// \ref ListGraph::changeTarget() "changeTarget()" and

   /// \ref ListGraph::reverseEdge() "reverseEdge()"

   /// of \ref ListGraph will \e not update the degree values correctly.

   ///

   /// \sa InDegMap

   template <typename _Graph>

   class OutDegMap  

     : protected AlterationNotifier<typename _Graph::Edge>::ObserverBase {

   public:

     typedef _Graph Graph;

     typedef int Value;

     typedef typename Graph::Node Key;

   private:

     class AutoNodeMap : public Graph::template NodeMap<int> {

     public:

       typedef typename Graph::template NodeMap<int> Parent;

       typedef typename Parent::Key Key;

       typedef typename Parent::Value Value;

       AutoNodeMap(const Graph& graph) : Parent(graph, 0) {}

       void add(const Key& key) {

 	Parent::add(key);

 	Parent::set(key, 0);

       }

     };

   public:

     /// \brief Constructor.

     ///

     /// Constructor for creating out-degree map.

     OutDegMap(const Graph& _graph) : graph(_graph), deg(_graph) {

       AlterationNotifier<typename _Graph::Edge>

 	::ObserverBase::attach(graph.getNotifier(typename _Graph::Edge()));

       for(typename _Graph::NodeIt it(graph); it != INVALID; ++it) {

 	deg[it] = countOutEdges(graph, it);

       }

     }

     virtual ~OutDegMap() {

       AlterationNotifier<typename _Graph::Edge>::

 	ObserverBase::detach();

     }

     /// Gives back the in-degree of a Node.

     int operator[](const Key& key) const {

       return deg[key];

     }

   protected:

     typedef typename Graph::Edge Edge;

     virtual void add(const Edge& edge) {

       ++deg[graph.source(edge)];

     }

     virtual void erase(const Edge& edge) {

       --deg[graph.source(edge)];

     }

     virtual void build() {

       for(typename _Graph::NodeIt it(graph); it != INVALID; ++it) {

 	deg[it] = countOutEdges(graph, it);

       }      

     }

     virtual void clear() {

       for(typename _Graph::NodeIt it(graph); it != INVALID; ++it) {

 	deg[it] = 0;

       }

     }

   private:

     const _Graph& graph;

     AutoNodeMap deg;

   };

   // Indicators for the tags

   template <typename Graph, typename Enable = void>

   struct NodeNumTagIndicator {

     static const bool value = false;

   };

   template <typename Graph>

   struct NodeNumTagIndicator<

     Graph, 

     typename enable_if<typename Graph::NodeNumTag, void>::type

   > {

     static const bool value = true;

   };

   template <typename Graph, typename Enable = void>

   struct EdgeNumTagIndicator {

     static const bool value = false;

   };

   template <typename Graph>

   struct EdgeNumTagIndicator<

     Graph, 

     typename enable_if<typename Graph::EdgeNumTag, void>::type

   > {

     static const bool value = true;

   };

   template <typename Graph, typename Enable = void>

   struct FindEdgeTagIndicator {

     static const bool value = false;

   };

   template <typename Graph>

   struct FindEdgeTagIndicator<

     Graph, 

     typename enable_if<typename Graph::FindEdgeTag, void>::type

   > {

     static const bool value = true;

   };

   /// @}

 } //END OF NAMESPACE LEMON

 #endif