/* -*- 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 <lemon/invalid.h>

#include <lemon/utility.h>

#include <lemon/maps.h>

#include <lemon/bits/alteration_notifier.h>

///\ingroup gutils

///\file

///\brief Graph utilities.

///

///\todo Please

///revise the documentation.

///

namespace lemon {

  /// \addtogroup gutils

  /// @{

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

  ///

  /// This function counts the items 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 structure 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);

  }

  /// 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...

  /// \bug Untested ...

  template <typename Graph>

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

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

				typename Graph::Edge prev = INVALID) 

  {

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

    //    if(prev==INVALID) g.first(e,u);

    if(prev==INVALID) e=typename Graph::OutEdgeIt(g,u);

    else ++e;

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

    return e;

  }

  /// \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 and it use 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 to an other graph.

  ///

  /// Class to copy a graph to an other graph. It can be used easier

  /// with 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 edge 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 mapping for each item

  /// in the graph.

  ///

  template <typename _Graph, typename _Item>

  class IdMap {

  public:

    typedef _Graph Graph;

    typedef int Value;

    typedef _Item Item;

    typedef _Item Key;

    typedef True NeedCopy;

    /// \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 the map.

    ///

    /// The class represents the inverse of the map.

    /// \see inverse()

    class InverseMap {

    public:

      typedef True NeedCopy;

      /// \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 map.

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

  };

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

  /// This type provides simple invertable map functions. 

  /// 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 mutable, continuous and immutable

  /// mapping for each item in the graph. The value for an item may mutated

  /// on each operation when the an item erased or added to graph.

  ///

  /// \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();

    }

    /// \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.

    ///

    /// The inverse map type.

    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.

      unsigned 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 True NeedCopy;

    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) {

      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 True NeedCopy;

    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) {

      return graph.target(e);

    }

  private:

    const Graph& graph;

  };

  /// \brief Returns a \ref TargetMap class

  ///

  /// This function just returns an \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 undirected edge.

  ///

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

  /// \author Balazs Dezso

  template <typename Graph>

  class ForwardMap {

  public:

    typedef True NeedCopy;

    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.edgeWithSource(key, graph.source(key));

    }

  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 undirected edge.

  ///

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

  /// \author Balazs Dezso

  template <typename Graph>

  class BackwardMap {

  public:

    typedef True NeedCopy;

    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.edgeWithSource(key, graph.target(key));

    }

  private:

    const Graph& graph;

  };

  /// \brief Returns a \ref BackwardMap class

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

  /// \relates BackwardMap

  template <typename Graph>

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

    return BackwardMap<Graph>(graph);

  }

  template <typename _Graph>

  class DegMapBase {

  public:

    typedef _Graph Graph;

  protected:

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

  };

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

  ///

  /// This map returns the in-degree of a node. Ones 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 updates automatically

  /// whenever the graph changes.

  ///

  /// \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: