diff -r d8475431bbbb -r 8e85e6bbefdf src/lemon/graph_utils.h
--- a/src/lemon/graph_utils.h	Sat May 21 21:04:57 2005 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,861 +0,0 @@
-/* -*- C++ -*-
- * src/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>
-
-///\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 structure 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 structure 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 edges in the graph.
-  ///
-  /// This function counts the 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;
-  }
-
-  /// 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 \ref concept::GraphBase "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;
-  }
-  
-  ///\e
-
-  ///\todo Please document.
-  ///
-  template <typename Graph>
-  inline int countOutEdges(const Graph& _g,  const typename Graph::Node& _n) {
-    return countNodeDegree<Graph, typename Graph::OutEdgeIt>(_g, _n);
-  }
-
-  ///\e
-
-  ///\todo Please document.
-  ///
-  template <typename Graph>
-  inline int countInEdges(const Graph& _g,  const typename Graph::Node& _n) {
-    return countNodeDegree<Graph, typename Graph::InEdgeIt>(_g, _n);
-  }
-
-  // graph copy
-
-  template <
-    typename DestinationGraph, 
-    typename SourceGraph, 
-    typename NodeBijection>
-  void copyNodes(DestinationGraph& _d, const SourceGraph& _s, 
-		 NodeBijection& _nb) {    
-    for (typename SourceGraph::NodeIt it(_s); it != INVALID; ++it) {
-      _nb[it] = _d.addNode();
-    }
-  }
-
-  template <
-    typename DestinationGraph, 
-    typename SourceGraph, 
-    typename NodeBijection,
-    typename EdgeBijection>
-  void copyEdges(DestinationGraph& _d, const SourceGraph& _s,
-		 const NodeBijection& _nb, EdgeBijection& _eb) {    
-    for (typename SourceGraph::EdgeIt it(_s); it != INVALID; ++it) {
-      _eb[it] = _d.addEdge(_nb[_s.source(it)], _nb[_s.target(it)]);
-    }
-  }
-
-  template <
-    typename DestinationGraph, 
-    typename SourceGraph, 
-    typename NodeBijection,
-    typename EdgeBijection>
-  void copyGraph(DestinationGraph& _d, const SourceGraph& _s, 
-		 NodeBijection& _nb, EdgeBijection& _eb) {
-    nodeCopy(_d, _s, _nb);
-    edgeCopy(_d, _s, _nb, _eb);
-  }
- 
-  template <
-    typename _DestinationGraph, 
-    typename _SourceGraph, 
-    typename _NodeBijection 
-    =typename _SourceGraph::template NodeMap<typename _DestinationGraph::Node>,
-    typename _EdgeBijection 
-    = typename _SourceGraph::template EdgeMap<typename _DestinationGraph::Edge>
-  >
-  class GraphCopy {
-  public:
-    
-    typedef _DestinationGraph DestinationGraph;
-    typedef _SourceGraph SourceGraph;
-
-    typedef _NodeBijection NodeBijection;
-    typedef _EdgeBijection EdgeBijection;
-    
-  protected:          
-    
-    NodeBijection node_bijection;
-    EdgeBijection edge_bijection;     
-
-  public:
-     
-    GraphCopy(DestinationGraph& _d, const SourceGraph& _s) {
-      copyGraph(_d, _s, node_bijection, edge_bijection);
-    }
-    
-    const NodeBijection& getNodeBijection() const {
-      return node_bijection;
-    }
-
-    const EdgeBijection& getEdgeBijection() const {
-      return edge_bijection;
-    }
-     
-  };
-
-
-  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 an 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 inversable graph-map type.
-
-  /// This type provides simple inversable map functions. 
-  /// The InversableMap wraps an arbitrary ReadWriteMap 
-  /// and if a key is setted to a new value then store it
-  /// in the inverse map.
-  /// \param _Graph The graph type.
-  /// \param _Map The map to extend with inversable 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);
-    }
-
-    /// \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();
-    }
-
-    /// \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];
-      }
-      
-    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 edge The edge 
-    /// \return The target of the edge 
-    Value operator[](const Key& key) {
-      return graph.target(key);
-    }
-
-  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);
-  }
-
-
-  /// @}
-
-} //END OF NAMESPACE LEMON
-
-#endif