lemon/graph_utils.h
author Alpar Juttner <alpar@cs.elte.hu>
Tue, 17 Jun 2008 12:28:49 +0100
changeset 174 2ec3c1bbc687
parent 157 2ccc1afc2c52
child 199 e3aba2c72be4
permissions -rw-r--r--
Merge
     1 /* -*- C++ -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library
     4  *
     5  * Copyright (C) 2003-2008
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 #ifndef LEMON_GRAPH_UTILS_H
    20 #define LEMON_GRAPH_UTILS_H
    21 
    22 #include <iterator>
    23 #include <vector>
    24 #include <map>
    25 #include <cmath>
    26 #include <algorithm>
    27 
    28 #include <lemon/bits/invalid.h>
    29 #include <lemon/bits/utility.h>
    30 #include <lemon/maps.h>
    31 #include <lemon/bits/traits.h>
    32 
    33 #include <lemon/bits/alteration_notifier.h>
    34 #include <lemon/bits/default_map.h>
    35 
    36 ///\ingroup gutils
    37 ///\file
    38 ///\brief Graph utilities.
    39 
    40 namespace lemon {
    41 
    42   /// \addtogroup gutils
    43   /// @{
    44 
    45   ///Creates convenience typedefs for the digraph types and iterators
    46 
    47   ///This \c \#define creates convenience typedefs for the following types
    48   ///of \c Digraph: \c Node,  \c NodeIt, \c Arc, \c ArcIt, \c InArcIt,
    49   ///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap, 
    50   ///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap.
    51   ///
    52   ///\note If the graph type is a dependent type, ie. the graph type depend
    53   ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
    54   ///macro.
    55 #define DIGRAPH_TYPEDEFS(Digraph)					\
    56   typedef Digraph::Node Node;						\
    57   typedef Digraph::NodeIt NodeIt;					\
    58   typedef Digraph::Arc Arc;						\
    59   typedef Digraph::ArcIt ArcIt;						\
    60   typedef Digraph::InArcIt InArcIt;					\
    61   typedef Digraph::OutArcIt OutArcIt;					\
    62   typedef Digraph::NodeMap<bool> BoolNodeMap;				\
    63   typedef Digraph::NodeMap<int> IntNodeMap;				\
    64   typedef Digraph::NodeMap<double> DoubleNodeMap;			\
    65   typedef Digraph::ArcMap<bool> BoolArcMap;				\
    66   typedef Digraph::ArcMap<int> IntArcMap;				\
    67   typedef Digraph::ArcMap<double> DoubleArcMap
    68 
    69   ///Creates convenience typedefs for the digraph types and iterators
    70 
    71   ///\see DIGRAPH_TYPEDEFS
    72   ///
    73   ///\note Use this macro, if the graph type is a dependent type,
    74   ///ie. the graph type depend on a template parameter.
    75 #define TEMPLATE_DIGRAPH_TYPEDEFS(Digraph)				\
    76   typedef typename Digraph::Node Node;					\
    77   typedef typename Digraph::NodeIt NodeIt;				\
    78   typedef typename Digraph::Arc Arc;					\
    79   typedef typename Digraph::ArcIt ArcIt;				\
    80   typedef typename Digraph::InArcIt InArcIt;				\
    81   typedef typename Digraph::OutArcIt OutArcIt;				\
    82   typedef typename Digraph::template NodeMap<bool> BoolNodeMap;		\
    83   typedef typename Digraph::template NodeMap<int> IntNodeMap;		\
    84   typedef typename Digraph::template NodeMap<double> DoubleNodeMap;	\
    85   typedef typename Digraph::template ArcMap<bool> BoolArcMap;		\
    86   typedef typename Digraph::template ArcMap<int> IntArcMap;		\
    87   typedef typename Digraph::template ArcMap<double> DoubleArcMap
    88   
    89   ///Creates convenience typedefs for the graph types and iterators
    90 
    91   ///This \c \#define creates the same convenience typedefs as defined
    92   ///by \ref DIGRAPH_TYPEDEFS(Graph) and six more, namely it creates
    93   ///\c Edge, \c EdgeIt, \c IncEdgeIt, \c BoolEdgeMap, \c IntEdgeMap,
    94   ///\c DoubleEdgeMap.
    95   ///
    96   ///\note If the graph type is a dependent type, ie. the graph type depend
    97   ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
    98   ///macro.
    99 #define GRAPH_TYPEDEFS(Graph)						\
   100   DIGRAPH_TYPEDEFS(Graph);						\
   101   typedef Graph::Edge Edge;						\
   102   typedef Graph::EdgeIt EdgeIt;						\
   103   typedef Graph::IncEdgeIt IncEdgeIt;					\
   104   typedef Graph::EdgeMap<bool> BoolEdgeMap;				\
   105   typedef Graph::EdgeMap<int> IntEdgeMap;				\
   106   typedef Graph::EdgeMap<double> DoubleEdgeMap
   107 
   108   ///Creates convenience typedefs for the graph types and iterators
   109 
   110   ///\see GRAPH_TYPEDEFS
   111   ///
   112   ///\note Use this macro, if the graph type is a dependent type,
   113   ///ie. the graph type depend on a template parameter.
   114 #define TEMPLATE_GRAPH_TYPEDEFS(Graph)					\
   115   TEMPLATE_DIGRAPH_TYPEDEFS(Graph);					\
   116   typedef typename Graph::Edge Edge;					\
   117   typedef typename Graph::EdgeIt EdgeIt;				\
   118   typedef typename Graph::IncEdgeIt IncEdgeIt;				\
   119   typedef typename Graph::template EdgeMap<bool> BoolEdgeMap;		\
   120   typedef typename Graph::template EdgeMap<int> IntEdgeMap;		\
   121   typedef typename Graph::template EdgeMap<double> DoubleEdgeMap
   122 
   123   /// \brief Function to count the items in the graph.
   124   ///
   125   /// This function counts the items (nodes, arcs etc) in the graph.
   126   /// The complexity of the function is O(n) because
   127   /// it iterates on all of the items.
   128   template <typename Graph, typename Item>
   129   inline int countItems(const Graph& g) {
   130     typedef typename ItemSetTraits<Graph, Item>::ItemIt ItemIt;
   131     int num = 0;
   132     for (ItemIt it(g); it != INVALID; ++it) {
   133       ++num;
   134     }
   135     return num;
   136   }
   137 
   138   // Node counting:
   139 
   140   namespace _graph_utils_bits {
   141     
   142     template <typename Graph, typename Enable = void>
   143     struct CountNodesSelector {
   144       static int count(const Graph &g) {
   145         return countItems<Graph, typename Graph::Node>(g);
   146       }
   147     };
   148 
   149     template <typename Graph>
   150     struct CountNodesSelector<
   151       Graph, typename 
   152       enable_if<typename Graph::NodeNumTag, void>::type> 
   153     {
   154       static int count(const Graph &g) {
   155         return g.nodeNum();
   156       }
   157     };    
   158   }
   159 
   160   /// \brief Function to count the nodes in the graph.
   161   ///
   162   /// This function counts the nodes in the graph.
   163   /// The complexity of the function is O(n) but for some
   164   /// graph structures it is specialized to run in O(1).
   165   ///
   166   /// If the graph contains a \e nodeNum() member function and a 
   167   /// \e NodeNumTag tag then this function calls directly the member
   168   /// function to query the cardinality of the node set.
   169   template <typename Graph>
   170   inline int countNodes(const Graph& g) {
   171     return _graph_utils_bits::CountNodesSelector<Graph>::count(g);
   172   }
   173 
   174   // Arc counting:
   175 
   176   namespace _graph_utils_bits {
   177     
   178     template <typename Graph, typename Enable = void>
   179     struct CountArcsSelector {
   180       static int count(const Graph &g) {
   181         return countItems<Graph, typename Graph::Arc>(g);
   182       }
   183     };
   184 
   185     template <typename Graph>
   186     struct CountArcsSelector<
   187       Graph, 
   188       typename enable_if<typename Graph::ArcNumTag, void>::type> 
   189     {
   190       static int count(const Graph &g) {
   191         return g.arcNum();
   192       }
   193     };    
   194   }
   195 
   196   /// \brief Function to count the arcs in the graph.
   197   ///
   198   /// This function counts the arcs in the graph.
   199   /// The complexity of the function is O(e) but for some
   200   /// graph structures it is specialized to run in O(1).
   201   ///
   202   /// If the graph contains a \e arcNum() member function and a 
   203   /// \e EdgeNumTag tag then this function calls directly the member
   204   /// function to query the cardinality of the arc set.
   205   template <typename Graph>
   206   inline int countArcs(const Graph& g) {
   207     return _graph_utils_bits::CountArcsSelector<Graph>::count(g);
   208   }
   209 
   210   // Edge counting:
   211   namespace _graph_utils_bits {
   212     
   213     template <typename Graph, typename Enable = void>
   214     struct CountEdgesSelector {
   215       static int count(const Graph &g) {
   216         return countItems<Graph, typename Graph::Edge>(g);
   217       }
   218     };
   219 
   220     template <typename Graph>
   221     struct CountEdgesSelector<
   222       Graph, 
   223       typename enable_if<typename Graph::EdgeNumTag, void>::type> 
   224     {
   225       static int count(const Graph &g) {
   226         return g.edgeNum();
   227       }
   228     };    
   229   }
   230 
   231   /// \brief Function to count the edges in the graph.
   232   ///
   233   /// This function counts the edges in the graph.
   234   /// The complexity of the function is O(m) but for some
   235   /// graph structures it is specialized to run in O(1).
   236   ///
   237   /// If the graph contains a \e edgeNum() member function and a 
   238   /// \e EdgeNumTag tag then this function calls directly the member
   239   /// function to query the cardinality of the edge set.
   240   template <typename Graph>
   241   inline int countEdges(const Graph& g) {
   242     return _graph_utils_bits::CountEdgesSelector<Graph>::count(g);
   243 
   244   }
   245 
   246 
   247   template <typename Graph, typename DegIt>
   248   inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {
   249     int num = 0;
   250     for (DegIt it(_g, _n); it != INVALID; ++it) {
   251       ++num;
   252     }
   253     return num;
   254   }
   255 
   256   /// \brief Function to count the number of the out-arcs from node \c n.
   257   ///
   258   /// This function counts the number of the out-arcs from node \c n
   259   /// in the graph.  
   260   template <typename Graph>
   261   inline int countOutArcs(const Graph& _g,  const typename Graph::Node& _n) {
   262     return countNodeDegree<Graph, typename Graph::OutArcIt>(_g, _n);
   263   }
   264 
   265   /// \brief Function to count the number of the in-arcs to node \c n.
   266   ///
   267   /// This function counts the number of the in-arcs to node \c n
   268   /// in the graph.  
   269   template <typename Graph>
   270   inline int countInArcs(const Graph& _g,  const typename Graph::Node& _n) {
   271     return countNodeDegree<Graph, typename Graph::InArcIt>(_g, _n);
   272   }
   273 
   274   /// \brief Function to count the number of the inc-edges to node \c n.
   275   ///
   276   /// This function counts the number of the inc-edges to node \c n
   277   /// in the graph.  
   278   template <typename Graph>
   279   inline int countIncEdges(const Graph& _g,  const typename Graph::Node& _n) {
   280     return countNodeDegree<Graph, typename Graph::IncEdgeIt>(_g, _n);
   281   }
   282 
   283   namespace _graph_utils_bits {
   284     
   285     template <typename Graph, typename Enable = void>
   286     struct FindArcSelector {
   287       typedef typename Graph::Node Node;
   288       typedef typename Graph::Arc Arc;
   289       static Arc find(const Graph &g, Node u, Node v, Arc e) {
   290         if (e == INVALID) {
   291           g.firstOut(e, u);
   292         } else {
   293           g.nextOut(e);
   294         }
   295         while (e != INVALID && g.target(e) != v) {
   296           g.nextOut(e);
   297         }
   298         return e;
   299       }
   300     };
   301 
   302     template <typename Graph>
   303     struct FindArcSelector<
   304       Graph, 
   305       typename enable_if<typename Graph::FindEdgeTag, void>::type> 
   306     {
   307       typedef typename Graph::Node Node;
   308       typedef typename Graph::Arc Arc;
   309       static Arc find(const Graph &g, Node u, Node v, Arc prev) {
   310         return g.findArc(u, v, prev);
   311       }
   312     };    
   313   }
   314 
   315   /// \brief Finds an arc between two nodes of a graph.
   316   ///
   317   /// Finds an arc from node \c u to node \c v in graph \c g.
   318   ///
   319   /// If \c prev is \ref INVALID (this is the default value), then
   320   /// it finds the first arc from \c u to \c v. Otherwise it looks for
   321   /// the next arc from \c u to \c v after \c prev.
   322   /// \return The found arc or \ref INVALID if there is no such an arc.
   323   ///
   324   /// Thus you can iterate through each arc from \c u to \c v as it follows.
   325   ///\code
   326   /// for(Arc e=findArc(g,u,v);e!=INVALID;e=findArc(g,u,v,e)) {
   327   ///   ...
   328   /// }
   329   ///\endcode
   330   ///
   331   ///\sa ArcLookUp
   332   ///\sa AllArcLookUp
   333   ///\sa DynArcLookUp
   334   ///\sa ConArcIt
   335   template <typename Graph>
   336   inline typename Graph::Arc 
   337   findArc(const Graph &g, typename Graph::Node u, typename Graph::Node v,
   338            typename Graph::Arc prev = INVALID) {
   339     return _graph_utils_bits::FindArcSelector<Graph>::find(g, u, v, prev);
   340   }
   341 
   342   /// \brief Iterator for iterating on arcs connected the same nodes.
   343   ///
   344   /// Iterator for iterating on arcs connected the same nodes. It is 
   345   /// higher level interface for the findArc() function. You can
   346   /// use it the following way:
   347   ///\code
   348   /// for (ConArcIt<Graph> it(g, src, trg); it != INVALID; ++it) {
   349   ///   ...
   350   /// }
   351   ///\endcode
   352   /// 
   353   ///\sa findArc()
   354   ///\sa ArcLookUp
   355   ///\sa AllArcLookUp
   356   ///\sa DynArcLookUp
   357   template <typename _Graph>
   358   class ConArcIt : public _Graph::Arc {
   359   public:
   360 
   361     typedef _Graph Graph;
   362     typedef typename Graph::Arc Parent;
   363 
   364     typedef typename Graph::Arc Arc;
   365     typedef typename Graph::Node Node;
   366 
   367     /// \brief Constructor.
   368     ///
   369     /// Construct a new ConArcIt iterating on the arcs which
   370     /// connects the \c u and \c v node.
   371     ConArcIt(const Graph& g, Node u, Node v) : _graph(g) {
   372       Parent::operator=(findArc(_graph, u, v));
   373     }
   374 
   375     /// \brief Constructor.
   376     ///
   377     /// Construct a new ConArcIt which continues the iterating from 
   378     /// the \c e arc.
   379     ConArcIt(const Graph& g, Arc a) : Parent(a), _graph(g) {}
   380     
   381     /// \brief Increment operator.
   382     ///
   383     /// It increments the iterator and gives back the next arc.
   384     ConArcIt& operator++() {
   385       Parent::operator=(findArc(_graph, _graph.source(*this), 
   386 				_graph.target(*this), *this));
   387       return *this;
   388     }
   389   private:
   390     const Graph& _graph;
   391   };
   392 
   393   namespace _graph_utils_bits {
   394     
   395     template <typename Graph, typename Enable = void>
   396     struct FindEdgeSelector {
   397       typedef typename Graph::Node Node;
   398       typedef typename Graph::Edge Edge;
   399       static Edge find(const Graph &g, Node u, Node v, Edge e) {
   400         bool b;
   401         if (u != v) {
   402           if (e == INVALID) {
   403             g.firstInc(e, b, u);
   404           } else {
   405             b = g.u(e) == u;
   406             g.nextInc(e, b);
   407           }
   408           while (e != INVALID && (b ? g.v(e) : g.u(e)) != v) {
   409             g.nextInc(e, b);
   410           }
   411         } else {
   412           if (e == INVALID) {
   413             g.firstInc(e, b, u);
   414           } else {
   415             b = true;
   416             g.nextInc(e, b);
   417           }
   418           while (e != INVALID && (!b || g.v(e) != v)) {
   419             g.nextInc(e, b);
   420           }
   421         }
   422         return e;
   423       }
   424     };
   425 
   426     template <typename Graph>
   427     struct FindEdgeSelector<
   428       Graph, 
   429       typename enable_if<typename Graph::FindEdgeTag, void>::type> 
   430     {
   431       typedef typename Graph::Node Node;
   432       typedef typename Graph::Edge Edge;
   433       static Edge find(const Graph &g, Node u, Node v, Edge prev) {
   434         return g.findEdge(u, v, prev);
   435       }
   436     };    
   437   }
   438 
   439   /// \brief Finds an edge between two nodes of a graph.
   440   ///
   441   /// Finds an edge from node \c u to node \c v in graph \c g.
   442   /// If the node \c u and node \c v is equal then each loop edge
   443   /// will be enumerated once.
   444   ///
   445   /// If \c prev is \ref INVALID (this is the default value), then
   446   /// it finds the first arc from \c u to \c v. Otherwise it looks for
   447   /// the next arc from \c u to \c v after \c prev.
   448   /// \return The found arc or \ref INVALID if there is no such an arc.
   449   ///
   450   /// Thus you can iterate through each arc from \c u to \c v as it follows.
   451   ///\code
   452   /// for(Edge e = findEdge(g,u,v); e != INVALID; 
   453   ///     e = findEdge(g,u,v,e)) {
   454   ///   ...
   455   /// }
   456   ///\endcode
   457   ///
   458   ///\sa ConEdgeIt
   459 
   460   template <typename Graph>
   461   inline typename Graph::Edge 
   462   findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,
   463             typename Graph::Edge p = INVALID) {
   464     return _graph_utils_bits::FindEdgeSelector<Graph>::find(g, u, v, p);
   465   }
   466 
   467   /// \brief Iterator for iterating on edges connected the same nodes.
   468   ///
   469   /// Iterator for iterating on edges connected the same nodes. It is 
   470   /// higher level interface for the findEdge() function. You can
   471   /// use it the following way:
   472   ///\code
   473   /// for (ConEdgeIt<Graph> it(g, src, trg); it != INVALID; ++it) {
   474   ///   ...
   475   /// }
   476   ///\endcode
   477   ///
   478   ///\sa findEdge()
   479   template <typename _Graph>
   480   class ConEdgeIt : public _Graph::Edge {
   481   public:
   482 
   483     typedef _Graph Graph;
   484     typedef typename Graph::Edge Parent;
   485 
   486     typedef typename Graph::Edge Edge;
   487     typedef typename Graph::Node Node;
   488 
   489     /// \brief Constructor.
   490     ///
   491     /// Construct a new ConEdgeIt iterating on the edges which
   492     /// connects the \c u and \c v node.
   493     ConEdgeIt(const Graph& g, Node u, Node v) : _graph(g) {
   494       Parent::operator=(findEdge(_graph, u, v));
   495     }
   496 
   497     /// \brief Constructor.
   498     ///
   499     /// Construct a new ConEdgeIt which continues the iterating from 
   500     /// the \c e edge.
   501     ConEdgeIt(const Graph& g, Edge e) : Parent(e), _graph(g) {}
   502     
   503     /// \brief Increment operator.
   504     ///
   505     /// It increments the iterator and gives back the next edge.
   506     ConEdgeIt& operator++() {
   507       Parent::operator=(findEdge(_graph, _graph.u(*this), 
   508 				 _graph.v(*this), *this));
   509       return *this;
   510     }
   511   private:
   512     const Graph& _graph;
   513   };
   514 
   515   namespace _graph_utils_bits {
   516 
   517     template <typename Digraph, typename Item, typename RefMap>
   518     class MapCopyBase {
   519     public:
   520       virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
   521       
   522       virtual ~MapCopyBase() {}
   523     };
   524 
   525     template <typename Digraph, typename Item, typename RefMap, 
   526               typename ToMap, typename FromMap>
   527     class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
   528     public:
   529 
   530       MapCopy(ToMap& tmap, const FromMap& map) 
   531         : _tmap(tmap), _map(map) {}
   532       
   533       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   534         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   535         for (ItemIt it(digraph); it != INVALID; ++it) {
   536           _tmap.set(refMap[it], _map[it]);
   537         }
   538       }
   539 
   540     private:
   541       ToMap& _tmap;
   542       const FromMap& _map;
   543     };
   544 
   545     template <typename Digraph, typename Item, typename RefMap, typename It>
   546     class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
   547     public:
   548 
   549       ItemCopy(It& it, const Item& item) : _it(it), _item(item) {}
   550       
   551       virtual void copy(const Digraph&, const RefMap& refMap) {
   552         _it = refMap[_item];
   553       }
   554 
   555     private:
   556       It& _it;
   557       Item _item;
   558     };
   559 
   560     template <typename Digraph, typename Item, typename RefMap, typename Ref>
   561     class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   562     public:
   563 
   564       RefCopy(Ref& map) : _map(map) {}
   565       
   566       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   567         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   568         for (ItemIt it(digraph); it != INVALID; ++it) {
   569           _map.set(it, refMap[it]);
   570         }
   571       }
   572 
   573     private:
   574       Ref& _map;
   575     };
   576 
   577     template <typename Digraph, typename Item, typename RefMap, 
   578               typename CrossRef>
   579     class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   580     public:
   581 
   582       CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
   583       
   584       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   585         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   586         for (ItemIt it(digraph); it != INVALID; ++it) {
   587           _cmap.set(refMap[it], it);
   588         }
   589       }
   590 
   591     private:
   592       CrossRef& _cmap;
   593     };
   594 
   595     template <typename Digraph, typename Enable = void>
   596     struct DigraphCopySelector {
   597       template <typename From, typename NodeRefMap, typename ArcRefMap>
   598       static void copy(Digraph &to, const From& from,
   599                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   600         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   601           nodeRefMap[it] = to.addNode();
   602         }
   603         for (typename From::ArcIt it(from); it != INVALID; ++it) {
   604           arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)], 
   605                                           nodeRefMap[from.target(it)]);
   606         }
   607       }
   608     };
   609 
   610     template <typename Digraph>
   611     struct DigraphCopySelector<
   612       Digraph, 
   613       typename enable_if<typename Digraph::BuildTag, void>::type> 
   614     {
   615       template <typename From, typename NodeRefMap, typename ArcRefMap>
   616       static void copy(Digraph &to, const From& from,
   617                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   618         to.build(from, nodeRefMap, arcRefMap);
   619       }
   620     };
   621 
   622     template <typename Graph, typename Enable = void>
   623     struct GraphCopySelector {
   624       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   625       static void copy(Graph &to, const From& from,
   626                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   627         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   628           nodeRefMap[it] = to.addNode();
   629         }
   630         for (typename From::EdgeIt it(from); it != INVALID; ++it) {
   631           edgeRefMap[it] = to.addArc(nodeRefMap[from.source(it)], 
   632 				       nodeRefMap[from.target(it)]);
   633         }
   634       }
   635     };
   636 
   637     template <typename Graph>
   638     struct GraphCopySelector<
   639       Graph, 
   640       typename enable_if<typename Graph::BuildTag, void>::type> 
   641     {
   642       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   643       static void copy(Graph &to, const From& from,
   644                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   645         to.build(from, nodeRefMap, edgeRefMap);
   646       }
   647     };
   648 
   649   }
   650 
   651   /// \brief Class to copy a digraph.
   652   ///
   653   /// Class to copy a digraph to another digraph (duplicate a digraph). The
   654   /// simplest way of using it is through the \c copyDigraph() function.
   655   ///
   656   /// This class not just make a copy of a graph, but it can create
   657   /// references and cross references between the nodes and arcs of
   658   /// the two graphs, it can copy maps for use with the newly created
   659   /// graph and copy nodes and arcs.
   660   ///
   661   /// To make a copy from a graph, first an instance of DigraphCopy
   662   /// should be created, then the data belongs to the graph should
   663   /// assigned to copy. In the end, the \c run() member should be
   664   /// called.
   665   ///
   666   /// The next code copies a graph with several data:
   667   ///\code
   668   ///  DigraphCopy<NewGraph, OrigGraph> dc(new_graph, orig_graph);
   669   ///  // create a reference for the nodes
   670   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   671   ///  dc.nodeRef(nr);
   672   ///  // create a cross reference (inverse) for the arcs
   673   ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);
   674   ///  dc.arcCrossRef(acr);
   675   ///  // copy an arc map
   676   ///  OrigGraph::ArcMap<double> oamap(orig_graph);
   677   ///  NewGraph::ArcMap<double> namap(new_graph);
   678   ///  dc.arcMap(namap, oamap);
   679   ///  // copy a node
   680   ///  OrigGraph::Node on;
   681   ///  NewGraph::Node nn;
   682   ///  dc.node(nn, on);
   683   ///  // Executions of copy
   684   ///  dc.run();
   685   ///\endcode
   686   template <typename To, typename From>
   687   class DigraphCopy {
   688   private:
   689 
   690     typedef typename From::Node Node;
   691     typedef typename From::NodeIt NodeIt;
   692     typedef typename From::Arc Arc;
   693     typedef typename From::ArcIt ArcIt;
   694 
   695     typedef typename To::Node TNode;
   696     typedef typename To::Arc TArc;
   697 
   698     typedef typename From::template NodeMap<TNode> NodeRefMap;
   699     typedef typename From::template ArcMap<TArc> ArcRefMap;
   700     
   701     
   702   public: 
   703 
   704 
   705     /// \brief Constructor for the DigraphCopy.
   706     ///
   707     /// It copies the content of the \c _from digraph into the
   708     /// \c _to digraph.
   709     DigraphCopy(To& to, const From& from) 
   710       : _from(from), _to(to) {}
   711 
   712     /// \brief Destructor of the DigraphCopy
   713     ///
   714     /// Destructor of the DigraphCopy
   715     ~DigraphCopy() {
   716       for (int i = 0; i < int(_node_maps.size()); ++i) {
   717         delete _node_maps[i];
   718       }
   719       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   720         delete _arc_maps[i];
   721       }
   722 
   723     }
   724 
   725     /// \brief Copies the node references into the given map.
   726     ///
   727     /// Copies the node references into the given map. The parameter
   728     /// should be a map, which key type is the Node type of the source
   729     /// graph, while the value type is the Node type of the
   730     /// destination graph.
   731     template <typename NodeRef>
   732     DigraphCopy& nodeRef(NodeRef& map) {
   733       _node_maps.push_back(new _graph_utils_bits::RefCopy<From, Node, 
   734 			   NodeRefMap, NodeRef>(map));
   735       return *this;
   736     }
   737 
   738     /// \brief Copies the node cross references into the given map.
   739     ///
   740     ///  Copies the node cross references (reverse references) into
   741     ///  the given map. The parameter should be a map, which key type
   742     ///  is the Node type of the destination graph, while the value type is
   743     ///  the Node type of the source graph.
   744     template <typename NodeCrossRef>
   745     DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
   746       _node_maps.push_back(new _graph_utils_bits::CrossRefCopy<From, Node,
   747 			   NodeRefMap, NodeCrossRef>(map));
   748       return *this;
   749     }
   750 
   751     /// \brief Make copy of the given map.
   752     ///
   753     /// Makes copy of the given map for the newly created digraph.
   754     /// The new map's key type is the destination graph's node type,
   755     /// and the copied map's key type is the source graph's node type.
   756     template <typename ToMap, typename FromMap>
   757     DigraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
   758       _node_maps.push_back(new _graph_utils_bits::MapCopy<From, Node, 
   759 			   NodeRefMap, ToMap, FromMap>(tmap, map));
   760       return *this;
   761     }
   762 
   763     /// \brief Make a copy of the given node.
   764     ///
   765     /// Make a copy of the given node.
   766     DigraphCopy& node(TNode& tnode, const Node& snode) {
   767       _node_maps.push_back(new _graph_utils_bits::ItemCopy<From, Node, 
   768 			   NodeRefMap, TNode>(tnode, snode));
   769       return *this;
   770     }
   771 
   772     /// \brief Copies the arc references into the given map.
   773     ///
   774     /// Copies the arc references into the given map.
   775     template <typename ArcRef>
   776     DigraphCopy& arcRef(ArcRef& map) {
   777       _arc_maps.push_back(new _graph_utils_bits::RefCopy<From, Arc, 
   778 			  ArcRefMap, ArcRef>(map));
   779       return *this;
   780     }
   781 
   782     /// \brief Copies the arc cross references into the given map.
   783     ///
   784     ///  Copies the arc cross references (reverse references) into
   785     ///  the given map.
   786     template <typename ArcCrossRef>
   787     DigraphCopy& arcCrossRef(ArcCrossRef& map) {
   788       _arc_maps.push_back(new _graph_utils_bits::CrossRefCopy<From, Arc,
   789 			  ArcRefMap, ArcCrossRef>(map));
   790       return *this;
   791     }
   792 
   793     /// \brief Make copy of the given map.
   794     ///
   795     /// Makes copy of the given map for the newly created digraph. 
   796     /// The new map's key type is the to digraph's arc type,
   797     /// and the copied map's key type is the from digraph's arc
   798     /// type.  
   799     template <typename ToMap, typename FromMap>
   800     DigraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
   801       _arc_maps.push_back(new _graph_utils_bits::MapCopy<From, Arc, 
   802 			  ArcRefMap, ToMap, FromMap>(tmap, map));
   803       return *this;
   804     }
   805 
   806     /// \brief Make a copy of the given arc.
   807     ///
   808     /// Make a copy of the given arc.
   809     DigraphCopy& arc(TArc& tarc, const Arc& sarc) {
   810       _arc_maps.push_back(new _graph_utils_bits::ItemCopy<From, Arc, 
   811 			  ArcRefMap, TArc>(tarc, sarc));
   812       return *this;
   813     }
   814 
   815     /// \brief Executes the copies.
   816     ///
   817     /// Executes the copies.
   818     void run() {
   819       NodeRefMap nodeRefMap(_from);
   820       ArcRefMap arcRefMap(_from);
   821       _graph_utils_bits::DigraphCopySelector<To>::
   822         copy(_to, _from, nodeRefMap, arcRefMap);
   823       for (int i = 0; i < int(_node_maps.size()); ++i) {
   824         _node_maps[i]->copy(_from, nodeRefMap);
   825       }
   826       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   827         _arc_maps[i]->copy(_from, arcRefMap);
   828       }      
   829     }
   830 
   831   protected:
   832 
   833 
   834     const From& _from;
   835     To& _to;
   836 
   837     std::vector<_graph_utils_bits::MapCopyBase<From, Node, NodeRefMap>* > 
   838     _node_maps;
   839 
   840     std::vector<_graph_utils_bits::MapCopyBase<From, Arc, ArcRefMap>* > 
   841     _arc_maps;
   842 
   843   };
   844 
   845   /// \brief Copy a digraph to another digraph.
   846   ///
   847   /// Copy a digraph to another digraph. The complete usage of the
   848   /// function is detailed in the DigraphCopy class, but a short
   849   /// example shows a basic work:
   850   ///\code
   851   /// copyDigraph(trg, src).nodeRef(nr).arcCrossRef(ecr).run();
   852   ///\endcode
   853   /// 
   854   /// After the copy the \c nr map will contain the mapping from the
   855   /// nodes of the \c from digraph to the nodes of the \c to digraph and
   856   /// \c ecr will contain the mapping from the arcs of the \c to digraph
   857   /// to the arcs of the \c from digraph.
   858   ///
   859   /// \see DigraphCopy 
   860   template <typename To, typename From>
   861   DigraphCopy<To, From> copyDigraph(To& to, const From& from) {
   862     return DigraphCopy<To, From>(to, from);
   863   }
   864 
   865   /// \brief Class to copy a graph.
   866   ///
   867   /// Class to copy a graph to another graph (duplicate a graph). The
   868   /// simplest way of using it is through the \c copyGraph() function.
   869   ///
   870   /// This class not just make a copy of a graph, but it can create
   871   /// references and cross references between the nodes, edges and arcs of
   872   /// the two graphs, it can copy maps for use with the newly created
   873   /// graph and copy nodes, edges and arcs.
   874   ///
   875   /// To make a copy from a graph, first an instance of GraphCopy
   876   /// should be created, then the data belongs to the graph should
   877   /// assigned to copy. In the end, the \c run() member should be
   878   /// called.
   879   ///
   880   /// The next code copies a graph with several data:
   881   ///\code
   882   ///  GraphCopy<NewGraph, OrigGraph> dc(new_graph, orig_graph);
   883   ///  // create a reference for the nodes
   884   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   885   ///  dc.nodeRef(nr);
   886   ///  // create a cross reference (inverse) for the edges
   887   ///  NewGraph::EdgeMap<OrigGraph::Arc> ecr(new_graph);
   888   ///  dc.edgeCrossRef(ecr);
   889   ///  // copy an arc map
   890   ///  OrigGraph::ArcMap<double> oamap(orig_graph);
   891   ///  NewGraph::ArcMap<double> namap(new_graph);
   892   ///  dc.arcMap(namap, oamap);
   893   ///  // copy a node
   894   ///  OrigGraph::Node on;
   895   ///  NewGraph::Node nn;
   896   ///  dc.node(nn, on);
   897   ///  // Executions of copy
   898   ///  dc.run();
   899   ///\endcode
   900   template <typename To, typename From>
   901   class GraphCopy {
   902   private:
   903 
   904     typedef typename From::Node Node;
   905     typedef typename From::NodeIt NodeIt;
   906     typedef typename From::Arc Arc;
   907     typedef typename From::ArcIt ArcIt;
   908     typedef typename From::Edge Edge;
   909     typedef typename From::EdgeIt EdgeIt;
   910 
   911     typedef typename To::Node TNode;
   912     typedef typename To::Arc TArc;
   913     typedef typename To::Edge TEdge;
   914 
   915     typedef typename From::template NodeMap<TNode> NodeRefMap;
   916     typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
   917 
   918     struct ArcRefMap {
   919       ArcRefMap(const To& to, const From& from,
   920 		const EdgeRefMap& edge_ref, const NodeRefMap& node_ref) 
   921         : _to(to), _from(from), 
   922           _edge_ref(edge_ref), _node_ref(node_ref) {}
   923 
   924       typedef typename From::Arc Key;
   925       typedef typename To::Arc Value;
   926 
   927       Value operator[](const Key& key) const {
   928         bool forward = 
   929           (_from.direction(key) == 
   930 	   (_node_ref[_from.source(key)] == _to.source(_edge_ref[key])));
   931 	return _to.direct(_edge_ref[key], forward); 
   932       }
   933       
   934       const To& _to;
   935       const From& _from;
   936       const EdgeRefMap& _edge_ref;
   937       const NodeRefMap& _node_ref;
   938     };
   939 
   940     
   941   public: 
   942 
   943 
   944     /// \brief Constructor for the GraphCopy.
   945     ///
   946     /// It copies the content of the \c _from graph into the
   947     /// \c _to graph.
   948     GraphCopy(To& to, const From& from) 
   949       : _from(from), _to(to) {}
   950 
   951     /// \brief Destructor of the GraphCopy
   952     ///
   953     /// Destructor of the GraphCopy
   954     ~GraphCopy() {
   955       for (int i = 0; i < int(_node_maps.size()); ++i) {
   956         delete _node_maps[i];
   957       }
   958       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   959         delete _arc_maps[i];
   960       }
   961       for (int i = 0; i < int(_edge_maps.size()); ++i) {
   962         delete _edge_maps[i];
   963       }
   964 
   965     }
   966 
   967     /// \brief Copies the node references into the given map.
   968     ///
   969     /// Copies the node references into the given map.
   970     template <typename NodeRef>
   971     GraphCopy& nodeRef(NodeRef& map) {
   972       _node_maps.push_back(new _graph_utils_bits::RefCopy<From, Node, 
   973 			   NodeRefMap, NodeRef>(map));
   974       return *this;
   975     }
   976 
   977     /// \brief Copies the node cross references into the given map.
   978     ///
   979     ///  Copies the node cross references (reverse references) into
   980     ///  the given map.
   981     template <typename NodeCrossRef>
   982     GraphCopy& nodeCrossRef(NodeCrossRef& map) {
   983       _node_maps.push_back(new _graph_utils_bits::CrossRefCopy<From, Node,
   984 			   NodeRefMap, NodeCrossRef>(map));
   985       return *this;
   986     }
   987 
   988     /// \brief Make copy of the given map.
   989     ///
   990     /// Makes copy of the given map for the newly created graph. 
   991     /// The new map's key type is the to graph's node type,
   992     /// and the copied map's key type is the from graph's node
   993     /// type.  
   994     template <typename ToMap, typename FromMap>
   995     GraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
   996       _node_maps.push_back(new _graph_utils_bits::MapCopy<From, Node, 
   997 			   NodeRefMap, ToMap, FromMap>(tmap, map));
   998       return *this;
   999     }
  1000 
  1001     /// \brief Make a copy of the given node.
  1002     ///
  1003     /// Make a copy of the given node.
  1004     GraphCopy& node(TNode& tnode, const Node& snode) {
  1005       _node_maps.push_back(new _graph_utils_bits::ItemCopy<From, Node, 
  1006 			   NodeRefMap, TNode>(tnode, snode));
  1007       return *this;
  1008     }
  1009 
  1010     /// \brief Copies the arc references into the given map.
  1011     ///
  1012     /// Copies the arc references into the given map.
  1013     template <typename ArcRef>
  1014     GraphCopy& arcRef(ArcRef& map) {
  1015       _arc_maps.push_back(new _graph_utils_bits::RefCopy<From, Arc, 
  1016 			  ArcRefMap, ArcRef>(map));
  1017       return *this;
  1018     }
  1019 
  1020     /// \brief Copies the arc cross references into the given map.
  1021     ///
  1022     ///  Copies the arc cross references (reverse references) into
  1023     ///  the given map.
  1024     template <typename ArcCrossRef>
  1025     GraphCopy& arcCrossRef(ArcCrossRef& map) {
  1026       _arc_maps.push_back(new _graph_utils_bits::CrossRefCopy<From, Arc,
  1027 			  ArcRefMap, ArcCrossRef>(map));
  1028       return *this;
  1029     }
  1030 
  1031     /// \brief Make copy of the given map.
  1032     ///
  1033     /// Makes copy of the given map for the newly created graph. 
  1034     /// The new map's key type is the to graph's arc type,
  1035     /// and the copied map's key type is the from graph's arc
  1036     /// type.  
  1037     template <typename ToMap, typename FromMap>
  1038     GraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
  1039       _arc_maps.push_back(new _graph_utils_bits::MapCopy<From, Arc, 
  1040 			  ArcRefMap, ToMap, FromMap>(tmap, map));
  1041       return *this;
  1042     }
  1043 
  1044     /// \brief Make a copy of the given arc.
  1045     ///
  1046     /// Make a copy of the given arc.
  1047     GraphCopy& arc(TArc& tarc, const Arc& sarc) {
  1048       _arc_maps.push_back(new _graph_utils_bits::ItemCopy<From, Arc, 
  1049 			  ArcRefMap, TArc>(tarc, sarc));
  1050       return *this;
  1051     }
  1052 
  1053     /// \brief Copies the edge references into the given map.
  1054     ///
  1055     /// Copies the edge references into the given map.
  1056     template <typename EdgeRef>
  1057     GraphCopy& edgeRef(EdgeRef& map) {
  1058       _edge_maps.push_back(new _graph_utils_bits::RefCopy<From, Edge, 
  1059 			   EdgeRefMap, EdgeRef>(map));
  1060       return *this;
  1061     }
  1062 
  1063     /// \brief Copies the edge cross references into the given map.
  1064     ///
  1065     /// Copies the edge cross references (reverse
  1066     /// references) into the given map.
  1067     template <typename EdgeCrossRef>
  1068     GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
  1069       _edge_maps.push_back(new _graph_utils_bits::CrossRefCopy<From, 
  1070 			   Edge, EdgeRefMap, EdgeCrossRef>(map));
  1071       return *this;
  1072     }
  1073 
  1074     /// \brief Make copy of the given map.
  1075     ///
  1076     /// Makes copy of the given map for the newly created graph. 
  1077     /// The new map's key type is the to graph's edge type,
  1078     /// and the copied map's key type is the from graph's edge
  1079     /// type.  
  1080     template <typename ToMap, typename FromMap>
  1081     GraphCopy& edgeMap(ToMap& tmap, const FromMap& map) {
  1082       _edge_maps.push_back(new _graph_utils_bits::MapCopy<From, Edge, 
  1083 			   EdgeRefMap, ToMap, FromMap>(tmap, map));
  1084       return *this;
  1085     }
  1086 
  1087     /// \brief Make a copy of the given edge.
  1088     ///
  1089     /// Make a copy of the given edge.
  1090     GraphCopy& edge(TEdge& tedge, const Edge& sedge) {
  1091       _edge_maps.push_back(new _graph_utils_bits::ItemCopy<From, Edge, 
  1092 			   EdgeRefMap, TEdge>(tedge, sedge));
  1093       return *this;
  1094     }
  1095 
  1096     /// \brief Executes the copies.
  1097     ///
  1098     /// Executes the copies.
  1099     void run() {
  1100       NodeRefMap nodeRefMap(_from);
  1101       EdgeRefMap edgeRefMap(_from);
  1102       ArcRefMap arcRefMap(_to, _from, edgeRefMap, nodeRefMap);
  1103       _graph_utils_bits::GraphCopySelector<To>::
  1104         copy(_to, _from, nodeRefMap, edgeRefMap);
  1105       for (int i = 0; i < int(_node_maps.size()); ++i) {
  1106         _node_maps[i]->copy(_from, nodeRefMap);
  1107       }
  1108       for (int i = 0; i < int(_edge_maps.size()); ++i) {
  1109         _edge_maps[i]->copy(_from, edgeRefMap);
  1110       }
  1111       for (int i = 0; i < int(_arc_maps.size()); ++i) {
  1112         _arc_maps[i]->copy(_from, arcRefMap);
  1113       }
  1114     }
  1115 
  1116   private:
  1117     
  1118     const From& _from;
  1119     To& _to;
  1120 
  1121     std::vector<_graph_utils_bits::MapCopyBase<From, Node, NodeRefMap>* > 
  1122     _node_maps;
  1123 
  1124     std::vector<_graph_utils_bits::MapCopyBase<From, Arc, ArcRefMap>* > 
  1125     _arc_maps;
  1126 
  1127     std::vector<_graph_utils_bits::MapCopyBase<From, Edge, EdgeRefMap>* > 
  1128     _edge_maps;
  1129 
  1130   };
  1131 
  1132   /// \brief Copy a graph to another graph.
  1133   ///
  1134   /// Copy a graph to another graph. The complete usage of the
  1135   /// function is detailed in the GraphCopy class, but a short
  1136   /// example shows a basic work:
  1137   ///\code
  1138   /// copyGraph(trg, src).nodeRef(nr).arcCrossRef(ecr).run();
  1139   ///\endcode
  1140   /// 
  1141   /// After the copy the \c nr map will contain the mapping from the
  1142   /// nodes of the \c from graph to the nodes of the \c to graph and
  1143   /// \c ecr will contain the mapping from the arcs of the \c to graph
  1144   /// to the arcs of the \c from graph.
  1145   ///
  1146   /// \see GraphCopy 
  1147   template <typename To, typename From>
  1148   GraphCopy<To, From> 
  1149   copyGraph(To& to, const From& from) {
  1150     return GraphCopy<To, From>(to, from);
  1151   }
  1152 
  1153   /// @}
  1154 
  1155   /// \addtogroup graph_maps
  1156   /// @{
  1157 
  1158   /// Provides an immutable and unique id for each item in the graph.
  1159 
  1160   /// The IdMap class provides a unique and immutable id for each item of the
  1161   /// same type (e.g. node) in the graph. This id is <ul><li>\b unique:
  1162   /// different items (nodes) get different ids <li>\b immutable: the id of an
  1163   /// item (node) does not change (even if you delete other nodes).  </ul>
  1164   /// Through this map you get access (i.e. can read) the inner id values of
  1165   /// the items stored in the graph. This map can be inverted with its member
  1166   /// class \c InverseMap or with the \c operator() member.
  1167   ///
  1168   template <typename _Graph, typename _Item>
  1169   class IdMap {
  1170   public:
  1171     typedef _Graph Graph;
  1172     typedef int Value;
  1173     typedef _Item Item;
  1174     typedef _Item Key;
  1175 
  1176     /// \brief Constructor.
  1177     ///
  1178     /// Constructor of the map.
  1179     explicit IdMap(const Graph& graph) : _graph(&graph) {}
  1180 
  1181     /// \brief Gives back the \e id of the item.
  1182     ///
  1183     /// Gives back the immutable and unique \e id of the item.
  1184     int operator[](const Item& item) const { return _graph->id(item);}
  1185 
  1186     /// \brief Gives back the item by its id.
  1187     ///
  1188     /// Gives back the item by its id.
  1189     Item operator()(int id) { return _graph->fromId(id, Item()); }
  1190 
  1191   private:
  1192     const Graph* _graph;
  1193 
  1194   public:
  1195 
  1196     /// \brief The class represents the inverse of its owner (IdMap).
  1197     ///
  1198     /// The class represents the inverse of its owner (IdMap).
  1199     /// \see inverse()
  1200     class InverseMap {
  1201     public:
  1202 
  1203       /// \brief Constructor.
  1204       ///
  1205       /// Constructor for creating an id-to-item map.
  1206       explicit InverseMap(const Graph& graph) : _graph(&graph) {}
  1207 
  1208       /// \brief Constructor.
  1209       ///
  1210       /// Constructor for creating an id-to-item map.
  1211       explicit InverseMap(const IdMap& map) : _graph(map._graph) {}
  1212 
  1213       /// \brief Gives back the given item from its id.
  1214       ///
  1215       /// Gives back the given item from its id.
  1216       /// 
  1217       Item operator[](int id) const { return _graph->fromId(id, Item());}
  1218 
  1219     private:
  1220       const Graph* _graph;
  1221     };
  1222 
  1223     /// \brief Gives back the inverse of the map.
  1224     ///
  1225     /// Gives back the inverse of the IdMap.
  1226     InverseMap inverse() const { return InverseMap(*_graph);} 
  1227 
  1228   };
  1229 
  1230   
  1231   /// \brief General invertable graph-map type.
  1232 
  1233   /// This type provides simple invertable graph-maps. 
  1234   /// The InvertableMap wraps an arbitrary ReadWriteMap 
  1235   /// and if a key is set to a new value then store it
  1236   /// in the inverse map.
  1237   ///
  1238   /// The values of the map can be accessed
  1239   /// with stl compatible forward iterator.
  1240   ///
  1241   /// \tparam _Graph The graph type.
  1242   /// \tparam _Item The item type of the graph.
  1243   /// \tparam _Value The value type of the map.
  1244   ///
  1245   /// \see IterableValueMap
  1246   template <typename _Graph, typename _Item, typename _Value>
  1247   class InvertableMap : protected DefaultMap<_Graph, _Item, _Value> {
  1248   private:
  1249     
  1250     typedef DefaultMap<_Graph, _Item, _Value> Map;
  1251     typedef _Graph Graph;
  1252 
  1253     typedef std::map<_Value, _Item> Container;
  1254     Container _inv_map;    
  1255 
  1256   public:
  1257  
  1258     /// The key type of InvertableMap (Node, Arc, Edge).
  1259     typedef typename Map::Key Key;
  1260     /// The value type of the InvertableMap.
  1261     typedef typename Map::Value Value;
  1262 
  1263 
  1264 
  1265     /// \brief Constructor.
  1266     ///
  1267     /// Construct a new InvertableMap for the graph.
  1268     ///
  1269     explicit InvertableMap(const Graph& graph) : Map(graph) {} 
  1270 
  1271     /// \brief Forward iterator for values.
  1272     ///
  1273     /// This iterator is an stl compatible forward
  1274     /// iterator on the values of the map. The values can
  1275     /// be accessed in the [beginValue, endValue) range.
  1276     ///
  1277     class ValueIterator 
  1278       : public std::iterator<std::forward_iterator_tag, Value> {
  1279       friend class InvertableMap;
  1280     private:
  1281       ValueIterator(typename Container::const_iterator _it) 
  1282         : it(_it) {}
  1283     public:
  1284       
  1285       ValueIterator() {}
  1286 
  1287       ValueIterator& operator++() { ++it; return *this; }
  1288       ValueIterator operator++(int) { 
  1289         ValueIterator tmp(*this); 
  1290         operator++();
  1291         return tmp; 
  1292       }
  1293 
  1294       const Value& operator*() const { return it->first; }
  1295       const Value* operator->() const { return &(it->first); }
  1296 
  1297       bool operator==(ValueIterator jt) const { return it == jt.it; }
  1298       bool operator!=(ValueIterator jt) const { return it != jt.it; }
  1299       
  1300     private:
  1301       typename Container::const_iterator it;
  1302     };
  1303 
  1304     /// \brief Returns an iterator to the first value.
  1305     ///
  1306     /// Returns an stl compatible iterator to the 
  1307     /// first value of the map. The values of the
  1308     /// map can be accessed in the [beginValue, endValue)
  1309     /// range.
  1310     ValueIterator beginValue() const {
  1311       return ValueIterator(_inv_map.begin());
  1312     }
  1313 
  1314     /// \brief Returns an iterator after the last value.
  1315     ///
  1316     /// Returns an stl compatible iterator after the 
  1317     /// last value of the map. The values of the
  1318     /// map can be accessed in the [beginValue, endValue)
  1319     /// range.
  1320     ValueIterator endValue() const {
  1321       return ValueIterator(_inv_map.end());
  1322     }
  1323     
  1324     /// \brief The setter function of the map.
  1325     ///
  1326     /// Sets the mapped value.
  1327     void set(const Key& key, const Value& val) {
  1328       Value oldval = Map::operator[](key);
  1329       typename Container::iterator it = _inv_map.find(oldval);
  1330       if (it != _inv_map.end() && it->second == key) {
  1331 	_inv_map.erase(it);
  1332       }      
  1333       _inv_map.insert(make_pair(val, key));
  1334       Map::set(key, val);
  1335     }
  1336 
  1337     /// \brief The getter function of the map.
  1338     ///
  1339     /// It gives back the value associated with the key.
  1340     typename MapTraits<Map>::ConstReturnValue 
  1341     operator[](const Key& key) const {
  1342       return Map::operator[](key);
  1343     }
  1344 
  1345     /// \brief Gives back the item by its value.
  1346     ///
  1347     /// Gives back the item by its value.
  1348     Key operator()(const Value& key) const {
  1349       typename Container::const_iterator it = _inv_map.find(key);
  1350       return it != _inv_map.end() ? it->second : INVALID;
  1351     }
  1352 
  1353   protected:
  1354 
  1355     /// \brief Erase the key from the map.
  1356     ///
  1357     /// Erase the key to the map. It is called by the
  1358     /// \c AlterationNotifier.
  1359     virtual void erase(const Key& key) {
  1360       Value val = Map::operator[](key);
  1361       typename Container::iterator it = _inv_map.find(val);
  1362       if (it != _inv_map.end() && it->second == key) {
  1363 	_inv_map.erase(it);
  1364       }
  1365       Map::erase(key);
  1366     }
  1367 
  1368     /// \brief Erase more keys from the map.
  1369     ///
  1370     /// Erase more keys from the map. It is called by the
  1371     /// \c AlterationNotifier.
  1372     virtual void erase(const std::vector<Key>& keys) {
  1373       for (int i = 0; i < int(keys.size()); ++i) {
  1374 	Value val = Map::operator[](keys[i]);
  1375 	typename Container::iterator it = _inv_map.find(val);
  1376 	if (it != _inv_map.end() && it->second == keys[i]) {
  1377 	  _inv_map.erase(it);
  1378 	}
  1379       }
  1380       Map::erase(keys);
  1381     }
  1382 
  1383     /// \brief Clear the keys from the map and inverse map.
  1384     ///
  1385     /// Clear the keys from the map and inverse map. It is called by the
  1386     /// \c AlterationNotifier.
  1387     virtual void clear() {
  1388       _inv_map.clear();
  1389       Map::clear();
  1390     }
  1391 
  1392   public:
  1393 
  1394     /// \brief The inverse map type.
  1395     ///
  1396     /// The inverse of this map. The subscript operator of the map
  1397     /// gives back always the item what was last assigned to the value. 
  1398     class InverseMap {
  1399     public:
  1400       /// \brief Constructor of the InverseMap.
  1401       ///
  1402       /// Constructor of the InverseMap.
  1403       explicit InverseMap(const InvertableMap& inverted) 
  1404         : _inverted(inverted) {}
  1405 
  1406       /// The value type of the InverseMap.
  1407       typedef typename InvertableMap::Key Value;
  1408       /// The key type of the InverseMap.
  1409       typedef typename InvertableMap::Value Key; 
  1410 
  1411       /// \brief Subscript operator. 
  1412       ///
  1413       /// Subscript operator. It gives back always the item 
  1414       /// what was last assigned to the value.
  1415       Value operator[](const Key& key) const {
  1416 	return _inverted(key);
  1417       }
  1418       
  1419     private:
  1420       const InvertableMap& _inverted;
  1421     };
  1422 
  1423     /// \brief It gives back the just readable inverse map.
  1424     ///
  1425     /// It gives back the just readable inverse map.
  1426     InverseMap inverse() const {
  1427       return InverseMap(*this);
  1428     } 
  1429 
  1430 
  1431     
  1432   };
  1433 
  1434   /// \brief Provides a mutable, continuous and unique descriptor for each 
  1435   /// item in the graph.
  1436   ///
  1437   /// The DescriptorMap class provides a unique and continuous (but mutable)
  1438   /// descriptor (id) for each item of the same type (e.g. node) in the
  1439   /// graph. This id is <ul><li>\b unique: different items (nodes) get
  1440   /// different ids <li>\b continuous: the range of the ids is the set of
  1441   /// integers between 0 and \c n-1, where \c n is the number of the items of
  1442   /// this type (e.g. nodes) (so the id of a node can change if you delete an
  1443   /// other node, i.e. this id is mutable).  </ul> This map can be inverted
  1444   /// with its member class \c InverseMap, or with the \c operator() member.
  1445   ///
  1446   /// \tparam _Graph The graph class the \c DescriptorMap belongs to.
  1447   /// \tparam _Item The Item is the Key of the Map. It may be Node, Arc or 
  1448   /// Edge.
  1449   template <typename _Graph, typename _Item>
  1450   class DescriptorMap : protected DefaultMap<_Graph, _Item, int> {
  1451 
  1452     typedef _Item Item;
  1453     typedef DefaultMap<_Graph, _Item, int> Map;
  1454 
  1455   public:
  1456     /// The graph class of DescriptorMap.
  1457     typedef _Graph Graph;
  1458 
  1459     /// The key type of DescriptorMap (Node, Arc, Edge).
  1460     typedef typename Map::Key Key;
  1461     /// The value type of DescriptorMap.
  1462     typedef typename Map::Value Value;
  1463 
  1464     /// \brief Constructor.
  1465     ///
  1466     /// Constructor for descriptor map.
  1467     explicit DescriptorMap(const Graph& _graph) : Map(_graph) {
  1468       Item it;
  1469       const typename Map::Notifier* nf = Map::notifier(); 
  1470       for (nf->first(it); it != INVALID; nf->next(it)) {
  1471 	Map::set(it, _inv_map.size());
  1472 	_inv_map.push_back(it);	
  1473       }      
  1474     }
  1475 
  1476   protected:
  1477 
  1478     /// \brief Add a new key to the map.
  1479     ///
  1480     /// Add a new key to the map. It is called by the
  1481     /// \c AlterationNotifier.
  1482     virtual void add(const Item& item) {
  1483       Map::add(item);
  1484       Map::set(item, _inv_map.size());
  1485       _inv_map.push_back(item);
  1486     }
  1487 
  1488     /// \brief Add more new keys to the map.
  1489     ///
  1490     /// Add more new keys to the map. It is called by the
  1491     /// \c AlterationNotifier.
  1492     virtual void add(const std::vector<Item>& items) {
  1493       Map::add(items);
  1494       for (int i = 0; i < int(items.size()); ++i) {
  1495 	Map::set(items[i], _inv_map.size());
  1496 	_inv_map.push_back(items[i]);
  1497       }
  1498     }
  1499 
  1500     /// \brief Erase the key from the map.
  1501     ///
  1502     /// Erase the key from the map. It is called by the
  1503     /// \c AlterationNotifier.
  1504     virtual void erase(const Item& item) {
  1505       Map::set(_inv_map.back(), Map::operator[](item));
  1506       _inv_map[Map::operator[](item)] = _inv_map.back();
  1507       _inv_map.pop_back();
  1508       Map::erase(item);
  1509     }
  1510 
  1511     /// \brief Erase more keys from the map.
  1512     ///
  1513     /// Erase more keys from the map. It is called by the
  1514     /// \c AlterationNotifier.
  1515     virtual void erase(const std::vector<Item>& items) {
  1516       for (int i = 0; i < int(items.size()); ++i) {
  1517 	Map::set(_inv_map.back(), Map::operator[](items[i]));
  1518 	_inv_map[Map::operator[](items[i])] = _inv_map.back();
  1519 	_inv_map.pop_back();
  1520       }
  1521       Map::erase(items);
  1522     }
  1523 
  1524     /// \brief Build the unique map.
  1525     ///
  1526     /// Build the unique map. It is called by the
  1527     /// \c AlterationNotifier.
  1528     virtual void build() {
  1529       Map::build();
  1530       Item it;
  1531       const typename Map::Notifier* nf = Map::notifier(); 
  1532       for (nf->first(it); it != INVALID; nf->next(it)) {
  1533 	Map::set(it, _inv_map.size());
  1534 	_inv_map.push_back(it);	
  1535       }      
  1536     }
  1537     
  1538     /// \brief Clear the keys from the map.
  1539     ///
  1540     /// Clear the keys from the map. It is called by the
  1541     /// \c AlterationNotifier.
  1542     virtual void clear() {
  1543       _inv_map.clear();
  1544       Map::clear();
  1545     }
  1546 
  1547   public:
  1548 
  1549     /// \brief Returns the maximal value plus one.
  1550     ///
  1551     /// Returns the maximal value plus one in the map.
  1552     unsigned int size() const {
  1553       return _inv_map.size();
  1554     }
  1555 
  1556     /// \brief Swaps the position of the two items in the map.
  1557     ///
  1558     /// Swaps the position of the two items in the map.
  1559     void swap(const Item& p, const Item& q) {
  1560       int pi = Map::operator[](p);
  1561       int qi = Map::operator[](q);
  1562       Map::set(p, qi);
  1563       _inv_map[qi] = p;
  1564       Map::set(q, pi);
  1565       _inv_map[pi] = q;
  1566     }
  1567 
  1568     /// \brief Gives back the \e descriptor of the item.
  1569     ///
  1570     /// Gives back the mutable and unique \e descriptor of the map.
  1571     int operator[](const Item& item) const {
  1572       return Map::operator[](item);
  1573     }
  1574 
  1575     /// \brief Gives back the item by its descriptor.
  1576     ///
  1577     /// Gives back th item by its descriptor.
  1578     Item operator()(int id) const {
  1579       return _inv_map[id];
  1580     }
  1581     
  1582   private:
  1583 
  1584     typedef std::vector<Item> Container;
  1585     Container _inv_map;
  1586 
  1587   public:
  1588     /// \brief The inverse map type of DescriptorMap.
  1589     ///
  1590     /// The inverse map type of DescriptorMap.
  1591     class InverseMap {
  1592     public:
  1593       /// \brief Constructor of the InverseMap.
  1594       ///
  1595       /// Constructor of the InverseMap.
  1596       explicit InverseMap(const DescriptorMap& inverted) 
  1597 	: _inverted(inverted) {}
  1598 
  1599 
  1600       /// The value type of the InverseMap.
  1601       typedef typename DescriptorMap::Key Value;
  1602       /// The key type of the InverseMap.
  1603       typedef typename DescriptorMap::Value Key; 
  1604 
  1605       /// \brief Subscript operator. 
  1606       ///
  1607       /// Subscript operator. It gives back the item 
  1608       /// that the descriptor belongs to currently.
  1609       Value operator[](const Key& key) const {
  1610 	return _inverted(key);
  1611       }
  1612 
  1613       /// \brief Size of the map.
  1614       ///
  1615       /// Returns the size of the map.
  1616       unsigned int size() const {
  1617 	return _inverted.size();
  1618       }
  1619       
  1620     private:
  1621       const DescriptorMap& _inverted;
  1622     };
  1623 
  1624     /// \brief Gives back the inverse of the map.
  1625     ///
  1626     /// Gives back the inverse of the map.
  1627     const InverseMap inverse() const {
  1628       return InverseMap(*this);
  1629     }
  1630   };
  1631 
  1632   /// \brief Returns the source of the given arc.
  1633   ///
  1634   /// The SourceMap gives back the source Node of the given arc. 
  1635   /// \see TargetMap
  1636   template <typename Digraph>
  1637   class SourceMap {
  1638   public:
  1639 
  1640     typedef typename Digraph::Node Value;
  1641     typedef typename Digraph::Arc Key;
  1642 
  1643     /// \brief Constructor
  1644     ///
  1645     /// Constructor
  1646     /// \param _digraph The digraph that the map belongs to.
  1647     explicit SourceMap(const Digraph& digraph) : _digraph(digraph) {}
  1648 
  1649     /// \brief The subscript operator.
  1650     ///
  1651     /// The subscript operator.
  1652     /// \param arc The arc 
  1653     /// \return The source of the arc 
  1654     Value operator[](const Key& arc) const {
  1655       return _digraph.source(arc);
  1656     }
  1657 
  1658   private:
  1659     const Digraph& _digraph;
  1660   };
  1661 
  1662   /// \brief Returns a \ref SourceMap class.
  1663   ///
  1664   /// This function just returns an \ref SourceMap class.
  1665   /// \relates SourceMap
  1666   template <typename Digraph>
  1667   inline SourceMap<Digraph> sourceMap(const Digraph& digraph) {
  1668     return SourceMap<Digraph>(digraph);
  1669   } 
  1670 
  1671   /// \brief Returns the target of the given arc.
  1672   ///
  1673   /// The TargetMap gives back the target Node of the given arc. 
  1674   /// \see SourceMap
  1675   template <typename Digraph>
  1676   class TargetMap {
  1677   public:
  1678 
  1679     typedef typename Digraph::Node Value;
  1680     typedef typename Digraph::Arc Key;
  1681 
  1682     /// \brief Constructor
  1683     ///
  1684     /// Constructor
  1685     /// \param _digraph The digraph that the map belongs to.
  1686     explicit TargetMap(const Digraph& digraph) : _digraph(digraph) {}
  1687 
  1688     /// \brief The subscript operator.
  1689     ///
  1690     /// The subscript operator.
  1691     /// \param e The arc 
  1692     /// \return The target of the arc 
  1693     Value operator[](const Key& e) const {
  1694       return _digraph.target(e);
  1695     }
  1696 
  1697   private:
  1698     const Digraph& _digraph;
  1699   };
  1700 
  1701   /// \brief Returns a \ref TargetMap class.
  1702   ///
  1703   /// This function just returns a \ref TargetMap class.
  1704   /// \relates TargetMap
  1705   template <typename Digraph>
  1706   inline TargetMap<Digraph> targetMap(const Digraph& digraph) {
  1707     return TargetMap<Digraph>(digraph);
  1708   }
  1709 
  1710   /// \brief Returns the "forward" directed arc view of an edge.
  1711   ///
  1712   /// Returns the "forward" directed arc view of an edge.
  1713   /// \see BackwardMap
  1714   template <typename Graph>
  1715   class ForwardMap {
  1716   public:
  1717 
  1718     typedef typename Graph::Arc Value;
  1719     typedef typename Graph::Edge Key;
  1720 
  1721     /// \brief Constructor
  1722     ///
  1723     /// Constructor
  1724     /// \param _graph The graph that the map belongs to.
  1725     explicit ForwardMap(const Graph& graph) : _graph(graph) {}
  1726 
  1727     /// \brief The subscript operator.
  1728     ///
  1729     /// The subscript operator.
  1730     /// \param key An edge 
  1731     /// \return The "forward" directed arc view of edge 
  1732     Value operator[](const Key& key) const {
  1733       return _graph.direct(key, true);
  1734     }
  1735 
  1736   private:
  1737     const Graph& _graph;
  1738   };
  1739 
  1740   /// \brief Returns a \ref ForwardMap class.
  1741   ///
  1742   /// This function just returns an \ref ForwardMap class.
  1743   /// \relates ForwardMap
  1744   template <typename Graph>
  1745   inline ForwardMap<Graph> forwardMap(const Graph& graph) {
  1746     return ForwardMap<Graph>(graph);
  1747   }
  1748 
  1749   /// \brief Returns the "backward" directed arc view of an edge.
  1750   ///
  1751   /// Returns the "backward" directed arc view of an edge.
  1752   /// \see ForwardMap
  1753   template <typename Graph>
  1754   class BackwardMap {
  1755   public:
  1756 
  1757     typedef typename Graph::Arc Value;
  1758     typedef typename Graph::Edge Key;
  1759 
  1760     /// \brief Constructor
  1761     ///
  1762     /// Constructor
  1763     /// \param _graph The graph that the map belongs to.
  1764     explicit BackwardMap(const Graph& graph) : _graph(graph) {}
  1765 
  1766     /// \brief The subscript operator.
  1767     ///
  1768     /// The subscript operator.
  1769     /// \param key An edge 
  1770     /// \return The "backward" directed arc view of edge 
  1771     Value operator[](const Key& key) const {
  1772       return _graph.direct(key, false);
  1773     }
  1774 
  1775   private:
  1776     const Graph& _graph;
  1777   };
  1778 
  1779   /// \brief Returns a \ref BackwardMap class
  1780 
  1781   /// This function just returns a \ref BackwardMap class.
  1782   /// \relates BackwardMap
  1783   template <typename Graph>
  1784   inline BackwardMap<Graph> backwardMap(const Graph& graph) {
  1785     return BackwardMap<Graph>(graph);
  1786   }
  1787 
  1788   /// \brief Potential difference map
  1789   ///
  1790   /// If there is an potential map on the nodes then we
  1791   /// can get an arc map as we get the substraction of the
  1792   /// values of the target and source.
  1793   template <typename Digraph, typename NodeMap>
  1794   class PotentialDifferenceMap {
  1795   public:
  1796     typedef typename Digraph::Arc Key;
  1797     typedef typename NodeMap::Value Value;
  1798 
  1799     /// \brief Constructor
  1800     ///
  1801     /// Contructor of the map
  1802     explicit PotentialDifferenceMap(const Digraph& digraph, 
  1803                                     const NodeMap& potential) 
  1804       : _digraph(digraph), _potential(potential) {}
  1805 
  1806     /// \brief Const subscription operator
  1807     ///
  1808     /// Const subscription operator
  1809     Value operator[](const Key& arc) const {
  1810       return _potential[_digraph.target(arc)] - 
  1811 	_potential[_digraph.source(arc)];
  1812     }
  1813 
  1814   private:
  1815     const Digraph& _digraph;
  1816     const NodeMap& _potential;
  1817   };
  1818 
  1819   /// \brief Returns a PotentialDifferenceMap.
  1820   ///
  1821   /// This function just returns a PotentialDifferenceMap.
  1822   /// \relates PotentialDifferenceMap
  1823   template <typename Digraph, typename NodeMap>
  1824   PotentialDifferenceMap<Digraph, NodeMap> 
  1825   potentialDifferenceMap(const Digraph& digraph, const NodeMap& potential) {
  1826     return PotentialDifferenceMap<Digraph, NodeMap>(digraph, potential);
  1827   }
  1828 
  1829   /// \brief Map of the node in-degrees.
  1830   ///
  1831   /// This map returns the in-degree of a node. Once it is constructed,
  1832   /// the degrees are stored in a standard NodeMap, so each query is done
  1833   /// in constant time. On the other hand, the values are updated automatically
  1834   /// whenever the digraph changes.
  1835   ///
  1836   /// \warning Besides addNode() and addArc(), a digraph structure may provide
  1837   /// alternative ways to modify the digraph. The correct behavior of InDegMap
  1838   /// is not guarantied if these additional features are used. For example
  1839   /// the functions \ref ListDigraph::changeSource() "changeSource()",
  1840   /// \ref ListDigraph::changeTarget() "changeTarget()" and
  1841   /// \ref ListDigraph::reverseArc() "reverseArc()"
  1842   /// of \ref ListDigraph will \e not update the degree values correctly.
  1843   ///
  1844   /// \sa OutDegMap
  1845 
  1846   template <typename _Digraph>
  1847   class InDegMap  
  1848     : protected ItemSetTraits<_Digraph, typename _Digraph::Arc>
  1849       ::ItemNotifier::ObserverBase {
  1850 
  1851   public:
  1852     
  1853     typedef _Digraph Digraph;
  1854     typedef int Value;
  1855     typedef typename Digraph::Node Key;
  1856 
  1857     typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
  1858     ::ItemNotifier::ObserverBase Parent;
  1859 
  1860   private:
  1861 
  1862     class AutoNodeMap : public DefaultMap<Digraph, Key, int> {
  1863     public:
  1864 
  1865       typedef DefaultMap<Digraph, Key, int> Parent;
  1866 
  1867       AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
  1868       
  1869       virtual void add(const Key& key) {
  1870 	Parent::add(key);
  1871 	Parent::set(key, 0);
  1872       }
  1873 
  1874       virtual void add(const std::vector<Key>& keys) {
  1875 	Parent::add(keys);
  1876 	for (int i = 0; i < int(keys.size()); ++i) {
  1877 	  Parent::set(keys[i], 0);
  1878 	}
  1879       }
  1880 
  1881       virtual void build() {
  1882 	Parent::build();
  1883 	Key it;
  1884 	typename Parent::Notifier* nf = Parent::notifier();
  1885 	for (nf->first(it); it != INVALID; nf->next(it)) {
  1886 	  Parent::set(it, 0);
  1887 	}
  1888       }
  1889     };
  1890 
  1891   public:
  1892 
  1893     /// \brief Constructor.
  1894     ///
  1895     /// Constructor for creating in-degree map.
  1896     explicit InDegMap(const Digraph& digraph) 
  1897       : _digraph(digraph), _deg(digraph) {
  1898       Parent::attach(_digraph.notifier(typename Digraph::Arc()));
  1899       
  1900       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  1901 	_deg[it] = countInArcs(_digraph, it);
  1902       }
  1903     }
  1904     
  1905     /// Gives back the in-degree of a Node.
  1906     int operator[](const Key& key) const {
  1907       return _deg[key];
  1908     }
  1909 
  1910   protected:
  1911     
  1912     typedef typename Digraph::Arc Arc;
  1913 
  1914     virtual void add(const Arc& arc) {
  1915       ++_deg[_digraph.target(arc)];
  1916     }
  1917 
  1918     virtual void add(const std::vector<Arc>& arcs) {
  1919       for (int i = 0; i < int(arcs.size()); ++i) {
  1920         ++_deg[_digraph.target(arcs[i])];
  1921       }
  1922     }
  1923 
  1924     virtual void erase(const Arc& arc) {
  1925       --_deg[_digraph.target(arc)];
  1926     }
  1927 
  1928     virtual void erase(const std::vector<Arc>& arcs) {
  1929       for (int i = 0; i < int(arcs.size()); ++i) {
  1930         --_deg[_digraph.target(arcs[i])];
  1931       }
  1932     }
  1933 
  1934     virtual void build() {
  1935       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  1936 	_deg[it] = countInArcs(_digraph, it);
  1937       }      
  1938     }
  1939 
  1940     virtual void clear() {
  1941       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  1942 	_deg[it] = 0;
  1943       }
  1944     }
  1945   private:
  1946     
  1947     const Digraph& _digraph;
  1948     AutoNodeMap _deg;
  1949   };
  1950 
  1951   /// \brief Map of the node out-degrees.
  1952   ///
  1953   /// This map returns the out-degree of a node. Once it is constructed,
  1954   /// the degrees are stored in a standard NodeMap, so each query is done
  1955   /// in constant time. On the other hand, the values are updated automatically
  1956   /// whenever the digraph changes.
  1957   ///
  1958   /// \warning Besides addNode() and addArc(), a digraph structure may provide
  1959   /// alternative ways to modify the digraph. The correct behavior of OutDegMap
  1960   /// is not guarantied if these additional features are used. For example
  1961   /// the functions \ref ListDigraph::changeSource() "changeSource()",
  1962   /// \ref ListDigraph::changeTarget() "changeTarget()" and
  1963   /// \ref ListDigraph::reverseArc() "reverseArc()"
  1964   /// of \ref ListDigraph will \e not update the degree values correctly.
  1965   ///
  1966   /// \sa InDegMap
  1967 
  1968   template <typename _Digraph>
  1969   class OutDegMap  
  1970     : protected ItemSetTraits<_Digraph, typename _Digraph::Arc>
  1971       ::ItemNotifier::ObserverBase {
  1972 
  1973   public:
  1974     
  1975     typedef _Digraph Digraph;
  1976     typedef int Value;
  1977     typedef typename Digraph::Node Key;
  1978 
  1979     typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
  1980     ::ItemNotifier::ObserverBase Parent;
  1981 
  1982   private:
  1983 
  1984     class AutoNodeMap : public DefaultMap<Digraph, Key, int> {
  1985     public:
  1986 
  1987       typedef DefaultMap<Digraph, Key, int> Parent;
  1988 
  1989       AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
  1990       
  1991       virtual void add(const Key& key) {
  1992 	Parent::add(key);
  1993 	Parent::set(key, 0);
  1994       }
  1995       virtual void add(const std::vector<Key>& keys) {
  1996 	Parent::add(keys);
  1997 	for (int i = 0; i < int(keys.size()); ++i) {
  1998 	  Parent::set(keys[i], 0);
  1999 	}
  2000       }
  2001       virtual void build() {
  2002 	Parent::build();
  2003 	Key it;
  2004 	typename Parent::Notifier* nf = Parent::notifier();
  2005 	for (nf->first(it); it != INVALID; nf->next(it)) {
  2006 	  Parent::set(it, 0);
  2007 	}
  2008       }
  2009     };
  2010 
  2011   public:
  2012 
  2013     /// \brief Constructor.
  2014     ///
  2015     /// Constructor for creating out-degree map.
  2016     explicit OutDegMap(const Digraph& digraph) 
  2017       : _digraph(digraph), _deg(digraph) {
  2018       Parent::attach(_digraph.notifier(typename Digraph::Arc()));
  2019       
  2020       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  2021 	_deg[it] = countOutArcs(_digraph, it);
  2022       }
  2023     }
  2024 
  2025     /// Gives back the out-degree of a Node.
  2026     int operator[](const Key& key) const {
  2027       return _deg[key];
  2028     }
  2029 
  2030   protected:
  2031     
  2032     typedef typename Digraph::Arc Arc;
  2033 
  2034     virtual void add(const Arc& arc) {
  2035       ++_deg[_digraph.source(arc)];
  2036     }
  2037 
  2038     virtual void add(const std::vector<Arc>& arcs) {
  2039       for (int i = 0; i < int(arcs.size()); ++i) {
  2040         ++_deg[_digraph.source(arcs[i])];
  2041       }
  2042     }
  2043 
  2044     virtual void erase(const Arc& arc) {
  2045       --_deg[_digraph.source(arc)];
  2046     }
  2047 
  2048     virtual void erase(const std::vector<Arc>& arcs) {
  2049       for (int i = 0; i < int(arcs.size()); ++i) {
  2050         --_deg[_digraph.source(arcs[i])];
  2051       }
  2052     }
  2053 
  2054     virtual void build() {
  2055       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  2056 	_deg[it] = countOutArcs(_digraph, it);
  2057       }      
  2058     }
  2059 
  2060     virtual void clear() {
  2061       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  2062 	_deg[it] = 0;
  2063       }
  2064     }
  2065   private:
  2066     
  2067     const Digraph& _digraph;
  2068     AutoNodeMap _deg;
  2069   };
  2070 
  2071 
  2072   ///Dynamic arc look up between given endpoints.
  2073   
  2074   ///\ingroup gutils
  2075   ///Using this class, you can find an arc in a digraph from a given
  2076   ///source to a given target in amortized time <em>O(log d)</em>,
  2077   ///where <em>d</em> is the out-degree of the source node.
  2078   ///
  2079   ///It is possible to find \e all parallel arcs between two nodes with
  2080   ///the \c findFirst() and \c findNext() members.
  2081   ///
  2082   ///See the \ref ArcLookUp and \ref AllArcLookUp classes if your
  2083   ///digraph is not changed so frequently.
  2084   ///
  2085   ///This class uses a self-adjusting binary search tree, Sleator's
  2086   ///and Tarjan's Splay tree for guarantee the logarithmic amortized
  2087   ///time bound for arc lookups. This class also guarantees the
  2088   ///optimal time bound in a constant factor for any distribution of
  2089   ///queries.
  2090   ///
  2091   ///\tparam G The type of the underlying digraph.  
  2092   ///
  2093   ///\sa ArcLookUp  
  2094   ///\sa AllArcLookUp  
  2095   template<class G>
  2096   class DynArcLookUp 
  2097     : protected ItemSetTraits<G, typename G::Arc>::ItemNotifier::ObserverBase
  2098   {
  2099   public:
  2100     typedef typename ItemSetTraits<G, typename G::Arc>
  2101     ::ItemNotifier::ObserverBase Parent;
  2102 
  2103     TEMPLATE_DIGRAPH_TYPEDEFS(G);
  2104     typedef G Digraph;
  2105 
  2106   protected:
  2107 
  2108     class AutoNodeMap : public DefaultMap<G, Node, Arc> {
  2109     public:
  2110 
  2111       typedef DefaultMap<G, Node, Arc> Parent;
  2112 
  2113       AutoNodeMap(const G& digraph) : Parent(digraph, INVALID) {}
  2114       
  2115       virtual void add(const Node& node) {
  2116 	Parent::add(node);
  2117 	Parent::set(node, INVALID);
  2118       }
  2119 
  2120       virtual void add(const std::vector<Node>& nodes) {
  2121 	Parent::add(nodes);
  2122 	for (int i = 0; i < int(nodes.size()); ++i) {
  2123 	  Parent::set(nodes[i], INVALID);
  2124 	}
  2125       }
  2126 
  2127       virtual void build() {
  2128 	Parent::build();
  2129 	Node it;
  2130 	typename Parent::Notifier* nf = Parent::notifier();
  2131 	for (nf->first(it); it != INVALID; nf->next(it)) {
  2132 	  Parent::set(it, INVALID);
  2133 	}
  2134       }
  2135     };
  2136 
  2137     const Digraph &_g;
  2138     AutoNodeMap _head;
  2139     typename Digraph::template ArcMap<Arc> _parent;
  2140     typename Digraph::template ArcMap<Arc> _left;
  2141     typename Digraph::template ArcMap<Arc> _right;
  2142     
  2143     class ArcLess {
  2144       const Digraph &g;
  2145     public:
  2146       ArcLess(const Digraph &_g) : g(_g) {}
  2147       bool operator()(Arc a,Arc b) const 
  2148       {
  2149 	return g.target(a)<g.target(b);
  2150       }
  2151     };
  2152     
  2153   public:
  2154     
  2155     ///Constructor
  2156 
  2157     ///Constructor.
  2158     ///
  2159     ///It builds up the search database.
  2160     DynArcLookUp(const Digraph &g) 
  2161       : _g(g),_head(g),_parent(g),_left(g),_right(g) 
  2162     { 
  2163       Parent::attach(_g.notifier(typename Digraph::Arc()));
  2164       refresh(); 
  2165     }
  2166     
  2167   protected:
  2168 
  2169     virtual void add(const Arc& arc) {
  2170       insert(arc);
  2171     }
  2172 
  2173     virtual void add(const std::vector<Arc>& arcs) {
  2174       for (int i = 0; i < int(arcs.size()); ++i) {
  2175 	insert(arcs[i]);
  2176       }
  2177     }
  2178 
  2179     virtual void erase(const Arc& arc) {
  2180       remove(arc);
  2181     }
  2182 
  2183     virtual void erase(const std::vector<Arc>& arcs) {
  2184       for (int i = 0; i < int(arcs.size()); ++i) {
  2185 	remove(arcs[i]);
  2186       }     
  2187     }
  2188 
  2189     virtual void build() {
  2190       refresh();
  2191     }
  2192 
  2193     virtual void clear() {
  2194       for(NodeIt n(_g);n!=INVALID;++n) {
  2195 	_head.set(n, INVALID);
  2196       }
  2197     }
  2198 
  2199     void insert(Arc arc) {
  2200       Node s = _g.source(arc);
  2201       Node t = _g.target(arc);
  2202       _left.set(arc, INVALID);
  2203       _right.set(arc, INVALID);
  2204       
  2205       Arc e = _head[s];
  2206       if (e == INVALID) {
  2207 	_head.set(s, arc);
  2208 	_parent.set(arc, INVALID);
  2209 	return;
  2210       }
  2211       while (true) {
  2212 	if (t < _g.target(e)) {
  2213 	  if (_left[e] == INVALID) {
  2214 	    _left.set(e, arc);
  2215 	    _parent.set(arc, e);
  2216 	    splay(arc);
  2217 	    return;
  2218 	  } else {
  2219 	    e = _left[e];
  2220 	  }
  2221 	} else {
  2222 	  if (_right[e] == INVALID) {
  2223 	    _right.set(e, arc);
  2224 	    _parent.set(arc, e);
  2225 	    splay(arc);
  2226 	    return;
  2227 	  } else {
  2228 	    e = _right[e];
  2229 	  }
  2230 	}
  2231       }
  2232     }
  2233 
  2234     void remove(Arc arc) {
  2235       if (_left[arc] == INVALID) {
  2236 	if (_right[arc] != INVALID) {
  2237 	  _parent.set(_right[arc], _parent[arc]);
  2238 	}
  2239 	if (_parent[arc] != INVALID) {
  2240 	  if (_left[_parent[arc]] == arc) {
  2241 	    _left.set(_parent[arc], _right[arc]);
  2242 	  } else {
  2243 	    _right.set(_parent[arc], _right[arc]);
  2244 	  }
  2245 	} else {
  2246 	  _head.set(_g.source(arc), _right[arc]);
  2247 	}
  2248       } else if (_right[arc] == INVALID) {
  2249 	_parent.set(_left[arc], _parent[arc]);
  2250 	if (_parent[arc] != INVALID) {
  2251 	  if (_left[_parent[arc]] == arc) {
  2252 	    _left.set(_parent[arc], _left[arc]);
  2253 	  } else {
  2254 	    _right.set(_parent[arc], _left[arc]);
  2255 	  }
  2256 	} else {
  2257 	  _head.set(_g.source(arc), _left[arc]);
  2258 	}
  2259       } else {
  2260 	Arc e = _left[arc];
  2261 	if (_right[e] != INVALID) {
  2262 	  e = _right[e];	  
  2263 	  while (_right[e] != INVALID) {
  2264 	    e = _right[e];
  2265 	  }
  2266 	  Arc s = _parent[e];
  2267 	  _right.set(_parent[e], _left[e]);
  2268 	  if (_left[e] != INVALID) {
  2269 	    _parent.set(_left[e], _parent[e]);
  2270 	  }
  2271 	  
  2272 	  _left.set(e, _left[arc]);
  2273 	  _parent.set(_left[arc], e);
  2274 	  _right.set(e, _right[arc]);
  2275 	  _parent.set(_right[arc], e);
  2276 
  2277 	  _parent.set(e, _parent[arc]);
  2278 	  if (_parent[arc] != INVALID) {
  2279 	    if (_left[_parent[arc]] == arc) {
  2280 	      _left.set(_parent[arc], e);
  2281 	    } else {
  2282 	      _right.set(_parent[arc], e);
  2283 	    }
  2284 	  }
  2285 	  splay(s);
  2286 	} else {
  2287 	  _right.set(e, _right[arc]);
  2288 	  _parent.set(_right[arc], e);
  2289 
  2290 	  if (_parent[arc] != INVALID) {
  2291 	    if (_left[_parent[arc]] == arc) {
  2292 	      _left.set(_parent[arc], e);
  2293 	    } else {
  2294 	      _right.set(_parent[arc], e);
  2295 	    }
  2296 	  } else {
  2297 	    _head.set(_g.source(arc), e);
  2298 	  }
  2299 	}
  2300       }
  2301     }
  2302 
  2303     Arc refreshRec(std::vector<Arc> &v,int a,int b) 
  2304     {
  2305       int m=(a+b)/2;
  2306       Arc me=v[m];
  2307       if (a < m) {
  2308 	Arc left = refreshRec(v,a,m-1);
  2309 	_left.set(me, left);
  2310 	_parent.set(left, me);
  2311       } else {
  2312 	_left.set(me, INVALID);
  2313       }
  2314       if (m < b) {
  2315 	Arc right = refreshRec(v,m+1,b);
  2316 	_right.set(me, right);
  2317 	_parent.set(right, me);
  2318       } else {
  2319 	_right.set(me, INVALID);
  2320       }
  2321       return me;
  2322     }
  2323 
  2324     void refresh() {
  2325       for(NodeIt n(_g);n!=INVALID;++n) {
  2326 	std::vector<Arc> v;
  2327 	for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
  2328 	if(v.size()) {
  2329 	  std::sort(v.begin(),v.end(),ArcLess(_g));
  2330 	  Arc head = refreshRec(v,0,v.size()-1);
  2331 	  _head.set(n, head);
  2332 	  _parent.set(head, INVALID);
  2333 	}
  2334 	else _head.set(n, INVALID);
  2335       }
  2336     }
  2337 
  2338     void zig(Arc v) {        
  2339       Arc w = _parent[v];
  2340       _parent.set(v, _parent[w]);
  2341       _parent.set(w, v);
  2342       _left.set(w, _right[v]);
  2343       _right.set(v, w);
  2344       if (_parent[v] != INVALID) {
  2345 	if (_right[_parent[v]] == w) {
  2346 	  _right.set(_parent[v], v);
  2347 	} else {
  2348 	  _left.set(_parent[v], v);
  2349 	}
  2350       }
  2351       if (_left[w] != INVALID){
  2352 	_parent.set(_left[w], w);
  2353       }
  2354     }
  2355 
  2356     void zag(Arc v) {        
  2357       Arc w = _parent[v];
  2358       _parent.set(v, _parent[w]);
  2359       _parent.set(w, v);
  2360       _right.set(w, _left[v]);
  2361       _left.set(v, w);
  2362       if (_parent[v] != INVALID){
  2363 	if (_left[_parent[v]] == w) {
  2364 	  _left.set(_parent[v], v);
  2365 	} else {
  2366 	  _right.set(_parent[v], v);
  2367 	}
  2368       }
  2369       if (_right[w] != INVALID){
  2370 	_parent.set(_right[w], w);
  2371       }
  2372     }
  2373 
  2374     void splay(Arc v) {
  2375       while (_parent[v] != INVALID) {
  2376 	if (v == _left[_parent[v]]) {
  2377 	  if (_parent[_parent[v]] == INVALID) {
  2378 	    zig(v);
  2379 	  } else {
  2380 	    if (_parent[v] == _left[_parent[_parent[v]]]) {
  2381 	      zig(_parent[v]);
  2382 	      zig(v);
  2383 	    } else {
  2384 	      zig(v);
  2385 	      zag(v);
  2386 	    }
  2387 	  }
  2388 	} else {
  2389 	  if (_parent[_parent[v]] == INVALID) {
  2390 	    zag(v);
  2391 	  } else {
  2392 	    if (_parent[v] == _left[_parent[_parent[v]]]) {
  2393 	      zag(v);
  2394 	      zig(v);
  2395 	    } else {
  2396 	      zag(_parent[v]);
  2397 	      zag(v);
  2398 	    }
  2399 	  }
  2400 	}
  2401       }
  2402       _head[_g.source(v)] = v;
  2403     }
  2404 
  2405 
  2406   public:
  2407     
  2408     ///Find an arc between two nodes.
  2409     
  2410     ///Find an arc between two nodes in time <em>O(</em>log<em>d)</em>, where
  2411     /// <em>d</em> is the number of outgoing arcs of \c s.
  2412     ///\param s The source node
  2413     ///\param t The target node
  2414     ///\return An arc from \c s to \c t if there exists,
  2415     ///\ref INVALID otherwise.
  2416     Arc operator()(Node s, Node t) const
  2417     {
  2418       Arc a = _head[s];
  2419       while (true) {
  2420 	if (_g.target(a) == t) {
  2421 	  const_cast<DynArcLookUp&>(*this).splay(a);
  2422 	  return a;
  2423 	} else if (t < _g.target(a)) {
  2424 	  if (_left[a] == INVALID) {
  2425 	    const_cast<DynArcLookUp&>(*this).splay(a);
  2426 	    return INVALID;
  2427 	  } else {
  2428 	    a = _left[a];
  2429 	  }
  2430 	} else  {
  2431 	  if (_right[a] == INVALID) {
  2432 	    const_cast<DynArcLookUp&>(*this).splay(a);
  2433 	    return INVALID;
  2434 	  } else {
  2435 	    a = _right[a];
  2436 	  }
  2437 	}
  2438       }
  2439     }
  2440 
  2441     ///Find the first arc between two nodes.
  2442     
  2443     ///Find the first arc between two nodes in time
  2444     /// <em>O(</em>log<em>d)</em>, where <em>d</em> is the number of
  2445     /// outgoing arcs of \c s.  
  2446     ///\param s The source node 
  2447     ///\param t The target node
  2448     ///\return An arc from \c s to \c t if there exists, \ref INVALID
  2449     /// otherwise.
  2450     Arc findFirst(Node s, Node t) const
  2451     {
  2452       Arc a = _head[s];
  2453       Arc r = INVALID;
  2454       while (true) {
  2455 	if (_g.target(a) < t) {
  2456 	  if (_right[a] == INVALID) {
  2457 	    const_cast<DynArcLookUp&>(*this).splay(a);
  2458 	    return r;
  2459 	  } else {
  2460 	    a = _right[a];
  2461 	  }
  2462 	} else {
  2463 	  if (_g.target(a) == t) {
  2464 	    r = a;
  2465 	  }
  2466 	  if (_left[a] == INVALID) {
  2467 	    const_cast<DynArcLookUp&>(*this).splay(a);
  2468 	    return r;
  2469 	  } else {
  2470 	    a = _left[a];
  2471 	  }
  2472 	}
  2473       }
  2474     }
  2475 
  2476     ///Find the next arc between two nodes.
  2477     
  2478     ///Find the next arc between two nodes in time
  2479     /// <em>O(</em>log<em>d)</em>, where <em>d</em> is the number of
  2480     /// outgoing arcs of \c s.  
  2481     ///\param s The source node 
  2482     ///\param t The target node
  2483     ///\return An arc from \c s to \c t if there exists, \ref INVALID
  2484     /// otherwise.
  2485 
  2486     ///\note If \c e is not the result of the previous \c findFirst()
  2487     ///operation then the amorized time bound can not be guaranteed.
  2488 #ifdef DOXYGEN
  2489     Arc findNext(Node s, Node t, Arc a) const
  2490 #else
  2491     Arc findNext(Node, Node t, Arc a) const
  2492 #endif
  2493     {
  2494       if (_right[a] != INVALID) {
  2495 	a = _right[a];
  2496 	while (_left[a] != INVALID) {
  2497 	  a = _left[a];
  2498 	}
  2499 	const_cast<DynArcLookUp&>(*this).splay(a);
  2500       } else {
  2501 	while (_parent[a] != INVALID && _right[_parent[a]] ==  a) {
  2502 	  a = _parent[a];
  2503 	}
  2504 	if (_parent[a] == INVALID) {
  2505 	  return INVALID;
  2506 	} else {
  2507 	  a = _parent[a];
  2508 	  const_cast<DynArcLookUp&>(*this).splay(a);
  2509 	}
  2510       }
  2511       if (_g.target(a) == t) return a;
  2512       else return INVALID;    
  2513     }
  2514 
  2515   };
  2516 
  2517   ///Fast arc look up between given endpoints.
  2518   
  2519   ///\ingroup gutils
  2520   ///Using this class, you can find an arc in a digraph from a given
  2521   ///source to a given target in time <em>O(log d)</em>,
  2522   ///where <em>d</em> is the out-degree of the source node.
  2523   ///
  2524   ///It is not possible to find \e all parallel arcs between two nodes.
  2525   ///Use \ref AllArcLookUp for this purpose.
  2526   ///
  2527   ///\warning This class is static, so you should refresh() (or at least
  2528   ///refresh(Node)) this data structure
  2529   ///whenever the digraph changes. This is a time consuming (superlinearly
  2530   ///proportional (<em>O(m</em>log<em>m)</em>) to the number of arcs).
  2531   ///
  2532   ///\tparam G The type of the underlying digraph.
  2533   ///
  2534   ///\sa DynArcLookUp
  2535   ///\sa AllArcLookUp  
  2536   template<class G>
  2537   class ArcLookUp 
  2538   {
  2539   public:
  2540     TEMPLATE_DIGRAPH_TYPEDEFS(G);
  2541     typedef G Digraph;
  2542 
  2543   protected:
  2544     const Digraph &_g;
  2545     typename Digraph::template NodeMap<Arc> _head;
  2546     typename Digraph::template ArcMap<Arc> _left;
  2547     typename Digraph::template ArcMap<Arc> _right;
  2548     
  2549     class ArcLess {
  2550       const Digraph &g;
  2551     public:
  2552       ArcLess(const Digraph &_g) : g(_g) {}
  2553       bool operator()(Arc a,Arc b) const 
  2554       {
  2555 	return g.target(a)<g.target(b);
  2556       }
  2557     };
  2558     
  2559   public:
  2560     
  2561     ///Constructor
  2562 
  2563     ///Constructor.
  2564     ///
  2565     ///It builds up the search database, which remains valid until the digraph
  2566     ///changes.
  2567     ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}
  2568     
  2569   private:
  2570     Arc refreshRec(std::vector<Arc> &v,int a,int b) 
  2571     {
  2572       int m=(a+b)/2;
  2573       Arc me=v[m];
  2574       _left[me] = a<m?refreshRec(v,a,m-1):INVALID;
  2575       _right[me] = m<b?refreshRec(v,m+1,b):INVALID;
  2576       return me;
  2577     }
  2578   public:
  2579     ///Refresh the data structure at a node.
  2580 
  2581     ///Build up the search database of node \c n.
  2582     ///
  2583     ///It runs in time <em>O(d</em>log<em>d)</em>, where <em>d</em> is
  2584     ///the number of the outgoing arcs of \c n.
  2585     void refresh(Node n) 
  2586     {
  2587       std::vector<Arc> v;
  2588       for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
  2589       if(v.size()) {
  2590 	std::sort(v.begin(),v.end(),ArcLess(_g));
  2591 	_head[n]=refreshRec(v,0,v.size()-1);
  2592       }
  2593       else _head[n]=INVALID;
  2594     }
  2595     ///Refresh the full data structure.
  2596 
  2597     ///Build up the full search database. In fact, it simply calls
  2598     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  2599     ///
  2600     ///It runs in time <em>O(m</em>log<em>D)</em>, where <em>m</em> is
  2601     ///the number of the arcs of \c n and <em>D</em> is the maximum
  2602     ///out-degree of the digraph.
  2603 
  2604     void refresh() 
  2605     {
  2606       for(NodeIt n(_g);n!=INVALID;++n) refresh(n);
  2607     }
  2608     
  2609     ///Find an arc between two nodes.
  2610     
  2611     ///Find an arc between two nodes in time <em>O(</em>log<em>d)</em>, where
  2612     /// <em>d</em> is the number of outgoing arcs of \c s.
  2613     ///\param s The source node
  2614     ///\param t The target node
  2615     ///\return An arc from \c s to \c t if there exists,
  2616     ///\ref INVALID otherwise.
  2617     ///
  2618     ///\warning If you change the digraph, refresh() must be called before using
  2619     ///this operator. If you change the outgoing arcs of
  2620     ///a single node \c n, then
  2621     ///\ref refresh(Node) "refresh(n)" is enough.
  2622     ///
  2623     Arc operator()(Node s, Node t) const
  2624     {
  2625       Arc e;
  2626       for(e=_head[s];
  2627 	  e!=INVALID&&_g.target(e)!=t;
  2628 	  e = t < _g.target(e)?_left[e]:_right[e]) ;
  2629       return e;
  2630     }
  2631 
  2632   };
  2633 
  2634   ///Fast look up of all arcs between given endpoints.
  2635   
  2636   ///\ingroup gutils
  2637   ///This class is the same as \ref ArcLookUp, with the addition
  2638   ///that it makes it possible to find all arcs between given endpoints.
  2639   ///
  2640   ///\warning This class is static, so you should refresh() (or at least
  2641   ///refresh(Node)) this data structure
  2642   ///whenever the digraph changes. This is a time consuming (superlinearly
  2643   ///proportional (<em>O(m</em>log<em>m)</em>) to the number of arcs).
  2644   ///
  2645   ///\tparam G The type of the underlying digraph.
  2646   ///
  2647   ///\sa DynArcLookUp
  2648   ///\sa ArcLookUp  
  2649   template<class G>
  2650   class AllArcLookUp : public ArcLookUp<G>
  2651   {
  2652     using ArcLookUp<G>::_g;
  2653     using ArcLookUp<G>::_right;
  2654     using ArcLookUp<G>::_left;
  2655     using ArcLookUp<G>::_head;
  2656 
  2657     TEMPLATE_DIGRAPH_TYPEDEFS(G);
  2658     typedef G Digraph;
  2659     
  2660     typename Digraph::template ArcMap<Arc> _next;
  2661     
  2662     Arc refreshNext(Arc head,Arc next=INVALID)
  2663     {
  2664       if(head==INVALID) return next;
  2665       else {
  2666 	next=refreshNext(_right[head],next);
  2667 // 	_next[head]=next;
  2668 	_next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
  2669 	  ? next : INVALID;
  2670 	return refreshNext(_left[head],head);
  2671       }
  2672     }
  2673     
  2674     void refreshNext()
  2675     {
  2676       for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
  2677     }
  2678     
  2679   public:
  2680     ///Constructor
  2681 
  2682     ///Constructor.
  2683     ///
  2684     ///It builds up the search database, which remains valid until the digraph
  2685     ///changes.
  2686     AllArcLookUp(const Digraph &g) : ArcLookUp<G>(g), _next(g) {refreshNext();}
  2687 
  2688     ///Refresh the data structure at a node.
  2689 
  2690     ///Build up the search database of node \c n.
  2691     ///
  2692     ///It runs in time <em>O(d</em>log<em>d)</em>, where <em>d</em> is
  2693     ///the number of the outgoing arcs of \c n.
  2694     
  2695     void refresh(Node n) 
  2696     {
  2697       ArcLookUp<G>::refresh(n);
  2698       refreshNext(_head[n]);
  2699     }
  2700     
  2701     ///Refresh the full data structure.
  2702 
  2703     ///Build up the full search database. In fact, it simply calls
  2704     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  2705     ///
  2706     ///It runs in time <em>O(m</em>log<em>D)</em>, where <em>m</em> is
  2707     ///the number of the arcs of \c n and <em>D</em> is the maximum
  2708     ///out-degree of the digraph.
  2709 
  2710     void refresh() 
  2711     {
  2712       for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
  2713     }
  2714     
  2715     ///Find an arc between two nodes.
  2716     
  2717     ///Find an arc between two nodes.
  2718     ///\param s The source node
  2719     ///\param t The target node
  2720     ///\param prev The previous arc between \c s and \c t. It it is INVALID or
  2721     ///not given, the operator finds the first appropriate arc.
  2722     ///\return An arc from \c s to \c t after \c prev or
  2723     ///\ref INVALID if there is no more.
  2724     ///
  2725     ///For example, you can count the number of arcs from \c u to \c v in the
  2726     ///following way.
  2727     ///\code
  2728     ///AllArcLookUp<ListDigraph> ae(g);
  2729     ///...
  2730     ///int n=0;
  2731     ///for(Arc e=ae(u,v);e!=INVALID;e=ae(u,v,e)) n++;
  2732     ///\endcode
  2733     ///
  2734     ///Finding the first arc take <em>O(</em>log<em>d)</em> time, where
  2735     /// <em>d</em> is the number of outgoing arcs of \c s. Then, the
  2736     ///consecutive arcs are found in constant time.
  2737     ///
  2738     ///\warning If you change the digraph, refresh() must be called before using
  2739     ///this operator. If you change the outgoing arcs of
  2740     ///a single node \c n, then
  2741     ///\ref refresh(Node) "refresh(n)" is enough.
  2742     ///
  2743 #ifdef DOXYGEN
  2744     Arc operator()(Node s, Node t, Arc prev=INVALID) const {}
  2745 #else
  2746     using ArcLookUp<G>::operator() ;
  2747     Arc operator()(Node s, Node t, Arc prev) const
  2748     {
  2749       return prev==INVALID?(*this)(s,t):_next[prev];
  2750     }
  2751 #endif
  2752       
  2753   };
  2754 
  2755   /// @}
  2756 
  2757 } //END OF NAMESPACE LEMON
  2758 
  2759 #endif