lemon/graph_utils.h
author Balazs Dezso <deba@inf.elte.hu>
Thu, 24 Apr 2008 13:53:09 +0100
changeset 149 2f7ae34e1333
parent 147 7c39a090cfc3
child 157 2ccc1afc2c52
permissions -rw-r--r--
Item validity checking for ListGraph and SmartGraph
     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   ///
   358   /// \author Balazs Dezso 
   359   template <typename _Graph>
   360   class ConArcIt : public _Graph::Arc {
   361   public:
   362 
   363     typedef _Graph Graph;
   364     typedef typename Graph::Arc Parent;
   365 
   366     typedef typename Graph::Arc Arc;
   367     typedef typename Graph::Node Node;
   368 
   369     /// \brief Constructor.
   370     ///
   371     /// Construct a new ConArcIt iterating on the arcs which
   372     /// connects the \c u and \c v node.
   373     ConArcIt(const Graph& g, Node u, Node v) : _graph(g) {
   374       Parent::operator=(findArc(_graph, u, v));
   375     }
   376 
   377     /// \brief Constructor.
   378     ///
   379     /// Construct a new ConArcIt which continues the iterating from 
   380     /// the \c e arc.
   381     ConArcIt(const Graph& g, Arc a) : Parent(a), _graph(g) {}
   382     
   383     /// \brief Increment operator.
   384     ///
   385     /// It increments the iterator and gives back the next arc.
   386     ConArcIt& operator++() {
   387       Parent::operator=(findArc(_graph, _graph.source(*this), 
   388 				_graph.target(*this), *this));
   389       return *this;
   390     }
   391   private:
   392     const Graph& _graph;
   393   };
   394 
   395   namespace _graph_utils_bits {
   396     
   397     template <typename Graph, typename Enable = void>
   398     struct FindEdgeSelector {
   399       typedef typename Graph::Node Node;
   400       typedef typename Graph::Edge Edge;
   401       static Edge find(const Graph &g, Node u, Node v, Edge e) {
   402         bool b;
   403         if (u != v) {
   404           if (e == INVALID) {
   405             g.firstInc(e, b, u);
   406           } else {
   407             b = g.source(e) == u;
   408             g.nextInc(e, b);
   409           }
   410           while (e != INVALID && (b ? g.target(e) : g.source(e)) != v) {
   411             g.nextInc(e, b);
   412           }
   413         } else {
   414           if (e == INVALID) {
   415             g.firstInc(e, b, u);
   416           } else {
   417             b = true;
   418             g.nextInc(e, b);
   419           }
   420           while (e != INVALID && (!b || g.target(e) != v)) {
   421             g.nextInc(e, b);
   422           }
   423         }
   424         return e;
   425       }
   426     };
   427 
   428     template <typename Graph>
   429     struct FindEdgeSelector<
   430       Graph, 
   431       typename enable_if<typename Graph::FindEdgeTag, void>::type> 
   432     {
   433       typedef typename Graph::Node Node;
   434       typedef typename Graph::Edge Edge;
   435       static Edge find(const Graph &g, Node u, Node v, Edge prev) {
   436         return g.findEdge(u, v, prev);
   437       }
   438     };    
   439   }
   440 
   441   /// \brief Finds an edge between two nodes of a graph.
   442   ///
   443   /// Finds an edge from node \c u to node \c v in graph \c g.
   444   /// If the node \c u and node \c v is equal then each loop edge
   445   /// will be enumerated once.
   446   ///
   447   /// If \c prev is \ref INVALID (this is the default value), then
   448   /// it finds the first arc from \c u to \c v. Otherwise it looks for
   449   /// the next arc from \c u to \c v after \c prev.
   450   /// \return The found arc or \ref INVALID if there is no such an arc.
   451   ///
   452   /// Thus you can iterate through each arc from \c u to \c v as it follows.
   453   ///\code
   454   /// for(Edge e = findEdge(g,u,v); e != INVALID; 
   455   ///     e = findEdge(g,u,v,e)) {
   456   ///   ...
   457   /// }
   458   ///\endcode
   459   ///
   460   ///\sa ConArcIt
   461 
   462   template <typename Graph>
   463   inline typename Graph::Edge 
   464   findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,
   465             typename Graph::Edge p = INVALID) {
   466     return _graph_utils_bits::FindEdgeSelector<Graph>::find(g, u, v, p);
   467   }
   468 
   469   /// \brief Iterator for iterating on edges connected the same nodes.
   470   ///
   471   /// Iterator for iterating on edges connected the same nodes. It is 
   472   /// higher level interface for the findEdge() function. You can
   473   /// use it the following way:
   474   ///\code
   475   /// for (ConEdgeIt<Graph> it(g, src, trg); it != INVALID; ++it) {
   476   ///   ...
   477   /// }
   478   ///\endcode
   479   ///
   480   ///\sa findEdge()
   481   ///
   482   /// \author Balazs Dezso 
   483   template <typename _Graph>
   484   class ConEdgeIt : public _Graph::Edge {
   485   public:
   486 
   487     typedef _Graph Graph;
   488     typedef typename Graph::Edge Parent;
   489 
   490     typedef typename Graph::Edge Edge;
   491     typedef typename Graph::Node Node;
   492 
   493     /// \brief Constructor.
   494     ///
   495     /// Construct a new ConEdgeIt iterating on the edges which
   496     /// connects the \c u and \c v node.
   497     ConEdgeIt(const Graph& g, Node u, Node v) : _graph(g) {
   498       Parent::operator=(findEdge(_graph, u, v));
   499     }
   500 
   501     /// \brief Constructor.
   502     ///
   503     /// Construct a new ConEdgeIt which continues the iterating from 
   504     /// the \c e edge.
   505     ConEdgeIt(const Graph& g, Edge e) : Parent(e), _graph(g) {}
   506     
   507     /// \brief Increment operator.
   508     ///
   509     /// It increments the iterator and gives back the next edge.
   510     ConEdgeIt& operator++() {
   511       Parent::operator=(findEdge(_graph, _graph.source(*this), 
   512 				 _graph.target(*this), *this));
   513       return *this;
   514     }
   515   private:
   516     const Graph& _graph;
   517   };
   518 
   519   namespace _graph_utils_bits {
   520 
   521     template <typename Digraph, typename Item, typename RefMap>
   522     class MapCopyBase {
   523     public:
   524       virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
   525       
   526       virtual ~MapCopyBase() {}
   527     };
   528 
   529     template <typename Digraph, typename Item, typename RefMap, 
   530               typename ToMap, typename FromMap>
   531     class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
   532     public:
   533 
   534       MapCopy(ToMap& tmap, const FromMap& map) 
   535         : _tmap(tmap), _map(map) {}
   536       
   537       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   538         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   539         for (ItemIt it(digraph); it != INVALID; ++it) {
   540           _tmap.set(refMap[it], _map[it]);
   541         }
   542       }
   543 
   544     private:
   545       ToMap& _tmap;
   546       const FromMap& _map;
   547     };
   548 
   549     template <typename Digraph, typename Item, typename RefMap, typename It>
   550     class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
   551     public:
   552 
   553       ItemCopy(It& it, const Item& item) : _it(it), _item(item) {}
   554       
   555       virtual void copy(const Digraph&, const RefMap& refMap) {
   556         _it = refMap[_item];
   557       }
   558 
   559     private:
   560       It& _it;
   561       Item _item;
   562     };
   563 
   564     template <typename Digraph, typename Item, typename RefMap, typename Ref>
   565     class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   566     public:
   567 
   568       RefCopy(Ref& map) : _map(map) {}
   569       
   570       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   571         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   572         for (ItemIt it(digraph); it != INVALID; ++it) {
   573           _map.set(it, refMap[it]);
   574         }
   575       }
   576 
   577     private:
   578       Ref& _map;
   579     };
   580 
   581     template <typename Digraph, typename Item, typename RefMap, 
   582               typename CrossRef>
   583     class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   584     public:
   585 
   586       CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
   587       
   588       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   589         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   590         for (ItemIt it(digraph); it != INVALID; ++it) {
   591           _cmap.set(refMap[it], it);
   592         }
   593       }
   594 
   595     private:
   596       CrossRef& _cmap;
   597     };
   598 
   599     template <typename Digraph, typename Enable = void>
   600     struct DigraphCopySelector {
   601       template <typename From, typename NodeRefMap, typename ArcRefMap>
   602       static void copy(Digraph &to, const From& from,
   603                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   604         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   605           nodeRefMap[it] = to.addNode();
   606         }
   607         for (typename From::ArcIt it(from); it != INVALID; ++it) {
   608           arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)], 
   609                                           nodeRefMap[from.target(it)]);
   610         }
   611       }
   612     };
   613 
   614     template <typename Digraph>
   615     struct DigraphCopySelector<
   616       Digraph, 
   617       typename enable_if<typename Digraph::BuildTag, void>::type> 
   618     {
   619       template <typename From, typename NodeRefMap, typename ArcRefMap>
   620       static void copy(Digraph &to, const From& from,
   621                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   622         to.build(from, nodeRefMap, arcRefMap);
   623       }
   624     };
   625 
   626     template <typename Graph, typename Enable = void>
   627     struct GraphCopySelector {
   628       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   629       static void copy(Graph &to, const From& from,
   630                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   631         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   632           nodeRefMap[it] = to.addNode();
   633         }
   634         for (typename From::EdgeIt it(from); it != INVALID; ++it) {
   635           edgeRefMap[it] = to.addArc(nodeRefMap[from.source(it)], 
   636 				       nodeRefMap[from.target(it)]);
   637         }
   638       }
   639     };
   640 
   641     template <typename Graph>
   642     struct GraphCopySelector<
   643       Graph, 
   644       typename enable_if<typename Graph::BuildTag, void>::type> 
   645     {
   646       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   647       static void copy(Graph &to, const From& from,
   648                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   649         to.build(from, nodeRefMap, edgeRefMap);
   650       }
   651     };
   652 
   653   }
   654 
   655   /// \brief Class to copy a digraph.
   656   ///
   657   /// Class to copy a digraph to another digraph (duplicate a digraph). The
   658   /// simplest way of using it is through the \c copyDigraph() function.
   659   ///
   660   /// This class not just make a copy of a graph, but it can create
   661   /// references and cross references between the nodes and arcs of
   662   /// the two graphs, it can copy maps for use with the newly created
   663   /// graph and copy nodes and arcs.
   664   ///
   665   /// To make a copy from a graph, first an instance of DigraphCopy
   666   /// should be created, then the data belongs to the graph should
   667   /// assigned to copy. In the end, the \c run() member should be
   668   /// called.
   669   ///
   670   /// The next code copies a graph with several data:
   671   ///\code
   672   ///  DigraphCopy<NewGraph, OrigGraph> dc(new_graph, orig_graph);
   673   ///  // create a reference for the nodes
   674   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   675   ///  dc.nodeRef(nr);
   676   ///  // create a cross reference (inverse) for the arcs
   677   ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);
   678   ///  dc.arcCrossRef(acr);
   679   ///  // copy an arc map
   680   ///  OrigGraph::ArcMap<double> oamap(orig_graph);
   681   ///  NewGraph::ArcMap<double> namap(new_graph);
   682   ///  dc.arcMap(namap, oamap);
   683   ///  // copy a node
   684   ///  OrigGraph::Node on;
   685   ///  NewGraph::Node nn;
   686   ///  dc.node(nn, on);
   687   ///  // Executions of copy
   688   ///  dc.run();
   689   ///\endcode
   690   template <typename To, typename From>
   691   class DigraphCopy {
   692   private:
   693 
   694     typedef typename From::Node Node;
   695     typedef typename From::NodeIt NodeIt;
   696     typedef typename From::Arc Arc;
   697     typedef typename From::ArcIt ArcIt;
   698 
   699     typedef typename To::Node TNode;
   700     typedef typename To::Arc TArc;
   701 
   702     typedef typename From::template NodeMap<TNode> NodeRefMap;
   703     typedef typename From::template ArcMap<TArc> ArcRefMap;
   704     
   705     
   706   public: 
   707 
   708 
   709     /// \brief Constructor for the DigraphCopy.
   710     ///
   711     /// It copies the content of the \c _from digraph into the
   712     /// \c _to digraph.
   713     DigraphCopy(To& to, const From& from) 
   714       : _from(from), _to(to) {}
   715 
   716     /// \brief Destructor of the DigraphCopy
   717     ///
   718     /// Destructor of the DigraphCopy
   719     ~DigraphCopy() {
   720       for (int i = 0; i < int(_node_maps.size()); ++i) {
   721         delete _node_maps[i];
   722       }
   723       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   724         delete _arc_maps[i];
   725       }
   726 
   727     }
   728 
   729     /// \brief Copies the node references into the given map.
   730     ///
   731     /// Copies the node references into the given map. The parameter
   732     /// should be a map, which key type is the Node type of the source
   733     /// graph, while the value type is the Node type of the
   734     /// destination graph.
   735     template <typename NodeRef>
   736     DigraphCopy& nodeRef(NodeRef& map) {
   737       _node_maps.push_back(new _graph_utils_bits::RefCopy<From, Node, 
   738 			   NodeRefMap, NodeRef>(map));
   739       return *this;
   740     }
   741 
   742     /// \brief Copies the node cross references into the given map.
   743     ///
   744     ///  Copies the node cross references (reverse references) into
   745     ///  the given map. The parameter should be a map, which key type
   746     ///  is the Node type of the destination graph, while the value type is
   747     ///  the Node type of the source graph.
   748     template <typename NodeCrossRef>
   749     DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
   750       _node_maps.push_back(new _graph_utils_bits::CrossRefCopy<From, Node,
   751 			   NodeRefMap, NodeCrossRef>(map));
   752       return *this;
   753     }
   754 
   755     /// \brief Make copy of the given map.
   756     ///
   757     /// Makes copy of the given map for the newly created digraph.
   758     /// The new map's key type is the destination graph's node type,
   759     /// and the copied map's key type is the source graph's node type.
   760     template <typename ToMap, typename FromMap>
   761     DigraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
   762       _node_maps.push_back(new _graph_utils_bits::MapCopy<From, Node, 
   763 			   NodeRefMap, ToMap, FromMap>(tmap, map));
   764       return *this;
   765     }
   766 
   767     /// \brief Make a copy of the given node.
   768     ///
   769     /// Make a copy of the given node.
   770     DigraphCopy& node(TNode& tnode, const Node& snode) {
   771       _node_maps.push_back(new _graph_utils_bits::ItemCopy<From, Node, 
   772 			   NodeRefMap, TNode>(tnode, snode));
   773       return *this;
   774     }
   775 
   776     /// \brief Copies the arc references into the given map.
   777     ///
   778     /// Copies the arc references into the given map.
   779     template <typename ArcRef>
   780     DigraphCopy& arcRef(ArcRef& map) {
   781       _arc_maps.push_back(new _graph_utils_bits::RefCopy<From, Arc, 
   782 			  ArcRefMap, ArcRef>(map));
   783       return *this;
   784     }
   785 
   786     /// \brief Copies the arc cross references into the given map.
   787     ///
   788     ///  Copies the arc cross references (reverse references) into
   789     ///  the given map.
   790     template <typename ArcCrossRef>
   791     DigraphCopy& arcCrossRef(ArcCrossRef& map) {
   792       _arc_maps.push_back(new _graph_utils_bits::CrossRefCopy<From, Arc,
   793 			  ArcRefMap, ArcCrossRef>(map));
   794       return *this;
   795     }
   796 
   797     /// \brief Make copy of the given map.
   798     ///
   799     /// Makes copy of the given map for the newly created digraph. 
   800     /// The new map's key type is the to digraph's arc type,
   801     /// and the copied map's key type is the from digraph's arc
   802     /// type.  
   803     template <typename ToMap, typename FromMap>
   804     DigraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
   805       _arc_maps.push_back(new _graph_utils_bits::MapCopy<From, Arc, 
   806 			  ArcRefMap, ToMap, FromMap>(tmap, map));
   807       return *this;
   808     }
   809 
   810     /// \brief Make a copy of the given arc.
   811     ///
   812     /// Make a copy of the given arc.
   813     DigraphCopy& arc(TArc& tarc, const Arc& sarc) {
   814       _arc_maps.push_back(new _graph_utils_bits::ItemCopy<From, Arc, 
   815 			  ArcRefMap, TArc>(tarc, sarc));
   816       return *this;
   817     }
   818 
   819     /// \brief Executes the copies.
   820     ///
   821     /// Executes the copies.
   822     void run() {
   823       NodeRefMap nodeRefMap(_from);
   824       ArcRefMap arcRefMap(_from);
   825       _graph_utils_bits::DigraphCopySelector<To>::
   826         copy(_to, _from, nodeRefMap, arcRefMap);
   827       for (int i = 0; i < int(_node_maps.size()); ++i) {
   828         _node_maps[i]->copy(_from, nodeRefMap);
   829       }
   830       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   831         _arc_maps[i]->copy(_from, arcRefMap);
   832       }      
   833     }
   834 
   835   protected:
   836 
   837 
   838     const From& _from;
   839     To& _to;
   840 
   841     std::vector<_graph_utils_bits::MapCopyBase<From, Node, NodeRefMap>* > 
   842     _node_maps;
   843 
   844     std::vector<_graph_utils_bits::MapCopyBase<From, Arc, ArcRefMap>* > 
   845     _arc_maps;
   846 
   847   };
   848 
   849   /// \brief Copy a digraph to another digraph.
   850   ///
   851   /// Copy a digraph to another digraph. The complete usage of the
   852   /// function is detailed in the DigraphCopy class, but a short
   853   /// example shows a basic work:
   854   ///\code
   855   /// copyDigraph(trg, src).nodeRef(nr).arcCrossRef(ecr).run();
   856   ///\endcode
   857   /// 
   858   /// After the copy the \c nr map will contain the mapping from the
   859   /// nodes of the \c from digraph to the nodes of the \c to digraph and
   860   /// \c ecr will contain the mapping from the arcs of the \c to digraph
   861   /// to the arcs of the \c from digraph.
   862   ///
   863   /// \see DigraphCopy 
   864   template <typename To, typename From>
   865   DigraphCopy<To, From> copyDigraph(To& to, const From& from) {
   866     return DigraphCopy<To, From>(to, from);
   867   }
   868 
   869   /// \brief Class to copy a graph.
   870   ///
   871   /// Class to copy a graph to another graph (duplicate a graph). The
   872   /// simplest way of using it is through the \c copyGraph() function.
   873   ///
   874   /// This class not just make a copy of a graph, but it can create
   875   /// references and cross references between the nodes, edges and arcs of
   876   /// the two graphs, it can copy maps for use with the newly created
   877   /// graph and copy nodes, edges and arcs.
   878   ///
   879   /// To make a copy from a graph, first an instance of GraphCopy
   880   /// should be created, then the data belongs to the graph should
   881   /// assigned to copy. In the end, the \c run() member should be
   882   /// called.
   883   ///
   884   /// The next code copies a graph with several data:
   885   ///\code
   886   ///  GraphCopy<NewGraph, OrigGraph> dc(new_graph, orig_graph);
   887   ///  // create a reference for the nodes
   888   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   889   ///  dc.nodeRef(nr);
   890   ///  // create a cross reference (inverse) for the edges
   891   ///  NewGraph::EdgeMap<OrigGraph::Arc> ecr(new_graph);
   892   ///  dc.edgeCrossRef(ecr);
   893   ///  // copy an arc map
   894   ///  OrigGraph::ArcMap<double> oamap(orig_graph);
   895   ///  NewGraph::ArcMap<double> namap(new_graph);
   896   ///  dc.arcMap(namap, oamap);
   897   ///  // copy a node
   898   ///  OrigGraph::Node on;
   899   ///  NewGraph::Node nn;
   900   ///  dc.node(nn, on);
   901   ///  // Executions of copy
   902   ///  dc.run();
   903   ///\endcode
   904   template <typename To, typename From>
   905   class GraphCopy {
   906   private:
   907 
   908     typedef typename From::Node Node;
   909     typedef typename From::NodeIt NodeIt;
   910     typedef typename From::Arc Arc;
   911     typedef typename From::ArcIt ArcIt;
   912     typedef typename From::Edge Edge;
   913     typedef typename From::EdgeIt EdgeIt;
   914 
   915     typedef typename To::Node TNode;
   916     typedef typename To::Arc TArc;
   917     typedef typename To::Edge TEdge;
   918 
   919     typedef typename From::template NodeMap<TNode> NodeRefMap;
   920     typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
   921 
   922     struct ArcRefMap {
   923       ArcRefMap(const To& to, const From& from,
   924 		const EdgeRefMap& edge_ref, const NodeRefMap& node_ref) 
   925         : _to(to), _from(from), 
   926           _edge_ref(edge_ref), _node_ref(node_ref) {}
   927 
   928       typedef typename From::Arc Key;
   929       typedef typename To::Arc Value;
   930 
   931       Value operator[](const Key& key) const {
   932         bool forward = 
   933           (_from.direction(key) == 
   934 	   (_node_ref[_from.source(key)] == _to.source(_edge_ref[key])));
   935 	return _to.direct(_edge_ref[key], forward); 
   936       }
   937       
   938       const To& _to;
   939       const From& _from;
   940       const EdgeRefMap& _edge_ref;
   941       const NodeRefMap& _node_ref;
   942     };
   943 
   944     
   945   public: 
   946 
   947 
   948     /// \brief Constructor for the GraphCopy.
   949     ///
   950     /// It copies the content of the \c _from graph into the
   951     /// \c _to graph.
   952     GraphCopy(To& to, const From& from) 
   953       : _from(from), _to(to) {}
   954 
   955     /// \brief Destructor of the GraphCopy
   956     ///
   957     /// Destructor of the GraphCopy
   958     ~GraphCopy() {
   959       for (int i = 0; i < int(_node_maps.size()); ++i) {
   960         delete _node_maps[i];
   961       }
   962       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   963         delete _arc_maps[i];
   964       }
   965       for (int i = 0; i < int(_edge_maps.size()); ++i) {
   966         delete _edge_maps[i];
   967       }
   968 
   969     }
   970 
   971     /// \brief Copies the node references into the given map.
   972     ///
   973     /// Copies the node references into the given map.
   974     template <typename NodeRef>
   975     GraphCopy& nodeRef(NodeRef& map) {
   976       _node_maps.push_back(new _graph_utils_bits::RefCopy<From, Node, 
   977 			   NodeRefMap, NodeRef>(map));
   978       return *this;
   979     }
   980 
   981     /// \brief Copies the node cross references into the given map.
   982     ///
   983     ///  Copies the node cross references (reverse references) into
   984     ///  the given map.
   985     template <typename NodeCrossRef>
   986     GraphCopy& nodeCrossRef(NodeCrossRef& map) {
   987       _node_maps.push_back(new _graph_utils_bits::CrossRefCopy<From, Node,
   988 			   NodeRefMap, NodeCrossRef>(map));
   989       return *this;
   990     }
   991 
   992     /// \brief Make copy of the given map.
   993     ///
   994     /// Makes copy of the given map for the newly created graph. 
   995     /// The new map's key type is the to graph's node type,
   996     /// and the copied map's key type is the from graph's node
   997     /// type.  
   998     template <typename ToMap, typename FromMap>
   999     GraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
  1000       _node_maps.push_back(new _graph_utils_bits::MapCopy<From, Node, 
  1001 			   NodeRefMap, ToMap, FromMap>(tmap, map));
  1002       return *this;
  1003     }
  1004 
  1005     /// \brief Make a copy of the given node.
  1006     ///
  1007     /// Make a copy of the given node.
  1008     GraphCopy& node(TNode& tnode, const Node& snode) {
  1009       _node_maps.push_back(new _graph_utils_bits::ItemCopy<From, Node, 
  1010 			   NodeRefMap, TNode>(tnode, snode));
  1011       return *this;
  1012     }
  1013 
  1014     /// \brief Copies the arc references into the given map.
  1015     ///
  1016     /// Copies the arc references into the given map.
  1017     template <typename ArcRef>
  1018     GraphCopy& arcRef(ArcRef& map) {
  1019       _arc_maps.push_back(new _graph_utils_bits::RefCopy<From, Arc, 
  1020 			  ArcRefMap, ArcRef>(map));
  1021       return *this;
  1022     }
  1023 
  1024     /// \brief Copies the arc cross references into the given map.
  1025     ///
  1026     ///  Copies the arc cross references (reverse references) into
  1027     ///  the given map.
  1028     template <typename ArcCrossRef>
  1029     GraphCopy& arcCrossRef(ArcCrossRef& map) {
  1030       _arc_maps.push_back(new _graph_utils_bits::CrossRefCopy<From, Arc,
  1031 			  ArcRefMap, ArcCrossRef>(map));
  1032       return *this;
  1033     }
  1034 
  1035     /// \brief Make copy of the given map.
  1036     ///
  1037     /// Makes copy of the given map for the newly created graph. 
  1038     /// The new map's key type is the to graph's arc type,
  1039     /// and the copied map's key type is the from graph's arc
  1040     /// type.  
  1041     template <typename ToMap, typename FromMap>
  1042     GraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
  1043       _arc_maps.push_back(new _graph_utils_bits::MapCopy<From, Arc, 
  1044 			  ArcRefMap, ToMap, FromMap>(tmap, map));
  1045       return *this;
  1046     }
  1047 
  1048     /// \brief Make a copy of the given arc.
  1049     ///
  1050     /// Make a copy of the given arc.
  1051     GraphCopy& arc(TArc& tarc, const Arc& sarc) {
  1052       _arc_maps.push_back(new _graph_utils_bits::ItemCopy<From, Arc, 
  1053 			  ArcRefMap, TArc>(tarc, sarc));
  1054       return *this;
  1055     }
  1056 
  1057     /// \brief Copies the edge references into the given map.
  1058     ///
  1059     /// Copies the edge references into the given map.
  1060     template <typename EdgeRef>
  1061     GraphCopy& edgeRef(EdgeRef& map) {
  1062       _edge_maps.push_back(new _graph_utils_bits::RefCopy<From, Edge, 
  1063 			   EdgeRefMap, EdgeRef>(map));
  1064       return *this;
  1065     }
  1066 
  1067     /// \brief Copies the edge cross references into the given map.
  1068     ///
  1069     /// Copies the edge cross references (reverse
  1070     /// references) into the given map.
  1071     template <typename EdgeCrossRef>
  1072     GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
  1073       _edge_maps.push_back(new _graph_utils_bits::CrossRefCopy<From, 
  1074 			   Edge, EdgeRefMap, EdgeCrossRef>(map));
  1075       return *this;
  1076     }
  1077 
  1078     /// \brief Make copy of the given map.
  1079     ///
  1080     /// Makes copy of the given map for the newly created graph. 
  1081     /// The new map's key type is the to graph's edge type,
  1082     /// and the copied map's key type is the from graph's edge
  1083     /// type.  
  1084     template <typename ToMap, typename FromMap>
  1085     GraphCopy& edgeMap(ToMap& tmap, const FromMap& map) {
  1086       _edge_maps.push_back(new _graph_utils_bits::MapCopy<From, Edge, 
  1087 			   EdgeRefMap, ToMap, FromMap>(tmap, map));
  1088       return *this;
  1089     }
  1090 
  1091     /// \brief Make a copy of the given edge.
  1092     ///
  1093     /// Make a copy of the given edge.
  1094     GraphCopy& edge(TEdge& tedge, const Edge& sedge) {
  1095       _edge_maps.push_back(new _graph_utils_bits::ItemCopy<From, Edge, 
  1096 			   EdgeRefMap, TEdge>(tedge, sedge));
  1097       return *this;
  1098     }
  1099 
  1100     /// \brief Executes the copies.
  1101     ///
  1102     /// Executes the copies.
  1103     void run() {
  1104       NodeRefMap nodeRefMap(_from);
  1105       EdgeRefMap edgeRefMap(_from);
  1106       ArcRefMap arcRefMap(_to, _from, edgeRefMap, nodeRefMap);
  1107       _graph_utils_bits::GraphCopySelector<To>::
  1108         copy(_to, _from, nodeRefMap, edgeRefMap);
  1109       for (int i = 0; i < int(_node_maps.size()); ++i) {
  1110         _node_maps[i]->copy(_from, nodeRefMap);
  1111       }
  1112       for (int i = 0; i < int(_edge_maps.size()); ++i) {
  1113         _edge_maps[i]->copy(_from, edgeRefMap);
  1114       }
  1115       for (int i = 0; i < int(_arc_maps.size()); ++i) {
  1116         _arc_maps[i]->copy(_from, arcRefMap);
  1117       }
  1118     }
  1119 
  1120   private:
  1121     
  1122     const From& _from;
  1123     To& _to;
  1124 
  1125     std::vector<_graph_utils_bits::MapCopyBase<From, Node, NodeRefMap>* > 
  1126     _node_maps;
  1127 
  1128     std::vector<_graph_utils_bits::MapCopyBase<From, Arc, ArcRefMap>* > 
  1129     _arc_maps;
  1130 
  1131     std::vector<_graph_utils_bits::MapCopyBase<From, Edge, EdgeRefMap>* > 
  1132     _edge_maps;
  1133 
  1134   };
  1135 
  1136   /// \brief Copy a graph to another graph.
  1137   ///
  1138   /// Copy a graph to another graph. The complete usage of the
  1139   /// function is detailed in the GraphCopy class, but a short
  1140   /// example shows a basic work:
  1141   ///\code
  1142   /// copyGraph(trg, src).nodeRef(nr).arcCrossRef(ecr).run();
  1143   ///\endcode
  1144   /// 
  1145   /// After the copy the \c nr map will contain the mapping from the
  1146   /// nodes of the \c from graph to the nodes of the \c to graph and
  1147   /// \c ecr will contain the mapping from the arcs of the \c to graph
  1148   /// to the arcs of the \c from graph.
  1149   ///
  1150   /// \see GraphCopy 
  1151   template <typename To, typename From>
  1152   GraphCopy<To, From> 
  1153   copyGraph(To& to, const From& from) {
  1154     return GraphCopy<To, From>(to, from);
  1155   }
  1156 
  1157   /// @}
  1158 
  1159   /// \addtogroup graph_maps
  1160   /// @{
  1161 
  1162   /// Provides an immutable and unique id for each item in the graph.
  1163 
  1164   /// The IdMap class provides a unique and immutable id for each item of the
  1165   /// same type (e.g. node) in the graph. This id is <ul><li>\b unique:
  1166   /// different items (nodes) get different ids <li>\b immutable: the id of an
  1167   /// item (node) does not change (even if you delete other nodes).  </ul>
  1168   /// Through this map you get access (i.e. can read) the inner id values of
  1169   /// the items stored in the graph. This map can be inverted with its member
  1170   /// class \c InverseMap or with the \c operator() member.
  1171   ///
  1172   template <typename _Graph, typename _Item>
  1173   class IdMap {
  1174   public:
  1175     typedef _Graph Graph;
  1176     typedef int Value;
  1177     typedef _Item Item;
  1178     typedef _Item Key;
  1179 
  1180     /// \brief Constructor.
  1181     ///
  1182     /// Constructor of the map.
  1183     explicit IdMap(const Graph& graph) : _graph(&graph) {}
  1184 
  1185     /// \brief Gives back the \e id of the item.
  1186     ///
  1187     /// Gives back the immutable and unique \e id of the item.
  1188     int operator[](const Item& item) const { return _graph->id(item);}
  1189 
  1190     /// \brief Gives back the item by its id.
  1191     ///
  1192     /// Gives back the item by its id.
  1193     Item operator()(int id) { return _graph->fromId(id, Item()); }
  1194 
  1195   private:
  1196     const Graph* _graph;
  1197 
  1198   public:
  1199 
  1200     /// \brief The class represents the inverse of its owner (IdMap).
  1201     ///
  1202     /// The class represents the inverse of its owner (IdMap).
  1203     /// \see inverse()
  1204     class InverseMap {
  1205     public:
  1206 
  1207       /// \brief Constructor.
  1208       ///
  1209       /// Constructor for creating an id-to-item map.
  1210       explicit InverseMap(const Graph& graph) : _graph(&graph) {}
  1211 
  1212       /// \brief Constructor.
  1213       ///
  1214       /// Constructor for creating an id-to-item map.
  1215       explicit InverseMap(const IdMap& map) : _graph(map._graph) {}
  1216 
  1217       /// \brief Gives back the given item from its id.
  1218       ///
  1219       /// Gives back the given item from its id.
  1220       /// 
  1221       Item operator[](int id) const { return _graph->fromId(id, Item());}
  1222 
  1223     private:
  1224       const Graph* _graph;
  1225     };
  1226 
  1227     /// \brief Gives back the inverse of the map.
  1228     ///
  1229     /// Gives back the inverse of the IdMap.
  1230     InverseMap inverse() const { return InverseMap(*_graph);} 
  1231 
  1232   };
  1233 
  1234   
  1235   /// \brief General invertable graph-map type.
  1236 
  1237   /// This type provides simple invertable graph-maps. 
  1238   /// The InvertableMap wraps an arbitrary ReadWriteMap 
  1239   /// and if a key is set to a new value then store it
  1240   /// in the inverse map.
  1241   ///
  1242   /// The values of the map can be accessed
  1243   /// with stl compatible forward iterator.
  1244   ///
  1245   /// \param _Graph The graph type.
  1246   /// \param _Item The item type of the graph.
  1247   /// \param _Value The value type of the map.
  1248   ///
  1249   /// \see IterableValueMap
  1250   template <typename _Graph, typename _Item, typename _Value>
  1251   class InvertableMap : protected DefaultMap<_Graph, _Item, _Value> {
  1252   private:
  1253     
  1254     typedef DefaultMap<_Graph, _Item, _Value> Map;
  1255     typedef _Graph Graph;
  1256 
  1257     typedef std::map<_Value, _Item> Container;
  1258     Container _inv_map;    
  1259 
  1260   public:
  1261  
  1262     /// The key type of InvertableMap (Node, Arc, Edge).
  1263     typedef typename Map::Key Key;
  1264     /// The value type of the InvertableMap.
  1265     typedef typename Map::Value Value;
  1266 
  1267 
  1268 
  1269     /// \brief Constructor.
  1270     ///
  1271     /// Construct a new InvertableMap for the graph.
  1272     ///
  1273     explicit InvertableMap(const Graph& graph) : Map(graph) {} 
  1274 
  1275     /// \brief Forward iterator for values.
  1276     ///
  1277     /// This iterator is an stl compatible forward
  1278     /// iterator on the values of the map. The values can
  1279     /// be accessed in the [beginValue, endValue) range.
  1280     ///
  1281     class ValueIterator 
  1282       : public std::iterator<std::forward_iterator_tag, Value> {
  1283       friend class InvertableMap;
  1284     private:
  1285       ValueIterator(typename Container::const_iterator _it) 
  1286         : it(_it) {}
  1287     public:
  1288       
  1289       ValueIterator() {}
  1290 
  1291       ValueIterator& operator++() { ++it; return *this; }
  1292       ValueIterator operator++(int) { 
  1293         ValueIterator tmp(*this); 
  1294         operator++();
  1295         return tmp; 
  1296       }
  1297 
  1298       const Value& operator*() const { return it->first; }
  1299       const Value* operator->() const { return &(it->first); }
  1300 
  1301       bool operator==(ValueIterator jt) const { return it == jt.it; }
  1302       bool operator!=(ValueIterator jt) const { return it != jt.it; }
  1303       
  1304     private:
  1305       typename Container::const_iterator it;
  1306     };
  1307 
  1308     /// \brief Returns an iterator to the first value.
  1309     ///
  1310     /// Returns an stl compatible iterator to the 
  1311     /// first value of the map. The values of the
  1312     /// map can be accessed in the [beginValue, endValue)
  1313     /// range.
  1314     ValueIterator beginValue() const {
  1315       return ValueIterator(_inv_map.begin());
  1316     }
  1317 
  1318     /// \brief Returns an iterator after the last value.
  1319     ///
  1320     /// Returns an stl compatible iterator after the 
  1321     /// last value of the map. The values of the
  1322     /// map can be accessed in the [beginValue, endValue)
  1323     /// range.
  1324     ValueIterator endValue() const {
  1325       return ValueIterator(_inv_map.end());
  1326     }
  1327     
  1328     /// \brief The setter function of the map.
  1329     ///
  1330     /// Sets the mapped value.
  1331     void set(const Key& key, const Value& val) {
  1332       Value oldval = Map::operator[](key);
  1333       typename Container::iterator it = _inv_map.find(oldval);
  1334       if (it != _inv_map.end() && it->second == key) {
  1335 	_inv_map.erase(it);
  1336       }      
  1337       _inv_map.insert(make_pair(val, key));
  1338       Map::set(key, val);
  1339     }
  1340 
  1341     /// \brief The getter function of the map.
  1342     ///
  1343     /// It gives back the value associated with the key.
  1344     typename MapTraits<Map>::ConstReturnValue 
  1345     operator[](const Key& key) const {
  1346       return Map::operator[](key);
  1347     }
  1348 
  1349     /// \brief Gives back the item by its value.
  1350     ///
  1351     /// Gives back the item by its value.
  1352     Key operator()(const Value& key) const {
  1353       typename Container::const_iterator it = _inv_map.find(key);
  1354       return it != _inv_map.end() ? it->second : INVALID;
  1355     }
  1356 
  1357   protected:
  1358 
  1359     /// \brief Erase the key from the map.
  1360     ///
  1361     /// Erase the key to the map. It is called by the
  1362     /// \c AlterationNotifier.
  1363     virtual void erase(const Key& key) {
  1364       Value val = Map::operator[](key);
  1365       typename Container::iterator it = _inv_map.find(val);
  1366       if (it != _inv_map.end() && it->second == key) {
  1367 	_inv_map.erase(it);
  1368       }
  1369       Map::erase(key);
  1370     }
  1371 
  1372     /// \brief Erase more keys from the map.
  1373     ///
  1374     /// Erase more keys from the map. It is called by the
  1375     /// \c AlterationNotifier.
  1376     virtual void erase(const std::vector<Key>& keys) {
  1377       for (int i = 0; i < int(keys.size()); ++i) {
  1378 	Value val = Map::operator[](keys[i]);
  1379 	typename Container::iterator it = _inv_map.find(val);
  1380 	if (it != _inv_map.end() && it->second == keys[i]) {
  1381 	  _inv_map.erase(it);
  1382 	}
  1383       }
  1384       Map::erase(keys);
  1385     }
  1386 
  1387     /// \brief Clear the keys from the map and inverse map.
  1388     ///
  1389     /// Clear the keys from the map and inverse map. It is called by the
  1390     /// \c AlterationNotifier.
  1391     virtual void clear() {
  1392       _inv_map.clear();
  1393       Map::clear();
  1394     }
  1395 
  1396   public:
  1397 
  1398     /// \brief The inverse map type.
  1399     ///
  1400     /// The inverse of this map. The subscript operator of the map
  1401     /// gives back always the item what was last assigned to the value. 
  1402     class InverseMap {
  1403     public:
  1404       /// \brief Constructor of the InverseMap.
  1405       ///
  1406       /// Constructor of the InverseMap.
  1407       explicit InverseMap(const InvertableMap& inverted) 
  1408         : _inverted(inverted) {}
  1409 
  1410       /// The value type of the InverseMap.
  1411       typedef typename InvertableMap::Key Value;
  1412       /// The key type of the InverseMap.
  1413       typedef typename InvertableMap::Value Key; 
  1414 
  1415       /// \brief Subscript operator. 
  1416       ///
  1417       /// Subscript operator. It gives back always the item 
  1418       /// what was last assigned to the value.
  1419       Value operator[](const Key& key) const {
  1420 	return _inverted(key);
  1421       }
  1422       
  1423     private:
  1424       const InvertableMap& _inverted;
  1425     };
  1426 
  1427     /// \brief It gives back the just readable inverse map.
  1428     ///
  1429     /// It gives back the just readable inverse map.
  1430     InverseMap inverse() const {
  1431       return InverseMap(*this);
  1432     } 
  1433 
  1434 
  1435     
  1436   };
  1437 
  1438   /// \brief Provides a mutable, continuous and unique descriptor for each 
  1439   /// item in the graph.
  1440   ///
  1441   /// The DescriptorMap class provides a unique and continuous (but mutable)
  1442   /// descriptor (id) for each item of the same type (e.g. node) in the
  1443   /// graph. This id is <ul><li>\b unique: different items (nodes) get
  1444   /// different ids <li>\b continuous: the range of the ids is the set of
  1445   /// integers between 0 and \c n-1, where \c n is the number of the items of
  1446   /// this type (e.g. nodes) (so the id of a node can change if you delete an
  1447   /// other node, i.e. this id is mutable).  </ul> This map can be inverted
  1448   /// with its member class \c InverseMap, or with the \c operator() member.
  1449   ///
  1450   /// \param _Graph The graph class the \c DescriptorMap belongs to.
  1451   /// \param _Item The Item is the Key of the Map. It may be Node, Arc or 
  1452   /// Edge.
  1453   template <typename _Graph, typename _Item>
  1454   class DescriptorMap : protected DefaultMap<_Graph, _Item, int> {
  1455 
  1456     typedef _Item Item;
  1457     typedef DefaultMap<_Graph, _Item, int> Map;
  1458 
  1459   public:
  1460     /// The graph class of DescriptorMap.
  1461     typedef _Graph Graph;
  1462 
  1463     /// The key type of DescriptorMap (Node, Arc, Edge).
  1464     typedef typename Map::Key Key;
  1465     /// The value type of DescriptorMap.
  1466     typedef typename Map::Value Value;
  1467 
  1468     /// \brief Constructor.
  1469     ///
  1470     /// Constructor for descriptor map.
  1471     explicit DescriptorMap(const Graph& _graph) : Map(_graph) {
  1472       Item it;
  1473       const typename Map::Notifier* nf = Map::notifier(); 
  1474       for (nf->first(it); it != INVALID; nf->next(it)) {
  1475 	Map::set(it, _inv_map.size());
  1476 	_inv_map.push_back(it);	
  1477       }      
  1478     }
  1479 
  1480   protected:
  1481 
  1482     /// \brief Add a new key to the map.
  1483     ///
  1484     /// Add a new key to the map. It is called by the
  1485     /// \c AlterationNotifier.
  1486     virtual void add(const Item& item) {
  1487       Map::add(item);
  1488       Map::set(item, _inv_map.size());
  1489       _inv_map.push_back(item);
  1490     }
  1491 
  1492     /// \brief Add more new keys to the map.
  1493     ///
  1494     /// Add more new keys to the map. It is called by the
  1495     /// \c AlterationNotifier.
  1496     virtual void add(const std::vector<Item>& items) {
  1497       Map::add(items);
  1498       for (int i = 0; i < int(items.size()); ++i) {
  1499 	Map::set(items[i], _inv_map.size());
  1500 	_inv_map.push_back(items[i]);
  1501       }
  1502     }
  1503 
  1504     /// \brief Erase the key from the map.
  1505     ///
  1506     /// Erase the key from the map. It is called by the
  1507     /// \c AlterationNotifier.
  1508     virtual void erase(const Item& item) {
  1509       Map::set(_inv_map.back(), Map::operator[](item));
  1510       _inv_map[Map::operator[](item)] = _inv_map.back();
  1511       _inv_map.pop_back();
  1512       Map::erase(item);
  1513     }
  1514 
  1515     /// \brief Erase more keys from the map.
  1516     ///
  1517     /// Erase more keys from the map. It is called by the
  1518     /// \c AlterationNotifier.
  1519     virtual void erase(const std::vector<Item>& items) {
  1520       for (int i = 0; i < int(items.size()); ++i) {
  1521 	Map::set(_inv_map.back(), Map::operator[](items[i]));
  1522 	_inv_map[Map::operator[](items[i])] = _inv_map.back();
  1523 	_inv_map.pop_back();
  1524       }
  1525       Map::erase(items);
  1526     }
  1527 
  1528     /// \brief Build the unique map.
  1529     ///
  1530     /// Build the unique map. It is called by the
  1531     /// \c AlterationNotifier.
  1532     virtual void build() {
  1533       Map::build();
  1534       Item it;
  1535       const typename Map::Notifier* nf = Map::notifier(); 
  1536       for (nf->first(it); it != INVALID; nf->next(it)) {
  1537 	Map::set(it, _inv_map.size());
  1538 	_inv_map.push_back(it);	
  1539       }      
  1540     }
  1541     
  1542     /// \brief Clear the keys from the map.
  1543     ///
  1544     /// Clear the keys from the map. It is called by the
  1545     /// \c AlterationNotifier.
  1546     virtual void clear() {
  1547       _inv_map.clear();
  1548       Map::clear();
  1549     }
  1550 
  1551   public:
  1552 
  1553     /// \brief Returns the maximal value plus one.
  1554     ///
  1555     /// Returns the maximal value plus one in the map.
  1556     unsigned int size() const {
  1557       return _inv_map.size();
  1558     }
  1559 
  1560     /// \brief Swaps the position of the two items in the map.
  1561     ///
  1562     /// Swaps the position of the two items in the map.
  1563     void swap(const Item& p, const Item& q) {
  1564       int pi = Map::operator[](p);
  1565       int qi = Map::operator[](q);
  1566       Map::set(p, qi);
  1567       _inv_map[qi] = p;
  1568       Map::set(q, pi);
  1569       _inv_map[pi] = q;
  1570     }
  1571 
  1572     /// \brief Gives back the \e descriptor of the item.
  1573     ///
  1574     /// Gives back the mutable and unique \e descriptor of the map.
  1575     int operator[](const Item& item) const {
  1576       return Map::operator[](item);
  1577     }
  1578 
  1579     /// \brief Gives back the item by its descriptor.
  1580     ///
  1581     /// Gives back th item by its descriptor.
  1582     Item operator()(int id) const {
  1583       return _inv_map[id];
  1584     }
  1585     
  1586   private:
  1587 
  1588     typedef std::vector<Item> Container;
  1589     Container _inv_map;
  1590 
  1591   public:
  1592     /// \brief The inverse map type of DescriptorMap.
  1593     ///
  1594     /// The inverse map type of DescriptorMap.
  1595     class InverseMap {
  1596     public:
  1597       /// \brief Constructor of the InverseMap.
  1598       ///
  1599       /// Constructor of the InverseMap.
  1600       explicit InverseMap(const DescriptorMap& inverted) 
  1601 	: _inverted(inverted) {}
  1602 
  1603 
  1604       /// The value type of the InverseMap.
  1605       typedef typename DescriptorMap::Key Value;
  1606       /// The key type of the InverseMap.
  1607       typedef typename DescriptorMap::Value Key; 
  1608 
  1609       /// \brief Subscript operator. 
  1610       ///
  1611       /// Subscript operator. It gives back the item 
  1612       /// that the descriptor belongs to currently.
  1613       Value operator[](const Key& key) const {
  1614 	return _inverted(key);
  1615       }
  1616 
  1617       /// \brief Size of the map.
  1618       ///
  1619       /// Returns the size of the map.
  1620       unsigned int size() const {
  1621 	return _inverted.size();
  1622       }
  1623       
  1624     private:
  1625       const DescriptorMap& _inverted;
  1626     };
  1627 
  1628     /// \brief Gives back the inverse of the map.
  1629     ///
  1630     /// Gives back the inverse of the map.
  1631     const InverseMap inverse() const {
  1632       return InverseMap(*this);
  1633     }
  1634   };
  1635 
  1636   /// \brief Returns the source of the given arc.
  1637   ///
  1638   /// The SourceMap gives back the source Node of the given arc. 
  1639   /// \see TargetMap
  1640   /// \author Balazs Dezso
  1641   template <typename Digraph>
  1642   class SourceMap {
  1643   public:
  1644 
  1645     typedef typename Digraph::Node Value;
  1646     typedef typename Digraph::Arc Key;
  1647 
  1648     /// \brief Constructor
  1649     ///
  1650     /// Constructor
  1651     /// \param _digraph The digraph that the map belongs to.
  1652     explicit SourceMap(const Digraph& digraph) : _digraph(digraph) {}
  1653 
  1654     /// \brief The subscript operator.
  1655     ///
  1656     /// The subscript operator.
  1657     /// \param arc The arc 
  1658     /// \return The source of the arc 
  1659     Value operator[](const Key& arc) const {
  1660       return _digraph.source(arc);
  1661     }
  1662 
  1663   private:
  1664     const Digraph& _digraph;
  1665   };
  1666 
  1667   /// \brief Returns a \ref SourceMap class.
  1668   ///
  1669   /// This function just returns an \ref SourceMap class.
  1670   /// \relates SourceMap
  1671   template <typename Digraph>
  1672   inline SourceMap<Digraph> sourceMap(const Digraph& digraph) {
  1673     return SourceMap<Digraph>(digraph);
  1674   } 
  1675 
  1676   /// \brief Returns the target of the given arc.
  1677   ///
  1678   /// The TargetMap gives back the target Node of the given arc. 
  1679   /// \see SourceMap
  1680   /// \author Balazs Dezso
  1681   template <typename Digraph>
  1682   class TargetMap {
  1683   public:
  1684 
  1685     typedef typename Digraph::Node Value;
  1686     typedef typename Digraph::Arc Key;
  1687 
  1688     /// \brief Constructor
  1689     ///
  1690     /// Constructor
  1691     /// \param _digraph The digraph that the map belongs to.
  1692     explicit TargetMap(const Digraph& digraph) : _digraph(digraph) {}
  1693 
  1694     /// \brief The subscript operator.
  1695     ///
  1696     /// The subscript operator.
  1697     /// \param e The arc 
  1698     /// \return The target of the arc 
  1699     Value operator[](const Key& e) const {
  1700       return _digraph.target(e);
  1701     }
  1702 
  1703   private:
  1704     const Digraph& _digraph;
  1705   };
  1706 
  1707   /// \brief Returns a \ref TargetMap class.
  1708   ///
  1709   /// This function just returns a \ref TargetMap class.
  1710   /// \relates TargetMap
  1711   template <typename Digraph>
  1712   inline TargetMap<Digraph> targetMap(const Digraph& digraph) {
  1713     return TargetMap<Digraph>(digraph);
  1714   }
  1715 
  1716   /// \brief Returns the "forward" directed arc view of an edge.
  1717   ///
  1718   /// Returns the "forward" directed arc view of an edge.
  1719   /// \see BackwardMap
  1720   /// \author Balazs Dezso
  1721   template <typename Graph>
  1722   class ForwardMap {
  1723   public:
  1724 
  1725     typedef typename Graph::Arc Value;
  1726     typedef typename Graph::Edge Key;
  1727 
  1728     /// \brief Constructor
  1729     ///
  1730     /// Constructor
  1731     /// \param _graph The graph that the map belongs to.
  1732     explicit ForwardMap(const Graph& graph) : _graph(graph) {}
  1733 
  1734     /// \brief The subscript operator.
  1735     ///
  1736     /// The subscript operator.
  1737     /// \param key An edge 
  1738     /// \return The "forward" directed arc view of edge 
  1739     Value operator[](const Key& key) const {
  1740       return _graph.direct(key, true);
  1741     }
  1742 
  1743   private:
  1744     const Graph& _graph;
  1745   };
  1746 
  1747   /// \brief Returns a \ref ForwardMap class.
  1748   ///
  1749   /// This function just returns an \ref ForwardMap class.
  1750   /// \relates ForwardMap
  1751   template <typename Graph>
  1752   inline ForwardMap<Graph> forwardMap(const Graph& graph) {
  1753     return ForwardMap<Graph>(graph);
  1754   }
  1755 
  1756   /// \brief Returns the "backward" directed arc view of an edge.
  1757   ///
  1758   /// Returns the "backward" directed arc view of an edge.
  1759   /// \see ForwardMap
  1760   /// \author Balazs Dezso
  1761   template <typename Graph>
  1762   class BackwardMap {
  1763   public:
  1764 
  1765     typedef typename Graph::Arc Value;
  1766     typedef typename Graph::Edge Key;
  1767 
  1768     /// \brief Constructor
  1769     ///
  1770     /// Constructor
  1771     /// \param _graph The graph that the map belongs to.
  1772     explicit BackwardMap(const Graph& graph) : _graph(graph) {}
  1773 
  1774     /// \brief The subscript operator.
  1775     ///
  1776     /// The subscript operator.
  1777     /// \param key An edge 
  1778     /// \return The "backward" directed arc view of edge 
  1779     Value operator[](const Key& key) const {
  1780       return _graph.direct(key, false);
  1781     }
  1782 
  1783   private:
  1784     const Graph& _graph;
  1785   };
  1786 
  1787   /// \brief Returns a \ref BackwardMap class
  1788 
  1789   /// This function just returns a \ref BackwardMap class.
  1790   /// \relates BackwardMap
  1791   template <typename Graph>
  1792   inline BackwardMap<Graph> backwardMap(const Graph& graph) {
  1793     return BackwardMap<Graph>(graph);
  1794   }
  1795 
  1796   /// \brief Potential difference map
  1797   ///
  1798   /// If there is an potential map on the nodes then we
  1799   /// can get an arc map as we get the substraction of the
  1800   /// values of the target and source.
  1801   template <typename Digraph, typename NodeMap>
  1802   class PotentialDifferenceMap {
  1803   public:
  1804     typedef typename Digraph::Arc Key;
  1805     typedef typename NodeMap::Value Value;
  1806 
  1807     /// \brief Constructor
  1808     ///
  1809     /// Contructor of the map
  1810     explicit PotentialDifferenceMap(const Digraph& digraph, 
  1811                                     const NodeMap& potential) 
  1812       : _digraph(digraph), _potential(potential) {}
  1813 
  1814     /// \brief Const subscription operator
  1815     ///
  1816     /// Const subscription operator
  1817     Value operator[](const Key& arc) const {
  1818       return _potential[_digraph.target(arc)] - 
  1819 	_potential[_digraph.source(arc)];
  1820     }
  1821 
  1822   private:
  1823     const Digraph& _digraph;
  1824     const NodeMap& _potential;
  1825   };
  1826 
  1827   /// \brief Returns a PotentialDifferenceMap.
  1828   ///
  1829   /// This function just returns a PotentialDifferenceMap.
  1830   /// \relates PotentialDifferenceMap
  1831   template <typename Digraph, typename NodeMap>
  1832   PotentialDifferenceMap<Digraph, NodeMap> 
  1833   potentialDifferenceMap(const Digraph& digraph, const NodeMap& potential) {
  1834     return PotentialDifferenceMap<Digraph, NodeMap>(digraph, potential);
  1835   }
  1836 
  1837   /// \brief Map of the node in-degrees.
  1838   ///
  1839   /// This map returns the in-degree of a node. Once it is constructed,
  1840   /// the degrees are stored in a standard NodeMap, so each query is done
  1841   /// in constant time. On the other hand, the values are updated automatically
  1842   /// whenever the digraph changes.
  1843   ///
  1844   /// \warning Besides addNode() and addArc(), a digraph structure may provide
  1845   /// alternative ways to modify the digraph. The correct behavior of InDegMap
  1846   /// is not guarantied if these additional features are used. For example
  1847   /// the functions \ref ListDigraph::changeSource() "changeSource()",
  1848   /// \ref ListDigraph::changeTarget() "changeTarget()" and
  1849   /// \ref ListDigraph::reverseArc() "reverseArc()"
  1850   /// of \ref ListDigraph will \e not update the degree values correctly.
  1851   ///
  1852   /// \sa OutDegMap
  1853 
  1854   template <typename _Digraph>
  1855   class InDegMap  
  1856     : protected ItemSetTraits<_Digraph, typename _Digraph::Arc>
  1857       ::ItemNotifier::ObserverBase {
  1858 
  1859   public:
  1860     
  1861     typedef _Digraph Digraph;
  1862     typedef int Value;
  1863     typedef typename Digraph::Node Key;
  1864 
  1865     typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
  1866     ::ItemNotifier::ObserverBase Parent;
  1867 
  1868   private:
  1869 
  1870     class AutoNodeMap : public DefaultMap<Digraph, Key, int> {
  1871     public:
  1872 
  1873       typedef DefaultMap<Digraph, Key, int> Parent;
  1874 
  1875       AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
  1876       
  1877       virtual void add(const Key& key) {
  1878 	Parent::add(key);
  1879 	Parent::set(key, 0);
  1880       }
  1881 
  1882       virtual void add(const std::vector<Key>& keys) {
  1883 	Parent::add(keys);
  1884 	for (int i = 0; i < int(keys.size()); ++i) {
  1885 	  Parent::set(keys[i], 0);
  1886 	}
  1887       }
  1888 
  1889       virtual void build() {
  1890 	Parent::build();
  1891 	Key it;
  1892 	typename Parent::Notifier* nf = Parent::notifier();
  1893 	for (nf->first(it); it != INVALID; nf->next(it)) {
  1894 	  Parent::set(it, 0);
  1895 	}
  1896       }
  1897     };
  1898 
  1899   public:
  1900 
  1901     /// \brief Constructor.
  1902     ///
  1903     /// Constructor for creating in-degree map.
  1904     explicit InDegMap(const Digraph& digraph) 
  1905       : _digraph(digraph), _deg(digraph) {
  1906       Parent::attach(_digraph.notifier(typename Digraph::Arc()));
  1907       
  1908       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  1909 	_deg[it] = countInArcs(_digraph, it);
  1910       }
  1911     }
  1912     
  1913     /// Gives back the in-degree of a Node.
  1914     int operator[](const Key& key) const {
  1915       return _deg[key];
  1916     }
  1917 
  1918   protected:
  1919     
  1920     typedef typename Digraph::Arc Arc;
  1921 
  1922     virtual void add(const Arc& arc) {
  1923       ++_deg[_digraph.target(arc)];
  1924     }
  1925 
  1926     virtual void add(const std::vector<Arc>& arcs) {
  1927       for (int i = 0; i < int(arcs.size()); ++i) {
  1928         ++_deg[_digraph.target(arcs[i])];
  1929       }
  1930     }
  1931 
  1932     virtual void erase(const Arc& arc) {
  1933       --_deg[_digraph.target(arc)];
  1934     }
  1935 
  1936     virtual void erase(const std::vector<Arc>& arcs) {
  1937       for (int i = 0; i < int(arcs.size()); ++i) {
  1938         --_deg[_digraph.target(arcs[i])];
  1939       }
  1940     }
  1941 
  1942     virtual void build() {
  1943       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  1944 	_deg[it] = countInArcs(_digraph, it);
  1945       }      
  1946     }
  1947 
  1948     virtual void clear() {
  1949       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  1950 	_deg[it] = 0;
  1951       }
  1952     }
  1953   private:
  1954     
  1955     const Digraph& _digraph;
  1956     AutoNodeMap _deg;
  1957   };
  1958 
  1959   /// \brief Map of the node out-degrees.
  1960   ///
  1961   /// This map returns the out-degree of a node. Once it is constructed,
  1962   /// the degrees are stored in a standard NodeMap, so each query is done
  1963   /// in constant time. On the other hand, the values are updated automatically
  1964   /// whenever the digraph changes.
  1965   ///
  1966   /// \warning Besides addNode() and addArc(), a digraph structure may provide
  1967   /// alternative ways to modify the digraph. The correct behavior of OutDegMap
  1968   /// is not guarantied if these additional features are used. For example
  1969   /// the functions \ref ListDigraph::changeSource() "changeSource()",
  1970   /// \ref ListDigraph::changeTarget() "changeTarget()" and
  1971   /// \ref ListDigraph::reverseArc() "reverseArc()"
  1972   /// of \ref ListDigraph will \e not update the degree values correctly.
  1973   ///
  1974   /// \sa InDegMap
  1975 
  1976   template <typename _Digraph>
  1977   class OutDegMap  
  1978     : protected ItemSetTraits<_Digraph, typename _Digraph::Arc>
  1979       ::ItemNotifier::ObserverBase {
  1980 
  1981   public:
  1982     
  1983     typedef _Digraph Digraph;
  1984     typedef int Value;
  1985     typedef typename Digraph::Node Key;
  1986 
  1987     typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
  1988     ::ItemNotifier::ObserverBase Parent;
  1989 
  1990   private:
  1991 
  1992     class AutoNodeMap : public DefaultMap<Digraph, Key, int> {
  1993     public:
  1994 
  1995       typedef DefaultMap<Digraph, Key, int> Parent;
  1996 
  1997       AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
  1998       
  1999       virtual void add(const Key& key) {
  2000 	Parent::add(key);
  2001 	Parent::set(key, 0);
  2002       }
  2003       virtual void add(const std::vector<Key>& keys) {
  2004 	Parent::add(keys);
  2005 	for (int i = 0; i < int(keys.size()); ++i) {
  2006 	  Parent::set(keys[i], 0);
  2007 	}
  2008       }
  2009       virtual void build() {
  2010 	Parent::build();
  2011 	Key it;
  2012 	typename Parent::Notifier* nf = Parent::notifier();
  2013 	for (nf->first(it); it != INVALID; nf->next(it)) {
  2014 	  Parent::set(it, 0);
  2015 	}
  2016       }
  2017     };
  2018 
  2019   public:
  2020 
  2021     /// \brief Constructor.
  2022     ///
  2023     /// Constructor for creating out-degree map.
  2024     explicit OutDegMap(const Digraph& digraph) 
  2025       : _digraph(digraph), _deg(digraph) {
  2026       Parent::attach(_digraph.notifier(typename Digraph::Arc()));
  2027       
  2028       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  2029 	_deg[it] = countOutArcs(_digraph, it);
  2030       }
  2031     }
  2032 
  2033     /// Gives back the out-degree of a Node.
  2034     int operator[](const Key& key) const {
  2035       return _deg[key];
  2036     }
  2037 
  2038   protected:
  2039     
  2040     typedef typename Digraph::Arc Arc;
  2041 
  2042     virtual void add(const Arc& arc) {
  2043       ++_deg[_digraph.source(arc)];
  2044     }
  2045 
  2046     virtual void add(const std::vector<Arc>& arcs) {
  2047       for (int i = 0; i < int(arcs.size()); ++i) {
  2048         ++_deg[_digraph.source(arcs[i])];
  2049       }
  2050     }
  2051 
  2052     virtual void erase(const Arc& arc) {
  2053       --_deg[_digraph.source(arc)];
  2054     }
  2055 
  2056     virtual void erase(const std::vector<Arc>& arcs) {
  2057       for (int i = 0; i < int(arcs.size()); ++i) {
  2058         --_deg[_digraph.source(arcs[i])];
  2059       }
  2060     }
  2061 
  2062     virtual void build() {
  2063       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  2064 	_deg[it] = countOutArcs(_digraph, it);
  2065       }      
  2066     }
  2067 
  2068     virtual void clear() {
  2069       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  2070 	_deg[it] = 0;
  2071       }
  2072     }
  2073   private:
  2074     
  2075     const Digraph& _digraph;
  2076     AutoNodeMap _deg;
  2077   };
  2078 
  2079 
  2080   ///Dynamic arc look up between given endpoints.
  2081   
  2082   ///\ingroup gutils
  2083   ///Using this class, you can find an arc in a digraph from a given
  2084   ///source to a given target in amortized time <em>O(log d)</em>,
  2085   ///where <em>d</em> is the out-degree of the source node.
  2086   ///
  2087   ///It is possible to find \e all parallel arcs between two nodes with
  2088   ///the \c findFirst() and \c findNext() members.
  2089   ///
  2090   ///See the \ref ArcLookUp and \ref AllArcLookUp classes if your
  2091   ///digraph is not changed so frequently.
  2092   ///
  2093   ///This class uses a self-adjusting binary search tree, Sleator's
  2094   ///and Tarjan's Splay tree for guarantee the logarithmic amortized
  2095   ///time bound for arc lookups. This class also guarantees the
  2096   ///optimal time bound in a constant factor for any distribution of
  2097   ///queries.
  2098   ///
  2099   ///\param G The type of the underlying digraph.  
  2100   ///
  2101   ///\sa ArcLookUp  
  2102   ///\sa AllArcLookUp  
  2103   template<class G>
  2104   class DynArcLookUp 
  2105     : protected ItemSetTraits<G, typename G::Arc>::ItemNotifier::ObserverBase
  2106   {
  2107   public:
  2108     typedef typename ItemSetTraits<G, typename G::Arc>
  2109     ::ItemNotifier::ObserverBase Parent;
  2110 
  2111     TEMPLATE_DIGRAPH_TYPEDEFS(G);
  2112     typedef G Digraph;
  2113 
  2114   protected:
  2115 
  2116     class AutoNodeMap : public DefaultMap<G, Node, Arc> {
  2117     public:
  2118 
  2119       typedef DefaultMap<G, Node, Arc> Parent;
  2120 
  2121       AutoNodeMap(const G& digraph) : Parent(digraph, INVALID) {}
  2122       
  2123       virtual void add(const Node& node) {
  2124 	Parent::add(node);
  2125 	Parent::set(node, INVALID);
  2126       }
  2127 
  2128       virtual void add(const std::vector<Node>& nodes) {
  2129 	Parent::add(nodes);
  2130 	for (int i = 0; i < int(nodes.size()); ++i) {
  2131 	  Parent::set(nodes[i], INVALID);
  2132 	}
  2133       }
  2134 
  2135       virtual void build() {
  2136 	Parent::build();
  2137 	Node it;
  2138 	typename Parent::Notifier* nf = Parent::notifier();
  2139 	for (nf->first(it); it != INVALID; nf->next(it)) {
  2140 	  Parent::set(it, INVALID);
  2141 	}
  2142       }
  2143     };
  2144 
  2145     const Digraph &_g;
  2146     AutoNodeMap _head;
  2147     typename Digraph::template ArcMap<Arc> _parent;
  2148     typename Digraph::template ArcMap<Arc> _left;
  2149     typename Digraph::template ArcMap<Arc> _right;
  2150     
  2151     class ArcLess {
  2152       const Digraph &g;
  2153     public:
  2154       ArcLess(const Digraph &_g) : g(_g) {}
  2155       bool operator()(Arc a,Arc b) const 
  2156       {
  2157 	return g.target(a)<g.target(b);
  2158       }
  2159     };
  2160     
  2161   public:
  2162     
  2163     ///Constructor
  2164 
  2165     ///Constructor.
  2166     ///
  2167     ///It builds up the search database.
  2168     DynArcLookUp(const Digraph &g) 
  2169       : _g(g),_head(g),_parent(g),_left(g),_right(g) 
  2170     { 
  2171       Parent::attach(_g.notifier(typename Digraph::Arc()));
  2172       refresh(); 
  2173     }
  2174     
  2175   protected:
  2176 
  2177     virtual void add(const Arc& arc) {
  2178       insert(arc);
  2179     }
  2180 
  2181     virtual void add(const std::vector<Arc>& arcs) {
  2182       for (int i = 0; i < int(arcs.size()); ++i) {
  2183 	insert(arcs[i]);
  2184       }
  2185     }
  2186 
  2187     virtual void erase(const Arc& arc) {
  2188       remove(arc);
  2189     }
  2190 
  2191     virtual void erase(const std::vector<Arc>& arcs) {
  2192       for (int i = 0; i < int(arcs.size()); ++i) {
  2193 	remove(arcs[i]);
  2194       }     
  2195     }
  2196 
  2197     virtual void build() {
  2198       refresh();
  2199     }
  2200 
  2201     virtual void clear() {
  2202       for(NodeIt n(_g);n!=INVALID;++n) {
  2203 	_head.set(n, INVALID);
  2204       }
  2205     }
  2206 
  2207     void insert(Arc arc) {
  2208       Node s = _g.source(arc);
  2209       Node t = _g.target(arc);
  2210       _left.set(arc, INVALID);
  2211       _right.set(arc, INVALID);
  2212       
  2213       Arc e = _head[s];
  2214       if (e == INVALID) {
  2215 	_head.set(s, arc);
  2216 	_parent.set(arc, INVALID);
  2217 	return;
  2218       }
  2219       while (true) {
  2220 	if (t < _g.target(e)) {
  2221 	  if (_left[e] == INVALID) {
  2222 	    _left.set(e, arc);
  2223 	    _parent.set(arc, e);
  2224 	    splay(arc);
  2225 	    return;
  2226 	  } else {
  2227 	    e = _left[e];
  2228 	  }
  2229 	} else {
  2230 	  if (_right[e] == INVALID) {
  2231 	    _right.set(e, arc);
  2232 	    _parent.set(arc, e);
  2233 	    splay(arc);
  2234 	    return;
  2235 	  } else {
  2236 	    e = _right[e];
  2237 	  }
  2238 	}
  2239       }
  2240     }
  2241 
  2242     void remove(Arc arc) {
  2243       if (_left[arc] == INVALID) {
  2244 	if (_right[arc] != INVALID) {
  2245 	  _parent.set(_right[arc], _parent[arc]);
  2246 	}
  2247 	if (_parent[arc] != INVALID) {
  2248 	  if (_left[_parent[arc]] == arc) {
  2249 	    _left.set(_parent[arc], _right[arc]);
  2250 	  } else {
  2251 	    _right.set(_parent[arc], _right[arc]);
  2252 	  }
  2253 	} else {
  2254 	  _head.set(_g.source(arc), _right[arc]);
  2255 	}
  2256       } else if (_right[arc] == INVALID) {
  2257 	_parent.set(_left[arc], _parent[arc]);
  2258 	if (_parent[arc] != INVALID) {
  2259 	  if (_left[_parent[arc]] == arc) {
  2260 	    _left.set(_parent[arc], _left[arc]);
  2261 	  } else {
  2262 	    _right.set(_parent[arc], _left[arc]);
  2263 	  }
  2264 	} else {
  2265 	  _head.set(_g.source(arc), _left[arc]);
  2266 	}
  2267       } else {
  2268 	Arc e = _left[arc];
  2269 	if (_right[e] != INVALID) {
  2270 	  e = _right[e];	  
  2271 	  while (_right[e] != INVALID) {
  2272 	    e = _right[e];
  2273 	  }
  2274 	  Arc s = _parent[e];
  2275 	  _right.set(_parent[e], _left[e]);
  2276 	  if (_left[e] != INVALID) {
  2277 	    _parent.set(_left[e], _parent[e]);
  2278 	  }
  2279 	  
  2280 	  _left.set(e, _left[arc]);
  2281 	  _parent.set(_left[arc], e);
  2282 	  _right.set(e, _right[arc]);
  2283 	  _parent.set(_right[arc], e);
  2284 
  2285 	  _parent.set(e, _parent[arc]);
  2286 	  if (_parent[arc] != INVALID) {
  2287 	    if (_left[_parent[arc]] == arc) {
  2288 	      _left.set(_parent[arc], e);
  2289 	    } else {
  2290 	      _right.set(_parent[arc], e);
  2291 	    }
  2292 	  }
  2293 	  splay(s);
  2294 	} else {
  2295 	  _right.set(e, _right[arc]);
  2296 	  _parent.set(_right[arc], e);
  2297 
  2298 	  if (_parent[arc] != INVALID) {
  2299 	    if (_left[_parent[arc]] == arc) {
  2300 	      _left.set(_parent[arc], e);
  2301 	    } else {
  2302 	      _right.set(_parent[arc], e);
  2303 	    }
  2304 	  } else {
  2305 	    _head.set(_g.source(arc), e);
  2306 	  }
  2307 	}
  2308       }
  2309     }
  2310 
  2311     Arc refreshRec(std::vector<Arc> &v,int a,int b) 
  2312     {
  2313       int m=(a+b)/2;
  2314       Arc me=v[m];
  2315       if (a < m) {
  2316 	Arc left = refreshRec(v,a,m-1);
  2317 	_left.set(me, left);
  2318 	_parent.set(left, me);
  2319       } else {
  2320 	_left.set(me, INVALID);
  2321       }
  2322       if (m < b) {
  2323 	Arc right = refreshRec(v,m+1,b);
  2324 	_right.set(me, right);
  2325 	_parent.set(right, me);
  2326       } else {
  2327 	_right.set(me, INVALID);
  2328       }
  2329       return me;
  2330     }
  2331 
  2332     void refresh() {
  2333       for(NodeIt n(_g);n!=INVALID;++n) {
  2334 	std::vector<Arc> v;
  2335 	for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
  2336 	if(v.size()) {
  2337 	  std::sort(v.begin(),v.end(),ArcLess(_g));
  2338 	  Arc head = refreshRec(v,0,v.size()-1);
  2339 	  _head.set(n, head);
  2340 	  _parent.set(head, INVALID);
  2341 	}
  2342 	else _head.set(n, INVALID);
  2343       }
  2344     }
  2345 
  2346     void zig(Arc v) {        
  2347       Arc w = _parent[v];
  2348       _parent.set(v, _parent[w]);
  2349       _parent.set(w, v);
  2350       _left.set(w, _right[v]);
  2351       _right.set(v, w);
  2352       if (_parent[v] != INVALID) {
  2353 	if (_right[_parent[v]] == w) {
  2354 	  _right.set(_parent[v], v);
  2355 	} else {
  2356 	  _left.set(_parent[v], v);
  2357 	}
  2358       }
  2359       if (_left[w] != INVALID){
  2360 	_parent.set(_left[w], w);
  2361       }
  2362     }
  2363 
  2364     void zag(Arc v) {        
  2365       Arc w = _parent[v];
  2366       _parent.set(v, _parent[w]);
  2367       _parent.set(w, v);
  2368       _right.set(w, _left[v]);
  2369       _left.set(v, w);
  2370       if (_parent[v] != INVALID){
  2371 	if (_left[_parent[v]] == w) {
  2372 	  _left.set(_parent[v], v);
  2373 	} else {
  2374 	  _right.set(_parent[v], v);
  2375 	}
  2376       }
  2377       if (_right[w] != INVALID){
  2378 	_parent.set(_right[w], w);
  2379       }
  2380     }
  2381 
  2382     void splay(Arc v) {
  2383       while (_parent[v] != INVALID) {
  2384 	if (v == _left[_parent[v]]) {
  2385 	  if (_parent[_parent[v]] == INVALID) {
  2386 	    zig(v);
  2387 	  } else {
  2388 	    if (_parent[v] == _left[_parent[_parent[v]]]) {
  2389 	      zig(_parent[v]);
  2390 	      zig(v);
  2391 	    } else {
  2392 	      zig(v);
  2393 	      zag(v);
  2394 	    }
  2395 	  }
  2396 	} else {
  2397 	  if (_parent[_parent[v]] == INVALID) {
  2398 	    zag(v);
  2399 	  } else {
  2400 	    if (_parent[v] == _left[_parent[_parent[v]]]) {
  2401 	      zag(v);
  2402 	      zig(v);
  2403 	    } else {
  2404 	      zag(_parent[v]);
  2405 	      zag(v);
  2406 	    }
  2407 	  }
  2408 	}
  2409       }
  2410       _head[_g.source(v)] = v;
  2411     }
  2412 
  2413 
  2414   public:
  2415     
  2416     ///Find an arc between two nodes.
  2417     
  2418     ///Find an arc between two nodes in time <em>O(</em>log<em>d)</em>, where
  2419     /// <em>d</em> is the number of outgoing arcs of \c s.
  2420     ///\param s The source node
  2421     ///\param t The target node
  2422     ///\return An arc from \c s to \c t if there exists,
  2423     ///\ref INVALID otherwise.
  2424     Arc operator()(Node s, Node t) const
  2425     {
  2426       Arc a = _head[s];
  2427       while (true) {
  2428 	if (_g.target(a) == t) {
  2429 	  const_cast<DynArcLookUp&>(*this).splay(a);
  2430 	  return a;
  2431 	} else if (t < _g.target(a)) {
  2432 	  if (_left[a] == INVALID) {
  2433 	    const_cast<DynArcLookUp&>(*this).splay(a);
  2434 	    return INVALID;
  2435 	  } else {
  2436 	    a = _left[a];
  2437 	  }
  2438 	} else  {
  2439 	  if (_right[a] == INVALID) {
  2440 	    const_cast<DynArcLookUp&>(*this).splay(a);
  2441 	    return INVALID;
  2442 	  } else {
  2443 	    a = _right[a];
  2444 	  }
  2445 	}
  2446       }
  2447     }
  2448 
  2449     ///Find the first arc between two nodes.
  2450     
  2451     ///Find the first arc between two nodes in time
  2452     /// <em>O(</em>log<em>d)</em>, where <em>d</em> is the number of
  2453     /// outgoing arcs of \c s.  
  2454     ///\param s The source node 
  2455     ///\param t The target node
  2456     ///\return An arc from \c s to \c t if there exists, \ref INVALID
  2457     /// otherwise.
  2458     Arc findFirst(Node s, Node t) const
  2459     {
  2460       Arc a = _head[s];
  2461       Arc r = INVALID;
  2462       while (true) {
  2463 	if (_g.target(a) < t) {
  2464 	  if (_right[a] == INVALID) {
  2465 	    const_cast<DynArcLookUp&>(*this).splay(a);
  2466 	    return r;
  2467 	  } else {
  2468 	    a = _right[a];
  2469 	  }
  2470 	} else {
  2471 	  if (_g.target(a) == t) {
  2472 	    r = a;
  2473 	  }
  2474 	  if (_left[a] == INVALID) {
  2475 	    const_cast<DynArcLookUp&>(*this).splay(a);
  2476 	    return r;
  2477 	  } else {
  2478 	    a = _left[a];
  2479 	  }
  2480 	}
  2481       }
  2482     }
  2483 
  2484     ///Find the next arc between two nodes.
  2485     
  2486     ///Find the next arc between two nodes in time
  2487     /// <em>O(</em>log<em>d)</em>, where <em>d</em> is the number of
  2488     /// outgoing arcs of \c s.  
  2489     ///\param s The source node 
  2490     ///\param t The target node
  2491     ///\return An arc from \c s to \c t if there exists, \ref INVALID
  2492     /// otherwise.
  2493 
  2494     ///\note If \c e is not the result of the previous \c findFirst()
  2495     ///operation then the amorized time bound can not be guaranteed.
  2496 #ifdef DOXYGEN
  2497     Arc findNext(Node s, Node t, Arc a) const
  2498 #else
  2499     Arc findNext(Node, Node t, Arc a) const
  2500 #endif
  2501     {
  2502       if (_right[a] != INVALID) {
  2503 	a = _right[a];
  2504 	while (_left[a] != INVALID) {
  2505 	  a = _left[a];
  2506 	}
  2507 	const_cast<DynArcLookUp&>(*this).splay(a);
  2508       } else {
  2509 	while (_parent[a] != INVALID && _right[_parent[a]] ==  a) {
  2510 	  a = _parent[a];
  2511 	}
  2512 	if (_parent[a] == INVALID) {
  2513 	  return INVALID;
  2514 	} else {
  2515 	  a = _parent[a];
  2516 	  const_cast<DynArcLookUp&>(*this).splay(a);
  2517 	}
  2518       }
  2519       if (_g.target(a) == t) return a;
  2520       else return INVALID;    
  2521     }
  2522 
  2523   };
  2524 
  2525   ///Fast arc look up between given endpoints.
  2526   
  2527   ///\ingroup gutils
  2528   ///Using this class, you can find an arc in a digraph from a given
  2529   ///source to a given target in time <em>O(log d)</em>,
  2530   ///where <em>d</em> is the out-degree of the source node.
  2531   ///
  2532   ///It is not possible to find \e all parallel arcs between two nodes.
  2533   ///Use \ref AllArcLookUp for this purpose.
  2534   ///
  2535   ///\warning This class is static, so you should refresh() (or at least
  2536   ///refresh(Node)) this data structure
  2537   ///whenever the digraph changes. This is a time consuming (superlinearly
  2538   ///proportional (<em>O(m</em>log<em>m)</em>) to the number of arcs).
  2539   ///
  2540   ///\param G The type of the underlying digraph.
  2541   ///
  2542   ///\sa DynArcLookUp
  2543   ///\sa AllArcLookUp  
  2544   template<class G>
  2545   class ArcLookUp 
  2546   {
  2547   public:
  2548     TEMPLATE_DIGRAPH_TYPEDEFS(G);
  2549     typedef G Digraph;
  2550 
  2551   protected:
  2552     const Digraph &_g;
  2553     typename Digraph::template NodeMap<Arc> _head;
  2554     typename Digraph::template ArcMap<Arc> _left;
  2555     typename Digraph::template ArcMap<Arc> _right;
  2556     
  2557     class ArcLess {
  2558       const Digraph &g;
  2559     public:
  2560       ArcLess(const Digraph &_g) : g(_g) {}
  2561       bool operator()(Arc a,Arc b) const 
  2562       {
  2563 	return g.target(a)<g.target(b);
  2564       }
  2565     };
  2566     
  2567   public:
  2568     
  2569     ///Constructor
  2570 
  2571     ///Constructor.
  2572     ///
  2573     ///It builds up the search database, which remains valid until the digraph
  2574     ///changes.
  2575     ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}
  2576     
  2577   private:
  2578     Arc refreshRec(std::vector<Arc> &v,int a,int b) 
  2579     {
  2580       int m=(a+b)/2;
  2581       Arc me=v[m];
  2582       _left[me] = a<m?refreshRec(v,a,m-1):INVALID;
  2583       _right[me] = m<b?refreshRec(v,m+1,b):INVALID;
  2584       return me;
  2585     }
  2586   public:
  2587     ///Refresh the data structure at a node.
  2588 
  2589     ///Build up the search database of node \c n.
  2590     ///
  2591     ///It runs in time <em>O(d</em>log<em>d)</em>, where <em>d</em> is
  2592     ///the number of the outgoing arcs of \c n.
  2593     void refresh(Node n) 
  2594     {
  2595       std::vector<Arc> v;
  2596       for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
  2597       if(v.size()) {
  2598 	std::sort(v.begin(),v.end(),ArcLess(_g));
  2599 	_head[n]=refreshRec(v,0,v.size()-1);
  2600       }
  2601       else _head[n]=INVALID;
  2602     }
  2603     ///Refresh the full data structure.
  2604 
  2605     ///Build up the full search database. In fact, it simply calls
  2606     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  2607     ///
  2608     ///It runs in time <em>O(m</em>log<em>D)</em>, where <em>m</em> is
  2609     ///the number of the arcs of \c n and <em>D</em> is the maximum
  2610     ///out-degree of the digraph.
  2611 
  2612     void refresh() 
  2613     {
  2614       for(NodeIt n(_g);n!=INVALID;++n) refresh(n);
  2615     }
  2616     
  2617     ///Find an arc between two nodes.
  2618     
  2619     ///Find an arc between two nodes in time <em>O(</em>log<em>d)</em>, where
  2620     /// <em>d</em> is the number of outgoing arcs of \c s.
  2621     ///\param s The source node
  2622     ///\param t The target node
  2623     ///\return An arc from \c s to \c t if there exists,
  2624     ///\ref INVALID otherwise.
  2625     ///
  2626     ///\warning If you change the digraph, refresh() must be called before using
  2627     ///this operator. If you change the outgoing arcs of
  2628     ///a single node \c n, then
  2629     ///\ref refresh(Node) "refresh(n)" is enough.
  2630     ///
  2631     Arc operator()(Node s, Node t) const
  2632     {
  2633       Arc e;
  2634       for(e=_head[s];
  2635 	  e!=INVALID&&_g.target(e)!=t;
  2636 	  e = t < _g.target(e)?_left[e]:_right[e]) ;
  2637       return e;
  2638     }
  2639 
  2640   };
  2641 
  2642   ///Fast look up of all arcs between given endpoints.
  2643   
  2644   ///\ingroup gutils
  2645   ///This class is the same as \ref ArcLookUp, with the addition
  2646   ///that it makes it possible to find all arcs between given endpoints.
  2647   ///
  2648   ///\warning This class is static, so you should refresh() (or at least
  2649   ///refresh(Node)) this data structure
  2650   ///whenever the digraph changes. This is a time consuming (superlinearly
  2651   ///proportional (<em>O(m</em>log<em>m)</em>) to the number of arcs).
  2652   ///
  2653   ///\param G The type of the underlying digraph.
  2654   ///
  2655   ///\sa DynArcLookUp
  2656   ///\sa ArcLookUp  
  2657   template<class G>
  2658   class AllArcLookUp : public ArcLookUp<G>
  2659   {
  2660     using ArcLookUp<G>::_g;
  2661     using ArcLookUp<G>::_right;
  2662     using ArcLookUp<G>::_left;
  2663     using ArcLookUp<G>::_head;
  2664 
  2665     TEMPLATE_DIGRAPH_TYPEDEFS(G);
  2666     typedef G Digraph;
  2667     
  2668     typename Digraph::template ArcMap<Arc> _next;
  2669     
  2670     Arc refreshNext(Arc head,Arc next=INVALID)
  2671     {
  2672       if(head==INVALID) return next;
  2673       else {
  2674 	next=refreshNext(_right[head],next);
  2675 // 	_next[head]=next;
  2676 	_next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
  2677 	  ? next : INVALID;
  2678 	return refreshNext(_left[head],head);
  2679       }
  2680     }
  2681     
  2682     void refreshNext()
  2683     {
  2684       for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
  2685     }
  2686     
  2687   public:
  2688     ///Constructor
  2689 
  2690     ///Constructor.
  2691     ///
  2692     ///It builds up the search database, which remains valid until the digraph
  2693     ///changes.
  2694     AllArcLookUp(const Digraph &g) : ArcLookUp<G>(g), _next(g) {refreshNext();}
  2695 
  2696     ///Refresh the data structure at a node.
  2697 
  2698     ///Build up the search database of node \c n.
  2699     ///
  2700     ///It runs in time <em>O(d</em>log<em>d)</em>, where <em>d</em> is
  2701     ///the number of the outgoing arcs of \c n.
  2702     
  2703     void refresh(Node n) 
  2704     {
  2705       ArcLookUp<G>::refresh(n);
  2706       refreshNext(_head[n]);
  2707     }
  2708     
  2709     ///Refresh the full data structure.
  2710 
  2711     ///Build up the full search database. In fact, it simply calls
  2712     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  2713     ///
  2714     ///It runs in time <em>O(m</em>log<em>D)</em>, where <em>m</em> is
  2715     ///the number of the arcs of \c n and <em>D</em> is the maximum
  2716     ///out-degree of the digraph.
  2717 
  2718     void refresh() 
  2719     {
  2720       for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
  2721     }
  2722     
  2723     ///Find an arc between two nodes.
  2724     
  2725     ///Find an arc between two nodes.
  2726     ///\param s The source node
  2727     ///\param t The target node
  2728     ///\param prev The previous arc between \c s and \c t. It it is INVALID or
  2729     ///not given, the operator finds the first appropriate arc.
  2730     ///\return An arc from \c s to \c t after \c prev or
  2731     ///\ref INVALID if there is no more.
  2732     ///
  2733     ///For example, you can count the number of arcs from \c u to \c v in the
  2734     ///following way.
  2735     ///\code
  2736     ///AllArcLookUp<ListDigraph> ae(g);
  2737     ///...
  2738     ///int n=0;
  2739     ///for(Arc e=ae(u,v);e!=INVALID;e=ae(u,v,e)) n++;
  2740     ///\endcode
  2741     ///
  2742     ///Finding the first arc take <em>O(</em>log<em>d)</em> time, where
  2743     /// <em>d</em> is the number of outgoing arcs of \c s. Then, the
  2744     ///consecutive arcs are found in constant time.
  2745     ///
  2746     ///\warning If you change the digraph, refresh() must be called before using
  2747     ///this operator. If you change the outgoing arcs of
  2748     ///a single node \c n, then
  2749     ///\ref refresh(Node) "refresh(n)" is enough.
  2750     ///
  2751 #ifdef DOXYGEN
  2752     Arc operator()(Node s, Node t, Arc prev=INVALID) const {}
  2753 #else
  2754     using ArcLookUp<G>::operator() ;
  2755     Arc operator()(Node s, Node t, Arc prev) const
  2756     {
  2757       return prev==INVALID?(*this)(s,t):_next[prev];
  2758     }
  2759 #endif
  2760       
  2761   };
  2762 
  2763   /// @}
  2764 
  2765 } //END OF NAMESPACE LEMON
  2766 
  2767 #endif