lemon/graph_utils.h
author Alpar Juttner <alpar@cs.elte.hu>
Sun, 13 Jul 2008 16:35:05 +0100
changeset 207 574b963d0275
parent 169 5b507a86ad72
child 209 765619b7cbb2
permissions -rw-r--r--
Merge
     1 /* -*- C++ -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library
     4  *
     5  * Copyright (C) 2003-2008
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 #ifndef LEMON_GRAPH_UTILS_H
    20 #define LEMON_GRAPH_UTILS_H
    21 
    22 #include <iterator>
    23 #include <vector>
    24 #include <map>
    25 #include <cmath>
    26 #include <algorithm>
    27 
    28 #include <lemon/bits/invalid.h>
    29 #include <lemon/bits/utility.h>
    30 #include <lemon/maps.h>
    31 #include <lemon/bits/traits.h>
    32 
    33 #include <lemon/bits/alteration_notifier.h>
    34 #include <lemon/bits/default_map.h>
    35 
    36 ///\ingroup gutils
    37 ///\file
    38 ///\brief Graph utilities.
    39 
    40 namespace lemon {
    41 
    42   /// \addtogroup gutils
    43   /// @{
    44 
    45   ///Creates convenience typedefs for the digraph types and iterators
    46 
    47   ///This \c \#define creates convenience typedefs for the following types
    48   ///of \c Digraph: \c Node,  \c NodeIt, \c Arc, \c ArcIt, \c InArcIt,
    49   ///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap, 
    50   ///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap.
    51   ///
    52   ///\note If the graph type is a dependent type, ie. the graph type depend
    53   ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
    54   ///macro.
    55 #define DIGRAPH_TYPEDEFS(Digraph)					\
    56   typedef Digraph::Node Node;						\
    57   typedef Digraph::NodeIt NodeIt;					\
    58   typedef Digraph::Arc Arc;						\
    59   typedef Digraph::ArcIt ArcIt;						\
    60   typedef Digraph::InArcIt InArcIt;					\
    61   typedef Digraph::OutArcIt OutArcIt;					\
    62   typedef Digraph::NodeMap<bool> BoolNodeMap;				\
    63   typedef Digraph::NodeMap<int> IntNodeMap;				\
    64   typedef Digraph::NodeMap<double> DoubleNodeMap;			\
    65   typedef Digraph::ArcMap<bool> BoolArcMap;				\
    66   typedef Digraph::ArcMap<int> IntArcMap;				\
    67   typedef Digraph::ArcMap<double> DoubleArcMap
    68 
    69   ///Creates convenience typedefs for the digraph types and iterators
    70 
    71   ///\see DIGRAPH_TYPEDEFS
    72   ///
    73   ///\note Use this macro, if the graph type is a dependent type,
    74   ///ie. the graph type depend on a template parameter.
    75 #define TEMPLATE_DIGRAPH_TYPEDEFS(Digraph)				\
    76   typedef typename Digraph::Node Node;					\
    77   typedef typename Digraph::NodeIt NodeIt;				\
    78   typedef typename Digraph::Arc Arc;					\
    79   typedef typename Digraph::ArcIt ArcIt;				\
    80   typedef typename Digraph::InArcIt InArcIt;				\
    81   typedef typename Digraph::OutArcIt OutArcIt;				\
    82   typedef typename Digraph::template NodeMap<bool> BoolNodeMap;		\
    83   typedef typename Digraph::template NodeMap<int> IntNodeMap;		\
    84   typedef typename Digraph::template NodeMap<double> DoubleNodeMap;	\
    85   typedef typename Digraph::template ArcMap<bool> BoolArcMap;		\
    86   typedef typename Digraph::template ArcMap<int> IntArcMap;		\
    87   typedef typename Digraph::template ArcMap<double> DoubleArcMap
    88   
    89   ///Creates convenience typedefs for the graph types and iterators
    90 
    91   ///This \c \#define creates the same convenience typedefs as defined
    92   ///by \ref DIGRAPH_TYPEDEFS(Graph) and six more, namely it creates
    93   ///\c Edge, \c EdgeIt, \c IncEdgeIt, \c BoolEdgeMap, \c IntEdgeMap,
    94   ///\c DoubleEdgeMap.
    95   ///
    96   ///\note If the graph type is a dependent type, ie. the graph type depend
    97   ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
    98   ///macro.
    99 #define GRAPH_TYPEDEFS(Graph)						\
   100   DIGRAPH_TYPEDEFS(Graph);						\
   101   typedef Graph::Edge Edge;						\
   102   typedef Graph::EdgeIt EdgeIt;						\
   103   typedef Graph::IncEdgeIt IncEdgeIt;					\
   104   typedef Graph::EdgeMap<bool> BoolEdgeMap;				\
   105   typedef Graph::EdgeMap<int> IntEdgeMap;				\
   106   typedef Graph::EdgeMap<double> DoubleEdgeMap
   107 
   108   ///Creates convenience typedefs for the graph types and iterators
   109 
   110   ///\see GRAPH_TYPEDEFS
   111   ///
   112   ///\note Use this macro, if the graph type is a dependent type,
   113   ///ie. the graph type depend on a template parameter.
   114 #define TEMPLATE_GRAPH_TYPEDEFS(Graph)					\
   115   TEMPLATE_DIGRAPH_TYPEDEFS(Graph);					\
   116   typedef typename Graph::Edge Edge;					\
   117   typedef typename Graph::EdgeIt EdgeIt;				\
   118   typedef typename Graph::IncEdgeIt IncEdgeIt;				\
   119   typedef typename Graph::template EdgeMap<bool> BoolEdgeMap;		\
   120   typedef typename Graph::template EdgeMap<int> IntEdgeMap;		\
   121   typedef typename Graph::template EdgeMap<double> DoubleEdgeMap
   122 
   123   /// \brief Function to count the items in the graph.
   124   ///
   125   /// This function counts the items (nodes, arcs etc) in the graph.
   126   /// The complexity of the function is O(n) because
   127   /// it iterates on all of the items.
   128   template <typename Graph, typename Item>
   129   inline int countItems(const Graph& g) {
   130     typedef typename ItemSetTraits<Graph, Item>::ItemIt ItemIt;
   131     int num = 0;
   132     for (ItemIt it(g); it != INVALID; ++it) {
   133       ++num;
   134     }
   135     return num;
   136   }
   137 
   138   // Node counting:
   139 
   140   namespace _graph_utils_bits {
   141     
   142     template <typename Graph, typename Enable = void>
   143     struct CountNodesSelector {
   144       static int count(const Graph &g) {
   145         return countItems<Graph, typename Graph::Node>(g);
   146       }
   147     };
   148 
   149     template <typename Graph>
   150     struct CountNodesSelector<
   151       Graph, typename 
   152       enable_if<typename Graph::NodeNumTag, void>::type> 
   153     {
   154       static int count(const Graph &g) {
   155         return g.nodeNum();
   156       }
   157     };    
   158   }
   159 
   160   /// \brief Function to count the nodes in the graph.
   161   ///
   162   /// This function counts the nodes in the graph.
   163   /// The complexity of the function is O(n) but for some
   164   /// graph structures it is specialized to run in O(1).
   165   ///
   166   /// If the graph contains a \e nodeNum() member function and a 
   167   /// \e NodeNumTag tag then this function calls directly the member
   168   /// function to query the cardinality of the node set.
   169   template <typename Graph>
   170   inline int countNodes(const Graph& g) {
   171     return _graph_utils_bits::CountNodesSelector<Graph>::count(g);
   172   }
   173 
   174   // Arc counting:
   175 
   176   namespace _graph_utils_bits {
   177     
   178     template <typename Graph, typename Enable = void>
   179     struct CountArcsSelector {
   180       static int count(const Graph &g) {
   181         return countItems<Graph, typename Graph::Arc>(g);
   182       }
   183     };
   184 
   185     template <typename Graph>
   186     struct CountArcsSelector<
   187       Graph, 
   188       typename enable_if<typename Graph::ArcNumTag, void>::type> 
   189     {
   190       static int count(const Graph &g) {
   191         return g.arcNum();
   192       }
   193     };    
   194   }
   195 
   196   /// \brief Function to count the arcs in the graph.
   197   ///
   198   /// This function counts the arcs in the graph.
   199   /// The complexity of the function is O(e) but for some
   200   /// graph structures it is specialized to run in O(1).
   201   ///
   202   /// If the graph contains a \e arcNum() member function and a 
   203   /// \e EdgeNumTag tag then this function calls directly the member
   204   /// function to query the cardinality of the arc set.
   205   template <typename Graph>
   206   inline int countArcs(const Graph& g) {
   207     return _graph_utils_bits::CountArcsSelector<Graph>::count(g);
   208   }
   209 
   210   // Edge counting:
   211   namespace _graph_utils_bits {
   212     
   213     template <typename Graph, typename Enable = void>
   214     struct CountEdgesSelector {
   215       static int count(const Graph &g) {
   216         return countItems<Graph, typename Graph::Edge>(g);
   217       }
   218     };
   219 
   220     template <typename Graph>
   221     struct CountEdgesSelector<
   222       Graph, 
   223       typename enable_if<typename Graph::EdgeNumTag, void>::type> 
   224     {
   225       static int count(const Graph &g) {
   226         return g.edgeNum();
   227       }
   228     };    
   229   }
   230 
   231   /// \brief Function to count the edges in the graph.
   232   ///
   233   /// This function counts the edges in the graph.
   234   /// The complexity of the function is O(m) but for some
   235   /// graph structures it is specialized to run in O(1).
   236   ///
   237   /// If the graph contains a \e edgeNum() member function and a 
   238   /// \e EdgeNumTag tag then this function calls directly the member
   239   /// function to query the cardinality of the edge set.
   240   template <typename Graph>
   241   inline int countEdges(const Graph& g) {
   242     return _graph_utils_bits::CountEdgesSelector<Graph>::count(g);
   243 
   244   }
   245 
   246 
   247   template <typename Graph, typename DegIt>
   248   inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {
   249     int num = 0;
   250     for (DegIt it(_g, _n); it != INVALID; ++it) {
   251       ++num;
   252     }
   253     return num;
   254   }
   255 
   256   /// \brief Function to count the number of the out-arcs from node \c n.
   257   ///
   258   /// This function counts the number of the out-arcs from node \c n
   259   /// in the graph.  
   260   template <typename Graph>
   261   inline int countOutArcs(const Graph& _g,  const typename Graph::Node& _n) {
   262     return countNodeDegree<Graph, typename Graph::OutArcIt>(_g, _n);
   263   }
   264 
   265   /// \brief Function to count the number of the in-arcs to node \c n.
   266   ///
   267   /// This function counts the number of the in-arcs to node \c n
   268   /// in the graph.  
   269   template <typename Graph>
   270   inline int countInArcs(const Graph& _g,  const typename Graph::Node& _n) {
   271     return countNodeDegree<Graph, typename Graph::InArcIt>(_g, _n);
   272   }
   273 
   274   /// \brief Function to count the number of the inc-edges to node \c n.
   275   ///
   276   /// This function counts the number of the inc-edges to node \c n
   277   /// in the graph.  
   278   template <typename Graph>
   279   inline int countIncEdges(const Graph& _g,  const typename Graph::Node& _n) {
   280     return countNodeDegree<Graph, typename Graph::IncEdgeIt>(_g, _n);
   281   }
   282 
   283   namespace _graph_utils_bits {
   284     
   285     template <typename Graph, typename Enable = void>
   286     struct FindArcSelector {
   287       typedef typename Graph::Node Node;
   288       typedef typename Graph::Arc Arc;
   289       static Arc find(const Graph &g, Node u, Node v, Arc e) {
   290         if (e == INVALID) {
   291           g.firstOut(e, u);
   292         } else {
   293           g.nextOut(e);
   294         }
   295         while (e != INVALID && g.target(e) != v) {
   296           g.nextOut(e);
   297         }
   298         return e;
   299       }
   300     };
   301 
   302     template <typename Graph>
   303     struct FindArcSelector<
   304       Graph, 
   305       typename enable_if<typename Graph::FindEdgeTag, void>::type> 
   306     {
   307       typedef typename Graph::Node Node;
   308       typedef typename Graph::Arc Arc;
   309       static Arc find(const Graph &g, Node u, Node v, Arc prev) {
   310         return g.findArc(u, v, prev);
   311       }
   312     };    
   313   }
   314 
   315   /// \brief Finds an arc between two nodes of a graph.
   316   ///
   317   /// Finds an arc from node \c u to node \c v in graph \c g.
   318   ///
   319   /// If \c prev is \ref INVALID (this is the default value), then
   320   /// it finds the first arc from \c u to \c v. Otherwise it looks for
   321   /// the next arc from \c u to \c v after \c prev.
   322   /// \return The found arc or \ref INVALID if there is no such an arc.
   323   ///
   324   /// Thus you can iterate through each arc from \c u to \c v as it follows.
   325   ///\code
   326   /// for(Arc e=findArc(g,u,v);e!=INVALID;e=findArc(g,u,v,e)) {
   327   ///   ...
   328   /// }
   329   ///\endcode
   330   ///
   331   ///\sa ArcLookUp
   332   ///\sa AllArcLookUp
   333   ///\sa DynArcLookUp
   334   ///\sa ConArcIt
   335   template <typename Graph>
   336   inline typename Graph::Arc 
   337   findArc(const Graph &g, typename Graph::Node u, typename Graph::Node v,
   338            typename Graph::Arc prev = INVALID) {
   339     return _graph_utils_bits::FindArcSelector<Graph>::find(g, u, v, prev);
   340   }
   341 
   342   /// \brief Iterator for iterating on arcs connected the same nodes.
   343   ///
   344   /// Iterator for iterating on arcs connected the same nodes. It is 
   345   /// higher level interface for the findArc() function. You can
   346   /// use it the following way:
   347   ///\code
   348   /// for (ConArcIt<Graph> it(g, src, trg); it != INVALID; ++it) {
   349   ///   ...
   350   /// }
   351   ///\endcode
   352   /// 
   353   ///\sa findArc()
   354   ///\sa ArcLookUp
   355   ///\sa AllArcLookUp
   356   ///\sa DynArcLookUp
   357   template <typename _Graph>
   358   class ConArcIt : public _Graph::Arc {
   359   public:
   360 
   361     typedef _Graph Graph;
   362     typedef typename Graph::Arc Parent;
   363 
   364     typedef typename Graph::Arc Arc;
   365     typedef typename Graph::Node Node;
   366 
   367     /// \brief Constructor.
   368     ///
   369     /// Construct a new ConArcIt iterating on the arcs which
   370     /// connects the \c u and \c v node.
   371     ConArcIt(const Graph& g, Node u, Node v) : _graph(g) {
   372       Parent::operator=(findArc(_graph, u, v));
   373     }
   374 
   375     /// \brief Constructor.
   376     ///
   377     /// Construct a new ConArcIt which continues the iterating from 
   378     /// the \c e arc.
   379     ConArcIt(const Graph& g, Arc a) : Parent(a), _graph(g) {}
   380     
   381     /// \brief Increment operator.
   382     ///
   383     /// It increments the iterator and gives back the next arc.
   384     ConArcIt& operator++() {
   385       Parent::operator=(findArc(_graph, _graph.source(*this), 
   386 				_graph.target(*this), *this));
   387       return *this;
   388     }
   389   private:
   390     const Graph& _graph;
   391   };
   392 
   393   namespace _graph_utils_bits {
   394     
   395     template <typename Graph, typename Enable = void>
   396     struct FindEdgeSelector {
   397       typedef typename Graph::Node Node;
   398       typedef typename Graph::Edge Edge;
   399       static Edge find(const Graph &g, Node u, Node v, Edge e) {
   400         bool b;
   401         if (u != v) {
   402           if (e == INVALID) {
   403             g.firstInc(e, b, u);
   404           } else {
   405             b = g.u(e) == u;
   406             g.nextInc(e, b);
   407           }
   408           while (e != INVALID && (b ? g.v(e) : g.u(e)) != v) {
   409             g.nextInc(e, b);
   410           }
   411         } else {
   412           if (e == INVALID) {
   413             g.firstInc(e, b, u);
   414           } else {
   415             b = true;
   416             g.nextInc(e, b);
   417           }
   418           while (e != INVALID && (!b || g.v(e) != v)) {
   419             g.nextInc(e, b);
   420           }
   421         }
   422         return e;
   423       }
   424     };
   425 
   426     template <typename Graph>
   427     struct FindEdgeSelector<
   428       Graph, 
   429       typename enable_if<typename Graph::FindEdgeTag, void>::type> 
   430     {
   431       typedef typename Graph::Node Node;
   432       typedef typename Graph::Edge Edge;
   433       static Edge find(const Graph &g, Node u, Node v, Edge prev) {
   434         return g.findEdge(u, v, prev);
   435       }
   436     };    
   437   }
   438 
   439   /// \brief Finds an edge between two nodes of a graph.
   440   ///
   441   /// Finds an edge from node \c u to node \c v in graph \c g.
   442   /// If the node \c u and node \c v is equal then each loop edge
   443   /// will be enumerated once.
   444   ///
   445   /// If \c prev is \ref INVALID (this is the default value), then
   446   /// it finds the first arc from \c u to \c v. Otherwise it looks for
   447   /// the next arc from \c u to \c v after \c prev.
   448   /// \return The found arc or \ref INVALID if there is no such an arc.
   449   ///
   450   /// Thus you can iterate through each arc from \c u to \c v as it follows.
   451   ///\code
   452   /// for(Edge e = findEdge(g,u,v); e != INVALID; 
   453   ///     e = findEdge(g,u,v,e)) {
   454   ///   ...
   455   /// }
   456   ///\endcode
   457   ///
   458   ///\sa ConEdgeIt
   459 
   460   template <typename Graph>
   461   inline typename Graph::Edge 
   462   findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,
   463             typename Graph::Edge p = INVALID) {
   464     return _graph_utils_bits::FindEdgeSelector<Graph>::find(g, u, v, p);
   465   }
   466 
   467   /// \brief Iterator for iterating on edges connected the same nodes.
   468   ///
   469   /// Iterator for iterating on edges connected the same nodes. It is 
   470   /// higher level interface for the findEdge() function. You can
   471   /// use it the following way:
   472   ///\code
   473   /// for (ConEdgeIt<Graph> it(g, src, trg); it != INVALID; ++it) {
   474   ///   ...
   475   /// }
   476   ///\endcode
   477   ///
   478   ///\sa findEdge()
   479   template <typename _Graph>
   480   class ConEdgeIt : public _Graph::Edge {
   481   public:
   482 
   483     typedef _Graph Graph;
   484     typedef typename Graph::Edge Parent;
   485 
   486     typedef typename Graph::Edge Edge;
   487     typedef typename Graph::Node Node;
   488 
   489     /// \brief Constructor.
   490     ///
   491     /// Construct a new ConEdgeIt iterating on the edges which
   492     /// connects the \c u and \c v node.
   493     ConEdgeIt(const Graph& g, Node u, Node v) : _graph(g) {
   494       Parent::operator=(findEdge(_graph, u, v));
   495     }
   496 
   497     /// \brief Constructor.
   498     ///
   499     /// Construct a new ConEdgeIt which continues the iterating from 
   500     /// the \c e edge.
   501     ConEdgeIt(const Graph& g, Edge e) : Parent(e), _graph(g) {}
   502     
   503     /// \brief Increment operator.
   504     ///
   505     /// It increments the iterator and gives back the next edge.
   506     ConEdgeIt& operator++() {
   507       Parent::operator=(findEdge(_graph, _graph.u(*this), 
   508 				 _graph.v(*this), *this));
   509       return *this;
   510     }
   511   private:
   512     const Graph& _graph;
   513   };
   514 
   515   namespace _graph_utils_bits {
   516 
   517     template <typename Digraph, typename Item, typename RefMap>
   518     class MapCopyBase {
   519     public:
   520       virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
   521       
   522       virtual ~MapCopyBase() {}
   523     };
   524 
   525     template <typename Digraph, typename Item, typename RefMap, 
   526               typename ToMap, typename FromMap>
   527     class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
   528     public:
   529 
   530       MapCopy(ToMap& tmap, const FromMap& map) 
   531         : _tmap(tmap), _map(map) {}
   532       
   533       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   534         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   535         for (ItemIt it(digraph); it != INVALID; ++it) {
   536           _tmap.set(refMap[it], _map[it]);
   537         }
   538       }
   539 
   540     private:
   541       ToMap& _tmap;
   542       const FromMap& _map;
   543     };
   544 
   545     template <typename Digraph, typename Item, typename RefMap, typename It>
   546     class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
   547     public:
   548 
   549       ItemCopy(It& it, const Item& item) : _it(it), _item(item) {}
   550       
   551       virtual void copy(const Digraph&, const RefMap& refMap) {
   552         _it = refMap[_item];
   553       }
   554 
   555     private:
   556       It& _it;
   557       Item _item;
   558     };
   559 
   560     template <typename Digraph, typename Item, typename RefMap, typename Ref>
   561     class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   562     public:
   563 
   564       RefCopy(Ref& map) : _map(map) {}
   565       
   566       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   567         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   568         for (ItemIt it(digraph); it != INVALID; ++it) {
   569           _map.set(it, refMap[it]);
   570         }
   571       }
   572 
   573     private:
   574       Ref& _map;
   575     };
   576 
   577     template <typename Digraph, typename Item, typename RefMap, 
   578               typename CrossRef>
   579     class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   580     public:
   581 
   582       CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
   583       
   584       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   585         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   586         for (ItemIt it(digraph); it != INVALID; ++it) {
   587           _cmap.set(refMap[it], it);
   588         }
   589       }
   590 
   591     private:
   592       CrossRef& _cmap;
   593     };
   594 
   595     template <typename Digraph, typename Enable = void>
   596     struct DigraphCopySelector {
   597       template <typename From, typename NodeRefMap, typename ArcRefMap>
   598       static void copy(Digraph &to, const From& from,
   599                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   600         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   601           nodeRefMap[it] = to.addNode();
   602         }
   603         for (typename From::ArcIt it(from); it != INVALID; ++it) {
   604           arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)], 
   605 				    nodeRefMap[from.target(it)]);
   606         }
   607       }
   608     };
   609 
   610     template <typename Digraph>
   611     struct DigraphCopySelector<
   612       Digraph, 
   613       typename enable_if<typename Digraph::BuildTag, void>::type> 
   614     {
   615       template <typename From, typename NodeRefMap, typename ArcRefMap>
   616       static void copy(Digraph &to, const From& from,
   617                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   618         to.build(from, nodeRefMap, arcRefMap);
   619       }
   620     };
   621 
   622     template <typename Graph, typename Enable = void>
   623     struct GraphCopySelector {
   624       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   625       static void copy(Graph &to, const From& from,
   626                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   627         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   628           nodeRefMap[it] = to.addNode();
   629         }
   630         for (typename From::EdgeIt it(from); it != INVALID; ++it) {
   631           edgeRefMap[it] = to.addEdge(nodeRefMap[from.u(it)], 
   632 				      nodeRefMap[from.v(it)]);
   633         }
   634       }
   635     };
   636 
   637     template <typename Graph>
   638     struct GraphCopySelector<
   639       Graph, 
   640       typename enable_if<typename Graph::BuildTag, void>::type> 
   641     {
   642       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   643       static void copy(Graph &to, const From& from,
   644                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   645         to.build(from, nodeRefMap, edgeRefMap);
   646       }
   647     };
   648 
   649   }
   650 
   651   /// \brief Class to copy a digraph.
   652   ///
   653   /// Class to copy a digraph to another digraph (duplicate a digraph). The
   654   /// simplest way of using it is through the \c copyDigraph() function.
   655   ///
   656   /// This class not just make a copy of a graph, but it can create
   657   /// references and cross references between the nodes and arcs of
   658   /// the two graphs, it can copy maps for use with the newly created
   659   /// graph and copy nodes and arcs.
   660   ///
   661   /// To make a copy from a graph, first an instance of DigraphCopy
   662   /// should be created, then the data belongs to the graph should
   663   /// assigned to copy. In the end, the \c run() member should be
   664   /// called.
   665   ///
   666   /// The next code copies a graph with several data:
   667   ///\code
   668   ///  DigraphCopy<NewGraph, OrigGraph> dc(new_graph, orig_graph);
   669   ///  // create a reference for the nodes
   670   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   671   ///  dc.nodeRef(nr);
   672   ///  // create a cross reference (inverse) for the arcs
   673   ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);
   674   ///  dc.arcCrossRef(acr);
   675   ///  // copy an arc map
   676   ///  OrigGraph::ArcMap<double> oamap(orig_graph);
   677   ///  NewGraph::ArcMap<double> namap(new_graph);
   678   ///  dc.arcMap(namap, oamap);
   679   ///  // copy a node
   680   ///  OrigGraph::Node on;
   681   ///  NewGraph::Node nn;
   682   ///  dc.node(nn, on);
   683   ///  // Executions of copy
   684   ///  dc.run();
   685   ///\endcode
   686   template <typename To, typename From>
   687   class DigraphCopy {
   688   private:
   689 
   690     typedef typename From::Node Node;
   691     typedef typename From::NodeIt NodeIt;
   692     typedef typename From::Arc Arc;
   693     typedef typename From::ArcIt ArcIt;
   694 
   695     typedef typename To::Node TNode;
   696     typedef typename To::Arc TArc;
   697 
   698     typedef typename From::template NodeMap<TNode> NodeRefMap;
   699     typedef typename From::template ArcMap<TArc> ArcRefMap;
   700     
   701     
   702   public: 
   703 
   704 
   705     /// \brief Constructor for the DigraphCopy.
   706     ///
   707     /// It copies the content of the \c _from digraph into the
   708     /// \c _to digraph.
   709     DigraphCopy(To& to, const From& from) 
   710       : _from(from), _to(to) {}
   711 
   712     /// \brief Destructor of the DigraphCopy
   713     ///
   714     /// Destructor of the DigraphCopy
   715     ~DigraphCopy() {
   716       for (int i = 0; i < int(_node_maps.size()); ++i) {
   717         delete _node_maps[i];
   718       }
   719       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   720         delete _arc_maps[i];
   721       }
   722 
   723     }
   724 
   725     /// \brief Copies the node references into the given map.
   726     ///
   727     /// Copies the node references into the given map. The parameter
   728     /// should be a map, which key type is the Node type of the source
   729     /// graph, while the value type is the Node type of the
   730     /// destination graph.
   731     template <typename NodeRef>
   732     DigraphCopy& nodeRef(NodeRef& map) {
   733       _node_maps.push_back(new _graph_utils_bits::RefCopy<From, Node, 
   734 			   NodeRefMap, NodeRef>(map));
   735       return *this;
   736     }
   737 
   738     /// \brief Copies the node cross references into the given map.
   739     ///
   740     ///  Copies the node cross references (reverse references) into
   741     ///  the given map. The parameter should be a map, which key type
   742     ///  is the Node type of the destination graph, while the value type is
   743     ///  the Node type of the source graph.
   744     template <typename NodeCrossRef>
   745     DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
   746       _node_maps.push_back(new _graph_utils_bits::CrossRefCopy<From, Node,
   747 			   NodeRefMap, NodeCrossRef>(map));
   748       return *this;
   749     }
   750 
   751     /// \brief Make copy of the given map.
   752     ///
   753     /// Makes copy of the given map for the newly created digraph.
   754     /// The new map's key type is the destination graph's node type,
   755     /// and the copied map's key type is the source graph's node type.
   756     template <typename ToMap, typename FromMap>
   757     DigraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
   758       _node_maps.push_back(new _graph_utils_bits::MapCopy<From, Node, 
   759 			   NodeRefMap, ToMap, FromMap>(tmap, map));
   760       return *this;
   761     }
   762 
   763     /// \brief Make a copy of the given node.
   764     ///
   765     /// Make a copy of the given node.
   766     DigraphCopy& node(TNode& tnode, const Node& snode) {
   767       _node_maps.push_back(new _graph_utils_bits::ItemCopy<From, Node, 
   768 			   NodeRefMap, TNode>(tnode, snode));
   769       return *this;
   770     }
   771 
   772     /// \brief Copies the arc references into the given map.
   773     ///
   774     /// Copies the arc references into the given map.
   775     template <typename ArcRef>
   776     DigraphCopy& arcRef(ArcRef& map) {
   777       _arc_maps.push_back(new _graph_utils_bits::RefCopy<From, Arc, 
   778 			  ArcRefMap, ArcRef>(map));
   779       return *this;
   780     }
   781 
   782     /// \brief Copies the arc cross references into the given map.
   783     ///
   784     ///  Copies the arc cross references (reverse references) into
   785     ///  the given map.
   786     template <typename ArcCrossRef>
   787     DigraphCopy& arcCrossRef(ArcCrossRef& map) {
   788       _arc_maps.push_back(new _graph_utils_bits::CrossRefCopy<From, Arc,
   789 			  ArcRefMap, ArcCrossRef>(map));
   790       return *this;
   791     }
   792 
   793     /// \brief Make copy of the given map.
   794     ///
   795     /// Makes copy of the given map for the newly created digraph. 
   796     /// The new map's key type is the to digraph's arc type,
   797     /// and the copied map's key type is the from digraph's arc
   798     /// type.  
   799     template <typename ToMap, typename FromMap>
   800     DigraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
   801       _arc_maps.push_back(new _graph_utils_bits::MapCopy<From, Arc, 
   802 			  ArcRefMap, ToMap, FromMap>(tmap, map));
   803       return *this;
   804     }
   805 
   806     /// \brief Make a copy of the given arc.
   807     ///
   808     /// Make a copy of the given arc.
   809     DigraphCopy& arc(TArc& tarc, const Arc& sarc) {
   810       _arc_maps.push_back(new _graph_utils_bits::ItemCopy<From, Arc, 
   811 			  ArcRefMap, TArc>(tarc, sarc));
   812       return *this;
   813     }
   814 
   815     /// \brief Executes the copies.
   816     ///
   817     /// Executes the copies.
   818     void run() {
   819       NodeRefMap nodeRefMap(_from);
   820       ArcRefMap arcRefMap(_from);
   821       _graph_utils_bits::DigraphCopySelector<To>::
   822         copy(_to, _from, nodeRefMap, arcRefMap);
   823       for (int i = 0; i < int(_node_maps.size()); ++i) {
   824         _node_maps[i]->copy(_from, nodeRefMap);
   825       }
   826       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   827         _arc_maps[i]->copy(_from, arcRefMap);
   828       }      
   829     }
   830 
   831   protected:
   832 
   833 
   834     const From& _from;
   835     To& _to;
   836 
   837     std::vector<_graph_utils_bits::MapCopyBase<From, Node, NodeRefMap>* > 
   838     _node_maps;
   839 
   840     std::vector<_graph_utils_bits::MapCopyBase<From, Arc, ArcRefMap>* > 
   841     _arc_maps;
   842 
   843   };
   844 
   845   /// \brief Copy a digraph to another digraph.
   846   ///
   847   /// Copy a digraph to another digraph. The complete usage of the
   848   /// function is detailed in the DigraphCopy class, but a short
   849   /// example shows a basic work:
   850   ///\code
   851   /// copyDigraph(trg, src).nodeRef(nr).arcCrossRef(ecr).run();
   852   ///\endcode
   853   /// 
   854   /// After the copy the \c nr map will contain the mapping from the
   855   /// nodes of the \c from digraph to the nodes of the \c to digraph and
   856   /// \c ecr will contain the mapping from the arcs of the \c to digraph
   857   /// to the arcs of the \c from digraph.
   858   ///
   859   /// \see DigraphCopy 
   860   template <typename To, typename From>
   861   DigraphCopy<To, From> copyDigraph(To& to, const From& from) {
   862     return DigraphCopy<To, From>(to, from);
   863   }
   864 
   865   /// \brief Class to copy a graph.
   866   ///
   867   /// Class to copy a graph to another graph (duplicate a graph). The
   868   /// simplest way of using it is through the \c copyGraph() function.
   869   ///
   870   /// This class not just make a copy of a graph, but it can create
   871   /// references and cross references between the nodes, edges and arcs of
   872   /// the two graphs, it can copy maps for use with the newly created
   873   /// graph and copy nodes, edges and arcs.
   874   ///
   875   /// To make a copy from a graph, first an instance of GraphCopy
   876   /// should be created, then the data belongs to the graph should
   877   /// assigned to copy. In the end, the \c run() member should be
   878   /// called.
   879   ///
   880   /// The next code copies a graph with several data:
   881   ///\code
   882   ///  GraphCopy<NewGraph, OrigGraph> dc(new_graph, orig_graph);
   883   ///  // create a reference for the nodes
   884   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   885   ///  dc.nodeRef(nr);
   886   ///  // create a cross reference (inverse) for the edges
   887   ///  NewGraph::EdgeMap<OrigGraph::Arc> ecr(new_graph);
   888   ///  dc.edgeCrossRef(ecr);
   889   ///  // copy an arc map
   890   ///  OrigGraph::ArcMap<double> oamap(orig_graph);
   891   ///  NewGraph::ArcMap<double> namap(new_graph);
   892   ///  dc.arcMap(namap, oamap);
   893   ///  // copy a node
   894   ///  OrigGraph::Node on;
   895   ///  NewGraph::Node nn;
   896   ///  dc.node(nn, on);
   897   ///  // Executions of copy
   898   ///  dc.run();
   899   ///\endcode
   900   template <typename To, typename From>
   901   class GraphCopy {
   902   private:
   903 
   904     typedef typename From::Node Node;
   905     typedef typename From::NodeIt NodeIt;
   906     typedef typename From::Arc Arc;
   907     typedef typename From::ArcIt ArcIt;
   908     typedef typename From::Edge Edge;
   909     typedef typename From::EdgeIt EdgeIt;
   910 
   911     typedef typename To::Node TNode;
   912     typedef typename To::Arc TArc;
   913     typedef typename To::Edge TEdge;
   914 
   915     typedef typename From::template NodeMap<TNode> NodeRefMap;
   916     typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
   917 
   918     struct ArcRefMap {
   919       ArcRefMap(const To& to, const From& from,
   920 		const EdgeRefMap& edge_ref, const NodeRefMap& node_ref) 
   921         : _to(to), _from(from), 
   922           _edge_ref(edge_ref), _node_ref(node_ref) {}
   923 
   924       typedef typename From::Arc Key;
   925       typedef typename To::Arc Value;
   926 
   927       Value operator[](const Key& key) const {
   928         bool forward = _from.u(key) != _from.v(key) ?
   929 	  _node_ref[_from.source(key)] == 
   930 	  _to.source(_to.direct(_edge_ref[key], true)) :
   931 	  _from.direction(key);
   932 	return _to.direct(_edge_ref[key], forward); 
   933       }
   934       
   935       const To& _to;
   936       const From& _from;
   937       const EdgeRefMap& _edge_ref;
   938       const NodeRefMap& _node_ref;
   939     };
   940 
   941     
   942   public: 
   943 
   944 
   945     /// \brief Constructor for the GraphCopy.
   946     ///
   947     /// It copies the content of the \c _from graph into the
   948     /// \c _to graph.
   949     GraphCopy(To& to, const From& from) 
   950       : _from(from), _to(to) {}
   951 
   952     /// \brief Destructor of the GraphCopy
   953     ///
   954     /// Destructor of the GraphCopy
   955     ~GraphCopy() {
   956       for (int i = 0; i < int(_node_maps.size()); ++i) {
   957         delete _node_maps[i];
   958       }
   959       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   960         delete _arc_maps[i];
   961       }
   962       for (int i = 0; i < int(_edge_maps.size()); ++i) {
   963         delete _edge_maps[i];
   964       }
   965 
   966     }
   967 
   968     /// \brief Copies the node references into the given map.
   969     ///
   970     /// Copies the node references into the given map.
   971     template <typename NodeRef>
   972     GraphCopy& nodeRef(NodeRef& map) {
   973       _node_maps.push_back(new _graph_utils_bits::RefCopy<From, Node, 
   974 			   NodeRefMap, NodeRef>(map));
   975       return *this;
   976     }
   977 
   978     /// \brief Copies the node cross references into the given map.
   979     ///
   980     ///  Copies the node cross references (reverse references) into
   981     ///  the given map.
   982     template <typename NodeCrossRef>
   983     GraphCopy& nodeCrossRef(NodeCrossRef& map) {
   984       _node_maps.push_back(new _graph_utils_bits::CrossRefCopy<From, Node,
   985 			   NodeRefMap, NodeCrossRef>(map));
   986       return *this;
   987     }
   988 
   989     /// \brief Make copy of the given map.
   990     ///
   991     /// Makes copy of the given map for the newly created graph. 
   992     /// The new map's key type is the to graph's node type,
   993     /// and the copied map's key type is the from graph's node
   994     /// type.  
   995     template <typename ToMap, typename FromMap>
   996     GraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
   997       _node_maps.push_back(new _graph_utils_bits::MapCopy<From, Node, 
   998 			   NodeRefMap, ToMap, FromMap>(tmap, map));
   999       return *this;
  1000     }
  1001 
  1002     /// \brief Make a copy of the given node.
  1003     ///
  1004     /// Make a copy of the given node.
  1005     GraphCopy& node(TNode& tnode, const Node& snode) {
  1006       _node_maps.push_back(new _graph_utils_bits::ItemCopy<From, Node, 
  1007 			   NodeRefMap, TNode>(tnode, snode));
  1008       return *this;
  1009     }
  1010 
  1011     /// \brief Copies the arc references into the given map.
  1012     ///
  1013     /// Copies the arc references into the given map.
  1014     template <typename ArcRef>
  1015     GraphCopy& arcRef(ArcRef& map) {
  1016       _arc_maps.push_back(new _graph_utils_bits::RefCopy<From, Arc, 
  1017 			  ArcRefMap, ArcRef>(map));
  1018       return *this;
  1019     }
  1020 
  1021     /// \brief Copies the arc cross references into the given map.
  1022     ///
  1023     ///  Copies the arc cross references (reverse references) into
  1024     ///  the given map.
  1025     template <typename ArcCrossRef>
  1026     GraphCopy& arcCrossRef(ArcCrossRef& map) {
  1027       _arc_maps.push_back(new _graph_utils_bits::CrossRefCopy<From, Arc,
  1028 			  ArcRefMap, ArcCrossRef>(map));
  1029       return *this;
  1030     }
  1031 
  1032     /// \brief Make copy of the given map.
  1033     ///
  1034     /// Makes copy of the given map for the newly created graph. 
  1035     /// The new map's key type is the to graph's arc type,
  1036     /// and the copied map's key type is the from graph's arc
  1037     /// type.  
  1038     template <typename ToMap, typename FromMap>
  1039     GraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
  1040       _arc_maps.push_back(new _graph_utils_bits::MapCopy<From, Arc, 
  1041 			  ArcRefMap, ToMap, FromMap>(tmap, map));
  1042       return *this;
  1043     }
  1044 
  1045     /// \brief Make a copy of the given arc.
  1046     ///
  1047     /// Make a copy of the given arc.
  1048     GraphCopy& arc(TArc& tarc, const Arc& sarc) {
  1049       _arc_maps.push_back(new _graph_utils_bits::ItemCopy<From, Arc, 
  1050 			  ArcRefMap, TArc>(tarc, sarc));
  1051       return *this;
  1052     }
  1053 
  1054     /// \brief Copies the edge references into the given map.
  1055     ///
  1056     /// Copies the edge references into the given map.
  1057     template <typename EdgeRef>
  1058     GraphCopy& edgeRef(EdgeRef& map) {
  1059       _edge_maps.push_back(new _graph_utils_bits::RefCopy<From, Edge, 
  1060 			   EdgeRefMap, EdgeRef>(map));
  1061       return *this;
  1062     }
  1063 
  1064     /// \brief Copies the edge cross references into the given map.
  1065     ///
  1066     /// Copies the edge cross references (reverse
  1067     /// references) into the given map.
  1068     template <typename EdgeCrossRef>
  1069     GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
  1070       _edge_maps.push_back(new _graph_utils_bits::CrossRefCopy<From, 
  1071 			   Edge, EdgeRefMap, EdgeCrossRef>(map));
  1072       return *this;
  1073     }
  1074 
  1075     /// \brief Make copy of the given map.
  1076     ///
  1077     /// Makes copy of the given map for the newly created graph. 
  1078     /// The new map's key type is the to graph's edge type,
  1079     /// and the copied map's key type is the from graph's edge
  1080     /// type.  
  1081     template <typename ToMap, typename FromMap>
  1082     GraphCopy& edgeMap(ToMap& tmap, const FromMap& map) {
  1083       _edge_maps.push_back(new _graph_utils_bits::MapCopy<From, Edge, 
  1084 			   EdgeRefMap, ToMap, FromMap>(tmap, map));
  1085       return *this;
  1086     }
  1087 
  1088     /// \brief Make a copy of the given edge.
  1089     ///
  1090     /// Make a copy of the given edge.
  1091     GraphCopy& edge(TEdge& tedge, const Edge& sedge) {
  1092       _edge_maps.push_back(new _graph_utils_bits::ItemCopy<From, Edge, 
  1093 			   EdgeRefMap, TEdge>(tedge, sedge));
  1094       return *this;
  1095     }
  1096 
  1097     /// \brief Executes the copies.
  1098     ///
  1099     /// Executes the copies.
  1100     void run() {
  1101       NodeRefMap nodeRefMap(_from);
  1102       EdgeRefMap edgeRefMap(_from);
  1103       ArcRefMap arcRefMap(_to, _from, edgeRefMap, nodeRefMap);
  1104       _graph_utils_bits::GraphCopySelector<To>::
  1105         copy(_to, _from, nodeRefMap, edgeRefMap);
  1106       for (int i = 0; i < int(_node_maps.size()); ++i) {
  1107         _node_maps[i]->copy(_from, nodeRefMap);
  1108       }
  1109       for (int i = 0; i < int(_edge_maps.size()); ++i) {
  1110         _edge_maps[i]->copy(_from, edgeRefMap);
  1111       }
  1112       for (int i = 0; i < int(_arc_maps.size()); ++i) {
  1113         _arc_maps[i]->copy(_from, arcRefMap);
  1114       }
  1115     }
  1116 
  1117   private:
  1118     
  1119     const From& _from;
  1120     To& _to;
  1121 
  1122     std::vector<_graph_utils_bits::MapCopyBase<From, Node, NodeRefMap>* > 
  1123     _node_maps;
  1124 
  1125     std::vector<_graph_utils_bits::MapCopyBase<From, Arc, ArcRefMap>* > 
  1126     _arc_maps;
  1127 
  1128     std::vector<_graph_utils_bits::MapCopyBase<From, Edge, EdgeRefMap>* > 
  1129     _edge_maps;
  1130 
  1131   };
  1132 
  1133   /// \brief Copy a graph to another graph.
  1134   ///
  1135   /// Copy a graph to another graph. The complete usage of the
  1136   /// function is detailed in the GraphCopy class, but a short
  1137   /// example shows a basic work:
  1138   ///\code
  1139   /// copyGraph(trg, src).nodeRef(nr).arcCrossRef(ecr).run();
  1140   ///\endcode
  1141   /// 
  1142   /// After the copy the \c nr map will contain the mapping from the
  1143   /// nodes of the \c from graph to the nodes of the \c to graph and
  1144   /// \c ecr will contain the mapping from the arcs of the \c to graph
  1145   /// to the arcs of the \c from graph.
  1146   ///
  1147   /// \see GraphCopy 
  1148   template <typename To, typename From>
  1149   GraphCopy<To, From> 
  1150   copyGraph(To& to, const From& from) {
  1151     return GraphCopy<To, From>(to, from);
  1152   }
  1153 
  1154   /// @}
  1155 
  1156   /// \addtogroup graph_maps
  1157   /// @{
  1158 
  1159   /// Provides an immutable and unique id for each item in the graph.
  1160 
  1161   /// The IdMap class provides a unique and immutable id for each item of the
  1162   /// same type (e.g. node) in the graph. This id is <ul><li>\b unique:
  1163   /// different items (nodes) get different ids <li>\b immutable: the id of an
  1164   /// item (node) does not change (even if you delete other nodes).  </ul>
  1165   /// Through this map you get access (i.e. can read) the inner id values of
  1166   /// the items stored in the graph. This map can be inverted with its member
  1167   /// class \c InverseMap or with the \c operator() member.
  1168   ///
  1169   template <typename _Graph, typename _Item>
  1170   class IdMap {
  1171   public:
  1172     typedef _Graph Graph;
  1173     typedef int Value;
  1174     typedef _Item Item;
  1175     typedef _Item Key;
  1176 
  1177     /// \brief Constructor.
  1178     ///
  1179     /// Constructor of the map.
  1180     explicit IdMap(const Graph& graph) : _graph(&graph) {}
  1181 
  1182     /// \brief Gives back the \e id of the item.
  1183     ///
  1184     /// Gives back the immutable and unique \e id of the item.
  1185     int operator[](const Item& item) const { return _graph->id(item);}
  1186 
  1187     /// \brief Gives back the item by its id.
  1188     ///
  1189     /// Gives back the item by its id.
  1190     Item operator()(int id) { return _graph->fromId(id, Item()); }
  1191 
  1192   private:
  1193     const Graph* _graph;
  1194 
  1195   public:
  1196 
  1197     /// \brief The class represents the inverse of its owner (IdMap).
  1198     ///
  1199     /// The class represents the inverse of its owner (IdMap).
  1200     /// \see inverse()
  1201     class InverseMap {
  1202     public:
  1203 
  1204       /// \brief Constructor.
  1205       ///
  1206       /// Constructor for creating an id-to-item map.
  1207       explicit InverseMap(const Graph& graph) : _graph(&graph) {}
  1208 
  1209       /// \brief Constructor.
  1210       ///
  1211       /// Constructor for creating an id-to-item map.
  1212       explicit InverseMap(const IdMap& map) : _graph(map._graph) {}
  1213 
  1214       /// \brief Gives back the given item from its id.
  1215       ///
  1216       /// Gives back the given item from its id.
  1217       /// 
  1218       Item operator[](int id) const { return _graph->fromId(id, Item());}
  1219 
  1220     private:
  1221       const Graph* _graph;
  1222     };
  1223 
  1224     /// \brief Gives back the inverse of the map.
  1225     ///
  1226     /// Gives back the inverse of the IdMap.
  1227     InverseMap inverse() const { return InverseMap(*_graph);} 
  1228 
  1229   };
  1230 
  1231   
  1232   /// \brief General invertable graph-map type.
  1233 
  1234   /// This type provides simple invertable graph-maps. 
  1235   /// The InvertableMap wraps an arbitrary ReadWriteMap 
  1236   /// and if a key is set to a new value then store it
  1237   /// in the inverse map.
  1238   ///
  1239   /// The values of the map can be accessed
  1240   /// with stl compatible forward iterator.
  1241   ///
  1242   /// \tparam _Graph The graph type.
  1243   /// \tparam _Item The item type of the graph.
  1244   /// \tparam _Value The value type of the map.
  1245   ///
  1246   /// \see IterableValueMap
  1247   template <typename _Graph, typename _Item, typename _Value>
  1248   class InvertableMap : protected DefaultMap<_Graph, _Item, _Value> {
  1249   private:
  1250     
  1251     typedef DefaultMap<_Graph, _Item, _Value> Map;
  1252     typedef _Graph Graph;
  1253 
  1254     typedef std::map<_Value, _Item> Container;
  1255     Container _inv_map;    
  1256 
  1257   public:
  1258  
  1259     /// The key type of InvertableMap (Node, Arc, Edge).
  1260     typedef typename Map::Key Key;
  1261     /// The value type of the InvertableMap.
  1262     typedef typename Map::Value Value;
  1263 
  1264 
  1265 
  1266     /// \brief Constructor.
  1267     ///
  1268     /// Construct a new InvertableMap for the graph.
  1269     ///
  1270     explicit InvertableMap(const Graph& graph) : Map(graph) {} 
  1271 
  1272     /// \brief Forward iterator for values.
  1273     ///
  1274     /// This iterator is an stl compatible forward
  1275     /// iterator on the values of the map. The values can
  1276     /// be accessed in the [beginValue, endValue) range.
  1277     ///
  1278     class ValueIterator 
  1279       : public std::iterator<std::forward_iterator_tag, Value> {
  1280       friend class InvertableMap;
  1281     private:
  1282       ValueIterator(typename Container::const_iterator _it) 
  1283         : it(_it) {}
  1284     public:
  1285       
  1286       ValueIterator() {}
  1287 
  1288       ValueIterator& operator++() { ++it; return *this; }
  1289       ValueIterator operator++(int) { 
  1290         ValueIterator tmp(*this); 
  1291         operator++();
  1292         return tmp; 
  1293       }
  1294 
  1295       const Value& operator*() const { return it->first; }
  1296       const Value* operator->() const { return &(it->first); }
  1297 
  1298       bool operator==(ValueIterator jt) const { return it == jt.it; }
  1299       bool operator!=(ValueIterator jt) const { return it != jt.it; }
  1300       
  1301     private:
  1302       typename Container::const_iterator it;
  1303     };
  1304 
  1305     /// \brief Returns an iterator to the first value.
  1306     ///
  1307     /// Returns an stl compatible iterator to the 
  1308     /// first value of the map. The values of the
  1309     /// map can be accessed in the [beginValue, endValue)
  1310     /// range.
  1311     ValueIterator beginValue() const {
  1312       return ValueIterator(_inv_map.begin());
  1313     }
  1314 
  1315     /// \brief Returns an iterator after the last value.
  1316     ///
  1317     /// Returns an stl compatible iterator after the 
  1318     /// last value of the map. The values of the
  1319     /// map can be accessed in the [beginValue, endValue)
  1320     /// range.
  1321     ValueIterator endValue() const {
  1322       return ValueIterator(_inv_map.end());
  1323     }
  1324     
  1325     /// \brief The setter function of the map.
  1326     ///
  1327     /// Sets the mapped value.
  1328     void set(const Key& key, const Value& val) {
  1329       Value oldval = Map::operator[](key);
  1330       typename Container::iterator it = _inv_map.find(oldval);
  1331       if (it != _inv_map.end() && it->second == key) {
  1332 	_inv_map.erase(it);
  1333       }      
  1334       _inv_map.insert(make_pair(val, key));
  1335       Map::set(key, val);
  1336     }
  1337 
  1338     /// \brief The getter function of the map.
  1339     ///
  1340     /// It gives back the value associated with the key.
  1341     typename MapTraits<Map>::ConstReturnValue 
  1342     operator[](const Key& key) const {
  1343       return Map::operator[](key);
  1344     }
  1345 
  1346     /// \brief Gives back the item by its value.
  1347     ///
  1348     /// Gives back the item by its value.
  1349     Key operator()(const Value& key) const {
  1350       typename Container::const_iterator it = _inv_map.find(key);
  1351       return it != _inv_map.end() ? it->second : INVALID;
  1352     }
  1353 
  1354   protected:
  1355 
  1356     /// \brief Erase the key from the map.
  1357     ///
  1358     /// Erase the key to the map. It is called by the
  1359     /// \c AlterationNotifier.
  1360     virtual void erase(const Key& key) {
  1361       Value val = Map::operator[](key);
  1362       typename Container::iterator it = _inv_map.find(val);
  1363       if (it != _inv_map.end() && it->second == key) {
  1364 	_inv_map.erase(it);
  1365       }
  1366       Map::erase(key);
  1367     }
  1368 
  1369     /// \brief Erase more keys from the map.
  1370     ///
  1371     /// Erase more keys from the map. It is called by the
  1372     /// \c AlterationNotifier.
  1373     virtual void erase(const std::vector<Key>& keys) {
  1374       for (int i = 0; i < int(keys.size()); ++i) {
  1375 	Value val = Map::operator[](keys[i]);
  1376 	typename Container::iterator it = _inv_map.find(val);
  1377 	if (it != _inv_map.end() && it->second == keys[i]) {
  1378 	  _inv_map.erase(it);
  1379 	}
  1380       }
  1381       Map::erase(keys);
  1382     }
  1383 
  1384     /// \brief Clear the keys from the map and inverse map.
  1385     ///
  1386     /// Clear the keys from the map and inverse map. It is called by the
  1387     /// \c AlterationNotifier.
  1388     virtual void clear() {
  1389       _inv_map.clear();
  1390       Map::clear();
  1391     }
  1392 
  1393   public:
  1394 
  1395     /// \brief The inverse map type.
  1396     ///
  1397     /// The inverse of this map. The subscript operator of the map
  1398     /// gives back always the item what was last assigned to the value. 
  1399     class InverseMap {
  1400     public:
  1401       /// \brief Constructor of the InverseMap.
  1402       ///
  1403       /// Constructor of the InverseMap.
  1404       explicit InverseMap(const InvertableMap& inverted) 
  1405         : _inverted(inverted) {}
  1406 
  1407       /// The value type of the InverseMap.
  1408       typedef typename InvertableMap::Key Value;
  1409       /// The key type of the InverseMap.
  1410       typedef typename InvertableMap::Value Key; 
  1411 
  1412       /// \brief Subscript operator. 
  1413       ///
  1414       /// Subscript operator. It gives back always the item 
  1415       /// what was last assigned to the value.
  1416       Value operator[](const Key& key) const {
  1417 	return _inverted(key);
  1418       }
  1419       
  1420     private:
  1421       const InvertableMap& _inverted;
  1422     };
  1423 
  1424     /// \brief It gives back the just readable inverse map.
  1425     ///
  1426     /// It gives back the just readable inverse map.
  1427     InverseMap inverse() const {
  1428       return InverseMap(*this);
  1429     } 
  1430 
  1431 
  1432     
  1433   };
  1434 
  1435   /// \brief Provides a mutable, continuous and unique descriptor for each 
  1436   /// item in the graph.
  1437   ///
  1438   /// The DescriptorMap class provides a unique and continuous (but mutable)
  1439   /// descriptor (id) for each item of the same type (e.g. node) in the
  1440   /// graph. This id is <ul><li>\b unique: different items (nodes) get
  1441   /// different ids <li>\b continuous: the range of the ids is the set of
  1442   /// integers between 0 and \c n-1, where \c n is the number of the items of
  1443   /// this type (e.g. nodes) (so the id of a node can change if you delete an
  1444   /// other node, i.e. this id is mutable).  </ul> This map can be inverted
  1445   /// with its member class \c InverseMap, or with the \c operator() member.
  1446   ///
  1447   /// \tparam _Graph The graph class the \c DescriptorMap belongs to.
  1448   /// \tparam _Item The Item is the Key of the Map. It may be Node, Arc or 
  1449   /// Edge.
  1450   template <typename _Graph, typename _Item>
  1451   class DescriptorMap : protected DefaultMap<_Graph, _Item, int> {
  1452 
  1453     typedef _Item Item;
  1454     typedef DefaultMap<_Graph, _Item, int> Map;
  1455 
  1456   public:
  1457     /// The graph class of DescriptorMap.
  1458     typedef _Graph Graph;
  1459 
  1460     /// The key type of DescriptorMap (Node, Arc, Edge).
  1461     typedef typename Map::Key Key;
  1462     /// The value type of DescriptorMap.
  1463     typedef typename Map::Value Value;
  1464 
  1465     /// \brief Constructor.
  1466     ///
  1467     /// Constructor for descriptor map.
  1468     explicit DescriptorMap(const Graph& _graph) : Map(_graph) {
  1469       Item it;
  1470       const typename Map::Notifier* nf = Map::notifier(); 
  1471       for (nf->first(it); it != INVALID; nf->next(it)) {
  1472 	Map::set(it, _inv_map.size());
  1473 	_inv_map.push_back(it);	
  1474       }      
  1475     }
  1476 
  1477   protected:
  1478 
  1479     /// \brief Add a new key to the map.
  1480     ///
  1481     /// Add a new key to the map. It is called by the
  1482     /// \c AlterationNotifier.
  1483     virtual void add(const Item& item) {
  1484       Map::add(item);
  1485       Map::set(item, _inv_map.size());
  1486       _inv_map.push_back(item);
  1487     }
  1488 
  1489     /// \brief Add more new keys to the map.
  1490     ///
  1491     /// Add more new keys to the map. It is called by the
  1492     /// \c AlterationNotifier.
  1493     virtual void add(const std::vector<Item>& items) {
  1494       Map::add(items);
  1495       for (int i = 0; i < int(items.size()); ++i) {
  1496 	Map::set(items[i], _inv_map.size());
  1497 	_inv_map.push_back(items[i]);
  1498       }
  1499     }
  1500 
  1501     /// \brief Erase the key from the map.
  1502     ///
  1503     /// Erase the key from the map. It is called by the
  1504     /// \c AlterationNotifier.
  1505     virtual void erase(const Item& item) {
  1506       Map::set(_inv_map.back(), Map::operator[](item));
  1507       _inv_map[Map::operator[](item)] = _inv_map.back();
  1508       _inv_map.pop_back();
  1509       Map::erase(item);
  1510     }
  1511 
  1512     /// \brief Erase more keys from the map.
  1513     ///
  1514     /// Erase more keys from the map. It is called by the
  1515     /// \c AlterationNotifier.
  1516     virtual void erase(const std::vector<Item>& items) {
  1517       for (int i = 0; i < int(items.size()); ++i) {
  1518 	Map::set(_inv_map.back(), Map::operator[](items[i]));
  1519 	_inv_map[Map::operator[](items[i])] = _inv_map.back();
  1520 	_inv_map.pop_back();
  1521       }
  1522       Map::erase(items);
  1523     }
  1524 
  1525     /// \brief Build the unique map.
  1526     ///
  1527     /// Build the unique map. It is called by the
  1528     /// \c AlterationNotifier.
  1529     virtual void build() {
  1530       Map::build();
  1531       Item it;
  1532       const typename Map::Notifier* nf = Map::notifier(); 
  1533       for (nf->first(it); it != INVALID; nf->next(it)) {
  1534 	Map::set(it, _inv_map.size());
  1535 	_inv_map.push_back(it);	
  1536       }      
  1537     }
  1538     
  1539     /// \brief Clear the keys from the map.
  1540     ///
  1541     /// Clear the keys from the map. It is called by the
  1542     /// \c AlterationNotifier.
  1543     virtual void clear() {
  1544       _inv_map.clear();
  1545       Map::clear();
  1546     }
  1547 
  1548   public:
  1549 
  1550     /// \brief Returns the maximal value plus one.
  1551     ///
  1552     /// Returns the maximal value plus one in the map.
  1553     unsigned int size() const {
  1554       return _inv_map.size();
  1555     }
  1556 
  1557     /// \brief Swaps the position of the two items in the map.
  1558     ///
  1559     /// Swaps the position of the two items in the map.
  1560     void swap(const Item& p, const Item& q) {
  1561       int pi = Map::operator[](p);
  1562       int qi = Map::operator[](q);
  1563       Map::set(p, qi);
  1564       _inv_map[qi] = p;
  1565       Map::set(q, pi);
  1566       _inv_map[pi] = q;
  1567     }
  1568 
  1569     /// \brief Gives back the \e descriptor of the item.
  1570     ///
  1571     /// Gives back the mutable and unique \e descriptor of the map.
  1572     int operator[](const Item& item) const {
  1573       return Map::operator[](item);
  1574     }
  1575 
  1576     /// \brief Gives back the item by its descriptor.
  1577     ///
  1578     /// Gives back th item by its descriptor.
  1579     Item operator()(int id) const {
  1580       return _inv_map[id];
  1581     }
  1582     
  1583   private:
  1584 
  1585     typedef std::vector<Item> Container;
  1586     Container _inv_map;
  1587 
  1588   public:
  1589     /// \brief The inverse map type of DescriptorMap.
  1590     ///
  1591     /// The inverse map type of DescriptorMap.
  1592     class InverseMap {
  1593     public:
  1594       /// \brief Constructor of the InverseMap.
  1595       ///
  1596       /// Constructor of the InverseMap.
  1597       explicit InverseMap(const DescriptorMap& inverted) 
  1598 	: _inverted(inverted) {}
  1599 
  1600 
  1601       /// The value type of the InverseMap.
  1602       typedef typename DescriptorMap::Key Value;
  1603       /// The key type of the InverseMap.
  1604       typedef typename DescriptorMap::Value Key; 
  1605 
  1606       /// \brief Subscript operator. 
  1607       ///
  1608       /// Subscript operator. It gives back the item 
  1609       /// that the descriptor belongs to currently.
  1610       Value operator[](const Key& key) const {
  1611 	return _inverted(key);
  1612       }
  1613 
  1614       /// \brief Size of the map.
  1615       ///
  1616       /// Returns the size of the map.
  1617       unsigned int size() const {
  1618 	return _inverted.size();
  1619       }
  1620       
  1621     private:
  1622       const DescriptorMap& _inverted;
  1623     };
  1624 
  1625     /// \brief Gives back the inverse of the map.
  1626     ///
  1627     /// Gives back the inverse of the map.
  1628     const InverseMap inverse() const {
  1629       return InverseMap(*this);
  1630     }
  1631   };
  1632 
  1633   /// \brief Returns the source of the given arc.
  1634   ///
  1635   /// The SourceMap gives back the source Node of the given arc. 
  1636   /// \see TargetMap
  1637   template <typename Digraph>
  1638   class SourceMap {
  1639   public:
  1640 
  1641     typedef typename Digraph::Node Value;
  1642     typedef typename Digraph::Arc Key;
  1643 
  1644     /// \brief Constructor
  1645     ///
  1646     /// Constructor
  1647     /// \param _digraph The digraph that the map belongs to.
  1648     explicit SourceMap(const Digraph& digraph) : _digraph(digraph) {}
  1649 
  1650     /// \brief The subscript operator.
  1651     ///
  1652     /// The subscript operator.
  1653     /// \param arc The arc 
  1654     /// \return The source of the arc 
  1655     Value operator[](const Key& arc) const {
  1656       return _digraph.source(arc);
  1657     }
  1658 
  1659   private:
  1660     const Digraph& _digraph;
  1661   };
  1662 
  1663   /// \brief Returns a \ref SourceMap class.
  1664   ///
  1665   /// This function just returns an \ref SourceMap class.
  1666   /// \relates SourceMap
  1667   template <typename Digraph>
  1668   inline SourceMap<Digraph> sourceMap(const Digraph& digraph) {
  1669     return SourceMap<Digraph>(digraph);
  1670   } 
  1671 
  1672   /// \brief Returns the target of the given arc.
  1673   ///
  1674   /// The TargetMap gives back the target Node of the given arc. 
  1675   /// \see SourceMap
  1676   template <typename Digraph>
  1677   class TargetMap {
  1678   public:
  1679 
  1680     typedef typename Digraph::Node Value;
  1681     typedef typename Digraph::Arc Key;
  1682 
  1683     /// \brief Constructor
  1684     ///
  1685     /// Constructor
  1686     /// \param _digraph The digraph that the map belongs to.
  1687     explicit TargetMap(const Digraph& digraph) : _digraph(digraph) {}
  1688 
  1689     /// \brief The subscript operator.
  1690     ///
  1691     /// The subscript operator.
  1692     /// \param e The arc 
  1693     /// \return The target of the arc 
  1694     Value operator[](const Key& e) const {
  1695       return _digraph.target(e);
  1696     }
  1697 
  1698   private:
  1699     const Digraph& _digraph;
  1700   };
  1701 
  1702   /// \brief Returns a \ref TargetMap class.
  1703   ///
  1704   /// This function just returns a \ref TargetMap class.
  1705   /// \relates TargetMap
  1706   template <typename Digraph>
  1707   inline TargetMap<Digraph> targetMap(const Digraph& digraph) {
  1708     return TargetMap<Digraph>(digraph);
  1709   }
  1710 
  1711   /// \brief Returns the "forward" directed arc view of an edge.
  1712   ///
  1713   /// Returns the "forward" directed arc view of an edge.
  1714   /// \see BackwardMap
  1715   template <typename Graph>
  1716   class ForwardMap {
  1717   public:
  1718 
  1719     typedef typename Graph::Arc Value;
  1720     typedef typename Graph::Edge Key;
  1721 
  1722     /// \brief Constructor
  1723     ///
  1724     /// Constructor
  1725     /// \param _graph The graph that the map belongs to.
  1726     explicit ForwardMap(const Graph& graph) : _graph(graph) {}
  1727 
  1728     /// \brief The subscript operator.
  1729     ///
  1730     /// The subscript operator.
  1731     /// \param key An edge 
  1732     /// \return The "forward" directed arc view of edge 
  1733     Value operator[](const Key& key) const {
  1734       return _graph.direct(key, true);
  1735     }
  1736 
  1737   private:
  1738     const Graph& _graph;
  1739   };
  1740 
  1741   /// \brief Returns a \ref ForwardMap class.
  1742   ///
  1743   /// This function just returns an \ref ForwardMap class.
  1744   /// \relates ForwardMap
  1745   template <typename Graph>
  1746   inline ForwardMap<Graph> forwardMap(const Graph& graph) {
  1747     return ForwardMap<Graph>(graph);
  1748   }
  1749 
  1750   /// \brief Returns the "backward" directed arc view of an edge.
  1751   ///
  1752   /// Returns the "backward" directed arc view of an edge.
  1753   /// \see ForwardMap
  1754   template <typename Graph>
  1755   class BackwardMap {
  1756   public:
  1757 
  1758     typedef typename Graph::Arc Value;
  1759     typedef typename Graph::Edge Key;
  1760 
  1761     /// \brief Constructor
  1762     ///
  1763     /// Constructor
  1764     /// \param _graph The graph that the map belongs to.
  1765     explicit BackwardMap(const Graph& graph) : _graph(graph) {}
  1766 
  1767     /// \brief The subscript operator.
  1768     ///
  1769     /// The subscript operator.
  1770     /// \param key An edge 
  1771     /// \return The "backward" directed arc view of edge 
  1772     Value operator[](const Key& key) const {
  1773       return _graph.direct(key, false);
  1774     }
  1775 
  1776   private:
  1777     const Graph& _graph;
  1778   };
  1779 
  1780   /// \brief Returns a \ref BackwardMap class
  1781 
  1782   /// This function just returns a \ref BackwardMap class.
  1783   /// \relates BackwardMap
  1784   template <typename Graph>
  1785   inline BackwardMap<Graph> backwardMap(const Graph& graph) {
  1786     return BackwardMap<Graph>(graph);
  1787   }
  1788 
  1789   /// \brief Potential difference map
  1790   ///
  1791   /// If there is an potential map on the nodes then we
  1792   /// can get an arc map as we get the substraction of the
  1793   /// values of the target and source.
  1794   template <typename Digraph, typename NodeMap>
  1795   class PotentialDifferenceMap {
  1796   public:
  1797     typedef typename Digraph::Arc Key;
  1798     typedef typename NodeMap::Value Value;
  1799 
  1800     /// \brief Constructor
  1801     ///
  1802     /// Contructor of the map
  1803     explicit PotentialDifferenceMap(const Digraph& digraph, 
  1804                                     const NodeMap& potential) 
  1805       : _digraph(digraph), _potential(potential) {}
  1806 
  1807     /// \brief Const subscription operator
  1808     ///
  1809     /// Const subscription operator
  1810     Value operator[](const Key& arc) const {
  1811       return _potential[_digraph.target(arc)] - 
  1812 	_potential[_digraph.source(arc)];
  1813     }
  1814 
  1815   private:
  1816     const Digraph& _digraph;
  1817     const NodeMap& _potential;
  1818   };
  1819 
  1820   /// \brief Returns a PotentialDifferenceMap.
  1821   ///
  1822   /// This function just returns a PotentialDifferenceMap.
  1823   /// \relates PotentialDifferenceMap
  1824   template <typename Digraph, typename NodeMap>
  1825   PotentialDifferenceMap<Digraph, NodeMap> 
  1826   potentialDifferenceMap(const Digraph& digraph, const NodeMap& potential) {
  1827     return PotentialDifferenceMap<Digraph, NodeMap>(digraph, potential);
  1828   }
  1829 
  1830   /// \brief Map of the node in-degrees.
  1831   ///
  1832   /// This map returns the in-degree of a node. Once it is constructed,
  1833   /// the degrees are stored in a standard NodeMap, so each query is done
  1834   /// in constant time. On the other hand, the values are updated automatically
  1835   /// whenever the digraph changes.
  1836   ///
  1837   /// \warning Besides addNode() and addArc(), a digraph structure may provide
  1838   /// alternative ways to modify the digraph. The correct behavior of InDegMap
  1839   /// is not guarantied if these additional features are used. For example
  1840   /// the functions \ref ListDigraph::changeSource() "changeSource()",
  1841   /// \ref ListDigraph::changeTarget() "changeTarget()" and
  1842   /// \ref ListDigraph::reverseArc() "reverseArc()"
  1843   /// of \ref ListDigraph will \e not update the degree values correctly.
  1844   ///
  1845   /// \sa OutDegMap
  1846 
  1847   template <typename _Digraph>
  1848   class InDegMap  
  1849     : protected ItemSetTraits<_Digraph, typename _Digraph::Arc>
  1850       ::ItemNotifier::ObserverBase {
  1851 
  1852   public:
  1853     
  1854     typedef _Digraph Digraph;
  1855     typedef int Value;
  1856     typedef typename Digraph::Node Key;
  1857 
  1858     typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
  1859     ::ItemNotifier::ObserverBase Parent;
  1860 
  1861   private:
  1862 
  1863     class AutoNodeMap : public DefaultMap<Digraph, Key, int> {
  1864     public:
  1865 
  1866       typedef DefaultMap<Digraph, Key, int> Parent;
  1867 
  1868       AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
  1869       
  1870       virtual void add(const Key& key) {
  1871 	Parent::add(key);
  1872 	Parent::set(key, 0);
  1873       }
  1874 
  1875       virtual void add(const std::vector<Key>& keys) {
  1876 	Parent::add(keys);
  1877 	for (int i = 0; i < int(keys.size()); ++i) {
  1878 	  Parent::set(keys[i], 0);
  1879 	}
  1880       }
  1881 
  1882       virtual void build() {
  1883 	Parent::build();
  1884 	Key it;
  1885 	typename Parent::Notifier* nf = Parent::notifier();
  1886 	for (nf->first(it); it != INVALID; nf->next(it)) {
  1887 	  Parent::set(it, 0);
  1888 	}
  1889       }
  1890     };
  1891 
  1892   public:
  1893 
  1894     /// \brief Constructor.
  1895     ///
  1896     /// Constructor for creating in-degree map.
  1897     explicit InDegMap(const Digraph& digraph) 
  1898       : _digraph(digraph), _deg(digraph) {
  1899       Parent::attach(_digraph.notifier(typename Digraph::Arc()));
  1900       
  1901       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  1902 	_deg[it] = countInArcs(_digraph, it);
  1903       }
  1904     }
  1905     
  1906     /// Gives back the in-degree of a Node.
  1907     int operator[](const Key& key) const {
  1908       return _deg[key];
  1909     }
  1910 
  1911   protected:
  1912     
  1913     typedef typename Digraph::Arc Arc;
  1914 
  1915     virtual void add(const Arc& arc) {
  1916       ++_deg[_digraph.target(arc)];
  1917     }
  1918 
  1919     virtual void add(const std::vector<Arc>& arcs) {
  1920       for (int i = 0; i < int(arcs.size()); ++i) {
  1921         ++_deg[_digraph.target(arcs[i])];
  1922       }
  1923     }
  1924 
  1925     virtual void erase(const Arc& arc) {
  1926       --_deg[_digraph.target(arc)];
  1927     }
  1928 
  1929     virtual void erase(const std::vector<Arc>& arcs) {
  1930       for (int i = 0; i < int(arcs.size()); ++i) {
  1931         --_deg[_digraph.target(arcs[i])];
  1932       }
  1933     }
  1934 
  1935     virtual void build() {
  1936       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  1937 	_deg[it] = countInArcs(_digraph, it);
  1938       }      
  1939     }
  1940 
  1941     virtual void clear() {
  1942       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  1943 	_deg[it] = 0;
  1944       }
  1945     }
  1946   private:
  1947     
  1948     const Digraph& _digraph;
  1949     AutoNodeMap _deg;
  1950   };
  1951 
  1952   /// \brief Map of the node out-degrees.
  1953   ///
  1954   /// This map returns the out-degree of a node. Once it is constructed,
  1955   /// the degrees are stored in a standard NodeMap, so each query is done
  1956   /// in constant time. On the other hand, the values are updated automatically
  1957   /// whenever the digraph changes.
  1958   ///
  1959   /// \warning Besides addNode() and addArc(), a digraph structure may provide
  1960   /// alternative ways to modify the digraph. The correct behavior of OutDegMap
  1961   /// is not guarantied if these additional features are used. For example
  1962   /// the functions \ref ListDigraph::changeSource() "changeSource()",
  1963   /// \ref ListDigraph::changeTarget() "changeTarget()" and
  1964   /// \ref ListDigraph::reverseArc() "reverseArc()"
  1965   /// of \ref ListDigraph will \e not update the degree values correctly.
  1966   ///
  1967   /// \sa InDegMap
  1968 
  1969   template <typename _Digraph>
  1970   class OutDegMap  
  1971     : protected ItemSetTraits<_Digraph, typename _Digraph::Arc>
  1972       ::ItemNotifier::ObserverBase {
  1973 
  1974   public:
  1975     
  1976     typedef _Digraph Digraph;
  1977     typedef int Value;
  1978     typedef typename Digraph::Node Key;
  1979 
  1980     typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
  1981     ::ItemNotifier::ObserverBase Parent;
  1982 
  1983   private:
  1984 
  1985     class AutoNodeMap : public DefaultMap<Digraph, Key, int> {
  1986     public:
  1987 
  1988       typedef DefaultMap<Digraph, Key, int> Parent;
  1989 
  1990       AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
  1991       
  1992       virtual void add(const Key& key) {
  1993 	Parent::add(key);
  1994 	Parent::set(key, 0);
  1995       }
  1996       virtual void add(const std::vector<Key>& keys) {
  1997 	Parent::add(keys);
  1998 	for (int i = 0; i < int(keys.size()); ++i) {
  1999 	  Parent::set(keys[i], 0);
  2000 	}
  2001       }
  2002       virtual void build() {
  2003 	Parent::build();
  2004 	Key it;
  2005 	typename Parent::Notifier* nf = Parent::notifier();
  2006 	for (nf->first(it); it != INVALID; nf->next(it)) {
  2007 	  Parent::set(it, 0);
  2008 	}
  2009       }
  2010     };
  2011 
  2012   public:
  2013 
  2014     /// \brief Constructor.
  2015     ///
  2016     /// Constructor for creating out-degree map.
  2017     explicit OutDegMap(const Digraph& digraph) 
  2018       : _digraph(digraph), _deg(digraph) {
  2019       Parent::attach(_digraph.notifier(typename Digraph::Arc()));
  2020       
  2021       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  2022 	_deg[it] = countOutArcs(_digraph, it);
  2023       }
  2024     }
  2025 
  2026     /// Gives back the out-degree of a Node.
  2027     int operator[](const Key& key) const {
  2028       return _deg[key];
  2029     }
  2030 
  2031   protected:
  2032     
  2033     typedef typename Digraph::Arc Arc;
  2034 
  2035     virtual void add(const Arc& arc) {
  2036       ++_deg[_digraph.source(arc)];
  2037     }
  2038 
  2039     virtual void add(const std::vector<Arc>& arcs) {
  2040       for (int i = 0; i < int(arcs.size()); ++i) {
  2041         ++_deg[_digraph.source(arcs[i])];
  2042       }
  2043     }
  2044 
  2045     virtual void erase(const Arc& arc) {
  2046       --_deg[_digraph.source(arc)];
  2047     }
  2048 
  2049     virtual void erase(const std::vector<Arc>& arcs) {
  2050       for (int i = 0; i < int(arcs.size()); ++i) {
  2051         --_deg[_digraph.source(arcs[i])];
  2052       }
  2053     }
  2054 
  2055     virtual void build() {
  2056       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  2057 	_deg[it] = countOutArcs(_digraph, it);
  2058       }      
  2059     }
  2060 
  2061     virtual void clear() {
  2062       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  2063 	_deg[it] = 0;
  2064       }
  2065     }
  2066   private:
  2067     
  2068     const Digraph& _digraph;
  2069     AutoNodeMap _deg;
  2070   };
  2071 
  2072 
  2073   ///Dynamic arc look up between given endpoints.
  2074   
  2075   ///\ingroup gutils
  2076   ///Using this class, you can find an arc in a digraph from a given
  2077   ///source to a given target in amortized time <em>O(log d)</em>,
  2078   ///where <em>d</em> is the out-degree of the source node.
  2079   ///
  2080   ///It is possible to find \e all parallel arcs between two nodes with
  2081   ///the \c findFirst() and \c findNext() members.
  2082   ///
  2083   ///See the \ref ArcLookUp and \ref AllArcLookUp classes if your
  2084   ///digraph is not changed so frequently.
  2085   ///
  2086   ///This class uses a self-adjusting binary search tree, Sleator's
  2087   ///and Tarjan's Splay tree for guarantee the logarithmic amortized
  2088   ///time bound for arc lookups. This class also guarantees the
  2089   ///optimal time bound in a constant factor for any distribution of
  2090   ///queries.
  2091   ///
  2092   ///\tparam G The type of the underlying digraph.  
  2093   ///
  2094   ///\sa ArcLookUp  
  2095   ///\sa AllArcLookUp  
  2096   template<class G>
  2097   class DynArcLookUp 
  2098     : protected ItemSetTraits<G, typename G::Arc>::ItemNotifier::ObserverBase
  2099   {
  2100   public:
  2101     typedef typename ItemSetTraits<G, typename G::Arc>
  2102     ::ItemNotifier::ObserverBase Parent;
  2103 
  2104     TEMPLATE_DIGRAPH_TYPEDEFS(G);
  2105     typedef G Digraph;
  2106 
  2107   protected:
  2108 
  2109     class AutoNodeMap : public DefaultMap<G, Node, Arc> {
  2110     public:
  2111 
  2112       typedef DefaultMap<G, Node, Arc> Parent;
  2113 
  2114       AutoNodeMap(const G& digraph) : Parent(digraph, INVALID) {}
  2115       
  2116       virtual void add(const Node& node) {
  2117 	Parent::add(node);
  2118 	Parent::set(node, INVALID);
  2119       }
  2120 
  2121       virtual void add(const std::vector<Node>& nodes) {
  2122 	Parent::add(nodes);
  2123 	for (int i = 0; i < int(nodes.size()); ++i) {
  2124 	  Parent::set(nodes[i], INVALID);
  2125 	}
  2126       }
  2127 
  2128       virtual void build() {
  2129 	Parent::build();
  2130 	Node it;
  2131 	typename Parent::Notifier* nf = Parent::notifier();
  2132 	for (nf->first(it); it != INVALID; nf->next(it)) {
  2133 	  Parent::set(it, INVALID);
  2134 	}
  2135       }
  2136     };
  2137 
  2138     const Digraph &_g;
  2139     AutoNodeMap _head;
  2140     typename Digraph::template ArcMap<Arc> _parent;
  2141     typename Digraph::template ArcMap<Arc> _left;
  2142     typename Digraph::template ArcMap<Arc> _right;
  2143     
  2144     class ArcLess {
  2145       const Digraph &g;
  2146     public:
  2147       ArcLess(const Digraph &_g) : g(_g) {}
  2148       bool operator()(Arc a,Arc b) const 
  2149       {
  2150 	return g.target(a)<g.target(b);
  2151       }
  2152     };
  2153     
  2154   public:
  2155     
  2156     ///Constructor
  2157 
  2158     ///Constructor.
  2159     ///
  2160     ///It builds up the search database.
  2161     DynArcLookUp(const Digraph &g) 
  2162       : _g(g),_head(g),_parent(g),_left(g),_right(g) 
  2163     { 
  2164       Parent::attach(_g.notifier(typename Digraph::Arc()));
  2165       refresh(); 
  2166     }
  2167     
  2168   protected:
  2169 
  2170     virtual void add(const Arc& arc) {
  2171       insert(arc);
  2172     }
  2173 
  2174     virtual void add(const std::vector<Arc>& arcs) {
  2175       for (int i = 0; i < int(arcs.size()); ++i) {
  2176 	insert(arcs[i]);
  2177       }
  2178     }
  2179 
  2180     virtual void erase(const Arc& arc) {
  2181       remove(arc);
  2182     }
  2183 
  2184     virtual void erase(const std::vector<Arc>& arcs) {
  2185       for (int i = 0; i < int(arcs.size()); ++i) {
  2186 	remove(arcs[i]);
  2187       }     
  2188     }
  2189 
  2190     virtual void build() {
  2191       refresh();
  2192     }
  2193 
  2194     virtual void clear() {
  2195       for(NodeIt n(_g);n!=INVALID;++n) {
  2196 	_head.set(n, INVALID);
  2197       }
  2198     }
  2199 
  2200     void insert(Arc arc) {
  2201       Node s = _g.source(arc);
  2202       Node t = _g.target(arc);
  2203       _left.set(arc, INVALID);
  2204       _right.set(arc, INVALID);
  2205       
  2206       Arc e = _head[s];
  2207       if (e == INVALID) {
  2208 	_head.set(s, arc);
  2209 	_parent.set(arc, INVALID);
  2210 	return;
  2211       }
  2212       while (true) {
  2213 	if (t < _g.target(e)) {
  2214 	  if (_left[e] == INVALID) {
  2215 	    _left.set(e, arc);
  2216 	    _parent.set(arc, e);
  2217 	    splay(arc);
  2218 	    return;
  2219 	  } else {
  2220 	    e = _left[e];
  2221 	  }
  2222 	} else {
  2223 	  if (_right[e] == INVALID) {
  2224 	    _right.set(e, arc);
  2225 	    _parent.set(arc, e);
  2226 	    splay(arc);
  2227 	    return;
  2228 	  } else {
  2229 	    e = _right[e];
  2230 	  }
  2231 	}
  2232       }
  2233     }
  2234 
  2235     void remove(Arc arc) {
  2236       if (_left[arc] == INVALID) {
  2237 	if (_right[arc] != INVALID) {
  2238 	  _parent.set(_right[arc], _parent[arc]);
  2239 	}
  2240 	if (_parent[arc] != INVALID) {
  2241 	  if (_left[_parent[arc]] == arc) {
  2242 	    _left.set(_parent[arc], _right[arc]);
  2243 	  } else {
  2244 	    _right.set(_parent[arc], _right[arc]);
  2245 	  }
  2246 	} else {
  2247 	  _head.set(_g.source(arc), _right[arc]);
  2248 	}
  2249       } else if (_right[arc] == INVALID) {
  2250 	_parent.set(_left[arc], _parent[arc]);
  2251 	if (_parent[arc] != INVALID) {
  2252 	  if (_left[_parent[arc]] == arc) {
  2253 	    _left.set(_parent[arc], _left[arc]);
  2254 	  } else {
  2255 	    _right.set(_parent[arc], _left[arc]);
  2256 	  }
  2257 	} else {
  2258 	  _head.set(_g.source(arc), _left[arc]);
  2259 	}
  2260       } else {
  2261 	Arc e = _left[arc];
  2262 	if (_right[e] != INVALID) {
  2263 	  e = _right[e];	  
  2264 	  while (_right[e] != INVALID) {
  2265 	    e = _right[e];
  2266 	  }
  2267 	  Arc s = _parent[e];
  2268 	  _right.set(_parent[e], _left[e]);
  2269 	  if (_left[e] != INVALID) {
  2270 	    _parent.set(_left[e], _parent[e]);
  2271 	  }
  2272 	  
  2273 	  _left.set(e, _left[arc]);
  2274 	  _parent.set(_left[arc], e);
  2275 	  _right.set(e, _right[arc]);
  2276 	  _parent.set(_right[arc], e);
  2277 
  2278 	  _parent.set(e, _parent[arc]);
  2279 	  if (_parent[arc] != INVALID) {
  2280 	    if (_left[_parent[arc]] == arc) {
  2281 	      _left.set(_parent[arc], e);
  2282 	    } else {
  2283 	      _right.set(_parent[arc], e);
  2284 	    }
  2285 	  }
  2286 	  splay(s);
  2287 	} else {
  2288 	  _right.set(e, _right[arc]);
  2289 	  _parent.set(_right[arc], e);
  2290 
  2291 	  if (_parent[arc] != INVALID) {
  2292 	    if (_left[_parent[arc]] == arc) {
  2293 	      _left.set(_parent[arc], e);
  2294 	    } else {
  2295 	      _right.set(_parent[arc], e);
  2296 	    }
  2297 	  } else {
  2298 	    _head.set(_g.source(arc), e);
  2299 	  }
  2300 	}
  2301       }
  2302     }
  2303 
  2304     Arc refreshRec(std::vector<Arc> &v,int a,int b) 
  2305     {
  2306       int m=(a+b)/2;
  2307       Arc me=v[m];
  2308       if (a < m) {
  2309 	Arc left = refreshRec(v,a,m-1);
  2310 	_left.set(me, left);
  2311 	_parent.set(left, me);
  2312       } else {
  2313 	_left.set(me, INVALID);
  2314       }
  2315       if (m < b) {
  2316 	Arc right = refreshRec(v,m+1,b);
  2317 	_right.set(me, right);
  2318 	_parent.set(right, me);
  2319       } else {
  2320 	_right.set(me, INVALID);
  2321       }
  2322       return me;
  2323     }
  2324 
  2325     void refresh() {
  2326       for(NodeIt n(_g);n!=INVALID;++n) {
  2327 	std::vector<Arc> v;
  2328 	for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
  2329 	if(v.size()) {
  2330 	  std::sort(v.begin(),v.end(),ArcLess(_g));
  2331 	  Arc head = refreshRec(v,0,v.size()-1);
  2332 	  _head.set(n, head);
  2333 	  _parent.set(head, INVALID);
  2334 	}
  2335 	else _head.set(n, INVALID);
  2336       }
  2337     }
  2338 
  2339     void zig(Arc v) {        
  2340       Arc w = _parent[v];
  2341       _parent.set(v, _parent[w]);
  2342       _parent.set(w, v);
  2343       _left.set(w, _right[v]);
  2344       _right.set(v, w);
  2345       if (_parent[v] != INVALID) {
  2346 	if (_right[_parent[v]] == w) {
  2347 	  _right.set(_parent[v], v);
  2348 	} else {
  2349 	  _left.set(_parent[v], v);
  2350 	}
  2351       }
  2352       if (_left[w] != INVALID){
  2353 	_parent.set(_left[w], w);
  2354       }
  2355     }
  2356 
  2357     void zag(Arc v) {        
  2358       Arc w = _parent[v];
  2359       _parent.set(v, _parent[w]);
  2360       _parent.set(w, v);
  2361       _right.set(w, _left[v]);
  2362       _left.set(v, w);
  2363       if (_parent[v] != INVALID){
  2364 	if (_left[_parent[v]] == w) {
  2365 	  _left.set(_parent[v], v);
  2366 	} else {
  2367 	  _right.set(_parent[v], v);
  2368 	}
  2369       }
  2370       if (_right[w] != INVALID){
  2371 	_parent.set(_right[w], w);
  2372       }
  2373     }
  2374 
  2375     void splay(Arc v) {
  2376       while (_parent[v] != INVALID) {
  2377 	if (v == _left[_parent[v]]) {
  2378 	  if (_parent[_parent[v]] == INVALID) {
  2379 	    zig(v);
  2380 	  } else {
  2381 	    if (_parent[v] == _left[_parent[_parent[v]]]) {
  2382 	      zig(_parent[v]);
  2383 	      zig(v);
  2384 	    } else {
  2385 	      zig(v);
  2386 	      zag(v);
  2387 	    }
  2388 	  }
  2389 	} else {
  2390 	  if (_parent[_parent[v]] == INVALID) {
  2391 	    zag(v);
  2392 	  } else {
  2393 	    if (_parent[v] == _left[_parent[_parent[v]]]) {
  2394 	      zag(v);
  2395 	      zig(v);
  2396 	    } else {
  2397 	      zag(_parent[v]);
  2398 	      zag(v);
  2399 	    }
  2400 	  }
  2401 	}
  2402       }
  2403       _head[_g.source(v)] = v;
  2404     }
  2405 
  2406 
  2407   public:
  2408     
  2409     ///Find an arc between two nodes.
  2410     
  2411     ///Find an arc between two nodes in time <em>O(</em>log<em>d)</em>, where
  2412     /// <em>d</em> is the number of outgoing arcs of \c s.
  2413     ///\param s The source node
  2414     ///\param t The target node
  2415     ///\return An arc from \c s to \c t if there exists,
  2416     ///\ref INVALID otherwise.
  2417     Arc operator()(Node s, Node t) const
  2418     {
  2419       Arc a = _head[s];
  2420       while (true) {
  2421 	if (_g.target(a) == t) {
  2422 	  const_cast<DynArcLookUp&>(*this).splay(a);
  2423 	  return a;
  2424 	} else if (t < _g.target(a)) {
  2425 	  if (_left[a] == INVALID) {
  2426 	    const_cast<DynArcLookUp&>(*this).splay(a);
  2427 	    return INVALID;
  2428 	  } else {
  2429 	    a = _left[a];
  2430 	  }
  2431 	} else  {
  2432 	  if (_right[a] == INVALID) {
  2433 	    const_cast<DynArcLookUp&>(*this).splay(a);
  2434 	    return INVALID;
  2435 	  } else {
  2436 	    a = _right[a];
  2437 	  }
  2438 	}
  2439       }
  2440     }
  2441 
  2442     ///Find the first arc between two nodes.
  2443     
  2444     ///Find the first arc between two nodes in time
  2445     /// <em>O(</em>log<em>d)</em>, where <em>d</em> is the number of
  2446     /// outgoing arcs of \c s.  
  2447     ///\param s The source node 
  2448     ///\param t The target node
  2449     ///\return An arc from \c s to \c t if there exists, \ref INVALID
  2450     /// otherwise.
  2451     Arc findFirst(Node s, Node t) const
  2452     {
  2453       Arc a = _head[s];
  2454       Arc r = INVALID;
  2455       while (true) {
  2456 	if (_g.target(a) < t) {
  2457 	  if (_right[a] == INVALID) {
  2458 	    const_cast<DynArcLookUp&>(*this).splay(a);
  2459 	    return r;
  2460 	  } else {
  2461 	    a = _right[a];
  2462 	  }
  2463 	} else {
  2464 	  if (_g.target(a) == t) {
  2465 	    r = a;
  2466 	  }
  2467 	  if (_left[a] == INVALID) {
  2468 	    const_cast<DynArcLookUp&>(*this).splay(a);
  2469 	    return r;
  2470 	  } else {
  2471 	    a = _left[a];
  2472 	  }
  2473 	}
  2474       }
  2475     }
  2476 
  2477     ///Find the next arc between two nodes.
  2478     
  2479     ///Find the next arc between two nodes in time
  2480     /// <em>O(</em>log<em>d)</em>, where <em>d</em> is the number of
  2481     /// outgoing arcs of \c s.  
  2482     ///\param s The source node 
  2483     ///\param t The target node
  2484     ///\return An arc from \c s to \c t if there exists, \ref INVALID
  2485     /// otherwise.
  2486 
  2487     ///\note If \c e is not the result of the previous \c findFirst()
  2488     ///operation then the amorized time bound can not be guaranteed.
  2489 #ifdef DOXYGEN
  2490     Arc findNext(Node s, Node t, Arc a) const
  2491 #else
  2492     Arc findNext(Node, Node t, Arc a) const
  2493 #endif
  2494     {
  2495       if (_right[a] != INVALID) {
  2496 	a = _right[a];
  2497 	while (_left[a] != INVALID) {
  2498 	  a = _left[a];
  2499 	}
  2500 	const_cast<DynArcLookUp&>(*this).splay(a);
  2501       } else {
  2502 	while (_parent[a] != INVALID && _right[_parent[a]] ==  a) {
  2503 	  a = _parent[a];
  2504 	}
  2505 	if (_parent[a] == INVALID) {
  2506 	  return INVALID;
  2507 	} else {
  2508 	  a = _parent[a];
  2509 	  const_cast<DynArcLookUp&>(*this).splay(a);
  2510 	}
  2511       }
  2512       if (_g.target(a) == t) return a;
  2513       else return INVALID;    
  2514     }
  2515 
  2516   };
  2517 
  2518   ///Fast arc look up between given endpoints.
  2519   
  2520   ///\ingroup gutils
  2521   ///Using this class, you can find an arc in a digraph from a given
  2522   ///source to a given target in time <em>O(log d)</em>,
  2523   ///where <em>d</em> is the out-degree of the source node.
  2524   ///
  2525   ///It is not possible to find \e all parallel arcs between two nodes.
  2526   ///Use \ref AllArcLookUp for this purpose.
  2527   ///
  2528   ///\warning This class is static, so you should refresh() (or at least
  2529   ///refresh(Node)) this data structure
  2530   ///whenever the digraph changes. This is a time consuming (superlinearly
  2531   ///proportional (<em>O(m</em>log<em>m)</em>) to the number of arcs).
  2532   ///
  2533   ///\tparam G The type of the underlying digraph.
  2534   ///
  2535   ///\sa DynArcLookUp
  2536   ///\sa AllArcLookUp  
  2537   template<class G>
  2538   class ArcLookUp 
  2539   {
  2540   public:
  2541     TEMPLATE_DIGRAPH_TYPEDEFS(G);
  2542     typedef G Digraph;
  2543 
  2544   protected:
  2545     const Digraph &_g;
  2546     typename Digraph::template NodeMap<Arc> _head;
  2547     typename Digraph::template ArcMap<Arc> _left;
  2548     typename Digraph::template ArcMap<Arc> _right;
  2549     
  2550     class ArcLess {
  2551       const Digraph &g;
  2552     public:
  2553       ArcLess(const Digraph &_g) : g(_g) {}
  2554       bool operator()(Arc a,Arc b) const 
  2555       {
  2556 	return g.target(a)<g.target(b);
  2557       }
  2558     };
  2559     
  2560   public:
  2561     
  2562     ///Constructor
  2563 
  2564     ///Constructor.
  2565     ///
  2566     ///It builds up the search database, which remains valid until the digraph
  2567     ///changes.
  2568     ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}
  2569     
  2570   private:
  2571     Arc refreshRec(std::vector<Arc> &v,int a,int b) 
  2572     {
  2573       int m=(a+b)/2;
  2574       Arc me=v[m];
  2575       _left[me] = a<m?refreshRec(v,a,m-1):INVALID;
  2576       _right[me] = m<b?refreshRec(v,m+1,b):INVALID;
  2577       return me;
  2578     }
  2579   public:
  2580     ///Refresh the data structure at a node.
  2581 
  2582     ///Build up the search database of node \c n.
  2583     ///
  2584     ///It runs in time <em>O(d</em>log<em>d)</em>, where <em>d</em> is
  2585     ///the number of the outgoing arcs of \c n.
  2586     void refresh(Node n) 
  2587     {
  2588       std::vector<Arc> v;
  2589       for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
  2590       if(v.size()) {
  2591 	std::sort(v.begin(),v.end(),ArcLess(_g));
  2592 	_head[n]=refreshRec(v,0,v.size()-1);
  2593       }
  2594       else _head[n]=INVALID;
  2595     }
  2596     ///Refresh the full data structure.
  2597 
  2598     ///Build up the full search database. In fact, it simply calls
  2599     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  2600     ///
  2601     ///It runs in time <em>O(m</em>log<em>D)</em>, where <em>m</em> is
  2602     ///the number of the arcs of \c n and <em>D</em> is the maximum
  2603     ///out-degree of the digraph.
  2604 
  2605     void refresh() 
  2606     {
  2607       for(NodeIt n(_g);n!=INVALID;++n) refresh(n);
  2608     }
  2609     
  2610     ///Find an arc between two nodes.
  2611     
  2612     ///Find an arc between two nodes in time <em>O(</em>log<em>d)</em>, where
  2613     /// <em>d</em> is the number of outgoing arcs of \c s.
  2614     ///\param s The source node
  2615     ///\param t The target node
  2616     ///\return An arc from \c s to \c t if there exists,
  2617     ///\ref INVALID otherwise.
  2618     ///
  2619     ///\warning If you change the digraph, refresh() must be called before using
  2620     ///this operator. If you change the outgoing arcs of
  2621     ///a single node \c n, then
  2622     ///\ref refresh(Node) "refresh(n)" is enough.
  2623     ///
  2624     Arc operator()(Node s, Node t) const
  2625     {
  2626       Arc e;
  2627       for(e=_head[s];
  2628 	  e!=INVALID&&_g.target(e)!=t;
  2629 	  e = t < _g.target(e)?_left[e]:_right[e]) ;
  2630       return e;
  2631     }
  2632 
  2633   };
  2634 
  2635   ///Fast look up of all arcs between given endpoints.
  2636   
  2637   ///\ingroup gutils
  2638   ///This class is the same as \ref ArcLookUp, with the addition
  2639   ///that it makes it possible to find all arcs between given endpoints.
  2640   ///
  2641   ///\warning This class is static, so you should refresh() (or at least
  2642   ///refresh(Node)) this data structure
  2643   ///whenever the digraph changes. This is a time consuming (superlinearly
  2644   ///proportional (<em>O(m</em>log<em>m)</em>) to the number of arcs).
  2645   ///
  2646   ///\tparam G The type of the underlying digraph.
  2647   ///
  2648   ///\sa DynArcLookUp
  2649   ///\sa ArcLookUp  
  2650   template<class G>
  2651   class AllArcLookUp : public ArcLookUp<G>
  2652   {
  2653     using ArcLookUp<G>::_g;
  2654     using ArcLookUp<G>::_right;
  2655     using ArcLookUp<G>::_left;
  2656     using ArcLookUp<G>::_head;
  2657 
  2658     TEMPLATE_DIGRAPH_TYPEDEFS(G);
  2659     typedef G Digraph;
  2660     
  2661     typename Digraph::template ArcMap<Arc> _next;
  2662     
  2663     Arc refreshNext(Arc head,Arc next=INVALID)
  2664     {
  2665       if(head==INVALID) return next;
  2666       else {
  2667 	next=refreshNext(_right[head],next);
  2668 // 	_next[head]=next;
  2669 	_next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
  2670 	  ? next : INVALID;
  2671 	return refreshNext(_left[head],head);
  2672       }
  2673     }
  2674     
  2675     void refreshNext()
  2676     {
  2677       for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
  2678     }
  2679     
  2680   public:
  2681     ///Constructor
  2682 
  2683     ///Constructor.
  2684     ///
  2685     ///It builds up the search database, which remains valid until the digraph
  2686     ///changes.
  2687     AllArcLookUp(const Digraph &g) : ArcLookUp<G>(g), _next(g) {refreshNext();}
  2688 
  2689     ///Refresh the data structure at a node.
  2690 
  2691     ///Build up the search database of node \c n.
  2692     ///
  2693     ///It runs in time <em>O(d</em>log<em>d)</em>, where <em>d</em> is
  2694     ///the number of the outgoing arcs of \c n.
  2695     
  2696     void refresh(Node n) 
  2697     {
  2698       ArcLookUp<G>::refresh(n);
  2699       refreshNext(_head[n]);
  2700     }
  2701     
  2702     ///Refresh the full data structure.
  2703 
  2704     ///Build up the full search database. In fact, it simply calls
  2705     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  2706     ///
  2707     ///It runs in time <em>O(m</em>log<em>D)</em>, where <em>m</em> is
  2708     ///the number of the arcs of \c n and <em>D</em> is the maximum
  2709     ///out-degree of the digraph.
  2710 
  2711     void refresh() 
  2712     {
  2713       for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
  2714     }
  2715     
  2716     ///Find an arc between two nodes.
  2717     
  2718     ///Find an arc between two nodes.
  2719     ///\param s The source node
  2720     ///\param t The target node
  2721     ///\param prev The previous arc between \c s and \c t. It it is INVALID or
  2722     ///not given, the operator finds the first appropriate arc.
  2723     ///\return An arc from \c s to \c t after \c prev or
  2724     ///\ref INVALID if there is no more.
  2725     ///
  2726     ///For example, you can count the number of arcs from \c u to \c v in the
  2727     ///following way.
  2728     ///\code
  2729     ///AllArcLookUp<ListDigraph> ae(g);
  2730     ///...
  2731     ///int n=0;
  2732     ///for(Arc e=ae(u,v);e!=INVALID;e=ae(u,v,e)) n++;
  2733     ///\endcode
  2734     ///
  2735     ///Finding the first arc take <em>O(</em>log<em>d)</em> time, where
  2736     /// <em>d</em> is the number of outgoing arcs of \c s. Then, the
  2737     ///consecutive arcs are found in constant time.
  2738     ///
  2739     ///\warning If you change the digraph, refresh() must be called before using
  2740     ///this operator. If you change the outgoing arcs of
  2741     ///a single node \c n, then
  2742     ///\ref refresh(Node) "refresh(n)" is enough.
  2743     ///
  2744 #ifdef DOXYGEN
  2745     Arc operator()(Node s, Node t, Arc prev=INVALID) const {}
  2746 #else
  2747     using ArcLookUp<G>::operator() ;
  2748     Arc operator()(Node s, Node t, Arc prev) const
  2749     {
  2750       return prev==INVALID?(*this)(s,t):_next[prev];
  2751     }
  2752 #endif
  2753       
  2754   };
  2755 
  2756   /// @}
  2757 
  2758 } //END OF NAMESPACE LEMON
  2759 
  2760 #endif