lemon/core.h
author Alpar Juttner <alpar@cs.elte.hu>
Thu, 09 Oct 2008 16:20:37 +0100
changeset 317 a0ab96ad65fe
parent 300 8c05947fc107
child 319 5e12d7734036
permissions -rw-r--r--
Merge
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     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_CORE_H
    20 #define LEMON_CORE_H
    21 
    22 #include <vector>
    23 #include <algorithm>
    24 
    25 #include <lemon/bits/enable_if.h>
    26 #include <lemon/bits/traits.h>
    27 
    28 ///\file
    29 ///\brief LEMON core utilities.
    30 ///
    31 ///This header file contains core utilities for LEMON.
    32 ///It is automatically included by all graph types, therefore it usually
    33 ///do not have to be included directly.
    34 
    35 namespace lemon {
    36 
    37   /// \brief Dummy type to make it easier to create invalid iterators.
    38   ///
    39   /// Dummy type to make it easier to create invalid iterators.
    40   /// See \ref INVALID for the usage.
    41   struct Invalid {
    42   public:
    43     bool operator==(Invalid) { return true;  }
    44     bool operator!=(Invalid) { return false; }
    45     bool operator< (Invalid) { return false; }
    46   };
    47 
    48   /// \brief Invalid iterators.
    49   ///
    50   /// \ref Invalid is a global type that converts to each iterator
    51   /// in such a way that the value of the target iterator will be invalid.
    52 #ifdef LEMON_ONLY_TEMPLATES
    53   const Invalid INVALID = Invalid();
    54 #else
    55   extern const Invalid INVALID;
    56 #endif
    57 
    58   /// \addtogroup gutils
    59   /// @{
    60 
    61   ///Create convenience typedefs for the digraph types and iterators
    62 
    63   ///This \c \#define creates convenient type definitions for the following
    64   ///types of \c Digraph: \c Node,  \c NodeIt, \c Arc, \c ArcIt, \c InArcIt,
    65   ///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap,
    66   ///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap.
    67   ///
    68   ///\note If the graph type is a dependent type, ie. the graph type depend
    69   ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
    70   ///macro.
    71 #define DIGRAPH_TYPEDEFS(Digraph)                                       \
    72   typedef Digraph::Node Node;                                           \
    73   typedef Digraph::NodeIt NodeIt;                                       \
    74   typedef Digraph::Arc Arc;                                             \
    75   typedef Digraph::ArcIt ArcIt;                                         \
    76   typedef Digraph::InArcIt InArcIt;                                     \
    77   typedef Digraph::OutArcIt OutArcIt;                                   \
    78   typedef Digraph::NodeMap<bool> BoolNodeMap;                           \
    79   typedef Digraph::NodeMap<int> IntNodeMap;                             \
    80   typedef Digraph::NodeMap<double> DoubleNodeMap;                       \
    81   typedef Digraph::ArcMap<bool> BoolArcMap;                             \
    82   typedef Digraph::ArcMap<int> IntArcMap;                               \
    83   typedef Digraph::ArcMap<double> DoubleArcMap
    84 
    85   ///Create convenience typedefs for the digraph types and iterators
    86 
    87   ///\see DIGRAPH_TYPEDEFS
    88   ///
    89   ///\note Use this macro, if the graph type is a dependent type,
    90   ///ie. the graph type depend on a template parameter.
    91 #define TEMPLATE_DIGRAPH_TYPEDEFS(Digraph)                              \
    92   typedef typename Digraph::Node Node;                                  \
    93   typedef typename Digraph::NodeIt NodeIt;                              \
    94   typedef typename Digraph::Arc Arc;                                    \
    95   typedef typename Digraph::ArcIt ArcIt;                                \
    96   typedef typename Digraph::InArcIt InArcIt;                            \
    97   typedef typename Digraph::OutArcIt OutArcIt;                          \
    98   typedef typename Digraph::template NodeMap<bool> BoolNodeMap;         \
    99   typedef typename Digraph::template NodeMap<int> IntNodeMap;           \
   100   typedef typename Digraph::template NodeMap<double> DoubleNodeMap;     \
   101   typedef typename Digraph::template ArcMap<bool> BoolArcMap;           \
   102   typedef typename Digraph::template ArcMap<int> IntArcMap;             \
   103   typedef typename Digraph::template ArcMap<double> DoubleArcMap
   104 
   105   ///Create convenience typedefs for the graph types and iterators
   106 
   107   ///This \c \#define creates the same convenient type definitions as defined
   108   ///by \ref DIGRAPH_TYPEDEFS(Graph) and six more, namely it creates
   109   ///\c Edge, \c EdgeIt, \c IncEdgeIt, \c BoolEdgeMap, \c IntEdgeMap,
   110   ///\c DoubleEdgeMap.
   111   ///
   112   ///\note If the graph type is a dependent type, ie. the graph type depend
   113   ///on a template parameter, then use \c TEMPLATE_GRAPH_TYPEDEFS()
   114   ///macro.
   115 #define GRAPH_TYPEDEFS(Graph)                                           \
   116   DIGRAPH_TYPEDEFS(Graph);                                              \
   117   typedef Graph::Edge Edge;                                             \
   118   typedef Graph::EdgeIt EdgeIt;                                         \
   119   typedef Graph::IncEdgeIt IncEdgeIt;                                   \
   120   typedef Graph::EdgeMap<bool> BoolEdgeMap;                             \
   121   typedef Graph::EdgeMap<int> IntEdgeMap;                               \
   122   typedef Graph::EdgeMap<double> DoubleEdgeMap
   123 
   124   ///Create convenience typedefs for the graph types and iterators
   125 
   126   ///\see GRAPH_TYPEDEFS
   127   ///
   128   ///\note Use this macro, if the graph type is a dependent type,
   129   ///ie. the graph type depend on a template parameter.
   130 #define TEMPLATE_GRAPH_TYPEDEFS(Graph)                                  \
   131   TEMPLATE_DIGRAPH_TYPEDEFS(Graph);                                     \
   132   typedef typename Graph::Edge Edge;                                    \
   133   typedef typename Graph::EdgeIt EdgeIt;                                \
   134   typedef typename Graph::IncEdgeIt IncEdgeIt;                          \
   135   typedef typename Graph::template EdgeMap<bool> BoolEdgeMap;           \
   136   typedef typename Graph::template EdgeMap<int> IntEdgeMap;             \
   137   typedef typename Graph::template EdgeMap<double> DoubleEdgeMap
   138 
   139   /// \brief Function to count the items in a graph.
   140   ///
   141   /// This function counts the items (nodes, arcs etc.) in a graph.
   142   /// The complexity of the function is linear because
   143   /// it iterates on all of the items.
   144   template <typename Graph, typename Item>
   145   inline int countItems(const Graph& g) {
   146     typedef typename ItemSetTraits<Graph, Item>::ItemIt ItemIt;
   147     int num = 0;
   148     for (ItemIt it(g); it != INVALID; ++it) {
   149       ++num;
   150     }
   151     return num;
   152   }
   153 
   154   // Node counting:
   155 
   156   namespace _core_bits {
   157 
   158     template <typename Graph, typename Enable = void>
   159     struct CountNodesSelector {
   160       static int count(const Graph &g) {
   161         return countItems<Graph, typename Graph::Node>(g);
   162       }
   163     };
   164 
   165     template <typename Graph>
   166     struct CountNodesSelector<
   167       Graph, typename
   168       enable_if<typename Graph::NodeNumTag, void>::type>
   169     {
   170       static int count(const Graph &g) {
   171         return g.nodeNum();
   172       }
   173     };
   174   }
   175 
   176   /// \brief Function to count the nodes in the graph.
   177   ///
   178   /// This function counts the nodes in the graph.
   179   /// The complexity of the function is <em>O</em>(<em>n</em>), but for some
   180   /// graph structures it is specialized to run in <em>O</em>(1).
   181   ///
   182   /// \note If the graph contains a \c nodeNum() member function and a
   183   /// \c NodeNumTag tag then this function calls directly the member
   184   /// function to query the cardinality of the node set.
   185   template <typename Graph>
   186   inline int countNodes(const Graph& g) {
   187     return _core_bits::CountNodesSelector<Graph>::count(g);
   188   }
   189 
   190   // Arc counting:
   191 
   192   namespace _core_bits {
   193 
   194     template <typename Graph, typename Enable = void>
   195     struct CountArcsSelector {
   196       static int count(const Graph &g) {
   197         return countItems<Graph, typename Graph::Arc>(g);
   198       }
   199     };
   200 
   201     template <typename Graph>
   202     struct CountArcsSelector<
   203       Graph,
   204       typename enable_if<typename Graph::ArcNumTag, void>::type>
   205     {
   206       static int count(const Graph &g) {
   207         return g.arcNum();
   208       }
   209     };
   210   }
   211 
   212   /// \brief Function to count the arcs in the graph.
   213   ///
   214   /// This function counts the arcs in the graph.
   215   /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
   216   /// graph structures it is specialized to run in <em>O</em>(1).
   217   ///
   218   /// \note If the graph contains a \c arcNum() member function and a
   219   /// \c ArcNumTag tag then this function calls directly the member
   220   /// function to query the cardinality of the arc set.
   221   template <typename Graph>
   222   inline int countArcs(const Graph& g) {
   223     return _core_bits::CountArcsSelector<Graph>::count(g);
   224   }
   225 
   226   // Edge counting:
   227 
   228   namespace _core_bits {
   229 
   230     template <typename Graph, typename Enable = void>
   231     struct CountEdgesSelector {
   232       static int count(const Graph &g) {
   233         return countItems<Graph, typename Graph::Edge>(g);
   234       }
   235     };
   236 
   237     template <typename Graph>
   238     struct CountEdgesSelector<
   239       Graph,
   240       typename enable_if<typename Graph::EdgeNumTag, void>::type>
   241     {
   242       static int count(const Graph &g) {
   243         return g.edgeNum();
   244       }
   245     };
   246   }
   247 
   248   /// \brief Function to count the edges in the graph.
   249   ///
   250   /// This function counts the edges in the graph.
   251   /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
   252   /// graph structures it is specialized to run in <em>O</em>(1).
   253   ///
   254   /// \note If the graph contains a \c edgeNum() member function and a
   255   /// \c EdgeNumTag tag then this function calls directly the member
   256   /// function to query the cardinality of the edge set.
   257   template <typename Graph>
   258   inline int countEdges(const Graph& g) {
   259     return _core_bits::CountEdgesSelector<Graph>::count(g);
   260 
   261   }
   262 
   263 
   264   template <typename Graph, typename DegIt>
   265   inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {
   266     int num = 0;
   267     for (DegIt it(_g, _n); it != INVALID; ++it) {
   268       ++num;
   269     }
   270     return num;
   271   }
   272 
   273   /// \brief Function to count the number of the out-arcs from node \c n.
   274   ///
   275   /// This function counts the number of the out-arcs from node \c n
   276   /// in the graph \c g.
   277   template <typename Graph>
   278   inline int countOutArcs(const Graph& g,  const typename Graph::Node& n) {
   279     return countNodeDegree<Graph, typename Graph::OutArcIt>(g, n);
   280   }
   281 
   282   /// \brief Function to count the number of the in-arcs to node \c n.
   283   ///
   284   /// This function counts the number of the in-arcs to node \c n
   285   /// in the graph \c g.
   286   template <typename Graph>
   287   inline int countInArcs(const Graph& g,  const typename Graph::Node& n) {
   288     return countNodeDegree<Graph, typename Graph::InArcIt>(g, n);
   289   }
   290 
   291   /// \brief Function to count the number of the inc-edges to node \c n.
   292   ///
   293   /// This function counts the number of the inc-edges to node \c n
   294   /// in the undirected graph \c g.
   295   template <typename Graph>
   296   inline int countIncEdges(const Graph& g,  const typename Graph::Node& n) {
   297     return countNodeDegree<Graph, typename Graph::IncEdgeIt>(g, n);
   298   }
   299 
   300   namespace _core_bits {
   301 
   302     template <typename Digraph, typename Item, typename RefMap>
   303     class MapCopyBase {
   304     public:
   305       virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
   306 
   307       virtual ~MapCopyBase() {}
   308     };
   309 
   310     template <typename Digraph, typename Item, typename RefMap,
   311               typename FromMap, typename ToMap>
   312     class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
   313     public:
   314 
   315       MapCopy(const FromMap& map, ToMap& tmap)
   316         : _map(map), _tmap(tmap) {}
   317 
   318       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   319         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   320         for (ItemIt it(digraph); it != INVALID; ++it) {
   321           _tmap.set(refMap[it], _map[it]);
   322         }
   323       }
   324 
   325     private:
   326       const FromMap& _map;
   327       ToMap& _tmap;
   328     };
   329 
   330     template <typename Digraph, typename Item, typename RefMap, typename It>
   331     class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
   332     public:
   333 
   334       ItemCopy(const Item& item, It& it) : _item(item), _it(it) {}
   335 
   336       virtual void copy(const Digraph&, const RefMap& refMap) {
   337         _it = refMap[_item];
   338       }
   339 
   340     private:
   341       Item _item;
   342       It& _it;
   343     };
   344 
   345     template <typename Digraph, typename Item, typename RefMap, typename Ref>
   346     class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   347     public:
   348 
   349       RefCopy(Ref& map) : _map(map) {}
   350 
   351       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   352         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   353         for (ItemIt it(digraph); it != INVALID; ++it) {
   354           _map.set(it, refMap[it]);
   355         }
   356       }
   357 
   358     private:
   359       Ref& _map;
   360     };
   361 
   362     template <typename Digraph, typename Item, typename RefMap,
   363               typename CrossRef>
   364     class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   365     public:
   366 
   367       CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
   368 
   369       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   370         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   371         for (ItemIt it(digraph); it != INVALID; ++it) {
   372           _cmap.set(refMap[it], it);
   373         }
   374       }
   375 
   376     private:
   377       CrossRef& _cmap;
   378     };
   379 
   380     template <typename Digraph, typename Enable = void>
   381     struct DigraphCopySelector {
   382       template <typename From, typename NodeRefMap, typename ArcRefMap>
   383       static void copy(const From& from, Digraph &to,
   384                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   385         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   386           nodeRefMap[it] = to.addNode();
   387         }
   388         for (typename From::ArcIt it(from); it != INVALID; ++it) {
   389           arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)],
   390                                     nodeRefMap[from.target(it)]);
   391         }
   392       }
   393     };
   394 
   395     template <typename Digraph>
   396     struct DigraphCopySelector<
   397       Digraph,
   398       typename enable_if<typename Digraph::BuildTag, void>::type>
   399     {
   400       template <typename From, typename NodeRefMap, typename ArcRefMap>
   401       static void copy(const From& from, Digraph &to,
   402                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   403         to.build(from, nodeRefMap, arcRefMap);
   404       }
   405     };
   406 
   407     template <typename Graph, typename Enable = void>
   408     struct GraphCopySelector {
   409       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   410       static void copy(const From& from, Graph &to,
   411                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   412         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   413           nodeRefMap[it] = to.addNode();
   414         }
   415         for (typename From::EdgeIt it(from); it != INVALID; ++it) {
   416           edgeRefMap[it] = to.addEdge(nodeRefMap[from.u(it)],
   417                                       nodeRefMap[from.v(it)]);
   418         }
   419       }
   420     };
   421 
   422     template <typename Graph>
   423     struct GraphCopySelector<
   424       Graph,
   425       typename enable_if<typename Graph::BuildTag, void>::type>
   426     {
   427       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   428       static void copy(const From& from, Graph &to,
   429                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   430         to.build(from, nodeRefMap, edgeRefMap);
   431       }
   432     };
   433 
   434   }
   435 
   436   /// \brief Class to copy a digraph.
   437   ///
   438   /// Class to copy a digraph to another digraph (duplicate a digraph). The
   439   /// simplest way of using it is through the \c digraphCopy() function.
   440   ///
   441   /// This class not only make a copy of a digraph, but it can create
   442   /// references and cross references between the nodes and arcs of
   443   /// the two digraphs, and it can copy maps to use with the newly created
   444   /// digraph.
   445   ///
   446   /// To make a copy from a digraph, first an instance of DigraphCopy
   447   /// should be created, then the data belongs to the digraph should
   448   /// assigned to copy. In the end, the \c run() member should be
   449   /// called.
   450   ///
   451   /// The next code copies a digraph with several data:
   452   ///\code
   453   ///  DigraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
   454   ///  // Create references for the nodes
   455   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   456   ///  cg.nodeRef(nr);
   457   ///  // Create cross references (inverse) for the arcs
   458   ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);
   459   ///  cg.arcCrossRef(acr);
   460   ///  // Copy an arc map
   461   ///  OrigGraph::ArcMap<double> oamap(orig_graph);
   462   ///  NewGraph::ArcMap<double> namap(new_graph);
   463   ///  cg.arcMap(oamap, namap);
   464   ///  // Copy a node
   465   ///  OrigGraph::Node on;
   466   ///  NewGraph::Node nn;
   467   ///  cg.node(on, nn);
   468   ///  // Execute copying
   469   ///  cg.run();
   470   ///\endcode
   471   template <typename From, typename To>
   472   class DigraphCopy {
   473   private:
   474 
   475     typedef typename From::Node Node;
   476     typedef typename From::NodeIt NodeIt;
   477     typedef typename From::Arc Arc;
   478     typedef typename From::ArcIt ArcIt;
   479 
   480     typedef typename To::Node TNode;
   481     typedef typename To::Arc TArc;
   482 
   483     typedef typename From::template NodeMap<TNode> NodeRefMap;
   484     typedef typename From::template ArcMap<TArc> ArcRefMap;
   485 
   486   public:
   487 
   488     /// \brief Constructor of DigraphCopy.
   489     ///
   490     /// Constructor of DigraphCopy for copying the content of the
   491     /// \c from digraph into the \c to digraph.
   492     DigraphCopy(const From& from, To& to)
   493       : _from(from), _to(to) {}
   494 
   495     /// \brief Destructor of DigraphCopy
   496     ///
   497     /// Destructor of DigraphCopy.
   498     ~DigraphCopy() {
   499       for (int i = 0; i < int(_node_maps.size()); ++i) {
   500         delete _node_maps[i];
   501       }
   502       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   503         delete _arc_maps[i];
   504       }
   505 
   506     }
   507 
   508     /// \brief Copy the node references into the given map.
   509     ///
   510     /// This function copies the node references into the given map.
   511     /// The parameter should be a map, whose key type is the Node type of
   512     /// the source digraph, while the value type is the Node type of the
   513     /// destination digraph.
   514     template <typename NodeRef>
   515     DigraphCopy& nodeRef(NodeRef& map) {
   516       _node_maps.push_back(new _core_bits::RefCopy<From, Node,
   517                            NodeRefMap, NodeRef>(map));
   518       return *this;
   519     }
   520 
   521     /// \brief Copy the node cross references into the given map.
   522     ///
   523     /// This function copies the node cross references (reverse references)
   524     /// into the given map. The parameter should be a map, whose key type
   525     /// is the Node type of the destination digraph, while the value type is
   526     /// the Node type of the source digraph.
   527     template <typename NodeCrossRef>
   528     DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
   529       _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
   530                            NodeRefMap, NodeCrossRef>(map));
   531       return *this;
   532     }
   533 
   534     /// \brief Make a copy of the given node map.
   535     ///
   536     /// This function makes a copy of the given node map for the newly
   537     /// created digraph.
   538     /// The key type of the new map \c tmap should be the Node type of the
   539     /// destination digraph, and the key type of the original map \c map
   540     /// should be the Node type of the source digraph.
   541     template <typename FromMap, typename ToMap>
   542     DigraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
   543       _node_maps.push_back(new _core_bits::MapCopy<From, Node,
   544                            NodeRefMap, FromMap, ToMap>(map, tmap));
   545       return *this;
   546     }
   547 
   548     /// \brief Make a copy of the given node.
   549     ///
   550     /// This function makes a copy of the given node.
   551     DigraphCopy& node(const Node& node, TNode& tnode) {
   552       _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
   553                            NodeRefMap, TNode>(node, tnode));
   554       return *this;
   555     }
   556 
   557     /// \brief Copy the arc references into the given map.
   558     ///
   559     /// This function copies the arc references into the given map.
   560     /// The parameter should be a map, whose key type is the Arc type of
   561     /// the source digraph, while the value type is the Arc type of the
   562     /// destination digraph.
   563     template <typename ArcRef>
   564     DigraphCopy& arcRef(ArcRef& map) {
   565       _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
   566                           ArcRefMap, ArcRef>(map));
   567       return *this;
   568     }
   569 
   570     /// \brief Copy the arc cross references into the given map.
   571     ///
   572     /// This function copies the arc cross references (reverse references)
   573     /// into the given map. The parameter should be a map, whose key type
   574     /// is the Arc type of the destination digraph, while the value type is
   575     /// the Arc type of the source digraph.
   576     template <typename ArcCrossRef>
   577     DigraphCopy& arcCrossRef(ArcCrossRef& map) {
   578       _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
   579                           ArcRefMap, ArcCrossRef>(map));
   580       return *this;
   581     }
   582 
   583     /// \brief Make a copy of the given arc map.
   584     ///
   585     /// This function makes a copy of the given arc map for the newly
   586     /// created digraph.
   587     /// The key type of the new map \c tmap should be the Arc type of the
   588     /// destination digraph, and the key type of the original map \c map
   589     /// should be the Arc type of the source digraph.
   590     template <typename FromMap, typename ToMap>
   591     DigraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
   592       _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
   593                           ArcRefMap, FromMap, ToMap>(map, tmap));
   594       return *this;
   595     }
   596 
   597     /// \brief Make a copy of the given arc.
   598     ///
   599     /// This function makes a copy of the given arc.
   600     DigraphCopy& arc(const Arc& arc, TArc& tarc) {
   601       _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
   602                           ArcRefMap, TArc>(arc, tarc));
   603       return *this;
   604     }
   605 
   606     /// \brief Execute copying.
   607     ///
   608     /// This function executes the copying of the digraph along with the
   609     /// copying of the assigned data.
   610     void run() {
   611       NodeRefMap nodeRefMap(_from);
   612       ArcRefMap arcRefMap(_from);
   613       _core_bits::DigraphCopySelector<To>::
   614         copy(_from, _to, nodeRefMap, arcRefMap);
   615       for (int i = 0; i < int(_node_maps.size()); ++i) {
   616         _node_maps[i]->copy(_from, nodeRefMap);
   617       }
   618       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   619         _arc_maps[i]->copy(_from, arcRefMap);
   620       }
   621     }
   622 
   623   protected:
   624 
   625     const From& _from;
   626     To& _to;
   627 
   628     std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
   629       _node_maps;
   630 
   631     std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
   632       _arc_maps;
   633 
   634   };
   635 
   636   /// \brief Copy a digraph to another digraph.
   637   ///
   638   /// This function copies a digraph to another digraph.
   639   /// The complete usage of it is detailed in the DigraphCopy class, but
   640   /// a short example shows a basic work:
   641   ///\code
   642   /// digraphCopy(src, trg).nodeRef(nr).arcCrossRef(acr).run();
   643   ///\endcode
   644   ///
   645   /// After the copy the \c nr map will contain the mapping from the
   646   /// nodes of the \c from digraph to the nodes of the \c to digraph and
   647   /// \c acr will contain the mapping from the arcs of the \c to digraph
   648   /// to the arcs of the \c from digraph.
   649   ///
   650   /// \see DigraphCopy
   651   template <typename From, typename To>
   652   DigraphCopy<From, To> digraphCopy(const From& from, To& to) {
   653     return DigraphCopy<From, To>(from, to);
   654   }
   655 
   656   /// \brief Class to copy a graph.
   657   ///
   658   /// Class to copy a graph to another graph (duplicate a graph). The
   659   /// simplest way of using it is through the \c graphCopy() function.
   660   ///
   661   /// This class not only make a copy of a graph, but it can create
   662   /// references and cross references between the nodes, edges and arcs of
   663   /// the two graphs, and it can copy maps for using with the newly created
   664   /// graph.
   665   ///
   666   /// To make a copy from a graph, first an instance of GraphCopy
   667   /// should be created, then the data belongs to the graph should
   668   /// assigned to copy. In the end, the \c run() member should be
   669   /// called.
   670   ///
   671   /// The next code copies a graph with several data:
   672   ///\code
   673   ///  GraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
   674   ///  // Create references for the nodes
   675   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   676   ///  cg.nodeRef(nr);
   677   ///  // Create cross references (inverse) for the edges
   678   ///  NewGraph::EdgeMap<OrigGraph::Edge> ecr(new_graph);
   679   ///  cg.edgeCrossRef(ecr);
   680   ///  // Copy an edge map
   681   ///  OrigGraph::EdgeMap<double> oemap(orig_graph);
   682   ///  NewGraph::EdgeMap<double> nemap(new_graph);
   683   ///  cg.edgeMap(oemap, nemap);
   684   ///  // Copy a node
   685   ///  OrigGraph::Node on;
   686   ///  NewGraph::Node nn;
   687   ///  cg.node(on, nn);
   688   ///  // Execute copying
   689   ///  cg.run();
   690   ///\endcode
   691   template <typename From, typename To>
   692   class GraphCopy {
   693   private:
   694 
   695     typedef typename From::Node Node;
   696     typedef typename From::NodeIt NodeIt;
   697     typedef typename From::Arc Arc;
   698     typedef typename From::ArcIt ArcIt;
   699     typedef typename From::Edge Edge;
   700     typedef typename From::EdgeIt EdgeIt;
   701 
   702     typedef typename To::Node TNode;
   703     typedef typename To::Arc TArc;
   704     typedef typename To::Edge TEdge;
   705 
   706     typedef typename From::template NodeMap<TNode> NodeRefMap;
   707     typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
   708 
   709     struct ArcRefMap {
   710       ArcRefMap(const From& from, const To& to,
   711                 const EdgeRefMap& edge_ref, const NodeRefMap& node_ref)
   712         : _from(from), _to(to),
   713           _edge_ref(edge_ref), _node_ref(node_ref) {}
   714 
   715       typedef typename From::Arc Key;
   716       typedef typename To::Arc Value;
   717 
   718       Value operator[](const Key& key) const {
   719         bool forward = _from.u(key) != _from.v(key) ?
   720           _node_ref[_from.source(key)] ==
   721           _to.source(_to.direct(_edge_ref[key], true)) :
   722           _from.direction(key);
   723         return _to.direct(_edge_ref[key], forward);
   724       }
   725 
   726       const From& _from;
   727       const To& _to;
   728       const EdgeRefMap& _edge_ref;
   729       const NodeRefMap& _node_ref;
   730     };
   731 
   732   public:
   733 
   734     /// \brief Constructor of GraphCopy.
   735     ///
   736     /// Constructor of GraphCopy for copying the content of the
   737     /// \c from graph into the \c to graph.
   738     GraphCopy(const From& from, To& to)
   739       : _from(from), _to(to) {}
   740 
   741     /// \brief Destructor of GraphCopy
   742     ///
   743     /// Destructor of GraphCopy.
   744     ~GraphCopy() {
   745       for (int i = 0; i < int(_node_maps.size()); ++i) {
   746         delete _node_maps[i];
   747       }
   748       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   749         delete _arc_maps[i];
   750       }
   751       for (int i = 0; i < int(_edge_maps.size()); ++i) {
   752         delete _edge_maps[i];
   753       }
   754     }
   755 
   756     /// \brief Copy the node references into the given map.
   757     ///
   758     /// This function copies the node references into the given map.
   759     /// The parameter should be a map, whose key type is the Node type of
   760     /// the source graph, while the value type is the Node type of the
   761     /// destination graph.
   762     template <typename NodeRef>
   763     GraphCopy& nodeRef(NodeRef& map) {
   764       _node_maps.push_back(new _core_bits::RefCopy<From, Node,
   765                            NodeRefMap, NodeRef>(map));
   766       return *this;
   767     }
   768 
   769     /// \brief Copy the node cross references into the given map.
   770     ///
   771     /// This function copies the node cross references (reverse references)
   772     /// into the given map. The parameter should be a map, whose key type
   773     /// is the Node type of the destination graph, while the value type is
   774     /// the Node type of the source graph.
   775     template <typename NodeCrossRef>
   776     GraphCopy& nodeCrossRef(NodeCrossRef& map) {
   777       _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
   778                            NodeRefMap, NodeCrossRef>(map));
   779       return *this;
   780     }
   781 
   782     /// \brief Make a copy of the given node map.
   783     ///
   784     /// This function makes a copy of the given node map for the newly
   785     /// created graph.
   786     /// The key type of the new map \c tmap should be the Node type of the
   787     /// destination graph, and the key type of the original map \c map
   788     /// should be the Node type of the source graph.
   789     template <typename FromMap, typename ToMap>
   790     GraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
   791       _node_maps.push_back(new _core_bits::MapCopy<From, Node,
   792                            NodeRefMap, FromMap, ToMap>(map, tmap));
   793       return *this;
   794     }
   795 
   796     /// \brief Make a copy of the given node.
   797     ///
   798     /// This function makes a copy of the given node.
   799     GraphCopy& node(const Node& node, TNode& tnode) {
   800       _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
   801                            NodeRefMap, TNode>(node, tnode));
   802       return *this;
   803     }
   804 
   805     /// \brief Copy the arc references into the given map.
   806     ///
   807     /// This function copies the arc references into the given map.
   808     /// The parameter should be a map, whose key type is the Arc type of
   809     /// the source graph, while the value type is the Arc type of the
   810     /// destination graph.
   811     template <typename ArcRef>
   812     GraphCopy& arcRef(ArcRef& map) {
   813       _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
   814                           ArcRefMap, ArcRef>(map));
   815       return *this;
   816     }
   817 
   818     /// \brief Copy the arc cross references into the given map.
   819     ///
   820     /// This function copies the arc cross references (reverse references)
   821     /// into the given map. The parameter should be a map, whose key type
   822     /// is the Arc type of the destination graph, while the value type is
   823     /// the Arc type of the source graph.
   824     template <typename ArcCrossRef>
   825     GraphCopy& arcCrossRef(ArcCrossRef& map) {
   826       _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
   827                           ArcRefMap, ArcCrossRef>(map));
   828       return *this;
   829     }
   830 
   831     /// \brief Make a copy of the given arc map.
   832     ///
   833     /// This function makes a copy of the given arc map for the newly
   834     /// created graph.
   835     /// The key type of the new map \c tmap should be the Arc type of the
   836     /// destination graph, and the key type of the original map \c map
   837     /// should be the Arc type of the source graph.
   838     template <typename FromMap, typename ToMap>
   839     GraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
   840       _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
   841                           ArcRefMap, FromMap, ToMap>(map, tmap));
   842       return *this;
   843     }
   844 
   845     /// \brief Make a copy of the given arc.
   846     ///
   847     /// This function makes a copy of the given arc.
   848     GraphCopy& arc(const Arc& arc, TArc& tarc) {
   849       _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
   850                           ArcRefMap, TArc>(arc, tarc));
   851       return *this;
   852     }
   853 
   854     /// \brief Copy the edge references into the given map.
   855     ///
   856     /// This function copies the edge references into the given map.
   857     /// The parameter should be a map, whose key type is the Edge type of
   858     /// the source graph, while the value type is the Edge type of the
   859     /// destination graph.
   860     template <typename EdgeRef>
   861     GraphCopy& edgeRef(EdgeRef& map) {
   862       _edge_maps.push_back(new _core_bits::RefCopy<From, Edge,
   863                            EdgeRefMap, EdgeRef>(map));
   864       return *this;
   865     }
   866 
   867     /// \brief Copy the edge cross references into the given map.
   868     ///
   869     /// This function copies the edge cross references (reverse references)
   870     /// into the given map. The parameter should be a map, whose key type
   871     /// is the Edge type of the destination graph, while the value type is
   872     /// the Edge type of the source graph.
   873     template <typename EdgeCrossRef>
   874     GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
   875       _edge_maps.push_back(new _core_bits::CrossRefCopy<From,
   876                            Edge, EdgeRefMap, EdgeCrossRef>(map));
   877       return *this;
   878     }
   879 
   880     /// \brief Make a copy of the given edge map.
   881     ///
   882     /// This function makes a copy of the given edge map for the newly
   883     /// created graph.
   884     /// The key type of the new map \c tmap should be the Edge type of the
   885     /// destination graph, and the key type of the original map \c map
   886     /// should be the Edge type of the source graph.
   887     template <typename FromMap, typename ToMap>
   888     GraphCopy& edgeMap(const FromMap& map, ToMap& tmap) {
   889       _edge_maps.push_back(new _core_bits::MapCopy<From, Edge,
   890                            EdgeRefMap, FromMap, ToMap>(map, tmap));
   891       return *this;
   892     }
   893 
   894     /// \brief Make a copy of the given edge.
   895     ///
   896     /// This function makes a copy of the given edge.
   897     GraphCopy& edge(const Edge& edge, TEdge& tedge) {
   898       _edge_maps.push_back(new _core_bits::ItemCopy<From, Edge,
   899                            EdgeRefMap, TEdge>(edge, tedge));
   900       return *this;
   901     }
   902 
   903     /// \brief Execute copying.
   904     ///
   905     /// This function executes the copying of the graph along with the
   906     /// copying of the assigned data.
   907     void run() {
   908       NodeRefMap nodeRefMap(_from);
   909       EdgeRefMap edgeRefMap(_from);
   910       ArcRefMap arcRefMap(_from, _to, edgeRefMap, nodeRefMap);
   911       _core_bits::GraphCopySelector<To>::
   912         copy(_from, _to, nodeRefMap, edgeRefMap);
   913       for (int i = 0; i < int(_node_maps.size()); ++i) {
   914         _node_maps[i]->copy(_from, nodeRefMap);
   915       }
   916       for (int i = 0; i < int(_edge_maps.size()); ++i) {
   917         _edge_maps[i]->copy(_from, edgeRefMap);
   918       }
   919       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   920         _arc_maps[i]->copy(_from, arcRefMap);
   921       }
   922     }
   923 
   924   private:
   925 
   926     const From& _from;
   927     To& _to;
   928 
   929     std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
   930       _node_maps;
   931 
   932     std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
   933       _arc_maps;
   934 
   935     std::vector<_core_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
   936       _edge_maps;
   937 
   938   };
   939 
   940   /// \brief Copy a graph to another graph.
   941   ///
   942   /// This function copies a graph to another graph.
   943   /// The complete usage of it is detailed in the GraphCopy class,
   944   /// but a short example shows a basic work:
   945   ///\code
   946   /// graphCopy(src, trg).nodeRef(nr).edgeCrossRef(ecr).run();
   947   ///\endcode
   948   ///
   949   /// After the copy the \c nr map will contain the mapping from the
   950   /// nodes of the \c from graph to the nodes of the \c to graph and
   951   /// \c ecr will contain the mapping from the edges of the \c to graph
   952   /// to the edges of the \c from graph.
   953   ///
   954   /// \see GraphCopy
   955   template <typename From, typename To>
   956   GraphCopy<From, To>
   957   graphCopy(const From& from, To& to) {
   958     return GraphCopy<From, To>(from, to);
   959   }
   960 
   961   namespace _core_bits {
   962 
   963     template <typename Graph, typename Enable = void>
   964     struct FindArcSelector {
   965       typedef typename Graph::Node Node;
   966       typedef typename Graph::Arc Arc;
   967       static Arc find(const Graph &g, Node u, Node v, Arc e) {
   968         if (e == INVALID) {
   969           g.firstOut(e, u);
   970         } else {
   971           g.nextOut(e);
   972         }
   973         while (e != INVALID && g.target(e) != v) {
   974           g.nextOut(e);
   975         }
   976         return e;
   977       }
   978     };
   979 
   980     template <typename Graph>
   981     struct FindArcSelector<
   982       Graph,
   983       typename enable_if<typename Graph::FindArcTag, void>::type>
   984     {
   985       typedef typename Graph::Node Node;
   986       typedef typename Graph::Arc Arc;
   987       static Arc find(const Graph &g, Node u, Node v, Arc prev) {
   988         return g.findArc(u, v, prev);
   989       }
   990     };
   991   }
   992 
   993   /// \brief Find an arc between two nodes of a digraph.
   994   ///
   995   /// This function finds an arc from node \c u to node \c v in the
   996   /// digraph \c g.
   997   ///
   998   /// If \c prev is \ref INVALID (this is the default value), then
   999   /// it finds the first arc from \c u to \c v. Otherwise it looks for
  1000   /// the next arc from \c u to \c v after \c prev.
  1001   /// \return The found arc or \ref INVALID if there is no such an arc.
  1002   ///
  1003   /// Thus you can iterate through each arc from \c u to \c v as it follows.
  1004   ///\code
  1005   /// for(Arc e = findArc(g,u,v); e != INVALID; e = findArc(g,u,v,e)) {
  1006   ///   ...
  1007   /// }
  1008   ///\endcode
  1009   ///
  1010   /// \note \ref ConArcIt provides iterator interface for the same
  1011   /// functionality.
  1012   ///
  1013   ///\sa ConArcIt
  1014   ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
  1015   template <typename Graph>
  1016   inline typename Graph::Arc
  1017   findArc(const Graph &g, typename Graph::Node u, typename Graph::Node v,
  1018           typename Graph::Arc prev = INVALID) {
  1019     return _core_bits::FindArcSelector<Graph>::find(g, u, v, prev);
  1020   }
  1021 
  1022   /// \brief Iterator for iterating on parallel arcs connecting the same nodes.
  1023   ///
  1024   /// Iterator for iterating on parallel arcs connecting the same nodes. It is
  1025   /// a higher level interface for the \ref findArc() function. You can
  1026   /// use it the following way:
  1027   ///\code
  1028   /// for (ConArcIt<Graph> it(g, src, trg); it != INVALID; ++it) {
  1029   ///   ...
  1030   /// }
  1031   ///\endcode
  1032   ///
  1033   ///\sa findArc()
  1034   ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
  1035   template <typename _Graph>
  1036   class ConArcIt : public _Graph::Arc {
  1037   public:
  1038 
  1039     typedef _Graph Graph;
  1040     typedef typename Graph::Arc Parent;
  1041 
  1042     typedef typename Graph::Arc Arc;
  1043     typedef typename Graph::Node Node;
  1044 
  1045     /// \brief Constructor.
  1046     ///
  1047     /// Construct a new ConArcIt iterating on the arcs that
  1048     /// connects nodes \c u and \c v.
  1049     ConArcIt(const Graph& g, Node u, Node v) : _graph(g) {
  1050       Parent::operator=(findArc(_graph, u, v));
  1051     }
  1052 
  1053     /// \brief Constructor.
  1054     ///
  1055     /// Construct a new ConArcIt that continues the iterating from arc \c a.
  1056     ConArcIt(const Graph& g, Arc a) : Parent(a), _graph(g) {}
  1057 
  1058     /// \brief Increment operator.
  1059     ///
  1060     /// It increments the iterator and gives back the next arc.
  1061     ConArcIt& operator++() {
  1062       Parent::operator=(findArc(_graph, _graph.source(*this),
  1063                                 _graph.target(*this), *this));
  1064       return *this;
  1065     }
  1066   private:
  1067     const Graph& _graph;
  1068   };
  1069 
  1070   namespace _core_bits {
  1071 
  1072     template <typename Graph, typename Enable = void>
  1073     struct FindEdgeSelector {
  1074       typedef typename Graph::Node Node;
  1075       typedef typename Graph::Edge Edge;
  1076       static Edge find(const Graph &g, Node u, Node v, Edge e) {
  1077         bool b;
  1078         if (u != v) {
  1079           if (e == INVALID) {
  1080             g.firstInc(e, b, u);
  1081           } else {
  1082             b = g.u(e) == u;
  1083             g.nextInc(e, b);
  1084           }
  1085           while (e != INVALID && (b ? g.v(e) : g.u(e)) != v) {
  1086             g.nextInc(e, b);
  1087           }
  1088         } else {
  1089           if (e == INVALID) {
  1090             g.firstInc(e, b, u);
  1091           } else {
  1092             b = true;
  1093             g.nextInc(e, b);
  1094           }
  1095           while (e != INVALID && (!b || g.v(e) != v)) {
  1096             g.nextInc(e, b);
  1097           }
  1098         }
  1099         return e;
  1100       }
  1101     };
  1102 
  1103     template <typename Graph>
  1104     struct FindEdgeSelector<
  1105       Graph,
  1106       typename enable_if<typename Graph::FindEdgeTag, void>::type>
  1107     {
  1108       typedef typename Graph::Node Node;
  1109       typedef typename Graph::Edge Edge;
  1110       static Edge find(const Graph &g, Node u, Node v, Edge prev) {
  1111         return g.findEdge(u, v, prev);
  1112       }
  1113     };
  1114   }
  1115 
  1116   /// \brief Find an edge between two nodes of a graph.
  1117   ///
  1118   /// This function finds an edge from node \c u to node \c v in graph \c g.
  1119   /// If node \c u and node \c v is equal then each loop edge
  1120   /// will be enumerated once.
  1121   ///
  1122   /// If \c prev is \ref INVALID (this is the default value), then
  1123   /// it finds the first edge from \c u to \c v. Otherwise it looks for
  1124   /// the next edge from \c u to \c v after \c prev.
  1125   /// \return The found edge or \ref INVALID if there is no such an edge.
  1126   ///
  1127   /// Thus you can iterate through each edge between \c u and \c v
  1128   /// as it follows.
  1129   ///\code
  1130   /// for(Edge e = findEdge(g,u,v); e != INVALID; e = findEdge(g,u,v,e)) {
  1131   ///   ...
  1132   /// }
  1133   ///\endcode
  1134   ///
  1135   /// \note \ref ConEdgeIt provides iterator interface for the same
  1136   /// functionality.
  1137   ///
  1138   ///\sa ConEdgeIt
  1139   template <typename Graph>
  1140   inline typename Graph::Edge
  1141   findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,
  1142             typename Graph::Edge p = INVALID) {
  1143     return _core_bits::FindEdgeSelector<Graph>::find(g, u, v, p);
  1144   }
  1145 
  1146   /// \brief Iterator for iterating on parallel edges connecting the same nodes.
  1147   ///
  1148   /// Iterator for iterating on parallel edges connecting the same nodes.
  1149   /// It is a higher level interface for the findEdge() function. You can
  1150   /// use it the following way:
  1151   ///\code
  1152   /// for (ConEdgeIt<Graph> it(g, u, v); it != INVALID; ++it) {
  1153   ///   ...
  1154   /// }
  1155   ///\endcode
  1156   ///
  1157   ///\sa findEdge()
  1158   template <typename _Graph>
  1159   class ConEdgeIt : public _Graph::Edge {
  1160   public:
  1161 
  1162     typedef _Graph Graph;
  1163     typedef typename Graph::Edge Parent;
  1164 
  1165     typedef typename Graph::Edge Edge;
  1166     typedef typename Graph::Node Node;
  1167 
  1168     /// \brief Constructor.
  1169     ///
  1170     /// Construct a new ConEdgeIt iterating on the edges that
  1171     /// connects nodes \c u and \c v.
  1172     ConEdgeIt(const Graph& g, Node u, Node v) : _graph(g) {
  1173       Parent::operator=(findEdge(_graph, u, v));
  1174     }
  1175 
  1176     /// \brief Constructor.
  1177     ///
  1178     /// Construct a new ConEdgeIt that continues iterating from edge \c e.
  1179     ConEdgeIt(const Graph& g, Edge e) : Parent(e), _graph(g) {}
  1180 
  1181     /// \brief Increment operator.
  1182     ///
  1183     /// It increments the iterator and gives back the next edge.
  1184     ConEdgeIt& operator++() {
  1185       Parent::operator=(findEdge(_graph, _graph.u(*this),
  1186                                  _graph.v(*this), *this));
  1187       return *this;
  1188     }
  1189   private:
  1190     const Graph& _graph;
  1191   };
  1192 
  1193 
  1194   ///Dynamic arc look-up between given endpoints.
  1195 
  1196   ///Using this class, you can find an arc in a digraph from a given
  1197   ///source to a given target in amortized time <em>O</em>(log<em>d</em>),
  1198   ///where <em>d</em> is the out-degree of the source node.
  1199   ///
  1200   ///It is possible to find \e all parallel arcs between two nodes with
  1201   ///the \c operator() member.
  1202   ///
  1203   ///This is a dynamic data structure. Consider to use \ref ArcLookUp or
  1204   ///\ref AllArcLookUp if your digraph is not changed so frequently.
  1205   ///
  1206   ///This class uses a self-adjusting binary search tree, the Splay tree
  1207   ///of Sleator and Tarjan to guarantee the logarithmic amortized
  1208   ///time bound for arc look-ups. This class also guarantees the
  1209   ///optimal time bound in a constant factor for any distribution of
  1210   ///queries.
  1211   ///
  1212   ///\tparam G The type of the underlying digraph.
  1213   ///
  1214   ///\sa ArcLookUp
  1215   ///\sa AllArcLookUp
  1216   template<class G>
  1217   class DynArcLookUp
  1218     : protected ItemSetTraits<G, typename G::Arc>::ItemNotifier::ObserverBase
  1219   {
  1220   public:
  1221     typedef typename ItemSetTraits<G, typename G::Arc>
  1222     ::ItemNotifier::ObserverBase Parent;
  1223 
  1224     TEMPLATE_DIGRAPH_TYPEDEFS(G);
  1225     typedef G Digraph;
  1226 
  1227   protected:
  1228 
  1229     class AutoNodeMap : public ItemSetTraits<G, Node>::template Map<Arc>::Type {
  1230     public:
  1231 
  1232       typedef typename ItemSetTraits<G, Node>::template Map<Arc>::Type Parent;
  1233 
  1234       AutoNodeMap(const G& digraph) : Parent(digraph, INVALID) {}
  1235 
  1236       virtual void add(const Node& node) {
  1237         Parent::add(node);
  1238         Parent::set(node, INVALID);
  1239       }
  1240 
  1241       virtual void add(const std::vector<Node>& nodes) {
  1242         Parent::add(nodes);
  1243         for (int i = 0; i < int(nodes.size()); ++i) {
  1244           Parent::set(nodes[i], INVALID);
  1245         }
  1246       }
  1247 
  1248       virtual void build() {
  1249         Parent::build();
  1250         Node it;
  1251         typename Parent::Notifier* nf = Parent::notifier();
  1252         for (nf->first(it); it != INVALID; nf->next(it)) {
  1253           Parent::set(it, INVALID);
  1254         }
  1255       }
  1256     };
  1257 
  1258     const Digraph &_g;
  1259     AutoNodeMap _head;
  1260     typename Digraph::template ArcMap<Arc> _parent;
  1261     typename Digraph::template ArcMap<Arc> _left;
  1262     typename Digraph::template ArcMap<Arc> _right;
  1263 
  1264     class ArcLess {
  1265       const Digraph &g;
  1266     public:
  1267       ArcLess(const Digraph &_g) : g(_g) {}
  1268       bool operator()(Arc a,Arc b) const
  1269       {
  1270         return g.target(a)<g.target(b);
  1271       }
  1272     };
  1273 
  1274   public:
  1275 
  1276     ///Constructor
  1277 
  1278     ///Constructor.
  1279     ///
  1280     ///It builds up the search database.
  1281     DynArcLookUp(const Digraph &g)
  1282       : _g(g),_head(g),_parent(g),_left(g),_right(g)
  1283     {
  1284       Parent::attach(_g.notifier(typename Digraph::Arc()));
  1285       refresh();
  1286     }
  1287 
  1288   protected:
  1289 
  1290     virtual void add(const Arc& arc) {
  1291       insert(arc);
  1292     }
  1293 
  1294     virtual void add(const std::vector<Arc>& arcs) {
  1295       for (int i = 0; i < int(arcs.size()); ++i) {
  1296         insert(arcs[i]);
  1297       }
  1298     }
  1299 
  1300     virtual void erase(const Arc& arc) {
  1301       remove(arc);
  1302     }
  1303 
  1304     virtual void erase(const std::vector<Arc>& arcs) {
  1305       for (int i = 0; i < int(arcs.size()); ++i) {
  1306         remove(arcs[i]);
  1307       }
  1308     }
  1309 
  1310     virtual void build() {
  1311       refresh();
  1312     }
  1313 
  1314     virtual void clear() {
  1315       for(NodeIt n(_g);n!=INVALID;++n) {
  1316         _head.set(n, INVALID);
  1317       }
  1318     }
  1319 
  1320     void insert(Arc arc) {
  1321       Node s = _g.source(arc);
  1322       Node t = _g.target(arc);
  1323       _left.set(arc, INVALID);
  1324       _right.set(arc, INVALID);
  1325 
  1326       Arc e = _head[s];
  1327       if (e == INVALID) {
  1328         _head.set(s, arc);
  1329         _parent.set(arc, INVALID);
  1330         return;
  1331       }
  1332       while (true) {
  1333         if (t < _g.target(e)) {
  1334           if (_left[e] == INVALID) {
  1335             _left.set(e, arc);
  1336             _parent.set(arc, e);
  1337             splay(arc);
  1338             return;
  1339           } else {
  1340             e = _left[e];
  1341           }
  1342         } else {
  1343           if (_right[e] == INVALID) {
  1344             _right.set(e, arc);
  1345             _parent.set(arc, e);
  1346             splay(arc);
  1347             return;
  1348           } else {
  1349             e = _right[e];
  1350           }
  1351         }
  1352       }
  1353     }
  1354 
  1355     void remove(Arc arc) {
  1356       if (_left[arc] == INVALID) {
  1357         if (_right[arc] != INVALID) {
  1358           _parent.set(_right[arc], _parent[arc]);
  1359         }
  1360         if (_parent[arc] != INVALID) {
  1361           if (_left[_parent[arc]] == arc) {
  1362             _left.set(_parent[arc], _right[arc]);
  1363           } else {
  1364             _right.set(_parent[arc], _right[arc]);
  1365           }
  1366         } else {
  1367           _head.set(_g.source(arc), _right[arc]);
  1368         }
  1369       } else if (_right[arc] == INVALID) {
  1370         _parent.set(_left[arc], _parent[arc]);
  1371         if (_parent[arc] != INVALID) {
  1372           if (_left[_parent[arc]] == arc) {
  1373             _left.set(_parent[arc], _left[arc]);
  1374           } else {
  1375             _right.set(_parent[arc], _left[arc]);
  1376           }
  1377         } else {
  1378           _head.set(_g.source(arc), _left[arc]);
  1379         }
  1380       } else {
  1381         Arc e = _left[arc];
  1382         if (_right[e] != INVALID) {
  1383           e = _right[e];
  1384           while (_right[e] != INVALID) {
  1385             e = _right[e];
  1386           }
  1387           Arc s = _parent[e];
  1388           _right.set(_parent[e], _left[e]);
  1389           if (_left[e] != INVALID) {
  1390             _parent.set(_left[e], _parent[e]);
  1391           }
  1392 
  1393           _left.set(e, _left[arc]);
  1394           _parent.set(_left[arc], e);
  1395           _right.set(e, _right[arc]);
  1396           _parent.set(_right[arc], e);
  1397 
  1398           _parent.set(e, _parent[arc]);
  1399           if (_parent[arc] != INVALID) {
  1400             if (_left[_parent[arc]] == arc) {
  1401               _left.set(_parent[arc], e);
  1402             } else {
  1403               _right.set(_parent[arc], e);
  1404             }
  1405           }
  1406           splay(s);
  1407         } else {
  1408           _right.set(e, _right[arc]);
  1409           _parent.set(_right[arc], e);
  1410           _parent.set(e, _parent[arc]);
  1411 
  1412           if (_parent[arc] != INVALID) {
  1413             if (_left[_parent[arc]] == arc) {
  1414               _left.set(_parent[arc], e);
  1415             } else {
  1416               _right.set(_parent[arc], e);
  1417             }
  1418           } else {
  1419             _head.set(_g.source(arc), e);
  1420           }
  1421         }
  1422       }
  1423     }
  1424 
  1425     Arc refreshRec(std::vector<Arc> &v,int a,int b)
  1426     {
  1427       int m=(a+b)/2;
  1428       Arc me=v[m];
  1429       if (a < m) {
  1430         Arc left = refreshRec(v,a,m-1);
  1431         _left.set(me, left);
  1432         _parent.set(left, me);
  1433       } else {
  1434         _left.set(me, INVALID);
  1435       }
  1436       if (m < b) {
  1437         Arc right = refreshRec(v,m+1,b);
  1438         _right.set(me, right);
  1439         _parent.set(right, me);
  1440       } else {
  1441         _right.set(me, INVALID);
  1442       }
  1443       return me;
  1444     }
  1445 
  1446     void refresh() {
  1447       for(NodeIt n(_g);n!=INVALID;++n) {
  1448         std::vector<Arc> v;
  1449         for(OutArcIt a(_g,n);a!=INVALID;++a) v.push_back(a);
  1450         if (!v.empty()) {
  1451           std::sort(v.begin(),v.end(),ArcLess(_g));
  1452           Arc head = refreshRec(v,0,v.size()-1);
  1453           _head.set(n, head);
  1454           _parent.set(head, INVALID);
  1455         }
  1456         else _head.set(n, INVALID);
  1457       }
  1458     }
  1459 
  1460     void zig(Arc v) {
  1461       Arc w = _parent[v];
  1462       _parent.set(v, _parent[w]);
  1463       _parent.set(w, v);
  1464       _left.set(w, _right[v]);
  1465       _right.set(v, w);
  1466       if (_parent[v] != INVALID) {
  1467         if (_right[_parent[v]] == w) {
  1468           _right.set(_parent[v], v);
  1469         } else {
  1470           _left.set(_parent[v], v);
  1471         }
  1472       }
  1473       if (_left[w] != INVALID){
  1474         _parent.set(_left[w], w);
  1475       }
  1476     }
  1477 
  1478     void zag(Arc v) {
  1479       Arc w = _parent[v];
  1480       _parent.set(v, _parent[w]);
  1481       _parent.set(w, v);
  1482       _right.set(w, _left[v]);
  1483       _left.set(v, w);
  1484       if (_parent[v] != INVALID){
  1485         if (_left[_parent[v]] == w) {
  1486           _left.set(_parent[v], v);
  1487         } else {
  1488           _right.set(_parent[v], v);
  1489         }
  1490       }
  1491       if (_right[w] != INVALID){
  1492         _parent.set(_right[w], w);
  1493       }
  1494     }
  1495 
  1496     void splay(Arc v) {
  1497       while (_parent[v] != INVALID) {
  1498         if (v == _left[_parent[v]]) {
  1499           if (_parent[_parent[v]] == INVALID) {
  1500             zig(v);
  1501           } else {
  1502             if (_parent[v] == _left[_parent[_parent[v]]]) {
  1503               zig(_parent[v]);
  1504               zig(v);
  1505             } else {
  1506               zig(v);
  1507               zag(v);
  1508             }
  1509           }
  1510         } else {
  1511           if (_parent[_parent[v]] == INVALID) {
  1512             zag(v);
  1513           } else {
  1514             if (_parent[v] == _left[_parent[_parent[v]]]) {
  1515               zag(v);
  1516               zig(v);
  1517             } else {
  1518               zag(_parent[v]);
  1519               zag(v);
  1520             }
  1521           }
  1522         }
  1523       }
  1524       _head[_g.source(v)] = v;
  1525     }
  1526 
  1527 
  1528   public:
  1529 
  1530     ///Find an arc between two nodes.
  1531 
  1532     ///Find an arc between two nodes.
  1533     ///\param s The source node.
  1534     ///\param t The target node.
  1535     ///\param p The previous arc between \c s and \c t. It it is INVALID or
  1536     ///not given, the operator finds the first appropriate arc.
  1537     ///\return An arc from \c s to \c t after \c p or
  1538     ///\ref INVALID if there is no more.
  1539     ///
  1540     ///For example, you can count the number of arcs from \c u to \c v in the
  1541     ///following way.
  1542     ///\code
  1543     ///DynArcLookUp<ListDigraph> ae(g);
  1544     ///...
  1545     ///int n = 0;
  1546     ///for(Arc a = ae(u,v); a != INVALID; a = ae(u,v,a)) n++;
  1547     ///\endcode
  1548     ///
  1549     ///Finding the arcs take at most <em>O</em>(log<em>d</em>)
  1550     ///amortized time, specifically, the time complexity of the lookups
  1551     ///is equal to the optimal search tree implementation for the
  1552     ///current query distribution in a constant factor.
  1553     ///
  1554     ///\note This is a dynamic data structure, therefore the data
  1555     ///structure is updated after each graph alteration. Thus although
  1556     ///this data structure is theoretically faster than \ref ArcLookUp
  1557     ///and \ref AllArcLookUp, it often provides worse performance than
  1558     ///them.
  1559     Arc operator()(Node s, Node t, Arc p = INVALID) const  {
  1560       if (p == INVALID) {
  1561         Arc a = _head[s];
  1562         if (a == INVALID) return INVALID;
  1563         Arc r = INVALID;
  1564         while (true) {
  1565           if (_g.target(a) < t) {
  1566             if (_right[a] == INVALID) {
  1567               const_cast<DynArcLookUp&>(*this).splay(a);
  1568               return r;
  1569             } else {
  1570               a = _right[a];
  1571             }
  1572           } else {
  1573             if (_g.target(a) == t) {
  1574               r = a;
  1575             }
  1576             if (_left[a] == INVALID) {
  1577               const_cast<DynArcLookUp&>(*this).splay(a);
  1578               return r;
  1579             } else {
  1580               a = _left[a];
  1581             }
  1582           }
  1583         }
  1584       } else {
  1585         Arc a = p;
  1586         if (_right[a] != INVALID) {
  1587           a = _right[a];
  1588           while (_left[a] != INVALID) {
  1589             a = _left[a];
  1590           }
  1591           const_cast<DynArcLookUp&>(*this).splay(a);
  1592         } else {
  1593           while (_parent[a] != INVALID && _right[_parent[a]] ==  a) {
  1594             a = _parent[a];
  1595           }
  1596           if (_parent[a] == INVALID) {
  1597             return INVALID;
  1598           } else {
  1599             a = _parent[a];
  1600             const_cast<DynArcLookUp&>(*this).splay(a);
  1601           }
  1602         }
  1603         if (_g.target(a) == t) return a;
  1604         else return INVALID;
  1605       }
  1606     }
  1607 
  1608   };
  1609 
  1610   ///Fast arc look-up between given endpoints.
  1611 
  1612   ///Using this class, you can find an arc in a digraph from a given
  1613   ///source to a given target in time <em>O</em>(log<em>d</em>),
  1614   ///where <em>d</em> is the out-degree of the source node.
  1615   ///
  1616   ///It is not possible to find \e all parallel arcs between two nodes.
  1617   ///Use \ref AllArcLookUp for this purpose.
  1618   ///
  1619   ///\warning This class is static, so you should call refresh() (or at
  1620   ///least refresh(Node)) to refresh this data structure whenever the
  1621   ///digraph changes. This is a time consuming (superlinearly proportional
  1622   ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
  1623   ///
  1624   ///\tparam G The type of the underlying digraph.
  1625   ///
  1626   ///\sa DynArcLookUp
  1627   ///\sa AllArcLookUp
  1628   template<class G>
  1629   class ArcLookUp
  1630   {
  1631   public:
  1632     TEMPLATE_DIGRAPH_TYPEDEFS(G);
  1633     typedef G Digraph;
  1634 
  1635   protected:
  1636     const Digraph &_g;
  1637     typename Digraph::template NodeMap<Arc> _head;
  1638     typename Digraph::template ArcMap<Arc> _left;
  1639     typename Digraph::template ArcMap<Arc> _right;
  1640 
  1641     class ArcLess {
  1642       const Digraph &g;
  1643     public:
  1644       ArcLess(const Digraph &_g) : g(_g) {}
  1645       bool operator()(Arc a,Arc b) const
  1646       {
  1647         return g.target(a)<g.target(b);
  1648       }
  1649     };
  1650 
  1651   public:
  1652 
  1653     ///Constructor
  1654 
  1655     ///Constructor.
  1656     ///
  1657     ///It builds up the search database, which remains valid until the digraph
  1658     ///changes.
  1659     ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}
  1660 
  1661   private:
  1662     Arc refreshRec(std::vector<Arc> &v,int a,int b)
  1663     {
  1664       int m=(a+b)/2;
  1665       Arc me=v[m];
  1666       _left[me] = a<m?refreshRec(v,a,m-1):INVALID;
  1667       _right[me] = m<b?refreshRec(v,m+1,b):INVALID;
  1668       return me;
  1669     }
  1670   public:
  1671     ///Refresh the search data structure at a node.
  1672 
  1673     ///Build up the search database of node \c n.
  1674     ///
  1675     ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em>
  1676     ///is the number of the outgoing arcs of \c n.
  1677     void refresh(Node n)
  1678     {
  1679       std::vector<Arc> v;
  1680       for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
  1681       if(v.size()) {
  1682         std::sort(v.begin(),v.end(),ArcLess(_g));
  1683         _head[n]=refreshRec(v,0,v.size()-1);
  1684       }
  1685       else _head[n]=INVALID;
  1686     }
  1687     ///Refresh the full data structure.
  1688 
  1689     ///Build up the full search database. In fact, it simply calls
  1690     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  1691     ///
  1692     ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
  1693     ///the number of the arcs in the digraph and <em>D</em> is the maximum
  1694     ///out-degree of the digraph.
  1695     void refresh()
  1696     {
  1697       for(NodeIt n(_g);n!=INVALID;++n) refresh(n);
  1698     }
  1699 
  1700     ///Find an arc between two nodes.
  1701 
  1702     ///Find an arc between two nodes in time <em>O</em>(log<em>d</em>),
  1703     ///where <em>d</em> is the number of outgoing arcs of \c s.
  1704     ///\param s The source node.
  1705     ///\param t The target node.
  1706     ///\return An arc from \c s to \c t if there exists,
  1707     ///\ref INVALID otherwise.
  1708     ///
  1709     ///\warning If you change the digraph, refresh() must be called before using
  1710     ///this operator. If you change the outgoing arcs of
  1711     ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
  1712     Arc operator()(Node s, Node t) const
  1713     {
  1714       Arc e;
  1715       for(e=_head[s];
  1716           e!=INVALID&&_g.target(e)!=t;
  1717           e = t < _g.target(e)?_left[e]:_right[e]) ;
  1718       return e;
  1719     }
  1720 
  1721   };
  1722 
  1723   ///Fast look-up of all arcs between given endpoints.
  1724 
  1725   ///This class is the same as \ref ArcLookUp, with the addition
  1726   ///that it makes it possible to find all parallel arcs between given
  1727   ///endpoints.
  1728   ///
  1729   ///\warning This class is static, so you should call refresh() (or at
  1730   ///least refresh(Node)) to refresh this data structure whenever the
  1731   ///digraph changes. This is a time consuming (superlinearly proportional
  1732   ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
  1733   ///
  1734   ///\tparam G The type of the underlying digraph.
  1735   ///
  1736   ///\sa DynArcLookUp
  1737   ///\sa ArcLookUp
  1738   template<class G>
  1739   class AllArcLookUp : public ArcLookUp<G>
  1740   {
  1741     using ArcLookUp<G>::_g;
  1742     using ArcLookUp<G>::_right;
  1743     using ArcLookUp<G>::_left;
  1744     using ArcLookUp<G>::_head;
  1745 
  1746     TEMPLATE_DIGRAPH_TYPEDEFS(G);
  1747     typedef G Digraph;
  1748 
  1749     typename Digraph::template ArcMap<Arc> _next;
  1750 
  1751     Arc refreshNext(Arc head,Arc next=INVALID)
  1752     {
  1753       if(head==INVALID) return next;
  1754       else {
  1755         next=refreshNext(_right[head],next);
  1756         _next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
  1757           ? next : INVALID;
  1758         return refreshNext(_left[head],head);
  1759       }
  1760     }
  1761 
  1762     void refreshNext()
  1763     {
  1764       for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
  1765     }
  1766 
  1767   public:
  1768     ///Constructor
  1769 
  1770     ///Constructor.
  1771     ///
  1772     ///It builds up the search database, which remains valid until the digraph
  1773     ///changes.
  1774     AllArcLookUp(const Digraph &g) : ArcLookUp<G>(g), _next(g) {refreshNext();}
  1775 
  1776     ///Refresh the data structure at a node.
  1777 
  1778     ///Build up the search database of node \c n.
  1779     ///
  1780     ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em> is
  1781     ///the number of the outgoing arcs of \c n.
  1782     void refresh(Node n)
  1783     {
  1784       ArcLookUp<G>::refresh(n);
  1785       refreshNext(_head[n]);
  1786     }
  1787 
  1788     ///Refresh the full data structure.
  1789 
  1790     ///Build up the full search database. In fact, it simply calls
  1791     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  1792     ///
  1793     ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
  1794     ///the number of the arcs in the digraph and <em>D</em> is the maximum
  1795     ///out-degree of the digraph.
  1796     void refresh()
  1797     {
  1798       for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
  1799     }
  1800 
  1801     ///Find an arc between two nodes.
  1802 
  1803     ///Find an arc between two nodes.
  1804     ///\param s The source node.
  1805     ///\param t The target node.
  1806     ///\param prev The previous arc between \c s and \c t. It it is INVALID or
  1807     ///not given, the operator finds the first appropriate arc.
  1808     ///\return An arc from \c s to \c t after \c prev or
  1809     ///\ref INVALID if there is no more.
  1810     ///
  1811     ///For example, you can count the number of arcs from \c u to \c v in the
  1812     ///following way.
  1813     ///\code
  1814     ///AllArcLookUp<ListDigraph> ae(g);
  1815     ///...
  1816     ///int n = 0;
  1817     ///for(Arc a = ae(u,v); a != INVALID; a=ae(u,v,a)) n++;
  1818     ///\endcode
  1819     ///
  1820     ///Finding the first arc take <em>O</em>(log<em>d</em>) time,
  1821     ///where <em>d</em> is the number of outgoing arcs of \c s. Then the
  1822     ///consecutive arcs are found in constant time.
  1823     ///
  1824     ///\warning If you change the digraph, refresh() must be called before using
  1825     ///this operator. If you change the outgoing arcs of
  1826     ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
  1827     ///
  1828 #ifdef DOXYGEN
  1829     Arc operator()(Node s, Node t, Arc prev=INVALID) const {}
  1830 #else
  1831     using ArcLookUp<G>::operator() ;
  1832     Arc operator()(Node s, Node t, Arc prev) const
  1833     {
  1834       return prev==INVALID?(*this)(s,t):_next[prev];
  1835     }
  1836 #endif
  1837 
  1838   };
  1839 
  1840   /// @}
  1841 
  1842 } //namespace lemon
  1843 
  1844 #endif