lemon/core.h
author Alpar Juttner <alpar@cs.elte.hu>
Mon, 12 Apr 2010 17:05:49 +0200
changeset 887 ca4059d63236
parent 877 141f9c0db4a3
child 893 d395358592df
permissions -rw-r--r--
Merge bugfix #366
     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) 2003-2010
     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/config.h>
    26 #include <lemon/bits/enable_if.h>
    27 #include <lemon/bits/traits.h>
    28 #include <lemon/assert.h>
    29 
    30 // Disable the following warnings when compiling with MSVC:
    31 // C4250: 'class1' : inherits 'class2::member' via dominance
    32 // C4355: 'this' : used in base member initializer list
    33 // C4503: 'function' : decorated name length exceeded, name was truncated
    34 // C4800: 'type' : forcing value to bool 'true' or 'false' (performance warning)
    35 // C4996: 'function': was declared deprecated
    36 #ifdef _MSC_VER
    37 #pragma warning( disable : 4250 4355 4503 4800 4996 )
    38 #endif
    39 
    40 ///\file
    41 ///\brief LEMON core utilities.
    42 ///
    43 ///This header file contains core utilities for LEMON.
    44 ///It is automatically included by all graph types, therefore it usually
    45 ///do not have to be included directly.
    46 
    47 namespace lemon {
    48 
    49   /// \brief Dummy type to make it easier to create invalid iterators.
    50   ///
    51   /// Dummy type to make it easier to create invalid iterators.
    52   /// See \ref INVALID for the usage.
    53   struct Invalid {
    54   public:
    55     bool operator==(Invalid) { return true;  }
    56     bool operator!=(Invalid) { return false; }
    57     bool operator< (Invalid) { return false; }
    58   };
    59 
    60   /// \brief Invalid iterators.
    61   ///
    62   /// \ref Invalid is a global type that converts to each iterator
    63   /// in such a way that the value of the target iterator will be invalid.
    64 #ifdef LEMON_ONLY_TEMPLATES
    65   const Invalid INVALID = Invalid();
    66 #else
    67   extern const Invalid INVALID;
    68 #endif
    69 
    70   /// \addtogroup gutils
    71   /// @{
    72 
    73   ///Create convenience typedefs for the digraph types and iterators
    74 
    75   ///This \c \#define creates convenient type definitions for the following
    76   ///types of \c Digraph: \c Node,  \c NodeIt, \c Arc, \c ArcIt, \c InArcIt,
    77   ///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap,
    78   ///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap.
    79   ///
    80   ///\note If the graph type is a dependent type, ie. the graph type depend
    81   ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
    82   ///macro.
    83 #define DIGRAPH_TYPEDEFS(Digraph)                                       \
    84   typedef Digraph::Node Node;                                           \
    85   typedef Digraph::NodeIt NodeIt;                                       \
    86   typedef Digraph::Arc Arc;                                             \
    87   typedef Digraph::ArcIt ArcIt;                                         \
    88   typedef Digraph::InArcIt InArcIt;                                     \
    89   typedef Digraph::OutArcIt OutArcIt;                                   \
    90   typedef Digraph::NodeMap<bool> BoolNodeMap;                           \
    91   typedef Digraph::NodeMap<int> IntNodeMap;                             \
    92   typedef Digraph::NodeMap<double> DoubleNodeMap;                       \
    93   typedef Digraph::ArcMap<bool> BoolArcMap;                             \
    94   typedef Digraph::ArcMap<int> IntArcMap;                               \
    95   typedef Digraph::ArcMap<double> DoubleArcMap
    96 
    97   ///Create convenience typedefs for the digraph types and iterators
    98 
    99   ///\see DIGRAPH_TYPEDEFS
   100   ///
   101   ///\note Use this macro, if the graph type is a dependent type,
   102   ///ie. the graph type depend on a template parameter.
   103 #define TEMPLATE_DIGRAPH_TYPEDEFS(Digraph)                              \
   104   typedef typename Digraph::Node Node;                                  \
   105   typedef typename Digraph::NodeIt NodeIt;                              \
   106   typedef typename Digraph::Arc Arc;                                    \
   107   typedef typename Digraph::ArcIt ArcIt;                                \
   108   typedef typename Digraph::InArcIt InArcIt;                            \
   109   typedef typename Digraph::OutArcIt OutArcIt;                          \
   110   typedef typename Digraph::template NodeMap<bool> BoolNodeMap;         \
   111   typedef typename Digraph::template NodeMap<int> IntNodeMap;           \
   112   typedef typename Digraph::template NodeMap<double> DoubleNodeMap;     \
   113   typedef typename Digraph::template ArcMap<bool> BoolArcMap;           \
   114   typedef typename Digraph::template ArcMap<int> IntArcMap;             \
   115   typedef typename Digraph::template ArcMap<double> DoubleArcMap
   116 
   117   ///Create convenience typedefs for the graph types and iterators
   118 
   119   ///This \c \#define creates the same convenient type definitions as defined
   120   ///by \ref DIGRAPH_TYPEDEFS(Graph) and six more, namely it creates
   121   ///\c Edge, \c EdgeIt, \c IncEdgeIt, \c BoolEdgeMap, \c IntEdgeMap,
   122   ///\c DoubleEdgeMap.
   123   ///
   124   ///\note If the graph type is a dependent type, ie. the graph type depend
   125   ///on a template parameter, then use \c TEMPLATE_GRAPH_TYPEDEFS()
   126   ///macro.
   127 #define GRAPH_TYPEDEFS(Graph)                                           \
   128   DIGRAPH_TYPEDEFS(Graph);                                              \
   129   typedef Graph::Edge Edge;                                             \
   130   typedef Graph::EdgeIt EdgeIt;                                         \
   131   typedef Graph::IncEdgeIt IncEdgeIt;                                   \
   132   typedef Graph::EdgeMap<bool> BoolEdgeMap;                             \
   133   typedef Graph::EdgeMap<int> IntEdgeMap;                               \
   134   typedef Graph::EdgeMap<double> DoubleEdgeMap
   135 
   136   ///Create convenience typedefs for the graph types and iterators
   137 
   138   ///\see GRAPH_TYPEDEFS
   139   ///
   140   ///\note Use this macro, if the graph type is a dependent type,
   141   ///ie. the graph type depend on a template parameter.
   142 #define TEMPLATE_GRAPH_TYPEDEFS(Graph)                                  \
   143   TEMPLATE_DIGRAPH_TYPEDEFS(Graph);                                     \
   144   typedef typename Graph::Edge Edge;                                    \
   145   typedef typename Graph::EdgeIt EdgeIt;                                \
   146   typedef typename Graph::IncEdgeIt IncEdgeIt;                          \
   147   typedef typename Graph::template EdgeMap<bool> BoolEdgeMap;           \
   148   typedef typename Graph::template EdgeMap<int> IntEdgeMap;             \
   149   typedef typename Graph::template EdgeMap<double> DoubleEdgeMap
   150 
   151   /// \brief Function to count the items in a graph.
   152   ///
   153   /// This function counts the items (nodes, arcs etc.) in a graph.
   154   /// The complexity of the function is linear because
   155   /// it iterates on all of the items.
   156   template <typename Graph, typename Item>
   157   inline int countItems(const Graph& g) {
   158     typedef typename ItemSetTraits<Graph, Item>::ItemIt ItemIt;
   159     int num = 0;
   160     for (ItemIt it(g); it != INVALID; ++it) {
   161       ++num;
   162     }
   163     return num;
   164   }
   165 
   166   // Node counting:
   167 
   168   namespace _core_bits {
   169 
   170     template <typename Graph, typename Enable = void>
   171     struct CountNodesSelector {
   172       static int count(const Graph &g) {
   173         return countItems<Graph, typename Graph::Node>(g);
   174       }
   175     };
   176 
   177     template <typename Graph>
   178     struct CountNodesSelector<
   179       Graph, typename
   180       enable_if<typename Graph::NodeNumTag, void>::type>
   181     {
   182       static int count(const Graph &g) {
   183         return g.nodeNum();
   184       }
   185     };
   186   }
   187 
   188   /// \brief Function to count the nodes in the graph.
   189   ///
   190   /// This function counts the nodes in the graph.
   191   /// The complexity of the function is <em>O</em>(<em>n</em>), but for some
   192   /// graph structures it is specialized to run in <em>O</em>(1).
   193   ///
   194   /// \note If the graph contains a \c nodeNum() member function and a
   195   /// \c NodeNumTag tag then this function calls directly the member
   196   /// function to query the cardinality of the node set.
   197   template <typename Graph>
   198   inline int countNodes(const Graph& g) {
   199     return _core_bits::CountNodesSelector<Graph>::count(g);
   200   }
   201 
   202   // Arc counting:
   203 
   204   namespace _core_bits {
   205 
   206     template <typename Graph, typename Enable = void>
   207     struct CountArcsSelector {
   208       static int count(const Graph &g) {
   209         return countItems<Graph, typename Graph::Arc>(g);
   210       }
   211     };
   212 
   213     template <typename Graph>
   214     struct CountArcsSelector<
   215       Graph,
   216       typename enable_if<typename Graph::ArcNumTag, void>::type>
   217     {
   218       static int count(const Graph &g) {
   219         return g.arcNum();
   220       }
   221     };
   222   }
   223 
   224   /// \brief Function to count the arcs in the graph.
   225   ///
   226   /// This function counts the arcs in the graph.
   227   /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
   228   /// graph structures it is specialized to run in <em>O</em>(1).
   229   ///
   230   /// \note If the graph contains a \c arcNum() member function and a
   231   /// \c ArcNumTag tag then this function calls directly the member
   232   /// function to query the cardinality of the arc set.
   233   template <typename Graph>
   234   inline int countArcs(const Graph& g) {
   235     return _core_bits::CountArcsSelector<Graph>::count(g);
   236   }
   237 
   238   // Edge counting:
   239 
   240   namespace _core_bits {
   241 
   242     template <typename Graph, typename Enable = void>
   243     struct CountEdgesSelector {
   244       static int count(const Graph &g) {
   245         return countItems<Graph, typename Graph::Edge>(g);
   246       }
   247     };
   248 
   249     template <typename Graph>
   250     struct CountEdgesSelector<
   251       Graph,
   252       typename enable_if<typename Graph::EdgeNumTag, void>::type>
   253     {
   254       static int count(const Graph &g) {
   255         return g.edgeNum();
   256       }
   257     };
   258   }
   259 
   260   /// \brief Function to count the edges in the graph.
   261   ///
   262   /// This function counts the edges in the graph.
   263   /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
   264   /// graph structures it is specialized to run in <em>O</em>(1).
   265   ///
   266   /// \note If the graph contains a \c edgeNum() member function and a
   267   /// \c EdgeNumTag tag then this function calls directly the member
   268   /// function to query the cardinality of the edge set.
   269   template <typename Graph>
   270   inline int countEdges(const Graph& g) {
   271     return _core_bits::CountEdgesSelector<Graph>::count(g);
   272 
   273   }
   274 
   275 
   276   template <typename Graph, typename DegIt>
   277   inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {
   278     int num = 0;
   279     for (DegIt it(_g, _n); it != INVALID; ++it) {
   280       ++num;
   281     }
   282     return num;
   283   }
   284 
   285   /// \brief Function to count the number of the out-arcs from node \c n.
   286   ///
   287   /// This function counts the number of the out-arcs from node \c n
   288   /// in the graph \c g.
   289   template <typename Graph>
   290   inline int countOutArcs(const Graph& g,  const typename Graph::Node& n) {
   291     return countNodeDegree<Graph, typename Graph::OutArcIt>(g, n);
   292   }
   293 
   294   /// \brief Function to count the number of the in-arcs to node \c n.
   295   ///
   296   /// This function counts the number of the in-arcs to node \c n
   297   /// in the graph \c g.
   298   template <typename Graph>
   299   inline int countInArcs(const Graph& g,  const typename Graph::Node& n) {
   300     return countNodeDegree<Graph, typename Graph::InArcIt>(g, n);
   301   }
   302 
   303   /// \brief Function to count the number of the inc-edges to node \c n.
   304   ///
   305   /// This function counts the number of the inc-edges to node \c n
   306   /// in the undirected graph \c g.
   307   template <typename Graph>
   308   inline int countIncEdges(const Graph& g,  const typename Graph::Node& n) {
   309     return countNodeDegree<Graph, typename Graph::IncEdgeIt>(g, n);
   310   }
   311 
   312   namespace _core_bits {
   313 
   314     template <typename Digraph, typename Item, typename RefMap>
   315     class MapCopyBase {
   316     public:
   317       virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
   318 
   319       virtual ~MapCopyBase() {}
   320     };
   321 
   322     template <typename Digraph, typename Item, typename RefMap,
   323               typename FromMap, typename ToMap>
   324     class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
   325     public:
   326 
   327       MapCopy(const FromMap& map, ToMap& tmap)
   328         : _map(map), _tmap(tmap) {}
   329 
   330       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   331         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   332         for (ItemIt it(digraph); it != INVALID; ++it) {
   333           _tmap.set(refMap[it], _map[it]);
   334         }
   335       }
   336 
   337     private:
   338       const FromMap& _map;
   339       ToMap& _tmap;
   340     };
   341 
   342     template <typename Digraph, typename Item, typename RefMap, typename It>
   343     class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
   344     public:
   345 
   346       ItemCopy(const Item& item, It& it) : _item(item), _it(it) {}
   347 
   348       virtual void copy(const Digraph&, const RefMap& refMap) {
   349         _it = refMap[_item];
   350       }
   351 
   352     private:
   353       Item _item;
   354       It& _it;
   355     };
   356 
   357     template <typename Digraph, typename Item, typename RefMap, typename Ref>
   358     class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   359     public:
   360 
   361       RefCopy(Ref& map) : _map(map) {}
   362 
   363       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   364         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   365         for (ItemIt it(digraph); it != INVALID; ++it) {
   366           _map.set(it, refMap[it]);
   367         }
   368       }
   369 
   370     private:
   371       Ref& _map;
   372     };
   373 
   374     template <typename Digraph, typename Item, typename RefMap,
   375               typename CrossRef>
   376     class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   377     public:
   378 
   379       CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
   380 
   381       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   382         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   383         for (ItemIt it(digraph); it != INVALID; ++it) {
   384           _cmap.set(refMap[it], it);
   385         }
   386       }
   387 
   388     private:
   389       CrossRef& _cmap;
   390     };
   391 
   392     template <typename Digraph, typename Enable = void>
   393     struct DigraphCopySelector {
   394       template <typename From, typename NodeRefMap, typename ArcRefMap>
   395       static void copy(const From& from, Digraph &to,
   396                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   397         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   398           nodeRefMap[it] = to.addNode();
   399         }
   400         for (typename From::ArcIt it(from); it != INVALID; ++it) {
   401           arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)],
   402                                     nodeRefMap[from.target(it)]);
   403         }
   404       }
   405     };
   406 
   407     template <typename Digraph>
   408     struct DigraphCopySelector<
   409       Digraph,
   410       typename enable_if<typename Digraph::BuildTag, void>::type>
   411     {
   412       template <typename From, typename NodeRefMap, typename ArcRefMap>
   413       static void copy(const From& from, Digraph &to,
   414                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   415         to.build(from, nodeRefMap, arcRefMap);
   416       }
   417     };
   418 
   419     template <typename Graph, typename Enable = void>
   420     struct GraphCopySelector {
   421       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   422       static void copy(const From& from, Graph &to,
   423                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   424         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   425           nodeRefMap[it] = to.addNode();
   426         }
   427         for (typename From::EdgeIt it(from); it != INVALID; ++it) {
   428           edgeRefMap[it] = to.addEdge(nodeRefMap[from.u(it)],
   429                                       nodeRefMap[from.v(it)]);
   430         }
   431       }
   432     };
   433 
   434     template <typename Graph>
   435     struct GraphCopySelector<
   436       Graph,
   437       typename enable_if<typename Graph::BuildTag, void>::type>
   438     {
   439       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   440       static void copy(const From& from, Graph &to,
   441                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   442         to.build(from, nodeRefMap, edgeRefMap);
   443       }
   444     };
   445 
   446   }
   447 
   448   /// Check whether a graph is undirected.
   449   ///
   450   /// This function returns \c true if the given graph is undirected.
   451 #ifdef DOXYGEN
   452   template <typename GR>
   453   bool undirected(const GR& g) { return false; }
   454 #else
   455   template <typename GR>
   456   typename enable_if<UndirectedTagIndicator<GR>, bool>::type
   457   undirected(const GR&) {
   458     return true;
   459   }
   460   template <typename GR>
   461   typename disable_if<UndirectedTagIndicator<GR>, bool>::type
   462   undirected(const GR&) {
   463     return false;
   464   }
   465 #endif
   466 
   467   /// \brief Class to copy a digraph.
   468   ///
   469   /// Class to copy a digraph to another digraph (duplicate a digraph). The
   470   /// simplest way of using it is through the \c digraphCopy() function.
   471   ///
   472   /// This class not only make a copy of a digraph, but it can create
   473   /// references and cross references between the nodes and arcs of
   474   /// the two digraphs, and it can copy maps to use with the newly created
   475   /// digraph.
   476   ///
   477   /// To make a copy from a digraph, first an instance of DigraphCopy
   478   /// should be created, then the data belongs to the digraph should
   479   /// assigned to copy. In the end, the \c run() member should be
   480   /// called.
   481   ///
   482   /// The next code copies a digraph with several data:
   483   ///\code
   484   ///  DigraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
   485   ///  // Create references for the nodes
   486   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   487   ///  cg.nodeRef(nr);
   488   ///  // Create cross references (inverse) for the arcs
   489   ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);
   490   ///  cg.arcCrossRef(acr);
   491   ///  // Copy an arc map
   492   ///  OrigGraph::ArcMap<double> oamap(orig_graph);
   493   ///  NewGraph::ArcMap<double> namap(new_graph);
   494   ///  cg.arcMap(oamap, namap);
   495   ///  // Copy a node
   496   ///  OrigGraph::Node on;
   497   ///  NewGraph::Node nn;
   498   ///  cg.node(on, nn);
   499   ///  // Execute copying
   500   ///  cg.run();
   501   ///\endcode
   502   template <typename From, typename To>
   503   class DigraphCopy {
   504   private:
   505 
   506     typedef typename From::Node Node;
   507     typedef typename From::NodeIt NodeIt;
   508     typedef typename From::Arc Arc;
   509     typedef typename From::ArcIt ArcIt;
   510 
   511     typedef typename To::Node TNode;
   512     typedef typename To::Arc TArc;
   513 
   514     typedef typename From::template NodeMap<TNode> NodeRefMap;
   515     typedef typename From::template ArcMap<TArc> ArcRefMap;
   516 
   517   public:
   518 
   519     /// \brief Constructor of DigraphCopy.
   520     ///
   521     /// Constructor of DigraphCopy for copying the content of the
   522     /// \c from digraph into the \c to digraph.
   523     DigraphCopy(const From& from, To& to)
   524       : _from(from), _to(to) {}
   525 
   526     /// \brief Destructor of DigraphCopy
   527     ///
   528     /// Destructor of DigraphCopy.
   529     ~DigraphCopy() {
   530       for (int i = 0; i < int(_node_maps.size()); ++i) {
   531         delete _node_maps[i];
   532       }
   533       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   534         delete _arc_maps[i];
   535       }
   536 
   537     }
   538 
   539     /// \brief Copy the node references into the given map.
   540     ///
   541     /// This function copies the node references into the given map.
   542     /// The parameter should be a map, whose key type is the Node type of
   543     /// the source digraph, while the value type is the Node type of the
   544     /// destination digraph.
   545     template <typename NodeRef>
   546     DigraphCopy& nodeRef(NodeRef& map) {
   547       _node_maps.push_back(new _core_bits::RefCopy<From, Node,
   548                            NodeRefMap, NodeRef>(map));
   549       return *this;
   550     }
   551 
   552     /// \brief Copy the node cross references into the given map.
   553     ///
   554     /// This function copies the node cross references (reverse references)
   555     /// into the given map. The parameter should be a map, whose key type
   556     /// is the Node type of the destination digraph, while the value type is
   557     /// the Node type of the source digraph.
   558     template <typename NodeCrossRef>
   559     DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
   560       _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
   561                            NodeRefMap, NodeCrossRef>(map));
   562       return *this;
   563     }
   564 
   565     /// \brief Make a copy of the given node map.
   566     ///
   567     /// This function makes a copy of the given node map for the newly
   568     /// created digraph.
   569     /// The key type of the new map \c tmap should be the Node type of the
   570     /// destination digraph, and the key type of the original map \c map
   571     /// should be the Node type of the source digraph.
   572     template <typename FromMap, typename ToMap>
   573     DigraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
   574       _node_maps.push_back(new _core_bits::MapCopy<From, Node,
   575                            NodeRefMap, FromMap, ToMap>(map, tmap));
   576       return *this;
   577     }
   578 
   579     /// \brief Make a copy of the given node.
   580     ///
   581     /// This function makes a copy of the given node.
   582     DigraphCopy& node(const Node& node, TNode& tnode) {
   583       _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
   584                            NodeRefMap, TNode>(node, tnode));
   585       return *this;
   586     }
   587 
   588     /// \brief Copy the arc references into the given map.
   589     ///
   590     /// This function copies the arc references into the given map.
   591     /// The parameter should be a map, whose key type is the Arc type of
   592     /// the source digraph, while the value type is the Arc type of the
   593     /// destination digraph.
   594     template <typename ArcRef>
   595     DigraphCopy& arcRef(ArcRef& map) {
   596       _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
   597                           ArcRefMap, ArcRef>(map));
   598       return *this;
   599     }
   600 
   601     /// \brief Copy the arc cross references into the given map.
   602     ///
   603     /// This function copies the arc cross references (reverse references)
   604     /// into the given map. The parameter should be a map, whose key type
   605     /// is the Arc type of the destination digraph, while the value type is
   606     /// the Arc type of the source digraph.
   607     template <typename ArcCrossRef>
   608     DigraphCopy& arcCrossRef(ArcCrossRef& map) {
   609       _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
   610                           ArcRefMap, ArcCrossRef>(map));
   611       return *this;
   612     }
   613 
   614     /// \brief Make a copy of the given arc map.
   615     ///
   616     /// This function makes a copy of the given arc map for the newly
   617     /// created digraph.
   618     /// The key type of the new map \c tmap should be the Arc type of the
   619     /// destination digraph, and the key type of the original map \c map
   620     /// should be the Arc type of the source digraph.
   621     template <typename FromMap, typename ToMap>
   622     DigraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
   623       _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
   624                           ArcRefMap, FromMap, ToMap>(map, tmap));
   625       return *this;
   626     }
   627 
   628     /// \brief Make a copy of the given arc.
   629     ///
   630     /// This function makes a copy of the given arc.
   631     DigraphCopy& arc(const Arc& arc, TArc& tarc) {
   632       _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
   633                           ArcRefMap, TArc>(arc, tarc));
   634       return *this;
   635     }
   636 
   637     /// \brief Execute copying.
   638     ///
   639     /// This function executes the copying of the digraph along with the
   640     /// copying of the assigned data.
   641     void run() {
   642       NodeRefMap nodeRefMap(_from);
   643       ArcRefMap arcRefMap(_from);
   644       _core_bits::DigraphCopySelector<To>::
   645         copy(_from, _to, nodeRefMap, arcRefMap);
   646       for (int i = 0; i < int(_node_maps.size()); ++i) {
   647         _node_maps[i]->copy(_from, nodeRefMap);
   648       }
   649       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   650         _arc_maps[i]->copy(_from, arcRefMap);
   651       }
   652     }
   653 
   654   protected:
   655 
   656     const From& _from;
   657     To& _to;
   658 
   659     std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
   660       _node_maps;
   661 
   662     std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
   663       _arc_maps;
   664 
   665   };
   666 
   667   /// \brief Copy a digraph to another digraph.
   668   ///
   669   /// This function copies a digraph to another digraph.
   670   /// The complete usage of it is detailed in the DigraphCopy class, but
   671   /// a short example shows a basic work:
   672   ///\code
   673   /// digraphCopy(src, trg).nodeRef(nr).arcCrossRef(acr).run();
   674   ///\endcode
   675   ///
   676   /// After the copy the \c nr map will contain the mapping from the
   677   /// nodes of the \c from digraph to the nodes of the \c to digraph and
   678   /// \c acr will contain the mapping from the arcs of the \c to digraph
   679   /// to the arcs of the \c from digraph.
   680   ///
   681   /// \see DigraphCopy
   682   template <typename From, typename To>
   683   DigraphCopy<From, To> digraphCopy(const From& from, To& to) {
   684     return DigraphCopy<From, To>(from, to);
   685   }
   686 
   687   /// \brief Class to copy a graph.
   688   ///
   689   /// Class to copy a graph to another graph (duplicate a graph). The
   690   /// simplest way of using it is through the \c graphCopy() function.
   691   ///
   692   /// This class not only make a copy of a graph, but it can create
   693   /// references and cross references between the nodes, edges and arcs of
   694   /// the two graphs, and it can copy maps for using with the newly created
   695   /// graph.
   696   ///
   697   /// To make a copy from a graph, first an instance of GraphCopy
   698   /// should be created, then the data belongs to the graph should
   699   /// assigned to copy. In the end, the \c run() member should be
   700   /// called.
   701   ///
   702   /// The next code copies a graph with several data:
   703   ///\code
   704   ///  GraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
   705   ///  // Create references for the nodes
   706   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   707   ///  cg.nodeRef(nr);
   708   ///  // Create cross references (inverse) for the edges
   709   ///  NewGraph::EdgeMap<OrigGraph::Edge> ecr(new_graph);
   710   ///  cg.edgeCrossRef(ecr);
   711   ///  // Copy an edge map
   712   ///  OrigGraph::EdgeMap<double> oemap(orig_graph);
   713   ///  NewGraph::EdgeMap<double> nemap(new_graph);
   714   ///  cg.edgeMap(oemap, nemap);
   715   ///  // Copy a node
   716   ///  OrigGraph::Node on;
   717   ///  NewGraph::Node nn;
   718   ///  cg.node(on, nn);
   719   ///  // Execute copying
   720   ///  cg.run();
   721   ///\endcode
   722   template <typename From, typename To>
   723   class GraphCopy {
   724   private:
   725 
   726     typedef typename From::Node Node;
   727     typedef typename From::NodeIt NodeIt;
   728     typedef typename From::Arc Arc;
   729     typedef typename From::ArcIt ArcIt;
   730     typedef typename From::Edge Edge;
   731     typedef typename From::EdgeIt EdgeIt;
   732 
   733     typedef typename To::Node TNode;
   734     typedef typename To::Arc TArc;
   735     typedef typename To::Edge TEdge;
   736 
   737     typedef typename From::template NodeMap<TNode> NodeRefMap;
   738     typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
   739 
   740     struct ArcRefMap {
   741       ArcRefMap(const From& from, const To& to,
   742                 const EdgeRefMap& edge_ref, const NodeRefMap& node_ref)
   743         : _from(from), _to(to),
   744           _edge_ref(edge_ref), _node_ref(node_ref) {}
   745 
   746       typedef typename From::Arc Key;
   747       typedef typename To::Arc Value;
   748 
   749       Value operator[](const Key& key) const {
   750         bool forward = _from.u(key) != _from.v(key) ?
   751           _node_ref[_from.source(key)] ==
   752           _to.source(_to.direct(_edge_ref[key], true)) :
   753           _from.direction(key);
   754         return _to.direct(_edge_ref[key], forward);
   755       }
   756 
   757       const From& _from;
   758       const To& _to;
   759       const EdgeRefMap& _edge_ref;
   760       const NodeRefMap& _node_ref;
   761     };
   762 
   763   public:
   764 
   765     /// \brief Constructor of GraphCopy.
   766     ///
   767     /// Constructor of GraphCopy for copying the content of the
   768     /// \c from graph into the \c to graph.
   769     GraphCopy(const From& from, To& to)
   770       : _from(from), _to(to) {}
   771 
   772     /// \brief Destructor of GraphCopy
   773     ///
   774     /// Destructor of GraphCopy.
   775     ~GraphCopy() {
   776       for (int i = 0; i < int(_node_maps.size()); ++i) {
   777         delete _node_maps[i];
   778       }
   779       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   780         delete _arc_maps[i];
   781       }
   782       for (int i = 0; i < int(_edge_maps.size()); ++i) {
   783         delete _edge_maps[i];
   784       }
   785     }
   786 
   787     /// \brief Copy the node references into the given map.
   788     ///
   789     /// This function copies the node references into the given map.
   790     /// The parameter should be a map, whose key type is the Node type of
   791     /// the source graph, while the value type is the Node type of the
   792     /// destination graph.
   793     template <typename NodeRef>
   794     GraphCopy& nodeRef(NodeRef& map) {
   795       _node_maps.push_back(new _core_bits::RefCopy<From, Node,
   796                            NodeRefMap, NodeRef>(map));
   797       return *this;
   798     }
   799 
   800     /// \brief Copy the node cross references into the given map.
   801     ///
   802     /// This function copies the node cross references (reverse references)
   803     /// into the given map. The parameter should be a map, whose key type
   804     /// is the Node type of the destination graph, while the value type is
   805     /// the Node type of the source graph.
   806     template <typename NodeCrossRef>
   807     GraphCopy& nodeCrossRef(NodeCrossRef& map) {
   808       _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
   809                            NodeRefMap, NodeCrossRef>(map));
   810       return *this;
   811     }
   812 
   813     /// \brief Make a copy of the given node map.
   814     ///
   815     /// This function makes a copy of the given node map for the newly
   816     /// created graph.
   817     /// The key type of the new map \c tmap should be the Node type of the
   818     /// destination graph, and the key type of the original map \c map
   819     /// should be the Node type of the source graph.
   820     template <typename FromMap, typename ToMap>
   821     GraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
   822       _node_maps.push_back(new _core_bits::MapCopy<From, Node,
   823                            NodeRefMap, FromMap, ToMap>(map, tmap));
   824       return *this;
   825     }
   826 
   827     /// \brief Make a copy of the given node.
   828     ///
   829     /// This function makes a copy of the given node.
   830     GraphCopy& node(const Node& node, TNode& tnode) {
   831       _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
   832                            NodeRefMap, TNode>(node, tnode));
   833       return *this;
   834     }
   835 
   836     /// \brief Copy the arc references into the given map.
   837     ///
   838     /// This function copies the arc references into the given map.
   839     /// The parameter should be a map, whose key type is the Arc type of
   840     /// the source graph, while the value type is the Arc type of the
   841     /// destination graph.
   842     template <typename ArcRef>
   843     GraphCopy& arcRef(ArcRef& map) {
   844       _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
   845                           ArcRefMap, ArcRef>(map));
   846       return *this;
   847     }
   848 
   849     /// \brief Copy the arc cross references into the given map.
   850     ///
   851     /// This function copies the arc cross references (reverse references)
   852     /// into the given map. The parameter should be a map, whose key type
   853     /// is the Arc type of the destination graph, while the value type is
   854     /// the Arc type of the source graph.
   855     template <typename ArcCrossRef>
   856     GraphCopy& arcCrossRef(ArcCrossRef& map) {
   857       _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
   858                           ArcRefMap, ArcCrossRef>(map));
   859       return *this;
   860     }
   861 
   862     /// \brief Make a copy of the given arc map.
   863     ///
   864     /// This function makes a copy of the given arc map for the newly
   865     /// created graph.
   866     /// The key type of the new map \c tmap should be the Arc type of the
   867     /// destination graph, and the key type of the original map \c map
   868     /// should be the Arc type of the source graph.
   869     template <typename FromMap, typename ToMap>
   870     GraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
   871       _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
   872                           ArcRefMap, FromMap, ToMap>(map, tmap));
   873       return *this;
   874     }
   875 
   876     /// \brief Make a copy of the given arc.
   877     ///
   878     /// This function makes a copy of the given arc.
   879     GraphCopy& arc(const Arc& arc, TArc& tarc) {
   880       _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
   881                           ArcRefMap, TArc>(arc, tarc));
   882       return *this;
   883     }
   884 
   885     /// \brief Copy the edge references into the given map.
   886     ///
   887     /// This function copies the edge references into the given map.
   888     /// The parameter should be a map, whose key type is the Edge type of
   889     /// the source graph, while the value type is the Edge type of the
   890     /// destination graph.
   891     template <typename EdgeRef>
   892     GraphCopy& edgeRef(EdgeRef& map) {
   893       _edge_maps.push_back(new _core_bits::RefCopy<From, Edge,
   894                            EdgeRefMap, EdgeRef>(map));
   895       return *this;
   896     }
   897 
   898     /// \brief Copy the edge cross references into the given map.
   899     ///
   900     /// This function copies the edge cross references (reverse references)
   901     /// into the given map. The parameter should be a map, whose key type
   902     /// is the Edge type of the destination graph, while the value type is
   903     /// the Edge type of the source graph.
   904     template <typename EdgeCrossRef>
   905     GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
   906       _edge_maps.push_back(new _core_bits::CrossRefCopy<From,
   907                            Edge, EdgeRefMap, EdgeCrossRef>(map));
   908       return *this;
   909     }
   910 
   911     /// \brief Make a copy of the given edge map.
   912     ///
   913     /// This function makes a copy of the given edge map for the newly
   914     /// created graph.
   915     /// The key type of the new map \c tmap should be the Edge type of the
   916     /// destination graph, and the key type of the original map \c map
   917     /// should be the Edge type of the source graph.
   918     template <typename FromMap, typename ToMap>
   919     GraphCopy& edgeMap(const FromMap& map, ToMap& tmap) {
   920       _edge_maps.push_back(new _core_bits::MapCopy<From, Edge,
   921                            EdgeRefMap, FromMap, ToMap>(map, tmap));
   922       return *this;
   923     }
   924 
   925     /// \brief Make a copy of the given edge.
   926     ///
   927     /// This function makes a copy of the given edge.
   928     GraphCopy& edge(const Edge& edge, TEdge& tedge) {
   929       _edge_maps.push_back(new _core_bits::ItemCopy<From, Edge,
   930                            EdgeRefMap, TEdge>(edge, tedge));
   931       return *this;
   932     }
   933 
   934     /// \brief Execute copying.
   935     ///
   936     /// This function executes the copying of the graph along with the
   937     /// copying of the assigned data.
   938     void run() {
   939       NodeRefMap nodeRefMap(_from);
   940       EdgeRefMap edgeRefMap(_from);
   941       ArcRefMap arcRefMap(_from, _to, edgeRefMap, nodeRefMap);
   942       _core_bits::GraphCopySelector<To>::
   943         copy(_from, _to, nodeRefMap, edgeRefMap);
   944       for (int i = 0; i < int(_node_maps.size()); ++i) {
   945         _node_maps[i]->copy(_from, nodeRefMap);
   946       }
   947       for (int i = 0; i < int(_edge_maps.size()); ++i) {
   948         _edge_maps[i]->copy(_from, edgeRefMap);
   949       }
   950       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   951         _arc_maps[i]->copy(_from, arcRefMap);
   952       }
   953     }
   954 
   955   private:
   956 
   957     const From& _from;
   958     To& _to;
   959 
   960     std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
   961       _node_maps;
   962 
   963     std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
   964       _arc_maps;
   965 
   966     std::vector<_core_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
   967       _edge_maps;
   968 
   969   };
   970 
   971   /// \brief Copy a graph to another graph.
   972   ///
   973   /// This function copies a graph to another graph.
   974   /// The complete usage of it is detailed in the GraphCopy class,
   975   /// but a short example shows a basic work:
   976   ///\code
   977   /// graphCopy(src, trg).nodeRef(nr).edgeCrossRef(ecr).run();
   978   ///\endcode
   979   ///
   980   /// After the copy the \c nr map will contain the mapping from the
   981   /// nodes of the \c from graph to the nodes of the \c to graph and
   982   /// \c ecr will contain the mapping from the edges of the \c to graph
   983   /// to the edges of the \c from graph.
   984   ///
   985   /// \see GraphCopy
   986   template <typename From, typename To>
   987   GraphCopy<From, To>
   988   graphCopy(const From& from, To& to) {
   989     return GraphCopy<From, To>(from, to);
   990   }
   991 
   992   namespace _core_bits {
   993 
   994     template <typename Graph, typename Enable = void>
   995     struct FindArcSelector {
   996       typedef typename Graph::Node Node;
   997       typedef typename Graph::Arc Arc;
   998       static Arc find(const Graph &g, Node u, Node v, Arc e) {
   999         if (e == INVALID) {
  1000           g.firstOut(e, u);
  1001         } else {
  1002           g.nextOut(e);
  1003         }
  1004         while (e != INVALID && g.target(e) != v) {
  1005           g.nextOut(e);
  1006         }
  1007         return e;
  1008       }
  1009     };
  1010 
  1011     template <typename Graph>
  1012     struct FindArcSelector<
  1013       Graph,
  1014       typename enable_if<typename Graph::FindArcTag, void>::type>
  1015     {
  1016       typedef typename Graph::Node Node;
  1017       typedef typename Graph::Arc Arc;
  1018       static Arc find(const Graph &g, Node u, Node v, Arc prev) {
  1019         return g.findArc(u, v, prev);
  1020       }
  1021     };
  1022   }
  1023 
  1024   /// \brief Find an arc between two nodes of a digraph.
  1025   ///
  1026   /// This function finds an arc from node \c u to node \c v in the
  1027   /// digraph \c g.
  1028   ///
  1029   /// If \c prev is \ref INVALID (this is the default value), then
  1030   /// it finds the first arc from \c u to \c v. Otherwise it looks for
  1031   /// the next arc from \c u to \c v after \c prev.
  1032   /// \return The found arc or \ref INVALID if there is no such an arc.
  1033   ///
  1034   /// Thus you can iterate through each arc from \c u to \c v as it follows.
  1035   ///\code
  1036   /// for(Arc e = findArc(g,u,v); e != INVALID; e = findArc(g,u,v,e)) {
  1037   ///   ...
  1038   /// }
  1039   ///\endcode
  1040   ///
  1041   /// \note \ref ConArcIt provides iterator interface for the same
  1042   /// functionality.
  1043   ///
  1044   ///\sa ConArcIt
  1045   ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
  1046   template <typename Graph>
  1047   inline typename Graph::Arc
  1048   findArc(const Graph &g, typename Graph::Node u, typename Graph::Node v,
  1049           typename Graph::Arc prev = INVALID) {
  1050     return _core_bits::FindArcSelector<Graph>::find(g, u, v, prev);
  1051   }
  1052 
  1053   /// \brief Iterator for iterating on parallel arcs connecting the same nodes.
  1054   ///
  1055   /// Iterator for iterating on parallel arcs connecting the same nodes. It is
  1056   /// a higher level interface for the \ref findArc() function. You can
  1057   /// use it the following way:
  1058   ///\code
  1059   /// for (ConArcIt<Graph> it(g, src, trg); it != INVALID; ++it) {
  1060   ///   ...
  1061   /// }
  1062   ///\endcode
  1063   ///
  1064   ///\sa findArc()
  1065   ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
  1066   template <typename GR>
  1067   class ConArcIt : public GR::Arc {
  1068     typedef typename GR::Arc Parent;
  1069 
  1070   public:
  1071 
  1072     typedef typename GR::Arc Arc;
  1073     typedef typename GR::Node Node;
  1074 
  1075     /// \brief Constructor.
  1076     ///
  1077     /// Construct a new ConArcIt iterating on the arcs that
  1078     /// connects nodes \c u and \c v.
  1079     ConArcIt(const GR& g, Node u, Node v) : _graph(g) {
  1080       Parent::operator=(findArc(_graph, u, v));
  1081     }
  1082 
  1083     /// \brief Constructor.
  1084     ///
  1085     /// Construct a new ConArcIt that continues the iterating from arc \c a.
  1086     ConArcIt(const GR& g, Arc a) : Parent(a), _graph(g) {}
  1087 
  1088     /// \brief Increment operator.
  1089     ///
  1090     /// It increments the iterator and gives back the next arc.
  1091     ConArcIt& operator++() {
  1092       Parent::operator=(findArc(_graph, _graph.source(*this),
  1093                                 _graph.target(*this), *this));
  1094       return *this;
  1095     }
  1096   private:
  1097     const GR& _graph;
  1098   };
  1099 
  1100   namespace _core_bits {
  1101 
  1102     template <typename Graph, typename Enable = void>
  1103     struct FindEdgeSelector {
  1104       typedef typename Graph::Node Node;
  1105       typedef typename Graph::Edge Edge;
  1106       static Edge find(const Graph &g, Node u, Node v, Edge e) {
  1107         bool b;
  1108         if (u != v) {
  1109           if (e == INVALID) {
  1110             g.firstInc(e, b, u);
  1111           } else {
  1112             b = g.u(e) == u;
  1113             g.nextInc(e, b);
  1114           }
  1115           while (e != INVALID && (b ? g.v(e) : g.u(e)) != v) {
  1116             g.nextInc(e, b);
  1117           }
  1118         } else {
  1119           if (e == INVALID) {
  1120             g.firstInc(e, b, u);
  1121           } else {
  1122             b = true;
  1123             g.nextInc(e, b);
  1124           }
  1125           while (e != INVALID && (!b || g.v(e) != v)) {
  1126             g.nextInc(e, b);
  1127           }
  1128         }
  1129         return e;
  1130       }
  1131     };
  1132 
  1133     template <typename Graph>
  1134     struct FindEdgeSelector<
  1135       Graph,
  1136       typename enable_if<typename Graph::FindEdgeTag, void>::type>
  1137     {
  1138       typedef typename Graph::Node Node;
  1139       typedef typename Graph::Edge Edge;
  1140       static Edge find(const Graph &g, Node u, Node v, Edge prev) {
  1141         return g.findEdge(u, v, prev);
  1142       }
  1143     };
  1144   }
  1145 
  1146   /// \brief Find an edge between two nodes of a graph.
  1147   ///
  1148   /// This function finds an edge from node \c u to node \c v in graph \c g.
  1149   /// If node \c u and node \c v is equal then each loop edge
  1150   /// will be enumerated once.
  1151   ///
  1152   /// If \c prev is \ref INVALID (this is the default value), then
  1153   /// it finds the first edge from \c u to \c v. Otherwise it looks for
  1154   /// the next edge from \c u to \c v after \c prev.
  1155   /// \return The found edge or \ref INVALID if there is no such an edge.
  1156   ///
  1157   /// Thus you can iterate through each edge between \c u and \c v
  1158   /// as it follows.
  1159   ///\code
  1160   /// for(Edge e = findEdge(g,u,v); e != INVALID; e = findEdge(g,u,v,e)) {
  1161   ///   ...
  1162   /// }
  1163   ///\endcode
  1164   ///
  1165   /// \note \ref ConEdgeIt provides iterator interface for the same
  1166   /// functionality.
  1167   ///
  1168   ///\sa ConEdgeIt
  1169   template <typename Graph>
  1170   inline typename Graph::Edge
  1171   findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,
  1172             typename Graph::Edge p = INVALID) {
  1173     return _core_bits::FindEdgeSelector<Graph>::find(g, u, v, p);
  1174   }
  1175 
  1176   /// \brief Iterator for iterating on parallel edges connecting the same nodes.
  1177   ///
  1178   /// Iterator for iterating on parallel edges connecting the same nodes.
  1179   /// It is a higher level interface for the findEdge() function. You can
  1180   /// use it the following way:
  1181   ///\code
  1182   /// for (ConEdgeIt<Graph> it(g, u, v); it != INVALID; ++it) {
  1183   ///   ...
  1184   /// }
  1185   ///\endcode
  1186   ///
  1187   ///\sa findEdge()
  1188   template <typename GR>
  1189   class ConEdgeIt : public GR::Edge {
  1190     typedef typename GR::Edge Parent;
  1191 
  1192   public:
  1193 
  1194     typedef typename GR::Edge Edge;
  1195     typedef typename GR::Node Node;
  1196 
  1197     /// \brief Constructor.
  1198     ///
  1199     /// Construct a new ConEdgeIt iterating on the edges that
  1200     /// connects nodes \c u and \c v.
  1201     ConEdgeIt(const GR& g, Node u, Node v) : _graph(g), _u(u), _v(v) {
  1202       Parent::operator=(findEdge(_graph, _u, _v));
  1203     }
  1204 
  1205     /// \brief Constructor.
  1206     ///
  1207     /// Construct a new ConEdgeIt that continues iterating from edge \c e.
  1208     ConEdgeIt(const GR& g, Edge e) : Parent(e), _graph(g) {}
  1209 
  1210     /// \brief Increment operator.
  1211     ///
  1212     /// It increments the iterator and gives back the next edge.
  1213     ConEdgeIt& operator++() {
  1214       Parent::operator=(findEdge(_graph, _u, _v, *this));
  1215       return *this;
  1216     }
  1217   private:
  1218     const GR& _graph;
  1219     Node _u, _v;
  1220   };
  1221 
  1222 
  1223   ///Dynamic arc look-up between given endpoints.
  1224 
  1225   ///Using this class, you can find an arc in a digraph from a given
  1226   ///source to a given target in amortized time <em>O</em>(log<em>d</em>),
  1227   ///where <em>d</em> is the out-degree of the source node.
  1228   ///
  1229   ///It is possible to find \e all parallel arcs between two nodes with
  1230   ///the \c operator() member.
  1231   ///
  1232   ///This is a dynamic data structure. Consider to use \ref ArcLookUp or
  1233   ///\ref AllArcLookUp if your digraph is not changed so frequently.
  1234   ///
  1235   ///This class uses a self-adjusting binary search tree, the Splay tree
  1236   ///of Sleator and Tarjan to guarantee the logarithmic amortized
  1237   ///time bound for arc look-ups. This class also guarantees the
  1238   ///optimal time bound in a constant factor for any distribution of
  1239   ///queries.
  1240   ///
  1241   ///\tparam GR The type of the underlying digraph.
  1242   ///
  1243   ///\sa ArcLookUp
  1244   ///\sa AllArcLookUp
  1245   template <typename GR>
  1246   class DynArcLookUp
  1247     : protected ItemSetTraits<GR, typename GR::Arc>::ItemNotifier::ObserverBase
  1248   {
  1249     typedef typename ItemSetTraits<GR, typename GR::Arc>
  1250     ::ItemNotifier::ObserverBase Parent;
  1251 
  1252     TEMPLATE_DIGRAPH_TYPEDEFS(GR);
  1253 
  1254   public:
  1255 
  1256     /// The Digraph type
  1257     typedef GR Digraph;
  1258 
  1259   protected:
  1260 
  1261     class AutoNodeMap : public ItemSetTraits<GR, Node>::template Map<Arc>::Type
  1262     {
  1263       typedef typename ItemSetTraits<GR, Node>::template Map<Arc>::Type Parent;
  1264 
  1265     public:
  1266 
  1267       AutoNodeMap(const GR& digraph) : Parent(digraph, INVALID) {}
  1268 
  1269       virtual void add(const Node& node) {
  1270         Parent::add(node);
  1271         Parent::set(node, INVALID);
  1272       }
  1273 
  1274       virtual void add(const std::vector<Node>& nodes) {
  1275         Parent::add(nodes);
  1276         for (int i = 0; i < int(nodes.size()); ++i) {
  1277           Parent::set(nodes[i], INVALID);
  1278         }
  1279       }
  1280 
  1281       virtual void build() {
  1282         Parent::build();
  1283         Node it;
  1284         typename Parent::Notifier* nf = Parent::notifier();
  1285         for (nf->first(it); it != INVALID; nf->next(it)) {
  1286           Parent::set(it, INVALID);
  1287         }
  1288       }
  1289     };
  1290 
  1291     class ArcLess {
  1292       const Digraph &g;
  1293     public:
  1294       ArcLess(const Digraph &_g) : g(_g) {}
  1295       bool operator()(Arc a,Arc b) const
  1296       {
  1297         return g.target(a)<g.target(b);
  1298       }
  1299     };
  1300 
  1301   protected:
  1302 
  1303     const Digraph &_g;
  1304     AutoNodeMap _head;
  1305     typename Digraph::template ArcMap<Arc> _parent;
  1306     typename Digraph::template ArcMap<Arc> _left;
  1307     typename Digraph::template ArcMap<Arc> _right;
  1308 
  1309   public:
  1310 
  1311     ///Constructor
  1312 
  1313     ///Constructor.
  1314     ///
  1315     ///It builds up the search database.
  1316     DynArcLookUp(const Digraph &g)
  1317       : _g(g),_head(g),_parent(g),_left(g),_right(g)
  1318     {
  1319       Parent::attach(_g.notifier(typename Digraph::Arc()));
  1320       refresh();
  1321     }
  1322 
  1323   protected:
  1324 
  1325     virtual void add(const Arc& arc) {
  1326       insert(arc);
  1327     }
  1328 
  1329     virtual void add(const std::vector<Arc>& arcs) {
  1330       for (int i = 0; i < int(arcs.size()); ++i) {
  1331         insert(arcs[i]);
  1332       }
  1333     }
  1334 
  1335     virtual void erase(const Arc& arc) {
  1336       remove(arc);
  1337     }
  1338 
  1339     virtual void erase(const std::vector<Arc>& arcs) {
  1340       for (int i = 0; i < int(arcs.size()); ++i) {
  1341         remove(arcs[i]);
  1342       }
  1343     }
  1344 
  1345     virtual void build() {
  1346       refresh();
  1347     }
  1348 
  1349     virtual void clear() {
  1350       for(NodeIt n(_g);n!=INVALID;++n) {
  1351         _head[n] = INVALID;
  1352       }
  1353     }
  1354 
  1355     void insert(Arc arc) {
  1356       Node s = _g.source(arc);
  1357       Node t = _g.target(arc);
  1358       _left[arc] = INVALID;
  1359       _right[arc] = INVALID;
  1360 
  1361       Arc e = _head[s];
  1362       if (e == INVALID) {
  1363         _head[s] = arc;
  1364         _parent[arc] = INVALID;
  1365         return;
  1366       }
  1367       while (true) {
  1368         if (t < _g.target(e)) {
  1369           if (_left[e] == INVALID) {
  1370             _left[e] = arc;
  1371             _parent[arc] = e;
  1372             splay(arc);
  1373             return;
  1374           } else {
  1375             e = _left[e];
  1376           }
  1377         } else {
  1378           if (_right[e] == INVALID) {
  1379             _right[e] = arc;
  1380             _parent[arc] = e;
  1381             splay(arc);
  1382             return;
  1383           } else {
  1384             e = _right[e];
  1385           }
  1386         }
  1387       }
  1388     }
  1389 
  1390     void remove(Arc arc) {
  1391       if (_left[arc] == INVALID) {
  1392         if (_right[arc] != INVALID) {
  1393           _parent[_right[arc]] = _parent[arc];
  1394         }
  1395         if (_parent[arc] != INVALID) {
  1396           if (_left[_parent[arc]] == arc) {
  1397             _left[_parent[arc]] = _right[arc];
  1398           } else {
  1399             _right[_parent[arc]] = _right[arc];
  1400           }
  1401         } else {
  1402           _head[_g.source(arc)] = _right[arc];
  1403         }
  1404       } else if (_right[arc] == INVALID) {
  1405         _parent[_left[arc]] = _parent[arc];
  1406         if (_parent[arc] != INVALID) {
  1407           if (_left[_parent[arc]] == arc) {
  1408             _left[_parent[arc]] = _left[arc];
  1409           } else {
  1410             _right[_parent[arc]] = _left[arc];
  1411           }
  1412         } else {
  1413           _head[_g.source(arc)] = _left[arc];
  1414         }
  1415       } else {
  1416         Arc e = _left[arc];
  1417         if (_right[e] != INVALID) {
  1418           e = _right[e];
  1419           while (_right[e] != INVALID) {
  1420             e = _right[e];
  1421           }
  1422           Arc s = _parent[e];
  1423           _right[_parent[e]] = _left[e];
  1424           if (_left[e] != INVALID) {
  1425             _parent[_left[e]] = _parent[e];
  1426           }
  1427 
  1428           _left[e] = _left[arc];
  1429           _parent[_left[arc]] = e;
  1430           _right[e] = _right[arc];
  1431           _parent[_right[arc]] = e;
  1432 
  1433           _parent[e] = _parent[arc];
  1434           if (_parent[arc] != INVALID) {
  1435             if (_left[_parent[arc]] == arc) {
  1436               _left[_parent[arc]] = e;
  1437             } else {
  1438               _right[_parent[arc]] = e;
  1439             }
  1440           }
  1441           splay(s);
  1442         } else {
  1443           _right[e] = _right[arc];
  1444           _parent[_right[arc]] = e;
  1445           _parent[e] = _parent[arc];
  1446 
  1447           if (_parent[arc] != INVALID) {
  1448             if (_left[_parent[arc]] == arc) {
  1449               _left[_parent[arc]] = e;
  1450             } else {
  1451               _right[_parent[arc]] = e;
  1452             }
  1453           } else {
  1454             _head[_g.source(arc)] = e;
  1455           }
  1456         }
  1457       }
  1458     }
  1459 
  1460     Arc refreshRec(std::vector<Arc> &v,int a,int b)
  1461     {
  1462       int m=(a+b)/2;
  1463       Arc me=v[m];
  1464       if (a < m) {
  1465         Arc left = refreshRec(v,a,m-1);
  1466         _left[me] = left;
  1467         _parent[left] = me;
  1468       } else {
  1469         _left[me] = INVALID;
  1470       }
  1471       if (m < b) {
  1472         Arc right = refreshRec(v,m+1,b);
  1473         _right[me] = right;
  1474         _parent[right] = me;
  1475       } else {
  1476         _right[me] = INVALID;
  1477       }
  1478       return me;
  1479     }
  1480 
  1481     void refresh() {
  1482       for(NodeIt n(_g);n!=INVALID;++n) {
  1483         std::vector<Arc> v;
  1484         for(OutArcIt a(_g,n);a!=INVALID;++a) v.push_back(a);
  1485         if (!v.empty()) {
  1486           std::sort(v.begin(),v.end(),ArcLess(_g));
  1487           Arc head = refreshRec(v,0,v.size()-1);
  1488           _head[n] = head;
  1489           _parent[head] = INVALID;
  1490         }
  1491         else _head[n] = INVALID;
  1492       }
  1493     }
  1494 
  1495     void zig(Arc v) {
  1496       Arc w = _parent[v];
  1497       _parent[v] = _parent[w];
  1498       _parent[w] = v;
  1499       _left[w] = _right[v];
  1500       _right[v] = w;
  1501       if (_parent[v] != INVALID) {
  1502         if (_right[_parent[v]] == w) {
  1503           _right[_parent[v]] = v;
  1504         } else {
  1505           _left[_parent[v]] = v;
  1506         }
  1507       }
  1508       if (_left[w] != INVALID){
  1509         _parent[_left[w]] = w;
  1510       }
  1511     }
  1512 
  1513     void zag(Arc v) {
  1514       Arc w = _parent[v];
  1515       _parent[v] = _parent[w];
  1516       _parent[w] = v;
  1517       _right[w] = _left[v];
  1518       _left[v] = w;
  1519       if (_parent[v] != INVALID){
  1520         if (_left[_parent[v]] == w) {
  1521           _left[_parent[v]] = v;
  1522         } else {
  1523           _right[_parent[v]] = v;
  1524         }
  1525       }
  1526       if (_right[w] != INVALID){
  1527         _parent[_right[w]] = w;
  1528       }
  1529     }
  1530 
  1531     void splay(Arc v) {
  1532       while (_parent[v] != INVALID) {
  1533         if (v == _left[_parent[v]]) {
  1534           if (_parent[_parent[v]] == INVALID) {
  1535             zig(v);
  1536           } else {
  1537             if (_parent[v] == _left[_parent[_parent[v]]]) {
  1538               zig(_parent[v]);
  1539               zig(v);
  1540             } else {
  1541               zig(v);
  1542               zag(v);
  1543             }
  1544           }
  1545         } else {
  1546           if (_parent[_parent[v]] == INVALID) {
  1547             zag(v);
  1548           } else {
  1549             if (_parent[v] == _left[_parent[_parent[v]]]) {
  1550               zag(v);
  1551               zig(v);
  1552             } else {
  1553               zag(_parent[v]);
  1554               zag(v);
  1555             }
  1556           }
  1557         }
  1558       }
  1559       _head[_g.source(v)] = v;
  1560     }
  1561 
  1562 
  1563   public:
  1564 
  1565     ///Find an arc between two nodes.
  1566 
  1567     ///Find an arc between two nodes.
  1568     ///\param s The source node.
  1569     ///\param t The target node.
  1570     ///\param p The previous arc between \c s and \c t. It it is INVALID or
  1571     ///not given, the operator finds the first appropriate arc.
  1572     ///\return An arc from \c s to \c t after \c p or
  1573     ///\ref INVALID if there is no more.
  1574     ///
  1575     ///For example, you can count the number of arcs from \c u to \c v in the
  1576     ///following way.
  1577     ///\code
  1578     ///DynArcLookUp<ListDigraph> ae(g);
  1579     ///...
  1580     ///int n = 0;
  1581     ///for(Arc a = ae(u,v); a != INVALID; a = ae(u,v,a)) n++;
  1582     ///\endcode
  1583     ///
  1584     ///Finding the arcs take at most <em>O</em>(log<em>d</em>)
  1585     ///amortized time, specifically, the time complexity of the lookups
  1586     ///is equal to the optimal search tree implementation for the
  1587     ///current query distribution in a constant factor.
  1588     ///
  1589     ///\note This is a dynamic data structure, therefore the data
  1590     ///structure is updated after each graph alteration. Thus although
  1591     ///this data structure is theoretically faster than \ref ArcLookUp
  1592     ///and \ref AllArcLookUp, it often provides worse performance than
  1593     ///them.
  1594     Arc operator()(Node s, Node t, Arc p = INVALID) const  {
  1595       if (p == INVALID) {
  1596         Arc a = _head[s];
  1597         if (a == INVALID) return INVALID;
  1598         Arc r = INVALID;
  1599         while (true) {
  1600           if (_g.target(a) < t) {
  1601             if (_right[a] == INVALID) {
  1602               const_cast<DynArcLookUp&>(*this).splay(a);
  1603               return r;
  1604             } else {
  1605               a = _right[a];
  1606             }
  1607           } else {
  1608             if (_g.target(a) == t) {
  1609               r = a;
  1610             }
  1611             if (_left[a] == INVALID) {
  1612               const_cast<DynArcLookUp&>(*this).splay(a);
  1613               return r;
  1614             } else {
  1615               a = _left[a];
  1616             }
  1617           }
  1618         }
  1619       } else {
  1620         Arc a = p;
  1621         if (_right[a] != INVALID) {
  1622           a = _right[a];
  1623           while (_left[a] != INVALID) {
  1624             a = _left[a];
  1625           }
  1626           const_cast<DynArcLookUp&>(*this).splay(a);
  1627         } else {
  1628           while (_parent[a] != INVALID && _right[_parent[a]] ==  a) {
  1629             a = _parent[a];
  1630           }
  1631           if (_parent[a] == INVALID) {
  1632             return INVALID;
  1633           } else {
  1634             a = _parent[a];
  1635             const_cast<DynArcLookUp&>(*this).splay(a);
  1636           }
  1637         }
  1638         if (_g.target(a) == t) return a;
  1639         else return INVALID;
  1640       }
  1641     }
  1642 
  1643   };
  1644 
  1645   ///Fast arc look-up between given endpoints.
  1646 
  1647   ///Using this class, you can find an arc in a digraph from a given
  1648   ///source to a given target in time <em>O</em>(log<em>d</em>),
  1649   ///where <em>d</em> is the out-degree of the source node.
  1650   ///
  1651   ///It is not possible to find \e all parallel arcs between two nodes.
  1652   ///Use \ref AllArcLookUp for this purpose.
  1653   ///
  1654   ///\warning This class is static, so you should call refresh() (or at
  1655   ///least refresh(Node)) to refresh this data structure whenever the
  1656   ///digraph changes. This is a time consuming (superlinearly proportional
  1657   ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
  1658   ///
  1659   ///\tparam GR The type of the underlying digraph.
  1660   ///
  1661   ///\sa DynArcLookUp
  1662   ///\sa AllArcLookUp
  1663   template<class GR>
  1664   class ArcLookUp
  1665   {
  1666     TEMPLATE_DIGRAPH_TYPEDEFS(GR);
  1667 
  1668   public:
  1669 
  1670     /// The Digraph type
  1671     typedef GR Digraph;
  1672 
  1673   protected:
  1674     const Digraph &_g;
  1675     typename Digraph::template NodeMap<Arc> _head;
  1676     typename Digraph::template ArcMap<Arc> _left;
  1677     typename Digraph::template ArcMap<Arc> _right;
  1678 
  1679     class ArcLess {
  1680       const Digraph &g;
  1681     public:
  1682       ArcLess(const Digraph &_g) : g(_g) {}
  1683       bool operator()(Arc a,Arc b) const
  1684       {
  1685         return g.target(a)<g.target(b);
  1686       }
  1687     };
  1688 
  1689   public:
  1690 
  1691     ///Constructor
  1692 
  1693     ///Constructor.
  1694     ///
  1695     ///It builds up the search database, which remains valid until the digraph
  1696     ///changes.
  1697     ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}
  1698 
  1699   private:
  1700     Arc refreshRec(std::vector<Arc> &v,int a,int b)
  1701     {
  1702       int m=(a+b)/2;
  1703       Arc me=v[m];
  1704       _left[me] = a<m?refreshRec(v,a,m-1):INVALID;
  1705       _right[me] = m<b?refreshRec(v,m+1,b):INVALID;
  1706       return me;
  1707     }
  1708   public:
  1709     ///Refresh the search data structure at a node.
  1710 
  1711     ///Build up the search database of node \c n.
  1712     ///
  1713     ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em>
  1714     ///is the number of the outgoing arcs of \c n.
  1715     void refresh(Node n)
  1716     {
  1717       std::vector<Arc> v;
  1718       for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
  1719       if(v.size()) {
  1720         std::sort(v.begin(),v.end(),ArcLess(_g));
  1721         _head[n]=refreshRec(v,0,v.size()-1);
  1722       }
  1723       else _head[n]=INVALID;
  1724     }
  1725     ///Refresh the full data structure.
  1726 
  1727     ///Build up the full search database. In fact, it simply calls
  1728     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  1729     ///
  1730     ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
  1731     ///the number of the arcs in the digraph and <em>D</em> is the maximum
  1732     ///out-degree of the digraph.
  1733     void refresh()
  1734     {
  1735       for(NodeIt n(_g);n!=INVALID;++n) refresh(n);
  1736     }
  1737 
  1738     ///Find an arc between two nodes.
  1739 
  1740     ///Find an arc between two nodes in time <em>O</em>(log<em>d</em>),
  1741     ///where <em>d</em> is the number of outgoing arcs of \c s.
  1742     ///\param s The source node.
  1743     ///\param t The target node.
  1744     ///\return An arc from \c s to \c t if there exists,
  1745     ///\ref INVALID otherwise.
  1746     ///
  1747     ///\warning If you change the digraph, refresh() must be called before using
  1748     ///this operator. If you change the outgoing arcs of
  1749     ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
  1750     Arc operator()(Node s, Node t) const
  1751     {
  1752       Arc e;
  1753       for(e=_head[s];
  1754           e!=INVALID&&_g.target(e)!=t;
  1755           e = t < _g.target(e)?_left[e]:_right[e]) ;
  1756       return e;
  1757     }
  1758 
  1759   };
  1760 
  1761   ///Fast look-up of all arcs between given endpoints.
  1762 
  1763   ///This class is the same as \ref ArcLookUp, with the addition
  1764   ///that it makes it possible to find all parallel arcs between given
  1765   ///endpoints.
  1766   ///
  1767   ///\warning This class is static, so you should call refresh() (or at
  1768   ///least refresh(Node)) to refresh this data structure whenever the
  1769   ///digraph changes. This is a time consuming (superlinearly proportional
  1770   ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
  1771   ///
  1772   ///\tparam GR The type of the underlying digraph.
  1773   ///
  1774   ///\sa DynArcLookUp
  1775   ///\sa ArcLookUp
  1776   template<class GR>
  1777   class AllArcLookUp : public ArcLookUp<GR>
  1778   {
  1779     using ArcLookUp<GR>::_g;
  1780     using ArcLookUp<GR>::_right;
  1781     using ArcLookUp<GR>::_left;
  1782     using ArcLookUp<GR>::_head;
  1783 
  1784     TEMPLATE_DIGRAPH_TYPEDEFS(GR);
  1785 
  1786     typename GR::template ArcMap<Arc> _next;
  1787 
  1788     Arc refreshNext(Arc head,Arc next=INVALID)
  1789     {
  1790       if(head==INVALID) return next;
  1791       else {
  1792         next=refreshNext(_right[head],next);
  1793         _next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
  1794           ? next : INVALID;
  1795         return refreshNext(_left[head],head);
  1796       }
  1797     }
  1798 
  1799     void refreshNext()
  1800     {
  1801       for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
  1802     }
  1803 
  1804   public:
  1805 
  1806     /// The Digraph type
  1807     typedef GR Digraph;
  1808 
  1809     ///Constructor
  1810 
  1811     ///Constructor.
  1812     ///
  1813     ///It builds up the search database, which remains valid until the digraph
  1814     ///changes.
  1815     AllArcLookUp(const Digraph &g) : ArcLookUp<GR>(g), _next(g) {refreshNext();}
  1816 
  1817     ///Refresh the data structure at a node.
  1818 
  1819     ///Build up the search database of node \c n.
  1820     ///
  1821     ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em> is
  1822     ///the number of the outgoing arcs of \c n.
  1823     void refresh(Node n)
  1824     {
  1825       ArcLookUp<GR>::refresh(n);
  1826       refreshNext(_head[n]);
  1827     }
  1828 
  1829     ///Refresh the full data structure.
  1830 
  1831     ///Build up the full search database. In fact, it simply calls
  1832     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  1833     ///
  1834     ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
  1835     ///the number of the arcs in the digraph and <em>D</em> is the maximum
  1836     ///out-degree of the digraph.
  1837     void refresh()
  1838     {
  1839       for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
  1840     }
  1841 
  1842     ///Find an arc between two nodes.
  1843 
  1844     ///Find an arc between two nodes.
  1845     ///\param s The source node.
  1846     ///\param t The target node.
  1847     ///\param prev The previous arc between \c s and \c t. It it is INVALID or
  1848     ///not given, the operator finds the first appropriate arc.
  1849     ///\return An arc from \c s to \c t after \c prev or
  1850     ///\ref INVALID if there is no more.
  1851     ///
  1852     ///For example, you can count the number of arcs from \c u to \c v in the
  1853     ///following way.
  1854     ///\code
  1855     ///AllArcLookUp<ListDigraph> ae(g);
  1856     ///...
  1857     ///int n = 0;
  1858     ///for(Arc a = ae(u,v); a != INVALID; a=ae(u,v,a)) n++;
  1859     ///\endcode
  1860     ///
  1861     ///Finding the first arc take <em>O</em>(log<em>d</em>) time,
  1862     ///where <em>d</em> is the number of outgoing arcs of \c s. Then the
  1863     ///consecutive arcs are found in constant time.
  1864     ///
  1865     ///\warning If you change the digraph, refresh() must be called before using
  1866     ///this operator. If you change the outgoing arcs of
  1867     ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
  1868     ///
  1869 #ifdef DOXYGEN
  1870     Arc operator()(Node s, Node t, Arc prev=INVALID) const {}
  1871 #else
  1872     using ArcLookUp<GR>::operator() ;
  1873     Arc operator()(Node s, Node t, Arc prev) const
  1874     {
  1875       return prev==INVALID?(*this)(s,t):_next[prev];
  1876     }
  1877 #endif
  1878 
  1879   };
  1880 
  1881   /// @}
  1882 
  1883 } //namespace lemon
  1884 
  1885 #endif