lemon/core.h
author Peter Kovacs <kpeter@inf.elte.hu>
Sat, 30 Aug 2008 22:19:43 +0200
changeset 253 dbe309b5e855
parent 232 e39056157d24
child 282 dc9e8d2c0df9
permissions -rw-r--r--
Rename BoundingBox to Box (ticket #126)
     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   ///Creates convenience typedefs for the digraph types and iterators
    62 
    63   ///This \c \#define creates convenience typedefs for the following types
    64   ///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   ///Creates 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   ///Creates convenience typedefs for the graph types and iterators
   106 
   107   ///This \c \#define creates the same convenience typedefs 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_DIGRAPH_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   ///Creates 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 the graph.
   140   ///
   141   /// This function counts the items (nodes, arcs etc) in the graph.
   142   /// The complexity of the function is O(n) 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 O(n) but for some
   180   /// graph structures it is specialized to run in O(1).
   181   ///
   182   /// If the graph contains a \e nodeNum() member function and a
   183   /// \e 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 O(e) but for some
   216   /// graph structures it is specialized to run in O(1).
   217   ///
   218   /// If the graph contains a \e arcNum() member function and a
   219   /// \e EdgeNumTag 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   namespace _core_bits {
   228 
   229     template <typename Graph, typename Enable = void>
   230     struct CountEdgesSelector {
   231       static int count(const Graph &g) {
   232         return countItems<Graph, typename Graph::Edge>(g);
   233       }
   234     };
   235 
   236     template <typename Graph>
   237     struct CountEdgesSelector<
   238       Graph,
   239       typename enable_if<typename Graph::EdgeNumTag, void>::type>
   240     {
   241       static int count(const Graph &g) {
   242         return g.edgeNum();
   243       }
   244     };
   245   }
   246 
   247   /// \brief Function to count the edges in the graph.
   248   ///
   249   /// This function counts the edges in the graph.
   250   /// The complexity of the function is O(m) but for some
   251   /// graph structures it is specialized to run in O(1).
   252   ///
   253   /// If the graph contains a \e edgeNum() member function and a
   254   /// \e EdgeNumTag tag then this function calls directly the member
   255   /// function to query the cardinality of the edge set.
   256   template <typename Graph>
   257   inline int countEdges(const Graph& g) {
   258     return _core_bits::CountEdgesSelector<Graph>::count(g);
   259 
   260   }
   261 
   262 
   263   template <typename Graph, typename DegIt>
   264   inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {
   265     int num = 0;
   266     for (DegIt it(_g, _n); it != INVALID; ++it) {
   267       ++num;
   268     }
   269     return num;
   270   }
   271 
   272   /// \brief Function to count the number of the out-arcs from node \c n.
   273   ///
   274   /// This function counts the number of the out-arcs from node \c n
   275   /// in the graph.
   276   template <typename Graph>
   277   inline int countOutArcs(const Graph& _g,  const typename Graph::Node& _n) {
   278     return countNodeDegree<Graph, typename Graph::OutArcIt>(_g, _n);
   279   }
   280 
   281   /// \brief Function to count the number of the in-arcs to node \c n.
   282   ///
   283   /// This function counts the number of the in-arcs to node \c n
   284   /// in the graph.
   285   template <typename Graph>
   286   inline int countInArcs(const Graph& _g,  const typename Graph::Node& _n) {
   287     return countNodeDegree<Graph, typename Graph::InArcIt>(_g, _n);
   288   }
   289 
   290   /// \brief Function to count the number of the inc-edges to node \c n.
   291   ///
   292   /// This function counts the number of the inc-edges to node \c n
   293   /// in the graph.
   294   template <typename Graph>
   295   inline int countIncEdges(const Graph& _g,  const typename Graph::Node& _n) {
   296     return countNodeDegree<Graph, typename Graph::IncEdgeIt>(_g, _n);
   297   }
   298 
   299   namespace _core_bits {
   300 
   301     template <typename Digraph, typename Item, typename RefMap>
   302     class MapCopyBase {
   303     public:
   304       virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
   305 
   306       virtual ~MapCopyBase() {}
   307     };
   308 
   309     template <typename Digraph, typename Item, typename RefMap,
   310               typename ToMap, typename FromMap>
   311     class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
   312     public:
   313 
   314       MapCopy(ToMap& tmap, const FromMap& map)
   315         : _tmap(tmap), _map(map) {}
   316 
   317       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   318         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   319         for (ItemIt it(digraph); it != INVALID; ++it) {
   320           _tmap.set(refMap[it], _map[it]);
   321         }
   322       }
   323 
   324     private:
   325       ToMap& _tmap;
   326       const FromMap& _map;
   327     };
   328 
   329     template <typename Digraph, typename Item, typename RefMap, typename It>
   330     class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
   331     public:
   332 
   333       ItemCopy(It& it, const Item& item) : _it(it), _item(item) {}
   334 
   335       virtual void copy(const Digraph&, const RefMap& refMap) {
   336         _it = refMap[_item];
   337       }
   338 
   339     private:
   340       It& _it;
   341       Item _item;
   342     };
   343 
   344     template <typename Digraph, typename Item, typename RefMap, typename Ref>
   345     class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   346     public:
   347 
   348       RefCopy(Ref& map) : _map(map) {}
   349 
   350       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   351         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   352         for (ItemIt it(digraph); it != INVALID; ++it) {
   353           _map.set(it, refMap[it]);
   354         }
   355       }
   356 
   357     private:
   358       Ref& _map;
   359     };
   360 
   361     template <typename Digraph, typename Item, typename RefMap,
   362               typename CrossRef>
   363     class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   364     public:
   365 
   366       CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
   367 
   368       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   369         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   370         for (ItemIt it(digraph); it != INVALID; ++it) {
   371           _cmap.set(refMap[it], it);
   372         }
   373       }
   374 
   375     private:
   376       CrossRef& _cmap;
   377     };
   378 
   379     template <typename Digraph, typename Enable = void>
   380     struct DigraphCopySelector {
   381       template <typename From, typename NodeRefMap, typename ArcRefMap>
   382       static void copy(Digraph &to, const From& from,
   383                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   384         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   385           nodeRefMap[it] = to.addNode();
   386         }
   387         for (typename From::ArcIt it(from); it != INVALID; ++it) {
   388           arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)],
   389                                     nodeRefMap[from.target(it)]);
   390         }
   391       }
   392     };
   393 
   394     template <typename Digraph>
   395     struct DigraphCopySelector<
   396       Digraph,
   397       typename enable_if<typename Digraph::BuildTag, void>::type>
   398     {
   399       template <typename From, typename NodeRefMap, typename ArcRefMap>
   400       static void copy(Digraph &to, const From& from,
   401                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   402         to.build(from, nodeRefMap, arcRefMap);
   403       }
   404     };
   405 
   406     template <typename Graph, typename Enable = void>
   407     struct GraphCopySelector {
   408       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   409       static void copy(Graph &to, const From& from,
   410                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   411         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   412           nodeRefMap[it] = to.addNode();
   413         }
   414         for (typename From::EdgeIt it(from); it != INVALID; ++it) {
   415           edgeRefMap[it] = to.addEdge(nodeRefMap[from.u(it)],
   416                                       nodeRefMap[from.v(it)]);
   417         }
   418       }
   419     };
   420 
   421     template <typename Graph>
   422     struct GraphCopySelector<
   423       Graph,
   424       typename enable_if<typename Graph::BuildTag, void>::type>
   425     {
   426       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   427       static void copy(Graph &to, const From& from,
   428                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   429         to.build(from, nodeRefMap, edgeRefMap);
   430       }
   431     };
   432 
   433   }
   434 
   435   /// \brief Class to copy a digraph.
   436   ///
   437   /// Class to copy a digraph to another digraph (duplicate a digraph). The
   438   /// simplest way of using it is through the \c copyDigraph() function.
   439   ///
   440   /// This class not just make a copy of a graph, but it can create
   441   /// references and cross references between the nodes and arcs of
   442   /// the two graphs, it can copy maps for use with the newly created
   443   /// graph and copy nodes and arcs.
   444   ///
   445   /// To make a copy from a graph, first an instance of DigraphCopy
   446   /// should be created, then the data belongs to the graph should
   447   /// assigned to copy. In the end, the \c run() member should be
   448   /// called.
   449   ///
   450   /// The next code copies a graph with several data:
   451   ///\code
   452   ///  DigraphCopy<NewGraph, OrigGraph> dc(new_graph, orig_graph);
   453   ///  // create a reference for the nodes
   454   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   455   ///  dc.nodeRef(nr);
   456   ///  // create a cross reference (inverse) for the arcs
   457   ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);
   458   ///  dc.arcCrossRef(acr);
   459   ///  // copy an arc map
   460   ///  OrigGraph::ArcMap<double> oamap(orig_graph);
   461   ///  NewGraph::ArcMap<double> namap(new_graph);
   462   ///  dc.arcMap(namap, oamap);
   463   ///  // copy a node
   464   ///  OrigGraph::Node on;
   465   ///  NewGraph::Node nn;
   466   ///  dc.node(nn, on);
   467   ///  // Executions of copy
   468   ///  dc.run();
   469   ///\endcode
   470   template <typename To, typename From>
   471   class DigraphCopy {
   472   private:
   473 
   474     typedef typename From::Node Node;
   475     typedef typename From::NodeIt NodeIt;
   476     typedef typename From::Arc Arc;
   477     typedef typename From::ArcIt ArcIt;
   478 
   479     typedef typename To::Node TNode;
   480     typedef typename To::Arc TArc;
   481 
   482     typedef typename From::template NodeMap<TNode> NodeRefMap;
   483     typedef typename From::template ArcMap<TArc> ArcRefMap;
   484 
   485 
   486   public:
   487 
   488 
   489     /// \brief Constructor for the DigraphCopy.
   490     ///
   491     /// It copies the content of the \c _from digraph into the
   492     /// \c _to digraph.
   493     DigraphCopy(To& to, const From& from)
   494       : _from(from), _to(to) {}
   495 
   496     /// \brief Destructor of the DigraphCopy
   497     ///
   498     /// Destructor of the DigraphCopy
   499     ~DigraphCopy() {
   500       for (int i = 0; i < int(_node_maps.size()); ++i) {
   501         delete _node_maps[i];
   502       }
   503       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   504         delete _arc_maps[i];
   505       }
   506 
   507     }
   508 
   509     /// \brief Copies the node references into the given map.
   510     ///
   511     /// Copies the node references into the given map. The parameter
   512     /// should be a map, which key type is the Node type of the source
   513     /// graph, while the value type is the Node type of the
   514     /// destination graph.
   515     template <typename NodeRef>
   516     DigraphCopy& nodeRef(NodeRef& map) {
   517       _node_maps.push_back(new _core_bits::RefCopy<From, Node,
   518                            NodeRefMap, NodeRef>(map));
   519       return *this;
   520     }
   521 
   522     /// \brief Copies the node cross references into the given map.
   523     ///
   524     ///  Copies the node cross references (reverse references) into
   525     ///  the given map. The parameter should be a map, which key type
   526     ///  is the Node type of the destination graph, while the value type is
   527     ///  the Node type of the source graph.
   528     template <typename NodeCrossRef>
   529     DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
   530       _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
   531                            NodeRefMap, NodeCrossRef>(map));
   532       return *this;
   533     }
   534 
   535     /// \brief Make copy of the given map.
   536     ///
   537     /// Makes copy of the given map for the newly created digraph.
   538     /// The new map's key type is the destination graph's node type,
   539     /// and the copied map's key type is the source graph's node type.
   540     template <typename ToMap, typename FromMap>
   541     DigraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
   542       _node_maps.push_back(new _core_bits::MapCopy<From, Node,
   543                            NodeRefMap, ToMap, FromMap>(tmap, map));
   544       return *this;
   545     }
   546 
   547     /// \brief Make a copy of the given node.
   548     ///
   549     /// Make a copy of the given node.
   550     DigraphCopy& node(TNode& tnode, const Node& snode) {
   551       _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
   552                            NodeRefMap, TNode>(tnode, snode));
   553       return *this;
   554     }
   555 
   556     /// \brief Copies the arc references into the given map.
   557     ///
   558     /// Copies the arc references into the given map.
   559     template <typename ArcRef>
   560     DigraphCopy& arcRef(ArcRef& map) {
   561       _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
   562                           ArcRefMap, ArcRef>(map));
   563       return *this;
   564     }
   565 
   566     /// \brief Copies the arc cross references into the given map.
   567     ///
   568     ///  Copies the arc cross references (reverse references) into
   569     ///  the given map.
   570     template <typename ArcCrossRef>
   571     DigraphCopy& arcCrossRef(ArcCrossRef& map) {
   572       _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
   573                           ArcRefMap, ArcCrossRef>(map));
   574       return *this;
   575     }
   576 
   577     /// \brief Make copy of the given map.
   578     ///
   579     /// Makes copy of the given map for the newly created digraph.
   580     /// The new map's key type is the to digraph's arc type,
   581     /// and the copied map's key type is the from digraph's arc
   582     /// type.
   583     template <typename ToMap, typename FromMap>
   584     DigraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
   585       _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
   586                           ArcRefMap, ToMap, FromMap>(tmap, map));
   587       return *this;
   588     }
   589 
   590     /// \brief Make a copy of the given arc.
   591     ///
   592     /// Make a copy of the given arc.
   593     DigraphCopy& arc(TArc& tarc, const Arc& sarc) {
   594       _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
   595                           ArcRefMap, TArc>(tarc, sarc));
   596       return *this;
   597     }
   598 
   599     /// \brief Executes the copies.
   600     ///
   601     /// Executes the copies.
   602     void run() {
   603       NodeRefMap nodeRefMap(_from);
   604       ArcRefMap arcRefMap(_from);
   605       _core_bits::DigraphCopySelector<To>::
   606         copy(_to, _from, nodeRefMap, arcRefMap);
   607       for (int i = 0; i < int(_node_maps.size()); ++i) {
   608         _node_maps[i]->copy(_from, nodeRefMap);
   609       }
   610       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   611         _arc_maps[i]->copy(_from, arcRefMap);
   612       }
   613     }
   614 
   615   protected:
   616 
   617 
   618     const From& _from;
   619     To& _to;
   620 
   621     std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
   622     _node_maps;
   623 
   624     std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
   625     _arc_maps;
   626 
   627   };
   628 
   629   /// \brief Copy a digraph to another digraph.
   630   ///
   631   /// Copy a digraph to another digraph. The complete usage of the
   632   /// function is detailed in the DigraphCopy class, but a short
   633   /// example shows a basic work:
   634   ///\code
   635   /// copyDigraph(trg, src).nodeRef(nr).arcCrossRef(ecr).run();
   636   ///\endcode
   637   ///
   638   /// After the copy the \c nr map will contain the mapping from the
   639   /// nodes of the \c from digraph to the nodes of the \c to digraph and
   640   /// \c ecr will contain the mapping from the arcs of the \c to digraph
   641   /// to the arcs of the \c from digraph.
   642   ///
   643   /// \see DigraphCopy
   644   template <typename To, typename From>
   645   DigraphCopy<To, From> copyDigraph(To& to, const From& from) {
   646     return DigraphCopy<To, From>(to, from);
   647   }
   648 
   649   /// \brief Class to copy a graph.
   650   ///
   651   /// Class to copy a graph to another graph (duplicate a graph). The
   652   /// simplest way of using it is through the \c copyGraph() function.
   653   ///
   654   /// This class not just make a copy of a graph, but it can create
   655   /// references and cross references between the nodes, edges and arcs of
   656   /// the two graphs, it can copy maps for use with the newly created
   657   /// graph and copy nodes, edges and arcs.
   658   ///
   659   /// To make a copy from a graph, first an instance of GraphCopy
   660   /// should be created, then the data belongs to the graph should
   661   /// assigned to copy. In the end, the \c run() member should be
   662   /// called.
   663   ///
   664   /// The next code copies a graph with several data:
   665   ///\code
   666   ///  GraphCopy<NewGraph, OrigGraph> dc(new_graph, orig_graph);
   667   ///  // create a reference for the nodes
   668   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   669   ///  dc.nodeRef(nr);
   670   ///  // create a cross reference (inverse) for the edges
   671   ///  NewGraph::EdgeMap<OrigGraph::Arc> ecr(new_graph);
   672   ///  dc.edgeCrossRef(ecr);
   673   ///  // copy an arc map
   674   ///  OrigGraph::ArcMap<double> oamap(orig_graph);
   675   ///  NewGraph::ArcMap<double> namap(new_graph);
   676   ///  dc.arcMap(namap, oamap);
   677   ///  // copy a node
   678   ///  OrigGraph::Node on;
   679   ///  NewGraph::Node nn;
   680   ///  dc.node(nn, on);
   681   ///  // Executions of copy
   682   ///  dc.run();
   683   ///\endcode
   684   template <typename To, typename From>
   685   class GraphCopy {
   686   private:
   687 
   688     typedef typename From::Node Node;
   689     typedef typename From::NodeIt NodeIt;
   690     typedef typename From::Arc Arc;
   691     typedef typename From::ArcIt ArcIt;
   692     typedef typename From::Edge Edge;
   693     typedef typename From::EdgeIt EdgeIt;
   694 
   695     typedef typename To::Node TNode;
   696     typedef typename To::Arc TArc;
   697     typedef typename To::Edge TEdge;
   698 
   699     typedef typename From::template NodeMap<TNode> NodeRefMap;
   700     typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
   701 
   702     struct ArcRefMap {
   703       ArcRefMap(const To& to, const From& from,
   704                 const EdgeRefMap& edge_ref, const NodeRefMap& node_ref)
   705         : _to(to), _from(from),
   706           _edge_ref(edge_ref), _node_ref(node_ref) {}
   707 
   708       typedef typename From::Arc Key;
   709       typedef typename To::Arc Value;
   710 
   711       Value operator[](const Key& key) const {
   712         bool forward = _from.u(key) != _from.v(key) ?
   713           _node_ref[_from.source(key)] ==
   714           _to.source(_to.direct(_edge_ref[key], true)) :
   715           _from.direction(key);
   716         return _to.direct(_edge_ref[key], forward);
   717       }
   718 
   719       const To& _to;
   720       const From& _from;
   721       const EdgeRefMap& _edge_ref;
   722       const NodeRefMap& _node_ref;
   723     };
   724 
   725 
   726   public:
   727 
   728 
   729     /// \brief Constructor for the GraphCopy.
   730     ///
   731     /// It copies the content of the \c _from graph into the
   732     /// \c _to graph.
   733     GraphCopy(To& to, const From& from)
   734       : _from(from), _to(to) {}
   735 
   736     /// \brief Destructor of the GraphCopy
   737     ///
   738     /// Destructor of the GraphCopy
   739     ~GraphCopy() {
   740       for (int i = 0; i < int(_node_maps.size()); ++i) {
   741         delete _node_maps[i];
   742       }
   743       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   744         delete _arc_maps[i];
   745       }
   746       for (int i = 0; i < int(_edge_maps.size()); ++i) {
   747         delete _edge_maps[i];
   748       }
   749 
   750     }
   751 
   752     /// \brief Copies the node references into the given map.
   753     ///
   754     /// Copies the node references into the given map.
   755     template <typename NodeRef>
   756     GraphCopy& nodeRef(NodeRef& map) {
   757       _node_maps.push_back(new _core_bits::RefCopy<From, Node,
   758                            NodeRefMap, NodeRef>(map));
   759       return *this;
   760     }
   761 
   762     /// \brief Copies the node cross references into the given map.
   763     ///
   764     ///  Copies the node cross references (reverse references) into
   765     ///  the given map.
   766     template <typename NodeCrossRef>
   767     GraphCopy& nodeCrossRef(NodeCrossRef& map) {
   768       _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
   769                            NodeRefMap, NodeCrossRef>(map));
   770       return *this;
   771     }
   772 
   773     /// \brief Make copy of the given map.
   774     ///
   775     /// Makes copy of the given map for the newly created graph.
   776     /// The new map's key type is the to graph's node type,
   777     /// and the copied map's key type is the from graph's node
   778     /// type.
   779     template <typename ToMap, typename FromMap>
   780     GraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
   781       _node_maps.push_back(new _core_bits::MapCopy<From, Node,
   782                            NodeRefMap, ToMap, FromMap>(tmap, map));
   783       return *this;
   784     }
   785 
   786     /// \brief Make a copy of the given node.
   787     ///
   788     /// Make a copy of the given node.
   789     GraphCopy& node(TNode& tnode, const Node& snode) {
   790       _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
   791                            NodeRefMap, TNode>(tnode, snode));
   792       return *this;
   793     }
   794 
   795     /// \brief Copies the arc references into the given map.
   796     ///
   797     /// Copies the arc references into the given map.
   798     template <typename ArcRef>
   799     GraphCopy& arcRef(ArcRef& map) {
   800       _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
   801                           ArcRefMap, ArcRef>(map));
   802       return *this;
   803     }
   804 
   805     /// \brief Copies the arc cross references into the given map.
   806     ///
   807     ///  Copies the arc cross references (reverse references) into
   808     ///  the given map.
   809     template <typename ArcCrossRef>
   810     GraphCopy& arcCrossRef(ArcCrossRef& map) {
   811       _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
   812                           ArcRefMap, ArcCrossRef>(map));
   813       return *this;
   814     }
   815 
   816     /// \brief Make copy of the given map.
   817     ///
   818     /// Makes copy of the given map for the newly created graph.
   819     /// The new map's key type is the to graph's arc type,
   820     /// and the copied map's key type is the from graph's arc
   821     /// type.
   822     template <typename ToMap, typename FromMap>
   823     GraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
   824       _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
   825                           ArcRefMap, ToMap, FromMap>(tmap, map));
   826       return *this;
   827     }
   828 
   829     /// \brief Make a copy of the given arc.
   830     ///
   831     /// Make a copy of the given arc.
   832     GraphCopy& arc(TArc& tarc, const Arc& sarc) {
   833       _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
   834                           ArcRefMap, TArc>(tarc, sarc));
   835       return *this;
   836     }
   837 
   838     /// \brief Copies the edge references into the given map.
   839     ///
   840     /// Copies the edge references into the given map.
   841     template <typename EdgeRef>
   842     GraphCopy& edgeRef(EdgeRef& map) {
   843       _edge_maps.push_back(new _core_bits::RefCopy<From, Edge,
   844                            EdgeRefMap, EdgeRef>(map));
   845       return *this;
   846     }
   847 
   848     /// \brief Copies the edge cross references into the given map.
   849     ///
   850     /// Copies the edge cross references (reverse
   851     /// references) into the given map.
   852     template <typename EdgeCrossRef>
   853     GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
   854       _edge_maps.push_back(new _core_bits::CrossRefCopy<From,
   855                            Edge, EdgeRefMap, EdgeCrossRef>(map));
   856       return *this;
   857     }
   858 
   859     /// \brief Make copy of the given map.
   860     ///
   861     /// Makes copy of the given map for the newly created graph.
   862     /// The new map's key type is the to graph's edge type,
   863     /// and the copied map's key type is the from graph's edge
   864     /// type.
   865     template <typename ToMap, typename FromMap>
   866     GraphCopy& edgeMap(ToMap& tmap, const FromMap& map) {
   867       _edge_maps.push_back(new _core_bits::MapCopy<From, Edge,
   868                            EdgeRefMap, ToMap, FromMap>(tmap, map));
   869       return *this;
   870     }
   871 
   872     /// \brief Make a copy of the given edge.
   873     ///
   874     /// Make a copy of the given edge.
   875     GraphCopy& edge(TEdge& tedge, const Edge& sedge) {
   876       _edge_maps.push_back(new _core_bits::ItemCopy<From, Edge,
   877                            EdgeRefMap, TEdge>(tedge, sedge));
   878       return *this;
   879     }
   880 
   881     /// \brief Executes the copies.
   882     ///
   883     /// Executes the copies.
   884     void run() {
   885       NodeRefMap nodeRefMap(_from);
   886       EdgeRefMap edgeRefMap(_from);
   887       ArcRefMap arcRefMap(_to, _from, edgeRefMap, nodeRefMap);
   888       _core_bits::GraphCopySelector<To>::
   889         copy(_to, _from, nodeRefMap, edgeRefMap);
   890       for (int i = 0; i < int(_node_maps.size()); ++i) {
   891         _node_maps[i]->copy(_from, nodeRefMap);
   892       }
   893       for (int i = 0; i < int(_edge_maps.size()); ++i) {
   894         _edge_maps[i]->copy(_from, edgeRefMap);
   895       }
   896       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   897         _arc_maps[i]->copy(_from, arcRefMap);
   898       }
   899     }
   900 
   901   private:
   902 
   903     const From& _from;
   904     To& _to;
   905 
   906     std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
   907     _node_maps;
   908 
   909     std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
   910     _arc_maps;
   911 
   912     std::vector<_core_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
   913     _edge_maps;
   914 
   915   };
   916 
   917   /// \brief Copy a graph to another graph.
   918   ///
   919   /// Copy a graph to another graph. The complete usage of the
   920   /// function is detailed in the GraphCopy class, but a short
   921   /// example shows a basic work:
   922   ///\code
   923   /// copyGraph(trg, src).nodeRef(nr).arcCrossRef(ecr).run();
   924   ///\endcode
   925   ///
   926   /// After the copy the \c nr map will contain the mapping from the
   927   /// nodes of the \c from graph to the nodes of the \c to graph and
   928   /// \c ecr will contain the mapping from the arcs of the \c to graph
   929   /// to the arcs of the \c from graph.
   930   ///
   931   /// \see GraphCopy
   932   template <typename To, typename From>
   933   GraphCopy<To, From>
   934   copyGraph(To& to, const From& from) {
   935     return GraphCopy<To, From>(to, from);
   936   }
   937 
   938   namespace _core_bits {
   939 
   940     template <typename Graph, typename Enable = void>
   941     struct FindArcSelector {
   942       typedef typename Graph::Node Node;
   943       typedef typename Graph::Arc Arc;
   944       static Arc find(const Graph &g, Node u, Node v, Arc e) {
   945         if (e == INVALID) {
   946           g.firstOut(e, u);
   947         } else {
   948           g.nextOut(e);
   949         }
   950         while (e != INVALID && g.target(e) != v) {
   951           g.nextOut(e);
   952         }
   953         return e;
   954       }
   955     };
   956 
   957     template <typename Graph>
   958     struct FindArcSelector<
   959       Graph,
   960       typename enable_if<typename Graph::FindEdgeTag, void>::type>
   961     {
   962       typedef typename Graph::Node Node;
   963       typedef typename Graph::Arc Arc;
   964       static Arc find(const Graph &g, Node u, Node v, Arc prev) {
   965         return g.findArc(u, v, prev);
   966       }
   967     };
   968   }
   969 
   970   /// \brief Finds an arc between two nodes of a graph.
   971   ///
   972   /// Finds an arc from node \c u to node \c v in graph \c g.
   973   ///
   974   /// If \c prev is \ref INVALID (this is the default value), then
   975   /// it finds the first arc from \c u to \c v. Otherwise it looks for
   976   /// the next arc from \c u to \c v after \c prev.
   977   /// \return The found arc or \ref INVALID if there is no such an arc.
   978   ///
   979   /// Thus you can iterate through each arc from \c u to \c v as it follows.
   980   ///\code
   981   /// for(Arc e=findArc(g,u,v);e!=INVALID;e=findArc(g,u,v,e)) {
   982   ///   ...
   983   /// }
   984   ///\endcode
   985   ///
   986   ///\sa ArcLookUp
   987   ///\sa AllArcLookUp
   988   ///\sa DynArcLookUp
   989   ///\sa ConArcIt
   990   template <typename Graph>
   991   inline typename Graph::Arc
   992   findArc(const Graph &g, typename Graph::Node u, typename Graph::Node v,
   993           typename Graph::Arc prev = INVALID) {
   994     return _core_bits::FindArcSelector<Graph>::find(g, u, v, prev);
   995   }
   996 
   997   /// \brief Iterator for iterating on arcs connected the same nodes.
   998   ///
   999   /// Iterator for iterating on arcs connected the same nodes. It is
  1000   /// higher level interface for the findArc() function. You can
  1001   /// use it the following way:
  1002   ///\code
  1003   /// for (ConArcIt<Graph> it(g, src, trg); it != INVALID; ++it) {
  1004   ///   ...
  1005   /// }
  1006   ///\endcode
  1007   ///
  1008   ///\sa findArc()
  1009   ///\sa ArcLookUp
  1010   ///\sa AllArcLookUp
  1011   ///\sa DynArcLookUp
  1012   template <typename _Graph>
  1013   class ConArcIt : public _Graph::Arc {
  1014   public:
  1015 
  1016     typedef _Graph Graph;
  1017     typedef typename Graph::Arc Parent;
  1018 
  1019     typedef typename Graph::Arc Arc;
  1020     typedef typename Graph::Node Node;
  1021 
  1022     /// \brief Constructor.
  1023     ///
  1024     /// Construct a new ConArcIt iterating on the arcs which
  1025     /// connects the \c u and \c v node.
  1026     ConArcIt(const Graph& g, Node u, Node v) : _graph(g) {
  1027       Parent::operator=(findArc(_graph, u, v));
  1028     }
  1029 
  1030     /// \brief Constructor.
  1031     ///
  1032     /// Construct a new ConArcIt which continues the iterating from
  1033     /// the \c e arc.
  1034     ConArcIt(const Graph& g, Arc a) : Parent(a), _graph(g) {}
  1035 
  1036     /// \brief Increment operator.
  1037     ///
  1038     /// It increments the iterator and gives back the next arc.
  1039     ConArcIt& operator++() {
  1040       Parent::operator=(findArc(_graph, _graph.source(*this),
  1041                                 _graph.target(*this), *this));
  1042       return *this;
  1043     }
  1044   private:
  1045     const Graph& _graph;
  1046   };
  1047 
  1048   namespace _core_bits {
  1049 
  1050     template <typename Graph, typename Enable = void>
  1051     struct FindEdgeSelector {
  1052       typedef typename Graph::Node Node;
  1053       typedef typename Graph::Edge Edge;
  1054       static Edge find(const Graph &g, Node u, Node v, Edge e) {
  1055         bool b;
  1056         if (u != v) {
  1057           if (e == INVALID) {
  1058             g.firstInc(e, b, u);
  1059           } else {
  1060             b = g.u(e) == u;
  1061             g.nextInc(e, b);
  1062           }
  1063           while (e != INVALID && (b ? g.v(e) : g.u(e)) != v) {
  1064             g.nextInc(e, b);
  1065           }
  1066         } else {
  1067           if (e == INVALID) {
  1068             g.firstInc(e, b, u);
  1069           } else {
  1070             b = true;
  1071             g.nextInc(e, b);
  1072           }
  1073           while (e != INVALID && (!b || g.v(e) != v)) {
  1074             g.nextInc(e, b);
  1075           }
  1076         }
  1077         return e;
  1078       }
  1079     };
  1080 
  1081     template <typename Graph>
  1082     struct FindEdgeSelector<
  1083       Graph,
  1084       typename enable_if<typename Graph::FindEdgeTag, void>::type>
  1085     {
  1086       typedef typename Graph::Node Node;
  1087       typedef typename Graph::Edge Edge;
  1088       static Edge find(const Graph &g, Node u, Node v, Edge prev) {
  1089         return g.findEdge(u, v, prev);
  1090       }
  1091     };
  1092   }
  1093 
  1094   /// \brief Finds an edge between two nodes of a graph.
  1095   ///
  1096   /// Finds an edge from node \c u to node \c v in graph \c g.
  1097   /// If the node \c u and node \c v is equal then each loop edge
  1098   /// will be enumerated once.
  1099   ///
  1100   /// If \c prev is \ref INVALID (this is the default value), then
  1101   /// it finds the first arc from \c u to \c v. Otherwise it looks for
  1102   /// the next arc from \c u to \c v after \c prev.
  1103   /// \return The found arc or \ref INVALID if there is no such an arc.
  1104   ///
  1105   /// Thus you can iterate through each arc from \c u to \c v as it follows.
  1106   ///\code
  1107   /// for(Edge e = findEdge(g,u,v); e != INVALID;
  1108   ///     e = findEdge(g,u,v,e)) {
  1109   ///   ...
  1110   /// }
  1111   ///\endcode
  1112   ///
  1113   ///\sa ConEdgeIt
  1114 
  1115   template <typename Graph>
  1116   inline typename Graph::Edge
  1117   findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,
  1118             typename Graph::Edge p = INVALID) {
  1119     return _core_bits::FindEdgeSelector<Graph>::find(g, u, v, p);
  1120   }
  1121 
  1122   /// \brief Iterator for iterating on edges connected the same nodes.
  1123   ///
  1124   /// Iterator for iterating on edges connected the same nodes. It is
  1125   /// higher level interface for the findEdge() function. You can
  1126   /// use it the following way:
  1127   ///\code
  1128   /// for (ConEdgeIt<Graph> it(g, src, trg); it != INVALID; ++it) {
  1129   ///   ...
  1130   /// }
  1131   ///\endcode
  1132   ///
  1133   ///\sa findEdge()
  1134   template <typename _Graph>
  1135   class ConEdgeIt : public _Graph::Edge {
  1136   public:
  1137 
  1138     typedef _Graph Graph;
  1139     typedef typename Graph::Edge Parent;
  1140 
  1141     typedef typename Graph::Edge Edge;
  1142     typedef typename Graph::Node Node;
  1143 
  1144     /// \brief Constructor.
  1145     ///
  1146     /// Construct a new ConEdgeIt iterating on the edges which
  1147     /// connects the \c u and \c v node.
  1148     ConEdgeIt(const Graph& g, Node u, Node v) : _graph(g) {
  1149       Parent::operator=(findEdge(_graph, u, v));
  1150     }
  1151 
  1152     /// \brief Constructor.
  1153     ///
  1154     /// Construct a new ConEdgeIt which continues the iterating from
  1155     /// the \c e edge.
  1156     ConEdgeIt(const Graph& g, Edge e) : Parent(e), _graph(g) {}
  1157 
  1158     /// \brief Increment operator.
  1159     ///
  1160     /// It increments the iterator and gives back the next edge.
  1161     ConEdgeIt& operator++() {
  1162       Parent::operator=(findEdge(_graph, _graph.u(*this),
  1163                                  _graph.v(*this), *this));
  1164       return *this;
  1165     }
  1166   private:
  1167     const Graph& _graph;
  1168   };
  1169 
  1170 
  1171   ///Dynamic arc look up between given endpoints.
  1172 
  1173   ///Using this class, you can find an arc in a digraph from a given
  1174   ///source to a given target in amortized time <em>O(log</em>d<em>)</em>,
  1175   ///where <em>d</em> is the out-degree of the source node.
  1176   ///
  1177   ///It is possible to find \e all parallel arcs between two nodes with
  1178   ///the \c operator() member.
  1179   ///
  1180   ///See the \ref ArcLookUp and \ref AllArcLookUp classes if your
  1181   ///digraph is not changed so frequently.
  1182   ///
  1183   ///This class uses a self-adjusting binary search tree, Sleator's
  1184   ///and Tarjan's Splay tree for guarantee the logarithmic amortized
  1185   ///time bound for arc lookups. This class also guarantees the
  1186   ///optimal time bound in a constant factor for any distribution of
  1187   ///queries.
  1188   ///
  1189   ///\tparam G The type of the underlying digraph.
  1190   ///
  1191   ///\sa ArcLookUp
  1192   ///\sa AllArcLookUp
  1193   template<class G>
  1194   class DynArcLookUp
  1195     : protected ItemSetTraits<G, typename G::Arc>::ItemNotifier::ObserverBase
  1196   {
  1197   public:
  1198     typedef typename ItemSetTraits<G, typename G::Arc>
  1199     ::ItemNotifier::ObserverBase Parent;
  1200 
  1201     TEMPLATE_DIGRAPH_TYPEDEFS(G);
  1202     typedef G Digraph;
  1203 
  1204   protected:
  1205 
  1206     class AutoNodeMap : public ItemSetTraits<G, Node>::template Map<Arc>::Type {
  1207     public:
  1208 
  1209       typedef typename ItemSetTraits<G, Node>::template Map<Arc>::Type Parent;
  1210 
  1211       AutoNodeMap(const G& digraph) : Parent(digraph, INVALID) {}
  1212 
  1213       virtual void add(const Node& node) {
  1214         Parent::add(node);
  1215         Parent::set(node, INVALID);
  1216       }
  1217 
  1218       virtual void add(const std::vector<Node>& nodes) {
  1219         Parent::add(nodes);
  1220         for (int i = 0; i < int(nodes.size()); ++i) {
  1221           Parent::set(nodes[i], INVALID);
  1222         }
  1223       }
  1224 
  1225       virtual void build() {
  1226         Parent::build();
  1227         Node it;
  1228         typename Parent::Notifier* nf = Parent::notifier();
  1229         for (nf->first(it); it != INVALID; nf->next(it)) {
  1230           Parent::set(it, INVALID);
  1231         }
  1232       }
  1233     };
  1234 
  1235     const Digraph &_g;
  1236     AutoNodeMap _head;
  1237     typename Digraph::template ArcMap<Arc> _parent;
  1238     typename Digraph::template ArcMap<Arc> _left;
  1239     typename Digraph::template ArcMap<Arc> _right;
  1240 
  1241     class ArcLess {
  1242       const Digraph &g;
  1243     public:
  1244       ArcLess(const Digraph &_g) : g(_g) {}
  1245       bool operator()(Arc a,Arc b) const
  1246       {
  1247         return g.target(a)<g.target(b);
  1248       }
  1249     };
  1250 
  1251   public:
  1252 
  1253     ///Constructor
  1254 
  1255     ///Constructor.
  1256     ///
  1257     ///It builds up the search database.
  1258     DynArcLookUp(const Digraph &g)
  1259       : _g(g),_head(g),_parent(g),_left(g),_right(g)
  1260     {
  1261       Parent::attach(_g.notifier(typename Digraph::Arc()));
  1262       refresh();
  1263     }
  1264 
  1265   protected:
  1266 
  1267     virtual void add(const Arc& arc) {
  1268       insert(arc);
  1269     }
  1270 
  1271     virtual void add(const std::vector<Arc>& arcs) {
  1272       for (int i = 0; i < int(arcs.size()); ++i) {
  1273         insert(arcs[i]);
  1274       }
  1275     }
  1276 
  1277     virtual void erase(const Arc& arc) {
  1278       remove(arc);
  1279     }
  1280 
  1281     virtual void erase(const std::vector<Arc>& arcs) {
  1282       for (int i = 0; i < int(arcs.size()); ++i) {
  1283         remove(arcs[i]);
  1284       }
  1285     }
  1286 
  1287     virtual void build() {
  1288       refresh();
  1289     }
  1290 
  1291     virtual void clear() {
  1292       for(NodeIt n(_g);n!=INVALID;++n) {
  1293         _head.set(n, INVALID);
  1294       }
  1295     }
  1296 
  1297     void insert(Arc arc) {
  1298       Node s = _g.source(arc);
  1299       Node t = _g.target(arc);
  1300       _left.set(arc, INVALID);
  1301       _right.set(arc, INVALID);
  1302 
  1303       Arc e = _head[s];
  1304       if (e == INVALID) {
  1305         _head.set(s, arc);
  1306         _parent.set(arc, INVALID);
  1307         return;
  1308       }
  1309       while (true) {
  1310         if (t < _g.target(e)) {
  1311           if (_left[e] == INVALID) {
  1312             _left.set(e, arc);
  1313             _parent.set(arc, e);
  1314             splay(arc);
  1315             return;
  1316           } else {
  1317             e = _left[e];
  1318           }
  1319         } else {
  1320           if (_right[e] == INVALID) {
  1321             _right.set(e, arc);
  1322             _parent.set(arc, e);
  1323             splay(arc);
  1324             return;
  1325           } else {
  1326             e = _right[e];
  1327           }
  1328         }
  1329       }
  1330     }
  1331 
  1332     void remove(Arc arc) {
  1333       if (_left[arc] == INVALID) {
  1334         if (_right[arc] != INVALID) {
  1335           _parent.set(_right[arc], _parent[arc]);
  1336         }
  1337         if (_parent[arc] != INVALID) {
  1338           if (_left[_parent[arc]] == arc) {
  1339             _left.set(_parent[arc], _right[arc]);
  1340           } else {
  1341             _right.set(_parent[arc], _right[arc]);
  1342           }
  1343         } else {
  1344           _head.set(_g.source(arc), _right[arc]);
  1345         }
  1346       } else if (_right[arc] == INVALID) {
  1347         _parent.set(_left[arc], _parent[arc]);
  1348         if (_parent[arc] != INVALID) {
  1349           if (_left[_parent[arc]] == arc) {
  1350             _left.set(_parent[arc], _left[arc]);
  1351           } else {
  1352             _right.set(_parent[arc], _left[arc]);
  1353           }
  1354         } else {
  1355           _head.set(_g.source(arc), _left[arc]);
  1356         }
  1357       } else {
  1358         Arc e = _left[arc];
  1359         if (_right[e] != INVALID) {
  1360           e = _right[e];
  1361           while (_right[e] != INVALID) {
  1362             e = _right[e];
  1363           }
  1364           Arc s = _parent[e];
  1365           _right.set(_parent[e], _left[e]);
  1366           if (_left[e] != INVALID) {
  1367             _parent.set(_left[e], _parent[e]);
  1368           }
  1369 
  1370           _left.set(e, _left[arc]);
  1371           _parent.set(_left[arc], e);
  1372           _right.set(e, _right[arc]);
  1373           _parent.set(_right[arc], e);
  1374 
  1375           _parent.set(e, _parent[arc]);
  1376           if (_parent[arc] != INVALID) {
  1377             if (_left[_parent[arc]] == arc) {
  1378               _left.set(_parent[arc], e);
  1379             } else {
  1380               _right.set(_parent[arc], e);
  1381             }
  1382           }
  1383           splay(s);
  1384         } else {
  1385           _right.set(e, _right[arc]);
  1386           _parent.set(_right[arc], e);
  1387           _parent.set(e, _parent[arc]);
  1388 
  1389           if (_parent[arc] != INVALID) {
  1390             if (_left[_parent[arc]] == arc) {
  1391               _left.set(_parent[arc], e);
  1392             } else {
  1393               _right.set(_parent[arc], e);
  1394             }
  1395           } else {
  1396             _head.set(_g.source(arc), e);
  1397           }
  1398         }
  1399       }
  1400     }
  1401 
  1402     Arc refreshRec(std::vector<Arc> &v,int a,int b)
  1403     {
  1404       int m=(a+b)/2;
  1405       Arc me=v[m];
  1406       if (a < m) {
  1407         Arc left = refreshRec(v,a,m-1);
  1408         _left.set(me, left);
  1409         _parent.set(left, me);
  1410       } else {
  1411         _left.set(me, INVALID);
  1412       }
  1413       if (m < b) {
  1414         Arc right = refreshRec(v,m+1,b);
  1415         _right.set(me, right);
  1416         _parent.set(right, me);
  1417       } else {
  1418         _right.set(me, INVALID);
  1419       }
  1420       return me;
  1421     }
  1422 
  1423     void refresh() {
  1424       for(NodeIt n(_g);n!=INVALID;++n) {
  1425         std::vector<Arc> v;
  1426         for(OutArcIt a(_g,n);a!=INVALID;++a) v.push_back(a);
  1427         if (!v.empty()) {
  1428           std::sort(v.begin(),v.end(),ArcLess(_g));
  1429           Arc head = refreshRec(v,0,v.size()-1);
  1430           _head.set(n, head);
  1431           _parent.set(head, INVALID);
  1432         }
  1433         else _head.set(n, INVALID);
  1434       }
  1435     }
  1436 
  1437     void zig(Arc v) {
  1438       Arc w = _parent[v];
  1439       _parent.set(v, _parent[w]);
  1440       _parent.set(w, v);
  1441       _left.set(w, _right[v]);
  1442       _right.set(v, w);
  1443       if (_parent[v] != INVALID) {
  1444         if (_right[_parent[v]] == w) {
  1445           _right.set(_parent[v], v);
  1446         } else {
  1447           _left.set(_parent[v], v);
  1448         }
  1449       }
  1450       if (_left[w] != INVALID){
  1451         _parent.set(_left[w], w);
  1452       }
  1453     }
  1454 
  1455     void zag(Arc v) {
  1456       Arc w = _parent[v];
  1457       _parent.set(v, _parent[w]);
  1458       _parent.set(w, v);
  1459       _right.set(w, _left[v]);
  1460       _left.set(v, w);
  1461       if (_parent[v] != INVALID){
  1462         if (_left[_parent[v]] == w) {
  1463           _left.set(_parent[v], v);
  1464         } else {
  1465           _right.set(_parent[v], v);
  1466         }
  1467       }
  1468       if (_right[w] != INVALID){
  1469         _parent.set(_right[w], w);
  1470       }
  1471     }
  1472 
  1473     void splay(Arc v) {
  1474       while (_parent[v] != INVALID) {
  1475         if (v == _left[_parent[v]]) {
  1476           if (_parent[_parent[v]] == INVALID) {
  1477             zig(v);
  1478           } else {
  1479             if (_parent[v] == _left[_parent[_parent[v]]]) {
  1480               zig(_parent[v]);
  1481               zig(v);
  1482             } else {
  1483               zig(v);
  1484               zag(v);
  1485             }
  1486           }
  1487         } else {
  1488           if (_parent[_parent[v]] == INVALID) {
  1489             zag(v);
  1490           } else {
  1491             if (_parent[v] == _left[_parent[_parent[v]]]) {
  1492               zag(v);
  1493               zig(v);
  1494             } else {
  1495               zag(_parent[v]);
  1496               zag(v);
  1497             }
  1498           }
  1499         }
  1500       }
  1501       _head[_g.source(v)] = v;
  1502     }
  1503 
  1504 
  1505   public:
  1506 
  1507     ///Find an arc between two nodes.
  1508 
  1509     ///Find an arc between two nodes.
  1510     ///\param s The source node
  1511     ///\param t The target node
  1512     ///\param p The previous arc between \c s and \c t. It it is INVALID or
  1513     ///not given, the operator finds the first appropriate arc.
  1514     ///\return An arc from \c s to \c t after \c p or
  1515     ///\ref INVALID if there is no more.
  1516     ///
  1517     ///For example, you can count the number of arcs from \c u to \c v in the
  1518     ///following way.
  1519     ///\code
  1520     ///DynArcLookUp<ListDigraph> ae(g);
  1521     ///...
  1522     ///int n=0;
  1523     ///for(Arc e=ae(u,v);e!=INVALID;e=ae(u,v,e)) n++;
  1524     ///\endcode
  1525     ///
  1526     ///Finding the arcs take at most <em>O(</em>log<em>d)</em>
  1527     ///amortized time, specifically, the time complexity of the lookups
  1528     ///is equal to the optimal search tree implementation for the
  1529     ///current query distribution in a constant factor.
  1530     ///
  1531     ///\note This is a dynamic data structure, therefore the data
  1532     ///structure is updated after each graph alteration. However,
  1533     ///theoretically this data structure is faster than \c ArcLookUp
  1534     ///or AllEdgeLookup, but it often provides worse performance than
  1535     ///them.
  1536     ///
  1537     Arc operator()(Node s, Node t, Arc p = INVALID) const  {
  1538       if (p == INVALID) {
  1539         Arc a = _head[s];
  1540         if (a == INVALID) return INVALID;
  1541         Arc r = INVALID;
  1542         while (true) {
  1543           if (_g.target(a) < t) {
  1544             if (_right[a] == INVALID) {
  1545               const_cast<DynArcLookUp&>(*this).splay(a);
  1546               return r;
  1547             } else {
  1548               a = _right[a];
  1549             }
  1550           } else {
  1551             if (_g.target(a) == t) {
  1552               r = a;
  1553             }
  1554             if (_left[a] == INVALID) {
  1555               const_cast<DynArcLookUp&>(*this).splay(a);
  1556               return r;
  1557             } else {
  1558               a = _left[a];
  1559             }
  1560           }
  1561         }
  1562       } else {
  1563         Arc a = p;
  1564         if (_right[a] != INVALID) {
  1565           a = _right[a];
  1566           while (_left[a] != INVALID) {
  1567             a = _left[a];
  1568           }
  1569           const_cast<DynArcLookUp&>(*this).splay(a);
  1570         } else {
  1571           while (_parent[a] != INVALID && _right[_parent[a]] ==  a) {
  1572             a = _parent[a];
  1573           }
  1574           if (_parent[a] == INVALID) {
  1575             return INVALID;
  1576           } else {
  1577             a = _parent[a];
  1578             const_cast<DynArcLookUp&>(*this).splay(a);
  1579           }
  1580         }
  1581         if (_g.target(a) == t) return a;
  1582         else return INVALID;
  1583       }
  1584     }
  1585 
  1586   };
  1587 
  1588   ///Fast arc look up between given endpoints.
  1589 
  1590   ///Using this class, you can find an arc in a digraph from a given
  1591   ///source to a given target in time <em>O(log d)</em>,
  1592   ///where <em>d</em> is the out-degree of the source node.
  1593   ///
  1594   ///It is not possible to find \e all parallel arcs between two nodes.
  1595   ///Use \ref AllArcLookUp for this purpose.
  1596   ///
  1597   ///\warning This class is static, so you should refresh() (or at least
  1598   ///refresh(Node)) this data structure
  1599   ///whenever the digraph changes. This is a time consuming (superlinearly
  1600   ///proportional (<em>O(m</em>log<em>m)</em>) to the number of arcs).
  1601   ///
  1602   ///\tparam G The type of the underlying digraph.
  1603   ///
  1604   ///\sa DynArcLookUp
  1605   ///\sa AllArcLookUp
  1606   template<class G>
  1607   class ArcLookUp
  1608   {
  1609   public:
  1610     TEMPLATE_DIGRAPH_TYPEDEFS(G);
  1611     typedef G Digraph;
  1612 
  1613   protected:
  1614     const Digraph &_g;
  1615     typename Digraph::template NodeMap<Arc> _head;
  1616     typename Digraph::template ArcMap<Arc> _left;
  1617     typename Digraph::template ArcMap<Arc> _right;
  1618 
  1619     class ArcLess {
  1620       const Digraph &g;
  1621     public:
  1622       ArcLess(const Digraph &_g) : g(_g) {}
  1623       bool operator()(Arc a,Arc b) const
  1624       {
  1625         return g.target(a)<g.target(b);
  1626       }
  1627     };
  1628 
  1629   public:
  1630 
  1631     ///Constructor
  1632 
  1633     ///Constructor.
  1634     ///
  1635     ///It builds up the search database, which remains valid until the digraph
  1636     ///changes.
  1637     ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}
  1638 
  1639   private:
  1640     Arc refreshRec(std::vector<Arc> &v,int a,int b)
  1641     {
  1642       int m=(a+b)/2;
  1643       Arc me=v[m];
  1644       _left[me] = a<m?refreshRec(v,a,m-1):INVALID;
  1645       _right[me] = m<b?refreshRec(v,m+1,b):INVALID;
  1646       return me;
  1647     }
  1648   public:
  1649     ///Refresh the data structure at a node.
  1650 
  1651     ///Build up the search database of node \c n.
  1652     ///
  1653     ///It runs in time <em>O(d</em>log<em>d)</em>, where <em>d</em> is
  1654     ///the number of the outgoing arcs of \c n.
  1655     void refresh(Node n)
  1656     {
  1657       std::vector<Arc> v;
  1658       for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
  1659       if(v.size()) {
  1660         std::sort(v.begin(),v.end(),ArcLess(_g));
  1661         _head[n]=refreshRec(v,0,v.size()-1);
  1662       }
  1663       else _head[n]=INVALID;
  1664     }
  1665     ///Refresh the full data structure.
  1666 
  1667     ///Build up the full search database. In fact, it simply calls
  1668     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  1669     ///
  1670     ///It runs in time <em>O(m</em>log<em>D)</em>, where <em>m</em> is
  1671     ///the number of the arcs of \c n and <em>D</em> is the maximum
  1672     ///out-degree of the digraph.
  1673 
  1674     void refresh()
  1675     {
  1676       for(NodeIt n(_g);n!=INVALID;++n) refresh(n);
  1677     }
  1678 
  1679     ///Find an arc between two nodes.
  1680 
  1681     ///Find an arc between two nodes in time <em>O(</em>log<em>d)</em>, where
  1682     /// <em>d</em> is the number of outgoing arcs of \c s.
  1683     ///\param s The source node
  1684     ///\param t The target node
  1685     ///\return An arc from \c s to \c t if there exists,
  1686     ///\ref INVALID otherwise.
  1687     ///
  1688     ///\warning If you change the digraph, refresh() must be called before using
  1689     ///this operator. If you change the outgoing arcs of
  1690     ///a single node \c n, then
  1691     ///\ref refresh(Node) "refresh(n)" is enough.
  1692     ///
  1693     Arc operator()(Node s, Node t) const
  1694     {
  1695       Arc e;
  1696       for(e=_head[s];
  1697           e!=INVALID&&_g.target(e)!=t;
  1698           e = t < _g.target(e)?_left[e]:_right[e]) ;
  1699       return e;
  1700     }
  1701 
  1702   };
  1703 
  1704   ///Fast look up of all arcs between given endpoints.
  1705 
  1706   ///This class is the same as \ref ArcLookUp, with the addition
  1707   ///that it makes it possible to find all arcs between given endpoints.
  1708   ///
  1709   ///\warning This class is static, so you should refresh() (or at least
  1710   ///refresh(Node)) this data structure
  1711   ///whenever the digraph changes. This is a time consuming (superlinearly
  1712   ///proportional (<em>O(m</em>log<em>m)</em>) to the number of arcs).
  1713   ///
  1714   ///\tparam G The type of the underlying digraph.
  1715   ///
  1716   ///\sa DynArcLookUp
  1717   ///\sa ArcLookUp
  1718   template<class G>
  1719   class AllArcLookUp : public ArcLookUp<G>
  1720   {
  1721     using ArcLookUp<G>::_g;
  1722     using ArcLookUp<G>::_right;
  1723     using ArcLookUp<G>::_left;
  1724     using ArcLookUp<G>::_head;
  1725 
  1726     TEMPLATE_DIGRAPH_TYPEDEFS(G);
  1727     typedef G Digraph;
  1728 
  1729     typename Digraph::template ArcMap<Arc> _next;
  1730 
  1731     Arc refreshNext(Arc head,Arc next=INVALID)
  1732     {
  1733       if(head==INVALID) return next;
  1734       else {
  1735         next=refreshNext(_right[head],next);
  1736 //         _next[head]=next;
  1737         _next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
  1738           ? next : INVALID;
  1739         return refreshNext(_left[head],head);
  1740       }
  1741     }
  1742 
  1743     void refreshNext()
  1744     {
  1745       for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
  1746     }
  1747 
  1748   public:
  1749     ///Constructor
  1750 
  1751     ///Constructor.
  1752     ///
  1753     ///It builds up the search database, which remains valid until the digraph
  1754     ///changes.
  1755     AllArcLookUp(const Digraph &g) : ArcLookUp<G>(g), _next(g) {refreshNext();}
  1756 
  1757     ///Refresh the data structure at a node.
  1758 
  1759     ///Build up the search database of node \c n.
  1760     ///
  1761     ///It runs in time <em>O(d</em>log<em>d)</em>, where <em>d</em> is
  1762     ///the number of the outgoing arcs of \c n.
  1763 
  1764     void refresh(Node n)
  1765     {
  1766       ArcLookUp<G>::refresh(n);
  1767       refreshNext(_head[n]);
  1768     }
  1769 
  1770     ///Refresh the full data structure.
  1771 
  1772     ///Build up the full search database. In fact, it simply calls
  1773     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  1774     ///
  1775     ///It runs in time <em>O(m</em>log<em>D)</em>, where <em>m</em> is
  1776     ///the number of the arcs of \c n and <em>D</em> is the maximum
  1777     ///out-degree of the digraph.
  1778 
  1779     void refresh()
  1780     {
  1781       for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
  1782     }
  1783 
  1784     ///Find an arc between two nodes.
  1785 
  1786     ///Find an arc between two nodes.
  1787     ///\param s The source node
  1788     ///\param t The target node
  1789     ///\param prev The previous arc between \c s and \c t. It it is INVALID or
  1790     ///not given, the operator finds the first appropriate arc.
  1791     ///\return An arc from \c s to \c t after \c prev or
  1792     ///\ref INVALID if there is no more.
  1793     ///
  1794     ///For example, you can count the number of arcs from \c u to \c v in the
  1795     ///following way.
  1796     ///\code
  1797     ///AllArcLookUp<ListDigraph> ae(g);
  1798     ///...
  1799     ///int n=0;
  1800     ///for(Arc e=ae(u,v);e!=INVALID;e=ae(u,v,e)) n++;
  1801     ///\endcode
  1802     ///
  1803     ///Finding the first arc take <em>O(</em>log<em>d)</em> time, where
  1804     /// <em>d</em> is the number of outgoing arcs of \c s. Then, the
  1805     ///consecutive arcs are found in constant time.
  1806     ///
  1807     ///\warning If you change the digraph, refresh() must be called before using
  1808     ///this operator. If you change the outgoing arcs of
  1809     ///a single node \c n, then
  1810     ///\ref refresh(Node) "refresh(n)" is enough.
  1811     ///
  1812 #ifdef DOXYGEN
  1813     Arc operator()(Node s, Node t, Arc prev=INVALID) const {}
  1814 #else
  1815     using ArcLookUp<G>::operator() ;
  1816     Arc operator()(Node s, Node t, Arc prev) const
  1817     {
  1818       return prev==INVALID?(*this)(s,t):_next[prev];
  1819     }
  1820 #endif
  1821 
  1822   };
  1823 
  1824   /// @}
  1825 
  1826 } //namespace lemon
  1827 
  1828 #endif