lemon/core.h
author Alpar Juttner <alpar@cs.elte.hu>
Mon, 23 Feb 2009 15:46:57 +0000
changeset 523 39aaeea2d471
parent 449 b0f74ca2e3ac
child 543 32fb28fc9d42
child 582 6a17a722b50e
permissions -rw-r--r--
Include /lemon/config.h globally (#230)
     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/core.h>
    26 #include <lemon/bits/enable_if.h>
    27 #include <lemon/bits/traits.h>
    28 #include <lemon/assert.h>
    29 
    30 ///\file
    31 ///\brief LEMON core utilities.
    32 ///
    33 ///This header file contains core utilities for LEMON.
    34 ///It is automatically included by all graph types, therefore it usually
    35 ///do not have to be included directly.
    36 
    37 namespace lemon {
    38 
    39   /// \brief Dummy type to make it easier to create invalid iterators.
    40   ///
    41   /// Dummy type to make it easier to create invalid iterators.
    42   /// See \ref INVALID for the usage.
    43   struct Invalid {
    44   public:
    45     bool operator==(Invalid) { return true;  }
    46     bool operator!=(Invalid) { return false; }
    47     bool operator< (Invalid) { return false; }
    48   };
    49 
    50   /// \brief Invalid iterators.
    51   ///
    52   /// \ref Invalid is a global type that converts to each iterator
    53   /// in such a way that the value of the target iterator will be invalid.
    54 #ifdef LEMON_ONLY_TEMPLATES
    55   const Invalid INVALID = Invalid();
    56 #else
    57   extern const Invalid INVALID;
    58 #endif
    59 
    60   /// \addtogroup gutils
    61   /// @{
    62 
    63   ///Create convenience typedefs for the digraph types and iterators
    64 
    65   ///This \c \#define creates convenient type definitions for the following
    66   ///types of \c Digraph: \c Node,  \c NodeIt, \c Arc, \c ArcIt, \c InArcIt,
    67   ///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap,
    68   ///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap.
    69   ///
    70   ///\note If the graph type is a dependent type, ie. the graph type depend
    71   ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
    72   ///macro.
    73 #define DIGRAPH_TYPEDEFS(Digraph)                                       \
    74   typedef Digraph::Node Node;                                           \
    75   typedef Digraph::NodeIt NodeIt;                                       \
    76   typedef Digraph::Arc Arc;                                             \
    77   typedef Digraph::ArcIt ArcIt;                                         \
    78   typedef Digraph::InArcIt InArcIt;                                     \
    79   typedef Digraph::OutArcIt OutArcIt;                                   \
    80   typedef Digraph::NodeMap<bool> BoolNodeMap;                           \
    81   typedef Digraph::NodeMap<int> IntNodeMap;                             \
    82   typedef Digraph::NodeMap<double> DoubleNodeMap;                       \
    83   typedef Digraph::ArcMap<bool> BoolArcMap;                             \
    84   typedef Digraph::ArcMap<int> IntArcMap;                               \
    85   typedef Digraph::ArcMap<double> DoubleArcMap
    86 
    87   ///Create convenience typedefs for the digraph types and iterators
    88 
    89   ///\see DIGRAPH_TYPEDEFS
    90   ///
    91   ///\note Use this macro, if the graph type is a dependent type,
    92   ///ie. the graph type depend on a template parameter.
    93 #define TEMPLATE_DIGRAPH_TYPEDEFS(Digraph)                              \
    94   typedef typename Digraph::Node Node;                                  \
    95   typedef typename Digraph::NodeIt NodeIt;                              \
    96   typedef typename Digraph::Arc Arc;                                    \
    97   typedef typename Digraph::ArcIt ArcIt;                                \
    98   typedef typename Digraph::InArcIt InArcIt;                            \
    99   typedef typename Digraph::OutArcIt OutArcIt;                          \
   100   typedef typename Digraph::template NodeMap<bool> BoolNodeMap;         \
   101   typedef typename Digraph::template NodeMap<int> IntNodeMap;           \
   102   typedef typename Digraph::template NodeMap<double> DoubleNodeMap;     \
   103   typedef typename Digraph::template ArcMap<bool> BoolArcMap;           \
   104   typedef typename Digraph::template ArcMap<int> IntArcMap;             \
   105   typedef typename Digraph::template ArcMap<double> DoubleArcMap
   106 
   107   ///Create convenience typedefs for the graph types and iterators
   108 
   109   ///This \c \#define creates the same convenient type definitions as defined
   110   ///by \ref DIGRAPH_TYPEDEFS(Graph) and six more, namely it creates
   111   ///\c Edge, \c EdgeIt, \c IncEdgeIt, \c BoolEdgeMap, \c IntEdgeMap,
   112   ///\c DoubleEdgeMap.
   113   ///
   114   ///\note If the graph type is a dependent type, ie. the graph type depend
   115   ///on a template parameter, then use \c TEMPLATE_GRAPH_TYPEDEFS()
   116   ///macro.
   117 #define GRAPH_TYPEDEFS(Graph)                                           \
   118   DIGRAPH_TYPEDEFS(Graph);                                              \
   119   typedef Graph::Edge Edge;                                             \
   120   typedef Graph::EdgeIt EdgeIt;                                         \
   121   typedef Graph::IncEdgeIt IncEdgeIt;                                   \
   122   typedef Graph::EdgeMap<bool> BoolEdgeMap;                             \
   123   typedef Graph::EdgeMap<int> IntEdgeMap;                               \
   124   typedef Graph::EdgeMap<double> DoubleEdgeMap
   125 
   126   ///Create convenience typedefs for the graph types and iterators
   127 
   128   ///\see GRAPH_TYPEDEFS
   129   ///
   130   ///\note Use this macro, if the graph type is a dependent type,
   131   ///ie. the graph type depend on a template parameter.
   132 #define TEMPLATE_GRAPH_TYPEDEFS(Graph)                                  \
   133   TEMPLATE_DIGRAPH_TYPEDEFS(Graph);                                     \
   134   typedef typename Graph::Edge Edge;                                    \
   135   typedef typename Graph::EdgeIt EdgeIt;                                \
   136   typedef typename Graph::IncEdgeIt IncEdgeIt;                          \
   137   typedef typename Graph::template EdgeMap<bool> BoolEdgeMap;           \
   138   typedef typename Graph::template EdgeMap<int> IntEdgeMap;             \
   139   typedef typename Graph::template EdgeMap<double> DoubleEdgeMap
   140 
   141   /// \brief Function to count the items in a graph.
   142   ///
   143   /// This function counts the items (nodes, arcs etc.) in a graph.
   144   /// The complexity of the function is linear because
   145   /// it iterates on all of the items.
   146   template <typename Graph, typename Item>
   147   inline int countItems(const Graph& g) {
   148     typedef typename ItemSetTraits<Graph, Item>::ItemIt ItemIt;
   149     int num = 0;
   150     for (ItemIt it(g); it != INVALID; ++it) {
   151       ++num;
   152     }
   153     return num;
   154   }
   155 
   156   // Node counting:
   157 
   158   namespace _core_bits {
   159 
   160     template <typename Graph, typename Enable = void>
   161     struct CountNodesSelector {
   162       static int count(const Graph &g) {
   163         return countItems<Graph, typename Graph::Node>(g);
   164       }
   165     };
   166 
   167     template <typename Graph>
   168     struct CountNodesSelector<
   169       Graph, typename
   170       enable_if<typename Graph::NodeNumTag, void>::type>
   171     {
   172       static int count(const Graph &g) {
   173         return g.nodeNum();
   174       }
   175     };
   176   }
   177 
   178   /// \brief Function to count the nodes in the graph.
   179   ///
   180   /// This function counts the nodes in the graph.
   181   /// The complexity of the function is <em>O</em>(<em>n</em>), but for some
   182   /// graph structures it is specialized to run in <em>O</em>(1).
   183   ///
   184   /// \note If the graph contains a \c nodeNum() member function and a
   185   /// \c NodeNumTag tag then this function calls directly the member
   186   /// function to query the cardinality of the node set.
   187   template <typename Graph>
   188   inline int countNodes(const Graph& g) {
   189     return _core_bits::CountNodesSelector<Graph>::count(g);
   190   }
   191 
   192   // Arc counting:
   193 
   194   namespace _core_bits {
   195 
   196     template <typename Graph, typename Enable = void>
   197     struct CountArcsSelector {
   198       static int count(const Graph &g) {
   199         return countItems<Graph, typename Graph::Arc>(g);
   200       }
   201     };
   202 
   203     template <typename Graph>
   204     struct CountArcsSelector<
   205       Graph,
   206       typename enable_if<typename Graph::ArcNumTag, void>::type>
   207     {
   208       static int count(const Graph &g) {
   209         return g.arcNum();
   210       }
   211     };
   212   }
   213 
   214   /// \brief Function to count the arcs in the graph.
   215   ///
   216   /// This function counts the arcs in the graph.
   217   /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
   218   /// graph structures it is specialized to run in <em>O</em>(1).
   219   ///
   220   /// \note If the graph contains a \c arcNum() member function and a
   221   /// \c ArcNumTag tag then this function calls directly the member
   222   /// function to query the cardinality of the arc set.
   223   template <typename Graph>
   224   inline int countArcs(const Graph& g) {
   225     return _core_bits::CountArcsSelector<Graph>::count(g);
   226   }
   227 
   228   // Edge counting:
   229 
   230   namespace _core_bits {
   231 
   232     template <typename Graph, typename Enable = void>
   233     struct CountEdgesSelector {
   234       static int count(const Graph &g) {
   235         return countItems<Graph, typename Graph::Edge>(g);
   236       }
   237     };
   238 
   239     template <typename Graph>
   240     struct CountEdgesSelector<
   241       Graph,
   242       typename enable_if<typename Graph::EdgeNumTag, void>::type>
   243     {
   244       static int count(const Graph &g) {
   245         return g.edgeNum();
   246       }
   247     };
   248   }
   249 
   250   /// \brief Function to count the edges in the graph.
   251   ///
   252   /// This function counts the edges in the graph.
   253   /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
   254   /// graph structures it is specialized to run in <em>O</em>(1).
   255   ///
   256   /// \note If the graph contains a \c edgeNum() member function and a
   257   /// \c EdgeNumTag tag then this function calls directly the member
   258   /// function to query the cardinality of the edge set.
   259   template <typename Graph>
   260   inline int countEdges(const Graph& g) {
   261     return _core_bits::CountEdgesSelector<Graph>::count(g);
   262 
   263   }
   264 
   265 
   266   template <typename Graph, typename DegIt>
   267   inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {
   268     int num = 0;
   269     for (DegIt it(_g, _n); it != INVALID; ++it) {
   270       ++num;
   271     }
   272     return num;
   273   }
   274 
   275   /// \brief Function to count the number of the out-arcs from node \c n.
   276   ///
   277   /// This function counts the number of the out-arcs from node \c n
   278   /// in the graph \c g.
   279   template <typename Graph>
   280   inline int countOutArcs(const Graph& g,  const typename Graph::Node& n) {
   281     return countNodeDegree<Graph, typename Graph::OutArcIt>(g, n);
   282   }
   283 
   284   /// \brief Function to count the number of the in-arcs to node \c n.
   285   ///
   286   /// This function counts the number of the in-arcs to node \c n
   287   /// in the graph \c g.
   288   template <typename Graph>
   289   inline int countInArcs(const Graph& g,  const typename Graph::Node& n) {
   290     return countNodeDegree<Graph, typename Graph::InArcIt>(g, n);
   291   }
   292 
   293   /// \brief Function to count the number of the inc-edges to node \c n.
   294   ///
   295   /// This function counts the number of the inc-edges to node \c n
   296   /// in the undirected graph \c g.
   297   template <typename Graph>
   298   inline int countIncEdges(const Graph& g,  const typename Graph::Node& n) {
   299     return countNodeDegree<Graph, typename Graph::IncEdgeIt>(g, n);
   300   }
   301 
   302   namespace _core_bits {
   303 
   304     template <typename Digraph, typename Item, typename RefMap>
   305     class MapCopyBase {
   306     public:
   307       virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
   308 
   309       virtual ~MapCopyBase() {}
   310     };
   311 
   312     template <typename Digraph, typename Item, typename RefMap,
   313               typename FromMap, typename ToMap>
   314     class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
   315     public:
   316 
   317       MapCopy(const FromMap& map, ToMap& tmap)
   318         : _map(map), _tmap(tmap) {}
   319 
   320       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   321         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   322         for (ItemIt it(digraph); it != INVALID; ++it) {
   323           _tmap.set(refMap[it], _map[it]);
   324         }
   325       }
   326 
   327     private:
   328       const FromMap& _map;
   329       ToMap& _tmap;
   330     };
   331 
   332     template <typename Digraph, typename Item, typename RefMap, typename It>
   333     class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
   334     public:
   335 
   336       ItemCopy(const Item& item, It& it) : _item(item), _it(it) {}
   337 
   338       virtual void copy(const Digraph&, const RefMap& refMap) {
   339         _it = refMap[_item];
   340       }
   341 
   342     private:
   343       Item _item;
   344       It& _it;
   345     };
   346 
   347     template <typename Digraph, typename Item, typename RefMap, typename Ref>
   348     class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   349     public:
   350 
   351       RefCopy(Ref& map) : _map(map) {}
   352 
   353       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   354         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   355         for (ItemIt it(digraph); it != INVALID; ++it) {
   356           _map.set(it, refMap[it]);
   357         }
   358       }
   359 
   360     private:
   361       Ref& _map;
   362     };
   363 
   364     template <typename Digraph, typename Item, typename RefMap,
   365               typename CrossRef>
   366     class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   367     public:
   368 
   369       CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
   370 
   371       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   372         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   373         for (ItemIt it(digraph); it != INVALID; ++it) {
   374           _cmap.set(refMap[it], it);
   375         }
   376       }
   377 
   378     private:
   379       CrossRef& _cmap;
   380     };
   381 
   382     template <typename Digraph, typename Enable = void>
   383     struct DigraphCopySelector {
   384       template <typename From, typename NodeRefMap, typename ArcRefMap>
   385       static void copy(const From& from, Digraph &to,
   386                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   387         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   388           nodeRefMap[it] = to.addNode();
   389         }
   390         for (typename From::ArcIt it(from); it != INVALID; ++it) {
   391           arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)],
   392                                     nodeRefMap[from.target(it)]);
   393         }
   394       }
   395     };
   396 
   397     template <typename Digraph>
   398     struct DigraphCopySelector<
   399       Digraph,
   400       typename enable_if<typename Digraph::BuildTag, void>::type>
   401     {
   402       template <typename From, typename NodeRefMap, typename ArcRefMap>
   403       static void copy(const From& from, Digraph &to,
   404                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   405         to.build(from, nodeRefMap, arcRefMap);
   406       }
   407     };
   408 
   409     template <typename Graph, typename Enable = void>
   410     struct GraphCopySelector {
   411       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   412       static void copy(const From& from, Graph &to,
   413                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   414         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   415           nodeRefMap[it] = to.addNode();
   416         }
   417         for (typename From::EdgeIt it(from); it != INVALID; ++it) {
   418           edgeRefMap[it] = to.addEdge(nodeRefMap[from.u(it)],
   419                                       nodeRefMap[from.v(it)]);
   420         }
   421       }
   422     };
   423 
   424     template <typename Graph>
   425     struct GraphCopySelector<
   426       Graph,
   427       typename enable_if<typename Graph::BuildTag, void>::type>
   428     {
   429       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   430       static void copy(const From& from, Graph &to,
   431                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   432         to.build(from, nodeRefMap, edgeRefMap);
   433       }
   434     };
   435 
   436   }
   437 
   438   /// \brief Class to copy a digraph.
   439   ///
   440   /// Class to copy a digraph to another digraph (duplicate a digraph). The
   441   /// simplest way of using it is through the \c digraphCopy() function.
   442   ///
   443   /// This class not only make a copy of a digraph, but it can create
   444   /// references and cross references between the nodes and arcs of
   445   /// the two digraphs, and it can copy maps to use with the newly created
   446   /// digraph.
   447   ///
   448   /// To make a copy from a digraph, first an instance of DigraphCopy
   449   /// should be created, then the data belongs to the digraph should
   450   /// assigned to copy. In the end, the \c run() member should be
   451   /// called.
   452   ///
   453   /// The next code copies a digraph with several data:
   454   ///\code
   455   ///  DigraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
   456   ///  // Create references for the nodes
   457   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   458   ///  cg.nodeRef(nr);
   459   ///  // Create cross references (inverse) for the arcs
   460   ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);
   461   ///  cg.arcCrossRef(acr);
   462   ///  // Copy an arc map
   463   ///  OrigGraph::ArcMap<double> oamap(orig_graph);
   464   ///  NewGraph::ArcMap<double> namap(new_graph);
   465   ///  cg.arcMap(oamap, namap);
   466   ///  // Copy a node
   467   ///  OrigGraph::Node on;
   468   ///  NewGraph::Node nn;
   469   ///  cg.node(on, nn);
   470   ///  // Execute copying
   471   ///  cg.run();
   472   ///\endcode
   473   template <typename From, typename To>
   474   class DigraphCopy {
   475   private:
   476 
   477     typedef typename From::Node Node;
   478     typedef typename From::NodeIt NodeIt;
   479     typedef typename From::Arc Arc;
   480     typedef typename From::ArcIt ArcIt;
   481 
   482     typedef typename To::Node TNode;
   483     typedef typename To::Arc TArc;
   484 
   485     typedef typename From::template NodeMap<TNode> NodeRefMap;
   486     typedef typename From::template ArcMap<TArc> ArcRefMap;
   487 
   488   public:
   489 
   490     /// \brief Constructor of DigraphCopy.
   491     ///
   492     /// Constructor of DigraphCopy for copying the content of the
   493     /// \c from digraph into the \c to digraph.
   494     DigraphCopy(const From& from, To& to)
   495       : _from(from), _to(to) {}
   496 
   497     /// \brief Destructor of DigraphCopy
   498     ///
   499     /// Destructor of DigraphCopy.
   500     ~DigraphCopy() {
   501       for (int i = 0; i < int(_node_maps.size()); ++i) {
   502         delete _node_maps[i];
   503       }
   504       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   505         delete _arc_maps[i];
   506       }
   507 
   508     }
   509 
   510     /// \brief Copy the node references into the given map.
   511     ///
   512     /// This function copies the node references into the given map.
   513     /// The parameter should be a map, whose key type is the Node type of
   514     /// the source digraph, while the value type is the Node type of the
   515     /// destination digraph.
   516     template <typename NodeRef>
   517     DigraphCopy& nodeRef(NodeRef& map) {
   518       _node_maps.push_back(new _core_bits::RefCopy<From, Node,
   519                            NodeRefMap, NodeRef>(map));
   520       return *this;
   521     }
   522 
   523     /// \brief Copy the node cross references into the given map.
   524     ///
   525     /// This function copies the node cross references (reverse references)
   526     /// into the given map. The parameter should be a map, whose key type
   527     /// is the Node type of the destination digraph, while the value type is
   528     /// the Node type of the source digraph.
   529     template <typename NodeCrossRef>
   530     DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
   531       _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
   532                            NodeRefMap, NodeCrossRef>(map));
   533       return *this;
   534     }
   535 
   536     /// \brief Make a copy of the given node map.
   537     ///
   538     /// This function makes a copy of the given node map for the newly
   539     /// created digraph.
   540     /// The key type of the new map \c tmap should be the Node type of the
   541     /// destination digraph, and the key type of the original map \c map
   542     /// should be the Node type of the source digraph.
   543     template <typename FromMap, typename ToMap>
   544     DigraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
   545       _node_maps.push_back(new _core_bits::MapCopy<From, Node,
   546                            NodeRefMap, FromMap, ToMap>(map, tmap));
   547       return *this;
   548     }
   549 
   550     /// \brief Make a copy of the given node.
   551     ///
   552     /// This function makes a copy of the given node.
   553     DigraphCopy& node(const Node& node, TNode& tnode) {
   554       _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
   555                            NodeRefMap, TNode>(node, tnode));
   556       return *this;
   557     }
   558 
   559     /// \brief Copy the arc references into the given map.
   560     ///
   561     /// This function copies the arc references into the given map.
   562     /// The parameter should be a map, whose key type is the Arc type of
   563     /// the source digraph, while the value type is the Arc type of the
   564     /// destination digraph.
   565     template <typename ArcRef>
   566     DigraphCopy& arcRef(ArcRef& map) {
   567       _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
   568                           ArcRefMap, ArcRef>(map));
   569       return *this;
   570     }
   571 
   572     /// \brief Copy the arc cross references into the given map.
   573     ///
   574     /// This function copies the arc cross references (reverse references)
   575     /// into the given map. The parameter should be a map, whose key type
   576     /// is the Arc type of the destination digraph, while the value type is
   577     /// the Arc type of the source digraph.
   578     template <typename ArcCrossRef>
   579     DigraphCopy& arcCrossRef(ArcCrossRef& map) {
   580       _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
   581                           ArcRefMap, ArcCrossRef>(map));
   582       return *this;
   583     }
   584 
   585     /// \brief Make a copy of the given arc map.
   586     ///
   587     /// This function makes a copy of the given arc map for the newly
   588     /// created digraph.
   589     /// The key type of the new map \c tmap should be the Arc type of the
   590     /// destination digraph, and the key type of the original map \c map
   591     /// should be the Arc type of the source digraph.
   592     template <typename FromMap, typename ToMap>
   593     DigraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
   594       _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
   595                           ArcRefMap, FromMap, ToMap>(map, tmap));
   596       return *this;
   597     }
   598 
   599     /// \brief Make a copy of the given arc.
   600     ///
   601     /// This function makes a copy of the given arc.
   602     DigraphCopy& arc(const Arc& arc, TArc& tarc) {
   603       _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
   604                           ArcRefMap, TArc>(arc, tarc));
   605       return *this;
   606     }
   607 
   608     /// \brief Execute copying.
   609     ///
   610     /// This function executes the copying of the digraph along with the
   611     /// copying of the assigned data.
   612     void run() {
   613       NodeRefMap nodeRefMap(_from);
   614       ArcRefMap arcRefMap(_from);
   615       _core_bits::DigraphCopySelector<To>::
   616         copy(_from, _to, nodeRefMap, arcRefMap);
   617       for (int i = 0; i < int(_node_maps.size()); ++i) {
   618         _node_maps[i]->copy(_from, nodeRefMap);
   619       }
   620       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   621         _arc_maps[i]->copy(_from, arcRefMap);
   622       }
   623     }
   624 
   625   protected:
   626 
   627     const From& _from;
   628     To& _to;
   629 
   630     std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
   631       _node_maps;
   632 
   633     std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
   634       _arc_maps;
   635 
   636   };
   637 
   638   /// \brief Copy a digraph to another digraph.
   639   ///
   640   /// This function copies a digraph to another digraph.
   641   /// The complete usage of it is detailed in the DigraphCopy class, but
   642   /// a short example shows a basic work:
   643   ///\code
   644   /// digraphCopy(src, trg).nodeRef(nr).arcCrossRef(acr).run();
   645   ///\endcode
   646   ///
   647   /// After the copy the \c nr map will contain the mapping from the
   648   /// nodes of the \c from digraph to the nodes of the \c to digraph and
   649   /// \c acr will contain the mapping from the arcs of the \c to digraph
   650   /// to the arcs of the \c from digraph.
   651   ///
   652   /// \see DigraphCopy
   653   template <typename From, typename To>
   654   DigraphCopy<From, To> digraphCopy(const From& from, To& to) {
   655     return DigraphCopy<From, To>(from, to);
   656   }
   657 
   658   /// \brief Class to copy a graph.
   659   ///
   660   /// Class to copy a graph to another graph (duplicate a graph). The
   661   /// simplest way of using it is through the \c graphCopy() function.
   662   ///
   663   /// This class not only make a copy of a graph, but it can create
   664   /// references and cross references between the nodes, edges and arcs of
   665   /// the two graphs, and it can copy maps for using with the newly created
   666   /// graph.
   667   ///
   668   /// To make a copy from a graph, first an instance of GraphCopy
   669   /// should be created, then the data belongs to the graph should
   670   /// assigned to copy. In the end, the \c run() member should be
   671   /// called.
   672   ///
   673   /// The next code copies a graph with several data:
   674   ///\code
   675   ///  GraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
   676   ///  // Create references for the nodes
   677   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   678   ///  cg.nodeRef(nr);
   679   ///  // Create cross references (inverse) for the edges
   680   ///  NewGraph::EdgeMap<OrigGraph::Edge> ecr(new_graph);
   681   ///  cg.edgeCrossRef(ecr);
   682   ///  // Copy an edge map
   683   ///  OrigGraph::EdgeMap<double> oemap(orig_graph);
   684   ///  NewGraph::EdgeMap<double> nemap(new_graph);
   685   ///  cg.edgeMap(oemap, nemap);
   686   ///  // Copy a node
   687   ///  OrigGraph::Node on;
   688   ///  NewGraph::Node nn;
   689   ///  cg.node(on, nn);
   690   ///  // Execute copying
   691   ///  cg.run();
   692   ///\endcode
   693   template <typename From, typename To>
   694   class GraphCopy {
   695   private:
   696 
   697     typedef typename From::Node Node;
   698     typedef typename From::NodeIt NodeIt;
   699     typedef typename From::Arc Arc;
   700     typedef typename From::ArcIt ArcIt;
   701     typedef typename From::Edge Edge;
   702     typedef typename From::EdgeIt EdgeIt;
   703 
   704     typedef typename To::Node TNode;
   705     typedef typename To::Arc TArc;
   706     typedef typename To::Edge TEdge;
   707 
   708     typedef typename From::template NodeMap<TNode> NodeRefMap;
   709     typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
   710 
   711     struct ArcRefMap {
   712       ArcRefMap(const From& from, const To& to,
   713                 const EdgeRefMap& edge_ref, const NodeRefMap& node_ref)
   714         : _from(from), _to(to),
   715           _edge_ref(edge_ref), _node_ref(node_ref) {}
   716 
   717       typedef typename From::Arc Key;
   718       typedef typename To::Arc Value;
   719 
   720       Value operator[](const Key& key) const {
   721         bool forward = _from.u(key) != _from.v(key) ?
   722           _node_ref[_from.source(key)] ==
   723           _to.source(_to.direct(_edge_ref[key], true)) :
   724           _from.direction(key);
   725         return _to.direct(_edge_ref[key], forward);
   726       }
   727 
   728       const From& _from;
   729       const To& _to;
   730       const EdgeRefMap& _edge_ref;
   731       const NodeRefMap& _node_ref;
   732     };
   733 
   734   public:
   735 
   736     /// \brief Constructor of GraphCopy.
   737     ///
   738     /// Constructor of GraphCopy for copying the content of the
   739     /// \c from graph into the \c to graph.
   740     GraphCopy(const From& from, To& to)
   741       : _from(from), _to(to) {}
   742 
   743     /// \brief Destructor of GraphCopy
   744     ///
   745     /// Destructor of GraphCopy.
   746     ~GraphCopy() {
   747       for (int i = 0; i < int(_node_maps.size()); ++i) {
   748         delete _node_maps[i];
   749       }
   750       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   751         delete _arc_maps[i];
   752       }
   753       for (int i = 0; i < int(_edge_maps.size()); ++i) {
   754         delete _edge_maps[i];
   755       }
   756     }
   757 
   758     /// \brief Copy the node references into the given map.
   759     ///
   760     /// This function copies the node references into the given map.
   761     /// The parameter should be a map, whose key type is the Node type of
   762     /// the source graph, while the value type is the Node type of the
   763     /// destination graph.
   764     template <typename NodeRef>
   765     GraphCopy& nodeRef(NodeRef& map) {
   766       _node_maps.push_back(new _core_bits::RefCopy<From, Node,
   767                            NodeRefMap, NodeRef>(map));
   768       return *this;
   769     }
   770 
   771     /// \brief Copy the node cross references into the given map.
   772     ///
   773     /// This function copies the node cross references (reverse references)
   774     /// into the given map. The parameter should be a map, whose key type
   775     /// is the Node type of the destination graph, while the value type is
   776     /// the Node type of the source graph.
   777     template <typename NodeCrossRef>
   778     GraphCopy& nodeCrossRef(NodeCrossRef& map) {
   779       _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
   780                            NodeRefMap, NodeCrossRef>(map));
   781       return *this;
   782     }
   783 
   784     /// \brief Make a copy of the given node map.
   785     ///
   786     /// This function makes a copy of the given node map for the newly
   787     /// created graph.
   788     /// The key type of the new map \c tmap should be the Node type of the
   789     /// destination graph, and the key type of the original map \c map
   790     /// should be the Node type of the source graph.
   791     template <typename FromMap, typename ToMap>
   792     GraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
   793       _node_maps.push_back(new _core_bits::MapCopy<From, Node,
   794                            NodeRefMap, FromMap, ToMap>(map, tmap));
   795       return *this;
   796     }
   797 
   798     /// \brief Make a copy of the given node.
   799     ///
   800     /// This function makes a copy of the given node.
   801     GraphCopy& node(const Node& node, TNode& tnode) {
   802       _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
   803                            NodeRefMap, TNode>(node, tnode));
   804       return *this;
   805     }
   806 
   807     /// \brief Copy the arc references into the given map.
   808     ///
   809     /// This function copies the arc references into the given map.
   810     /// The parameter should be a map, whose key type is the Arc type of
   811     /// the source graph, while the value type is the Arc type of the
   812     /// destination graph.
   813     template <typename ArcRef>
   814     GraphCopy& arcRef(ArcRef& map) {
   815       _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
   816                           ArcRefMap, ArcRef>(map));
   817       return *this;
   818     }
   819 
   820     /// \brief Copy the arc cross references into the given map.
   821     ///
   822     /// This function copies the arc cross references (reverse references)
   823     /// into the given map. The parameter should be a map, whose key type
   824     /// is the Arc type of the destination graph, while the value type is
   825     /// the Arc type of the source graph.
   826     template <typename ArcCrossRef>
   827     GraphCopy& arcCrossRef(ArcCrossRef& map) {
   828       _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
   829                           ArcRefMap, ArcCrossRef>(map));
   830       return *this;
   831     }
   832 
   833     /// \brief Make a copy of the given arc map.
   834     ///
   835     /// This function makes a copy of the given arc map for the newly
   836     /// created graph.
   837     /// The key type of the new map \c tmap should be the Arc type of the
   838     /// destination graph, and the key type of the original map \c map
   839     /// should be the Arc type of the source graph.
   840     template <typename FromMap, typename ToMap>
   841     GraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
   842       _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
   843                           ArcRefMap, FromMap, ToMap>(map, tmap));
   844       return *this;
   845     }
   846 
   847     /// \brief Make a copy of the given arc.
   848     ///
   849     /// This function makes a copy of the given arc.
   850     GraphCopy& arc(const Arc& arc, TArc& tarc) {
   851       _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
   852                           ArcRefMap, TArc>(arc, tarc));
   853       return *this;
   854     }
   855 
   856     /// \brief Copy the edge references into the given map.
   857     ///
   858     /// This function copies the edge references into the given map.
   859     /// The parameter should be a map, whose key type is the Edge type of
   860     /// the source graph, while the value type is the Edge type of the
   861     /// destination graph.
   862     template <typename EdgeRef>
   863     GraphCopy& edgeRef(EdgeRef& map) {
   864       _edge_maps.push_back(new _core_bits::RefCopy<From, Edge,
   865                            EdgeRefMap, EdgeRef>(map));
   866       return *this;
   867     }
   868 
   869     /// \brief Copy the edge cross references into the given map.
   870     ///
   871     /// This function copies the edge cross references (reverse references)
   872     /// into the given map. The parameter should be a map, whose key type
   873     /// is the Edge type of the destination graph, while the value type is
   874     /// the Edge type of the source graph.
   875     template <typename EdgeCrossRef>
   876     GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
   877       _edge_maps.push_back(new _core_bits::CrossRefCopy<From,
   878                            Edge, EdgeRefMap, EdgeCrossRef>(map));
   879       return *this;
   880     }
   881 
   882     /// \brief Make a copy of the given edge map.
   883     ///
   884     /// This function makes a copy of the given edge map for the newly
   885     /// created graph.
   886     /// The key type of the new map \c tmap should be the Edge type of the
   887     /// destination graph, and the key type of the original map \c map
   888     /// should be the Edge type of the source graph.
   889     template <typename FromMap, typename ToMap>
   890     GraphCopy& edgeMap(const FromMap& map, ToMap& tmap) {
   891       _edge_maps.push_back(new _core_bits::MapCopy<From, Edge,
   892                            EdgeRefMap, FromMap, ToMap>(map, tmap));
   893       return *this;
   894     }
   895 
   896     /// \brief Make a copy of the given edge.
   897     ///
   898     /// This function makes a copy of the given edge.
   899     GraphCopy& edge(const Edge& edge, TEdge& tedge) {
   900       _edge_maps.push_back(new _core_bits::ItemCopy<From, Edge,
   901                            EdgeRefMap, TEdge>(edge, tedge));
   902       return *this;
   903     }
   904 
   905     /// \brief Execute copying.
   906     ///
   907     /// This function executes the copying of the graph along with the
   908     /// copying of the assigned data.
   909     void run() {
   910       NodeRefMap nodeRefMap(_from);
   911       EdgeRefMap edgeRefMap(_from);
   912       ArcRefMap arcRefMap(_from, _to, edgeRefMap, nodeRefMap);
   913       _core_bits::GraphCopySelector<To>::
   914         copy(_from, _to, nodeRefMap, edgeRefMap);
   915       for (int i = 0; i < int(_node_maps.size()); ++i) {
   916         _node_maps[i]->copy(_from, nodeRefMap);
   917       }
   918       for (int i = 0; i < int(_edge_maps.size()); ++i) {
   919         _edge_maps[i]->copy(_from, edgeRefMap);
   920       }
   921       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   922         _arc_maps[i]->copy(_from, arcRefMap);
   923       }
   924     }
   925 
   926   private:
   927 
   928     const From& _from;
   929     To& _to;
   930 
   931     std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
   932       _node_maps;
   933 
   934     std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
   935       _arc_maps;
   936 
   937     std::vector<_core_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
   938       _edge_maps;
   939 
   940   };
   941 
   942   /// \brief Copy a graph to another graph.
   943   ///
   944   /// This function copies a graph to another graph.
   945   /// The complete usage of it is detailed in the GraphCopy class,
   946   /// but a short example shows a basic work:
   947   ///\code
   948   /// graphCopy(src, trg).nodeRef(nr).edgeCrossRef(ecr).run();
   949   ///\endcode
   950   ///
   951   /// After the copy the \c nr map will contain the mapping from the
   952   /// nodes of the \c from graph to the nodes of the \c to graph and
   953   /// \c ecr will contain the mapping from the edges of the \c to graph
   954   /// to the edges of the \c from graph.
   955   ///
   956   /// \see GraphCopy
   957   template <typename From, typename To>
   958   GraphCopy<From, To>
   959   graphCopy(const From& from, To& to) {
   960     return GraphCopy<From, To>(from, to);
   961   }
   962 
   963   namespace _core_bits {
   964 
   965     template <typename Graph, typename Enable = void>
   966     struct FindArcSelector {
   967       typedef typename Graph::Node Node;
   968       typedef typename Graph::Arc Arc;
   969       static Arc find(const Graph &g, Node u, Node v, Arc e) {
   970         if (e == INVALID) {
   971           g.firstOut(e, u);
   972         } else {
   973           g.nextOut(e);
   974         }
   975         while (e != INVALID && g.target(e) != v) {
   976           g.nextOut(e);
   977         }
   978         return e;
   979       }
   980     };
   981 
   982     template <typename Graph>
   983     struct FindArcSelector<
   984       Graph,
   985       typename enable_if<typename Graph::FindArcTag, void>::type>
   986     {
   987       typedef typename Graph::Node Node;
   988       typedef typename Graph::Arc Arc;
   989       static Arc find(const Graph &g, Node u, Node v, Arc prev) {
   990         return g.findArc(u, v, prev);
   991       }
   992     };
   993   }
   994 
   995   /// \brief Find an arc between two nodes of a digraph.
   996   ///
   997   /// This function finds an arc from node \c u to node \c v in the
   998   /// digraph \c g.
   999   ///
  1000   /// If \c prev is \ref INVALID (this is the default value), then
  1001   /// it finds the first arc from \c u to \c v. Otherwise it looks for
  1002   /// the next arc from \c u to \c v after \c prev.
  1003   /// \return The found arc or \ref INVALID if there is no such an arc.
  1004   ///
  1005   /// Thus you can iterate through each arc from \c u to \c v as it follows.
  1006   ///\code
  1007   /// for(Arc e = findArc(g,u,v); e != INVALID; e = findArc(g,u,v,e)) {
  1008   ///   ...
  1009   /// }
  1010   ///\endcode
  1011   ///
  1012   /// \note \ref ConArcIt provides iterator interface for the same
  1013   /// functionality.
  1014   ///
  1015   ///\sa ConArcIt
  1016   ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
  1017   template <typename Graph>
  1018   inline typename Graph::Arc
  1019   findArc(const Graph &g, typename Graph::Node u, typename Graph::Node v,
  1020           typename Graph::Arc prev = INVALID) {
  1021     return _core_bits::FindArcSelector<Graph>::find(g, u, v, prev);
  1022   }
  1023 
  1024   /// \brief Iterator for iterating on parallel arcs connecting the same nodes.
  1025   ///
  1026   /// Iterator for iterating on parallel arcs connecting the same nodes. It is
  1027   /// a higher level interface for the \ref findArc() function. You can
  1028   /// use it the following way:
  1029   ///\code
  1030   /// for (ConArcIt<Graph> it(g, src, trg); it != INVALID; ++it) {
  1031   ///   ...
  1032   /// }
  1033   ///\endcode
  1034   ///
  1035   ///\sa findArc()
  1036   ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
  1037   template <typename _Graph>
  1038   class ConArcIt : public _Graph::Arc {
  1039   public:
  1040 
  1041     typedef _Graph Graph;
  1042     typedef typename Graph::Arc Parent;
  1043 
  1044     typedef typename Graph::Arc Arc;
  1045     typedef typename Graph::Node Node;
  1046 
  1047     /// \brief Constructor.
  1048     ///
  1049     /// Construct a new ConArcIt iterating on the arcs that
  1050     /// connects nodes \c u and \c v.
  1051     ConArcIt(const Graph& g, Node u, Node v) : _graph(g) {
  1052       Parent::operator=(findArc(_graph, u, v));
  1053     }
  1054 
  1055     /// \brief Constructor.
  1056     ///
  1057     /// Construct a new ConArcIt that continues the iterating from arc \c a.
  1058     ConArcIt(const Graph& g, Arc a) : Parent(a), _graph(g) {}
  1059 
  1060     /// \brief Increment operator.
  1061     ///
  1062     /// It increments the iterator and gives back the next arc.
  1063     ConArcIt& operator++() {
  1064       Parent::operator=(findArc(_graph, _graph.source(*this),
  1065                                 _graph.target(*this), *this));
  1066       return *this;
  1067     }
  1068   private:
  1069     const Graph& _graph;
  1070   };
  1071 
  1072   namespace _core_bits {
  1073 
  1074     template <typename Graph, typename Enable = void>
  1075     struct FindEdgeSelector {
  1076       typedef typename Graph::Node Node;
  1077       typedef typename Graph::Edge Edge;
  1078       static Edge find(const Graph &g, Node u, Node v, Edge e) {
  1079         bool b;
  1080         if (u != v) {
  1081           if (e == INVALID) {
  1082             g.firstInc(e, b, u);
  1083           } else {
  1084             b = g.u(e) == u;
  1085             g.nextInc(e, b);
  1086           }
  1087           while (e != INVALID && (b ? g.v(e) : g.u(e)) != v) {
  1088             g.nextInc(e, b);
  1089           }
  1090         } else {
  1091           if (e == INVALID) {
  1092             g.firstInc(e, b, u);
  1093           } else {
  1094             b = true;
  1095             g.nextInc(e, b);
  1096           }
  1097           while (e != INVALID && (!b || g.v(e) != v)) {
  1098             g.nextInc(e, b);
  1099           }
  1100         }
  1101         return e;
  1102       }
  1103     };
  1104 
  1105     template <typename Graph>
  1106     struct FindEdgeSelector<
  1107       Graph,
  1108       typename enable_if<typename Graph::FindEdgeTag, void>::type>
  1109     {
  1110       typedef typename Graph::Node Node;
  1111       typedef typename Graph::Edge Edge;
  1112       static Edge find(const Graph &g, Node u, Node v, Edge prev) {
  1113         return g.findEdge(u, v, prev);
  1114       }
  1115     };
  1116   }
  1117 
  1118   /// \brief Find an edge between two nodes of a graph.
  1119   ///
  1120   /// This function finds an edge from node \c u to node \c v in graph \c g.
  1121   /// If node \c u and node \c v is equal then each loop edge
  1122   /// will be enumerated once.
  1123   ///
  1124   /// If \c prev is \ref INVALID (this is the default value), then
  1125   /// it finds the first edge from \c u to \c v. Otherwise it looks for
  1126   /// the next edge from \c u to \c v after \c prev.
  1127   /// \return The found edge or \ref INVALID if there is no such an edge.
  1128   ///
  1129   /// Thus you can iterate through each edge between \c u and \c v
  1130   /// as it follows.
  1131   ///\code
  1132   /// for(Edge e = findEdge(g,u,v); e != INVALID; e = findEdge(g,u,v,e)) {
  1133   ///   ...
  1134   /// }
  1135   ///\endcode
  1136   ///
  1137   /// \note \ref ConEdgeIt provides iterator interface for the same
  1138   /// functionality.
  1139   ///
  1140   ///\sa ConEdgeIt
  1141   template <typename Graph>
  1142   inline typename Graph::Edge
  1143   findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,
  1144             typename Graph::Edge p = INVALID) {
  1145     return _core_bits::FindEdgeSelector<Graph>::find(g, u, v, p);
  1146   }
  1147 
  1148   /// \brief Iterator for iterating on parallel edges connecting the same nodes.
  1149   ///
  1150   /// Iterator for iterating on parallel edges connecting the same nodes.
  1151   /// It is a higher level interface for the findEdge() function. You can
  1152   /// use it the following way:
  1153   ///\code
  1154   /// for (ConEdgeIt<Graph> it(g, u, v); it != INVALID; ++it) {
  1155   ///   ...
  1156   /// }
  1157   ///\endcode
  1158   ///
  1159   ///\sa findEdge()
  1160   template <typename _Graph>
  1161   class ConEdgeIt : public _Graph::Edge {
  1162   public:
  1163 
  1164     typedef _Graph Graph;
  1165     typedef typename Graph::Edge Parent;
  1166 
  1167     typedef typename Graph::Edge Edge;
  1168     typedef typename Graph::Node Node;
  1169 
  1170     /// \brief Constructor.
  1171     ///
  1172     /// Construct a new ConEdgeIt iterating on the edges that
  1173     /// connects nodes \c u and \c v.
  1174     ConEdgeIt(const Graph& g, Node u, Node v) : _graph(g), _u(u), _v(v) {
  1175       Parent::operator=(findEdge(_graph, _u, _v));
  1176     }
  1177 
  1178     /// \brief Constructor.
  1179     ///
  1180     /// Construct a new ConEdgeIt that continues iterating from edge \c e.
  1181     ConEdgeIt(const Graph& g, Edge e) : Parent(e), _graph(g) {}
  1182 
  1183     /// \brief Increment operator.
  1184     ///
  1185     /// It increments the iterator and gives back the next edge.
  1186     ConEdgeIt& operator++() {
  1187       Parent::operator=(findEdge(_graph, _u, _v, *this));
  1188       return *this;
  1189     }
  1190   private:
  1191     const Graph& _graph;
  1192     Node _u, _v;
  1193   };
  1194 
  1195 
  1196   ///Dynamic arc look-up between given endpoints.
  1197 
  1198   ///Using this class, you can find an arc in a digraph from a given
  1199   ///source to a given target in amortized time <em>O</em>(log<em>d</em>),
  1200   ///where <em>d</em> is the out-degree of the source node.
  1201   ///
  1202   ///It is possible to find \e all parallel arcs between two nodes with
  1203   ///the \c operator() member.
  1204   ///
  1205   ///This is a dynamic data structure. Consider to use \ref ArcLookUp or
  1206   ///\ref AllArcLookUp if your digraph is not changed so frequently.
  1207   ///
  1208   ///This class uses a self-adjusting binary search tree, the Splay tree
  1209   ///of Sleator and Tarjan to guarantee the logarithmic amortized
  1210   ///time bound for arc look-ups. This class also guarantees the
  1211   ///optimal time bound in a constant factor for any distribution of
  1212   ///queries.
  1213   ///
  1214   ///\tparam G The type of the underlying digraph.
  1215   ///
  1216   ///\sa ArcLookUp
  1217   ///\sa AllArcLookUp
  1218   template<class G>
  1219   class DynArcLookUp
  1220     : protected ItemSetTraits<G, typename G::Arc>::ItemNotifier::ObserverBase
  1221   {
  1222   public:
  1223     typedef typename ItemSetTraits<G, typename G::Arc>
  1224     ::ItemNotifier::ObserverBase Parent;
  1225 
  1226     TEMPLATE_DIGRAPH_TYPEDEFS(G);
  1227     typedef G Digraph;
  1228 
  1229   protected:
  1230 
  1231     class AutoNodeMap : public ItemSetTraits<G, Node>::template Map<Arc>::Type {
  1232     public:
  1233 
  1234       typedef typename ItemSetTraits<G, Node>::template Map<Arc>::Type Parent;
  1235 
  1236       AutoNodeMap(const G& digraph) : Parent(digraph, INVALID) {}
  1237 
  1238       virtual void add(const Node& node) {
  1239         Parent::add(node);
  1240         Parent::set(node, INVALID);
  1241       }
  1242 
  1243       virtual void add(const std::vector<Node>& nodes) {
  1244         Parent::add(nodes);
  1245         for (int i = 0; i < int(nodes.size()); ++i) {
  1246           Parent::set(nodes[i], INVALID);
  1247         }
  1248       }
  1249 
  1250       virtual void build() {
  1251         Parent::build();
  1252         Node it;
  1253         typename Parent::Notifier* nf = Parent::notifier();
  1254         for (nf->first(it); it != INVALID; nf->next(it)) {
  1255           Parent::set(it, INVALID);
  1256         }
  1257       }
  1258     };
  1259 
  1260     const Digraph &_g;
  1261     AutoNodeMap _head;
  1262     typename Digraph::template ArcMap<Arc> _parent;
  1263     typename Digraph::template ArcMap<Arc> _left;
  1264     typename Digraph::template ArcMap<Arc> _right;
  1265 
  1266     class ArcLess {
  1267       const Digraph &g;
  1268     public:
  1269       ArcLess(const Digraph &_g) : g(_g) {}
  1270       bool operator()(Arc a,Arc b) const
  1271       {
  1272         return g.target(a)<g.target(b);
  1273       }
  1274     };
  1275 
  1276   public:
  1277 
  1278     ///Constructor
  1279 
  1280     ///Constructor.
  1281     ///
  1282     ///It builds up the search database.
  1283     DynArcLookUp(const Digraph &g)
  1284       : _g(g),_head(g),_parent(g),_left(g),_right(g)
  1285     {
  1286       Parent::attach(_g.notifier(typename Digraph::Arc()));
  1287       refresh();
  1288     }
  1289 
  1290   protected:
  1291 
  1292     virtual void add(const Arc& arc) {
  1293       insert(arc);
  1294     }
  1295 
  1296     virtual void add(const std::vector<Arc>& arcs) {
  1297       for (int i = 0; i < int(arcs.size()); ++i) {
  1298         insert(arcs[i]);
  1299       }
  1300     }
  1301 
  1302     virtual void erase(const Arc& arc) {
  1303       remove(arc);
  1304     }
  1305 
  1306     virtual void erase(const std::vector<Arc>& arcs) {
  1307       for (int i = 0; i < int(arcs.size()); ++i) {
  1308         remove(arcs[i]);
  1309       }
  1310     }
  1311 
  1312     virtual void build() {
  1313       refresh();
  1314     }
  1315 
  1316     virtual void clear() {
  1317       for(NodeIt n(_g);n!=INVALID;++n) {
  1318         _head.set(n, INVALID);
  1319       }
  1320     }
  1321 
  1322     void insert(Arc arc) {
  1323       Node s = _g.source(arc);
  1324       Node t = _g.target(arc);
  1325       _left.set(arc, INVALID);
  1326       _right.set(arc, INVALID);
  1327 
  1328       Arc e = _head[s];
  1329       if (e == INVALID) {
  1330         _head.set(s, arc);
  1331         _parent.set(arc, INVALID);
  1332         return;
  1333       }
  1334       while (true) {
  1335         if (t < _g.target(e)) {
  1336           if (_left[e] == INVALID) {
  1337             _left.set(e, arc);
  1338             _parent.set(arc, e);
  1339             splay(arc);
  1340             return;
  1341           } else {
  1342             e = _left[e];
  1343           }
  1344         } else {
  1345           if (_right[e] == INVALID) {
  1346             _right.set(e, arc);
  1347             _parent.set(arc, e);
  1348             splay(arc);
  1349             return;
  1350           } else {
  1351             e = _right[e];
  1352           }
  1353         }
  1354       }
  1355     }
  1356 
  1357     void remove(Arc arc) {
  1358       if (_left[arc] == INVALID) {
  1359         if (_right[arc] != INVALID) {
  1360           _parent.set(_right[arc], _parent[arc]);
  1361         }
  1362         if (_parent[arc] != INVALID) {
  1363           if (_left[_parent[arc]] == arc) {
  1364             _left.set(_parent[arc], _right[arc]);
  1365           } else {
  1366             _right.set(_parent[arc], _right[arc]);
  1367           }
  1368         } else {
  1369           _head.set(_g.source(arc), _right[arc]);
  1370         }
  1371       } else if (_right[arc] == INVALID) {
  1372         _parent.set(_left[arc], _parent[arc]);
  1373         if (_parent[arc] != INVALID) {
  1374           if (_left[_parent[arc]] == arc) {
  1375             _left.set(_parent[arc], _left[arc]);
  1376           } else {
  1377             _right.set(_parent[arc], _left[arc]);
  1378           }
  1379         } else {
  1380           _head.set(_g.source(arc), _left[arc]);
  1381         }
  1382       } else {
  1383         Arc e = _left[arc];
  1384         if (_right[e] != INVALID) {
  1385           e = _right[e];
  1386           while (_right[e] != INVALID) {
  1387             e = _right[e];
  1388           }
  1389           Arc s = _parent[e];
  1390           _right.set(_parent[e], _left[e]);
  1391           if (_left[e] != INVALID) {
  1392             _parent.set(_left[e], _parent[e]);
  1393           }
  1394 
  1395           _left.set(e, _left[arc]);
  1396           _parent.set(_left[arc], e);
  1397           _right.set(e, _right[arc]);
  1398           _parent.set(_right[arc], e);
  1399 
  1400           _parent.set(e, _parent[arc]);
  1401           if (_parent[arc] != INVALID) {
  1402             if (_left[_parent[arc]] == arc) {
  1403               _left.set(_parent[arc], e);
  1404             } else {
  1405               _right.set(_parent[arc], e);
  1406             }
  1407           }
  1408           splay(s);
  1409         } else {
  1410           _right.set(e, _right[arc]);
  1411           _parent.set(_right[arc], e);
  1412           _parent.set(e, _parent[arc]);
  1413 
  1414           if (_parent[arc] != INVALID) {
  1415             if (_left[_parent[arc]] == arc) {
  1416               _left.set(_parent[arc], e);
  1417             } else {
  1418               _right.set(_parent[arc], e);
  1419             }
  1420           } else {
  1421             _head.set(_g.source(arc), e);
  1422           }
  1423         }
  1424       }
  1425     }
  1426 
  1427     Arc refreshRec(std::vector<Arc> &v,int a,int b)
  1428     {
  1429       int m=(a+b)/2;
  1430       Arc me=v[m];
  1431       if (a < m) {
  1432         Arc left = refreshRec(v,a,m-1);
  1433         _left.set(me, left);
  1434         _parent.set(left, me);
  1435       } else {
  1436         _left.set(me, INVALID);
  1437       }
  1438       if (m < b) {
  1439         Arc right = refreshRec(v,m+1,b);
  1440         _right.set(me, right);
  1441         _parent.set(right, me);
  1442       } else {
  1443         _right.set(me, INVALID);
  1444       }
  1445       return me;
  1446     }
  1447 
  1448     void refresh() {
  1449       for(NodeIt n(_g);n!=INVALID;++n) {
  1450         std::vector<Arc> v;
  1451         for(OutArcIt a(_g,n);a!=INVALID;++a) v.push_back(a);
  1452         if (!v.empty()) {
  1453           std::sort(v.begin(),v.end(),ArcLess(_g));
  1454           Arc head = refreshRec(v,0,v.size()-1);
  1455           _head.set(n, head);
  1456           _parent.set(head, INVALID);
  1457         }
  1458         else _head.set(n, INVALID);
  1459       }
  1460     }
  1461 
  1462     void zig(Arc v) {
  1463       Arc w = _parent[v];
  1464       _parent.set(v, _parent[w]);
  1465       _parent.set(w, v);
  1466       _left.set(w, _right[v]);
  1467       _right.set(v, w);
  1468       if (_parent[v] != INVALID) {
  1469         if (_right[_parent[v]] == w) {
  1470           _right.set(_parent[v], v);
  1471         } else {
  1472           _left.set(_parent[v], v);
  1473         }
  1474       }
  1475       if (_left[w] != INVALID){
  1476         _parent.set(_left[w], w);
  1477       }
  1478     }
  1479 
  1480     void zag(Arc v) {
  1481       Arc w = _parent[v];
  1482       _parent.set(v, _parent[w]);
  1483       _parent.set(w, v);
  1484       _right.set(w, _left[v]);
  1485       _left.set(v, w);
  1486       if (_parent[v] != INVALID){
  1487         if (_left[_parent[v]] == w) {
  1488           _left.set(_parent[v], v);
  1489         } else {
  1490           _right.set(_parent[v], v);
  1491         }
  1492       }
  1493       if (_right[w] != INVALID){
  1494         _parent.set(_right[w], w);
  1495       }
  1496     }
  1497 
  1498     void splay(Arc v) {
  1499       while (_parent[v] != INVALID) {
  1500         if (v == _left[_parent[v]]) {
  1501           if (_parent[_parent[v]] == INVALID) {
  1502             zig(v);
  1503           } else {
  1504             if (_parent[v] == _left[_parent[_parent[v]]]) {
  1505               zig(_parent[v]);
  1506               zig(v);
  1507             } else {
  1508               zig(v);
  1509               zag(v);
  1510             }
  1511           }
  1512         } else {
  1513           if (_parent[_parent[v]] == INVALID) {
  1514             zag(v);
  1515           } else {
  1516             if (_parent[v] == _left[_parent[_parent[v]]]) {
  1517               zag(v);
  1518               zig(v);
  1519             } else {
  1520               zag(_parent[v]);
  1521               zag(v);
  1522             }
  1523           }
  1524         }
  1525       }
  1526       _head[_g.source(v)] = v;
  1527     }
  1528 
  1529 
  1530   public:
  1531 
  1532     ///Find an arc between two nodes.
  1533 
  1534     ///Find an arc between two nodes.
  1535     ///\param s The source node.
  1536     ///\param t The target node.
  1537     ///\param p The previous arc between \c s and \c t. It it is INVALID or
  1538     ///not given, the operator finds the first appropriate arc.
  1539     ///\return An arc from \c s to \c t after \c p or
  1540     ///\ref INVALID if there is no more.
  1541     ///
  1542     ///For example, you can count the number of arcs from \c u to \c v in the
  1543     ///following way.
  1544     ///\code
  1545     ///DynArcLookUp<ListDigraph> ae(g);
  1546     ///...
  1547     ///int n = 0;
  1548     ///for(Arc a = ae(u,v); a != INVALID; a = ae(u,v,a)) n++;
  1549     ///\endcode
  1550     ///
  1551     ///Finding the arcs take at most <em>O</em>(log<em>d</em>)
  1552     ///amortized time, specifically, the time complexity of the lookups
  1553     ///is equal to the optimal search tree implementation for the
  1554     ///current query distribution in a constant factor.
  1555     ///
  1556     ///\note This is a dynamic data structure, therefore the data
  1557     ///structure is updated after each graph alteration. Thus although
  1558     ///this data structure is theoretically faster than \ref ArcLookUp
  1559     ///and \ref AllArcLookUp, it often provides worse performance than
  1560     ///them.
  1561     Arc operator()(Node s, Node t, Arc p = INVALID) const  {
  1562       if (p == INVALID) {
  1563         Arc a = _head[s];
  1564         if (a == INVALID) return INVALID;
  1565         Arc r = INVALID;
  1566         while (true) {
  1567           if (_g.target(a) < t) {
  1568             if (_right[a] == INVALID) {
  1569               const_cast<DynArcLookUp&>(*this).splay(a);
  1570               return r;
  1571             } else {
  1572               a = _right[a];
  1573             }
  1574           } else {
  1575             if (_g.target(a) == t) {
  1576               r = a;
  1577             }
  1578             if (_left[a] == INVALID) {
  1579               const_cast<DynArcLookUp&>(*this).splay(a);
  1580               return r;
  1581             } else {
  1582               a = _left[a];
  1583             }
  1584           }
  1585         }
  1586       } else {
  1587         Arc a = p;
  1588         if (_right[a] != INVALID) {
  1589           a = _right[a];
  1590           while (_left[a] != INVALID) {
  1591             a = _left[a];
  1592           }
  1593           const_cast<DynArcLookUp&>(*this).splay(a);
  1594         } else {
  1595           while (_parent[a] != INVALID && _right[_parent[a]] ==  a) {
  1596             a = _parent[a];
  1597           }
  1598           if (_parent[a] == INVALID) {
  1599             return INVALID;
  1600           } else {
  1601             a = _parent[a];
  1602             const_cast<DynArcLookUp&>(*this).splay(a);
  1603           }
  1604         }
  1605         if (_g.target(a) == t) return a;
  1606         else return INVALID;
  1607       }
  1608     }
  1609 
  1610   };
  1611 
  1612   ///Fast arc look-up between given endpoints.
  1613 
  1614   ///Using this class, you can find an arc in a digraph from a given
  1615   ///source to a given target in time <em>O</em>(log<em>d</em>),
  1616   ///where <em>d</em> is the out-degree of the source node.
  1617   ///
  1618   ///It is not possible to find \e all parallel arcs between two nodes.
  1619   ///Use \ref AllArcLookUp for this purpose.
  1620   ///
  1621   ///\warning This class is static, so you should call refresh() (or at
  1622   ///least refresh(Node)) to refresh this data structure whenever the
  1623   ///digraph changes. This is a time consuming (superlinearly proportional
  1624   ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
  1625   ///
  1626   ///\tparam G The type of the underlying digraph.
  1627   ///
  1628   ///\sa DynArcLookUp
  1629   ///\sa AllArcLookUp
  1630   template<class G>
  1631   class ArcLookUp
  1632   {
  1633   public:
  1634     TEMPLATE_DIGRAPH_TYPEDEFS(G);
  1635     typedef G Digraph;
  1636 
  1637   protected:
  1638     const Digraph &_g;
  1639     typename Digraph::template NodeMap<Arc> _head;
  1640     typename Digraph::template ArcMap<Arc> _left;
  1641     typename Digraph::template ArcMap<Arc> _right;
  1642 
  1643     class ArcLess {
  1644       const Digraph &g;
  1645     public:
  1646       ArcLess(const Digraph &_g) : g(_g) {}
  1647       bool operator()(Arc a,Arc b) const
  1648       {
  1649         return g.target(a)<g.target(b);
  1650       }
  1651     };
  1652 
  1653   public:
  1654 
  1655     ///Constructor
  1656 
  1657     ///Constructor.
  1658     ///
  1659     ///It builds up the search database, which remains valid until the digraph
  1660     ///changes.
  1661     ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}
  1662 
  1663   private:
  1664     Arc refreshRec(std::vector<Arc> &v,int a,int b)
  1665     {
  1666       int m=(a+b)/2;
  1667       Arc me=v[m];
  1668       _left[me] = a<m?refreshRec(v,a,m-1):INVALID;
  1669       _right[me] = m<b?refreshRec(v,m+1,b):INVALID;
  1670       return me;
  1671     }
  1672   public:
  1673     ///Refresh the search data structure at a node.
  1674 
  1675     ///Build up the search database of node \c n.
  1676     ///
  1677     ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em>
  1678     ///is the number of the outgoing arcs of \c n.
  1679     void refresh(Node n)
  1680     {
  1681       std::vector<Arc> v;
  1682       for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
  1683       if(v.size()) {
  1684         std::sort(v.begin(),v.end(),ArcLess(_g));
  1685         _head[n]=refreshRec(v,0,v.size()-1);
  1686       }
  1687       else _head[n]=INVALID;
  1688     }
  1689     ///Refresh the full data structure.
  1690 
  1691     ///Build up the full search database. In fact, it simply calls
  1692     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  1693     ///
  1694     ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
  1695     ///the number of the arcs in the digraph and <em>D</em> is the maximum
  1696     ///out-degree of the digraph.
  1697     void refresh()
  1698     {
  1699       for(NodeIt n(_g);n!=INVALID;++n) refresh(n);
  1700     }
  1701 
  1702     ///Find an arc between two nodes.
  1703 
  1704     ///Find an arc between two nodes in time <em>O</em>(log<em>d</em>),
  1705     ///where <em>d</em> is the number of outgoing arcs of \c s.
  1706     ///\param s The source node.
  1707     ///\param t The target node.
  1708     ///\return An arc from \c s to \c t if there exists,
  1709     ///\ref INVALID otherwise.
  1710     ///
  1711     ///\warning If you change the digraph, refresh() must be called before using
  1712     ///this operator. If you change the outgoing arcs of
  1713     ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
  1714     Arc operator()(Node s, Node t) const
  1715     {
  1716       Arc e;
  1717       for(e=_head[s];
  1718           e!=INVALID&&_g.target(e)!=t;
  1719           e = t < _g.target(e)?_left[e]:_right[e]) ;
  1720       return e;
  1721     }
  1722 
  1723   };
  1724 
  1725   ///Fast look-up of all arcs between given endpoints.
  1726 
  1727   ///This class is the same as \ref ArcLookUp, with the addition
  1728   ///that it makes it possible to find all parallel arcs between given
  1729   ///endpoints.
  1730   ///
  1731   ///\warning This class is static, so you should call refresh() (or at
  1732   ///least refresh(Node)) to refresh this data structure whenever the
  1733   ///digraph changes. This is a time consuming (superlinearly proportional
  1734   ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
  1735   ///
  1736   ///\tparam G The type of the underlying digraph.
  1737   ///
  1738   ///\sa DynArcLookUp
  1739   ///\sa ArcLookUp
  1740   template<class G>
  1741   class AllArcLookUp : public ArcLookUp<G>
  1742   {
  1743     using ArcLookUp<G>::_g;
  1744     using ArcLookUp<G>::_right;
  1745     using ArcLookUp<G>::_left;
  1746     using ArcLookUp<G>::_head;
  1747 
  1748     TEMPLATE_DIGRAPH_TYPEDEFS(G);
  1749     typedef G Digraph;
  1750 
  1751     typename Digraph::template ArcMap<Arc> _next;
  1752 
  1753     Arc refreshNext(Arc head,Arc next=INVALID)
  1754     {
  1755       if(head==INVALID) return next;
  1756       else {
  1757         next=refreshNext(_right[head],next);
  1758         _next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
  1759           ? next : INVALID;
  1760         return refreshNext(_left[head],head);
  1761       }
  1762     }
  1763 
  1764     void refreshNext()
  1765     {
  1766       for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
  1767     }
  1768 
  1769   public:
  1770     ///Constructor
  1771 
  1772     ///Constructor.
  1773     ///
  1774     ///It builds up the search database, which remains valid until the digraph
  1775     ///changes.
  1776     AllArcLookUp(const Digraph &g) : ArcLookUp<G>(g), _next(g) {refreshNext();}
  1777 
  1778     ///Refresh the data structure at a node.
  1779 
  1780     ///Build up the search database of node \c n.
  1781     ///
  1782     ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em> is
  1783     ///the number of the outgoing arcs of \c n.
  1784     void refresh(Node n)
  1785     {
  1786       ArcLookUp<G>::refresh(n);
  1787       refreshNext(_head[n]);
  1788     }
  1789 
  1790     ///Refresh the full data structure.
  1791 
  1792     ///Build up the full search database. In fact, it simply calls
  1793     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  1794     ///
  1795     ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
  1796     ///the number of the arcs in the digraph and <em>D</em> is the maximum
  1797     ///out-degree of the digraph.
  1798     void refresh()
  1799     {
  1800       for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
  1801     }
  1802 
  1803     ///Find an arc between two nodes.
  1804 
  1805     ///Find an arc between two nodes.
  1806     ///\param s The source node.
  1807     ///\param t The target node.
  1808     ///\param prev The previous arc between \c s and \c t. It it is INVALID or
  1809     ///not given, the operator finds the first appropriate arc.
  1810     ///\return An arc from \c s to \c t after \c prev or
  1811     ///\ref INVALID if there is no more.
  1812     ///
  1813     ///For example, you can count the number of arcs from \c u to \c v in the
  1814     ///following way.
  1815     ///\code
  1816     ///AllArcLookUp<ListDigraph> ae(g);
  1817     ///...
  1818     ///int n = 0;
  1819     ///for(Arc a = ae(u,v); a != INVALID; a=ae(u,v,a)) n++;
  1820     ///\endcode
  1821     ///
  1822     ///Finding the first arc take <em>O</em>(log<em>d</em>) time,
  1823     ///where <em>d</em> is the number of outgoing arcs of \c s. Then the
  1824     ///consecutive arcs are found in constant time.
  1825     ///
  1826     ///\warning If you change the digraph, refresh() must be called before using
  1827     ///this operator. If you change the outgoing arcs of
  1828     ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
  1829     ///
  1830 #ifdef DOXYGEN
  1831     Arc operator()(Node s, Node t, Arc prev=INVALID) const {}
  1832 #else
  1833     using ArcLookUp<G>::operator() ;
  1834     Arc operator()(Node s, Node t, Arc prev) const
  1835     {
  1836       return prev==INVALID?(*this)(s,t):_next[prev];
  1837     }
  1838 #endif
  1839 
  1840   };
  1841 
  1842   /// @}
  1843 
  1844 } //namespace lemon
  1845 
  1846 #endif