lemon/core.h
author Akos Ladanyi <ladanyi@tmit.bme.hu>
Thu, 28 May 2009 12:11:50 +0100
changeset 718 da70af8844b9
parent 686 72ac25ad276e
child 956 141f9c0db4a3
child 984 9f22c22fe227
permissions -rw-r--r--
Suppress MSVC warnings using pragmas (#295)
     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) 2003-2009
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 #ifndef LEMON_CORE_H
    20 #define LEMON_CORE_H
    21 
    22 #include <vector>
    23 #include <algorithm>
    24 
    25 #include <lemon/config.h>
    26 #include <lemon/bits/enable_if.h>
    27 #include <lemon/bits/traits.h>
    28 #include <lemon/assert.h>
    29 
    30 // Disable the following warnings when compiling with MSVC:
    31 // C4250: 'class1' : inherits 'class2::member' via dominance
    32 // C4355: 'this' : used in base member initializer list
    33 // C4503: 'function' : decorated name length exceeded, name was truncated
    34 // C4800: 'type' : forcing value to bool 'true' or 'false' (performance warning)
    35 // C4996: 'function': was declared deprecated
    36 #ifdef _MSC_VER
    37 #pragma warning( disable : 4250 4355 4503 4800 4996 )
    38 #endif
    39 
    40 ///\file
    41 ///\brief LEMON core utilities.
    42 ///
    43 ///This header file contains core utilities for LEMON.
    44 ///It is automatically included by all graph types, therefore it usually
    45 ///do not have to be included directly.
    46 
    47 namespace lemon {
    48 
    49   /// \brief Dummy type to make it easier to create invalid iterators.
    50   ///
    51   /// Dummy type to make it easier to create invalid iterators.
    52   /// See \ref INVALID for the usage.
    53   struct Invalid {
    54   public:
    55     bool operator==(Invalid) { return true;  }
    56     bool operator!=(Invalid) { return false; }
    57     bool operator< (Invalid) { return false; }
    58   };
    59 
    60   /// \brief Invalid iterators.
    61   ///
    62   /// \ref Invalid is a global type that converts to each iterator
    63   /// in such a way that the value of the target iterator will be invalid.
    64 #ifdef LEMON_ONLY_TEMPLATES
    65   const Invalid INVALID = Invalid();
    66 #else
    67   extern const Invalid INVALID;
    68 #endif
    69 
    70   /// \addtogroup gutils
    71   /// @{
    72 
    73   ///Create convenience typedefs for the digraph types and iterators
    74 
    75   ///This \c \#define creates convenient type definitions for the following
    76   ///types of \c Digraph: \c Node,  \c NodeIt, \c Arc, \c ArcIt, \c InArcIt,
    77   ///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap,
    78   ///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap.
    79   ///
    80   ///\note If the graph type is a dependent type, ie. the graph type depend
    81   ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
    82   ///macro.
    83 #define DIGRAPH_TYPEDEFS(Digraph)                                       \
    84   typedef Digraph::Node Node;                                           \
    85   typedef Digraph::NodeIt NodeIt;                                       \
    86   typedef Digraph::Arc Arc;                                             \
    87   typedef Digraph::ArcIt ArcIt;                                         \
    88   typedef Digraph::InArcIt InArcIt;                                     \
    89   typedef Digraph::OutArcIt OutArcIt;                                   \
    90   typedef Digraph::NodeMap<bool> BoolNodeMap;                           \
    91   typedef Digraph::NodeMap<int> IntNodeMap;                             \
    92   typedef Digraph::NodeMap<double> DoubleNodeMap;                       \
    93   typedef Digraph::ArcMap<bool> BoolArcMap;                             \
    94   typedef Digraph::ArcMap<int> IntArcMap;                               \
    95   typedef Digraph::ArcMap<double> DoubleArcMap
    96 
    97   ///Create convenience typedefs for the digraph types and iterators
    98 
    99   ///\see DIGRAPH_TYPEDEFS
   100   ///
   101   ///\note Use this macro, if the graph type is a dependent type,
   102   ///ie. the graph type depend on a template parameter.
   103 #define TEMPLATE_DIGRAPH_TYPEDEFS(Digraph)                              \
   104   typedef typename Digraph::Node Node;                                  \
   105   typedef typename Digraph::NodeIt NodeIt;                              \
   106   typedef typename Digraph::Arc Arc;                                    \
   107   typedef typename Digraph::ArcIt ArcIt;                                \
   108   typedef typename Digraph::InArcIt InArcIt;                            \
   109   typedef typename Digraph::OutArcIt OutArcIt;                          \
   110   typedef typename Digraph::template NodeMap<bool> BoolNodeMap;         \
   111   typedef typename Digraph::template NodeMap<int> IntNodeMap;           \
   112   typedef typename Digraph::template NodeMap<double> DoubleNodeMap;     \
   113   typedef typename Digraph::template ArcMap<bool> BoolArcMap;           \
   114   typedef typename Digraph::template ArcMap<int> IntArcMap;             \
   115   typedef typename Digraph::template ArcMap<double> DoubleArcMap
   116 
   117   ///Create convenience typedefs for the graph types and iterators
   118 
   119   ///This \c \#define creates the same convenient type definitions as defined
   120   ///by \ref DIGRAPH_TYPEDEFS(Graph) and six more, namely it creates
   121   ///\c Edge, \c EdgeIt, \c IncEdgeIt, \c BoolEdgeMap, \c IntEdgeMap,
   122   ///\c DoubleEdgeMap.
   123   ///
   124   ///\note If the graph type is a dependent type, ie. the graph type depend
   125   ///on a template parameter, then use \c TEMPLATE_GRAPH_TYPEDEFS()
   126   ///macro.
   127 #define GRAPH_TYPEDEFS(Graph)                                           \
   128   DIGRAPH_TYPEDEFS(Graph);                                              \
   129   typedef Graph::Edge Edge;                                             \
   130   typedef Graph::EdgeIt EdgeIt;                                         \
   131   typedef Graph::IncEdgeIt IncEdgeIt;                                   \
   132   typedef Graph::EdgeMap<bool> BoolEdgeMap;                             \
   133   typedef Graph::EdgeMap<int> IntEdgeMap;                               \
   134   typedef Graph::EdgeMap<double> DoubleEdgeMap
   135 
   136   ///Create convenience typedefs for the graph types and iterators
   137 
   138   ///\see GRAPH_TYPEDEFS
   139   ///
   140   ///\note Use this macro, if the graph type is a dependent type,
   141   ///ie. the graph type depend on a template parameter.
   142 #define TEMPLATE_GRAPH_TYPEDEFS(Graph)                                  \
   143   TEMPLATE_DIGRAPH_TYPEDEFS(Graph);                                     \
   144   typedef typename Graph::Edge Edge;                                    \
   145   typedef typename Graph::EdgeIt EdgeIt;                                \
   146   typedef typename Graph::IncEdgeIt IncEdgeIt;                          \
   147   typedef typename Graph::template EdgeMap<bool> BoolEdgeMap;           \
   148   typedef typename Graph::template EdgeMap<int> IntEdgeMap;             \
   149   typedef typename Graph::template EdgeMap<double> DoubleEdgeMap
   150 
   151   /// \brief Function to count the items in a graph.
   152   ///
   153   /// This function counts the items (nodes, arcs etc.) in a graph.
   154   /// The complexity of the function is linear because
   155   /// it iterates on all of the items.
   156   template <typename Graph, typename Item>
   157   inline int countItems(const Graph& g) {
   158     typedef typename ItemSetTraits<Graph, Item>::ItemIt ItemIt;
   159     int num = 0;
   160     for (ItemIt it(g); it != INVALID; ++it) {
   161       ++num;
   162     }
   163     return num;
   164   }
   165 
   166   // Node counting:
   167 
   168   namespace _core_bits {
   169 
   170     template <typename Graph, typename Enable = void>
   171     struct CountNodesSelector {
   172       static int count(const Graph &g) {
   173         return countItems<Graph, typename Graph::Node>(g);
   174       }
   175     };
   176 
   177     template <typename Graph>
   178     struct CountNodesSelector<
   179       Graph, typename
   180       enable_if<typename Graph::NodeNumTag, void>::type>
   181     {
   182       static int count(const Graph &g) {
   183         return g.nodeNum();
   184       }
   185     };
   186   }
   187 
   188   /// \brief Function to count the nodes in the graph.
   189   ///
   190   /// This function counts the nodes in the graph.
   191   /// The complexity of the function is <em>O</em>(<em>n</em>), but for some
   192   /// graph structures it is specialized to run in <em>O</em>(1).
   193   ///
   194   /// \note If the graph contains a \c nodeNum() member function and a
   195   /// \c NodeNumTag tag then this function calls directly the member
   196   /// function to query the cardinality of the node set.
   197   template <typename Graph>
   198   inline int countNodes(const Graph& g) {
   199     return _core_bits::CountNodesSelector<Graph>::count(g);
   200   }
   201 
   202   // Arc counting:
   203 
   204   namespace _core_bits {
   205 
   206     template <typename Graph, typename Enable = void>
   207     struct CountArcsSelector {
   208       static int count(const Graph &g) {
   209         return countItems<Graph, typename Graph::Arc>(g);
   210       }
   211     };
   212 
   213     template <typename Graph>
   214     struct CountArcsSelector<
   215       Graph,
   216       typename enable_if<typename Graph::ArcNumTag, void>::type>
   217     {
   218       static int count(const Graph &g) {
   219         return g.arcNum();
   220       }
   221     };
   222   }
   223 
   224   /// \brief Function to count the arcs in the graph.
   225   ///
   226   /// This function counts the arcs in the graph.
   227   /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
   228   /// graph structures it is specialized to run in <em>O</em>(1).
   229   ///
   230   /// \note If the graph contains a \c arcNum() member function and a
   231   /// \c ArcNumTag tag then this function calls directly the member
   232   /// function to query the cardinality of the arc set.
   233   template <typename Graph>
   234   inline int countArcs(const Graph& g) {
   235     return _core_bits::CountArcsSelector<Graph>::count(g);
   236   }
   237 
   238   // Edge counting:
   239 
   240   namespace _core_bits {
   241 
   242     template <typename Graph, typename Enable = void>
   243     struct CountEdgesSelector {
   244       static int count(const Graph &g) {
   245         return countItems<Graph, typename Graph::Edge>(g);
   246       }
   247     };
   248 
   249     template <typename Graph>
   250     struct CountEdgesSelector<
   251       Graph,
   252       typename enable_if<typename Graph::EdgeNumTag, void>::type>
   253     {
   254       static int count(const Graph &g) {
   255         return g.edgeNum();
   256       }
   257     };
   258   }
   259 
   260   /// \brief Function to count the edges in the graph.
   261   ///
   262   /// This function counts the edges in the graph.
   263   /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
   264   /// graph structures it is specialized to run in <em>O</em>(1).
   265   ///
   266   /// \note If the graph contains a \c edgeNum() member function and a
   267   /// \c EdgeNumTag tag then this function calls directly the member
   268   /// function to query the cardinality of the edge set.
   269   template <typename Graph>
   270   inline int countEdges(const Graph& g) {
   271     return _core_bits::CountEdgesSelector<Graph>::count(g);
   272 
   273   }
   274 
   275 
   276   template <typename Graph, typename DegIt>
   277   inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {
   278     int num = 0;
   279     for (DegIt it(_g, _n); it != INVALID; ++it) {
   280       ++num;
   281     }
   282     return num;
   283   }
   284 
   285   /// \brief Function to count the number of the out-arcs from node \c n.
   286   ///
   287   /// This function counts the number of the out-arcs from node \c n
   288   /// in the graph \c g.
   289   template <typename Graph>
   290   inline int countOutArcs(const Graph& g,  const typename Graph::Node& n) {
   291     return countNodeDegree<Graph, typename Graph::OutArcIt>(g, n);
   292   }
   293 
   294   /// \brief Function to count the number of the in-arcs to node \c n.
   295   ///
   296   /// This function counts the number of the in-arcs to node \c n
   297   /// in the graph \c g.
   298   template <typename Graph>
   299   inline int countInArcs(const Graph& g,  const typename Graph::Node& n) {
   300     return countNodeDegree<Graph, typename Graph::InArcIt>(g, n);
   301   }
   302 
   303   /// \brief Function to count the number of the inc-edges to node \c n.
   304   ///
   305   /// This function counts the number of the inc-edges to node \c n
   306   /// in the undirected graph \c g.
   307   template <typename Graph>
   308   inline int countIncEdges(const Graph& g,  const typename Graph::Node& n) {
   309     return countNodeDegree<Graph, typename Graph::IncEdgeIt>(g, n);
   310   }
   311 
   312   namespace _core_bits {
   313 
   314     template <typename Digraph, typename Item, typename RefMap>
   315     class MapCopyBase {
   316     public:
   317       virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
   318 
   319       virtual ~MapCopyBase() {}
   320     };
   321 
   322     template <typename Digraph, typename Item, typename RefMap,
   323               typename FromMap, typename ToMap>
   324     class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
   325     public:
   326 
   327       MapCopy(const FromMap& map, ToMap& tmap)
   328         : _map(map), _tmap(tmap) {}
   329 
   330       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   331         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   332         for (ItemIt it(digraph); it != INVALID; ++it) {
   333           _tmap.set(refMap[it], _map[it]);
   334         }
   335       }
   336 
   337     private:
   338       const FromMap& _map;
   339       ToMap& _tmap;
   340     };
   341 
   342     template <typename Digraph, typename Item, typename RefMap, typename It>
   343     class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
   344     public:
   345 
   346       ItemCopy(const Item& item, It& it) : _item(item), _it(it) {}
   347 
   348       virtual void copy(const Digraph&, const RefMap& refMap) {
   349         _it = refMap[_item];
   350       }
   351 
   352     private:
   353       Item _item;
   354       It& _it;
   355     };
   356 
   357     template <typename Digraph, typename Item, typename RefMap, typename Ref>
   358     class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   359     public:
   360 
   361       RefCopy(Ref& map) : _map(map) {}
   362 
   363       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   364         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   365         for (ItemIt it(digraph); it != INVALID; ++it) {
   366           _map.set(it, refMap[it]);
   367         }
   368       }
   369 
   370     private:
   371       Ref& _map;
   372     };
   373 
   374     template <typename Digraph, typename Item, typename RefMap,
   375               typename CrossRef>
   376     class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   377     public:
   378 
   379       CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
   380 
   381       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   382         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   383         for (ItemIt it(digraph); it != INVALID; ++it) {
   384           _cmap.set(refMap[it], it);
   385         }
   386       }
   387 
   388     private:
   389       CrossRef& _cmap;
   390     };
   391 
   392     template <typename Digraph, typename Enable = void>
   393     struct DigraphCopySelector {
   394       template <typename From, typename NodeRefMap, typename ArcRefMap>
   395       static void copy(const From& from, Digraph &to,
   396                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   397         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   398           nodeRefMap[it] = to.addNode();
   399         }
   400         for (typename From::ArcIt it(from); it != INVALID; ++it) {
   401           arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)],
   402                                     nodeRefMap[from.target(it)]);
   403         }
   404       }
   405     };
   406 
   407     template <typename Digraph>
   408     struct DigraphCopySelector<
   409       Digraph,
   410       typename enable_if<typename Digraph::BuildTag, void>::type>
   411     {
   412       template <typename From, typename NodeRefMap, typename ArcRefMap>
   413       static void copy(const From& from, Digraph &to,
   414                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   415         to.build(from, nodeRefMap, arcRefMap);
   416       }
   417     };
   418 
   419     template <typename Graph, typename Enable = void>
   420     struct GraphCopySelector {
   421       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   422       static void copy(const From& from, Graph &to,
   423                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   424         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   425           nodeRefMap[it] = to.addNode();
   426         }
   427         for (typename From::EdgeIt it(from); it != INVALID; ++it) {
   428           edgeRefMap[it] = to.addEdge(nodeRefMap[from.u(it)],
   429                                       nodeRefMap[from.v(it)]);
   430         }
   431       }
   432     };
   433 
   434     template <typename Graph>
   435     struct GraphCopySelector<
   436       Graph,
   437       typename enable_if<typename Graph::BuildTag, void>::type>
   438     {
   439       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   440       static void copy(const From& from, Graph &to,
   441                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   442         to.build(from, nodeRefMap, edgeRefMap);
   443       }
   444     };
   445 
   446   }
   447 
   448   /// \brief Class to copy a digraph.
   449   ///
   450   /// Class to copy a digraph to another digraph (duplicate a digraph). The
   451   /// simplest way of using it is through the \c digraphCopy() function.
   452   ///
   453   /// This class not only make a copy of a digraph, but it can create
   454   /// references and cross references between the nodes and arcs of
   455   /// the two digraphs, and it can copy maps to use with the newly created
   456   /// digraph.
   457   ///
   458   /// To make a copy from a digraph, first an instance of DigraphCopy
   459   /// should be created, then the data belongs to the digraph should
   460   /// assigned to copy. In the end, the \c run() member should be
   461   /// called.
   462   ///
   463   /// The next code copies a digraph with several data:
   464   ///\code
   465   ///  DigraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
   466   ///  // Create references for the nodes
   467   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   468   ///  cg.nodeRef(nr);
   469   ///  // Create cross references (inverse) for the arcs
   470   ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);
   471   ///  cg.arcCrossRef(acr);
   472   ///  // Copy an arc map
   473   ///  OrigGraph::ArcMap<double> oamap(orig_graph);
   474   ///  NewGraph::ArcMap<double> namap(new_graph);
   475   ///  cg.arcMap(oamap, namap);
   476   ///  // Copy a node
   477   ///  OrigGraph::Node on;
   478   ///  NewGraph::Node nn;
   479   ///  cg.node(on, nn);
   480   ///  // Execute copying
   481   ///  cg.run();
   482   ///\endcode
   483   template <typename From, typename To>
   484   class DigraphCopy {
   485   private:
   486 
   487     typedef typename From::Node Node;
   488     typedef typename From::NodeIt NodeIt;
   489     typedef typename From::Arc Arc;
   490     typedef typename From::ArcIt ArcIt;
   491 
   492     typedef typename To::Node TNode;
   493     typedef typename To::Arc TArc;
   494 
   495     typedef typename From::template NodeMap<TNode> NodeRefMap;
   496     typedef typename From::template ArcMap<TArc> ArcRefMap;
   497 
   498   public:
   499 
   500     /// \brief Constructor of DigraphCopy.
   501     ///
   502     /// Constructor of DigraphCopy for copying the content of the
   503     /// \c from digraph into the \c to digraph.
   504     DigraphCopy(const From& from, To& to)
   505       : _from(from), _to(to) {}
   506 
   507     /// \brief Destructor of DigraphCopy
   508     ///
   509     /// Destructor of DigraphCopy.
   510     ~DigraphCopy() {
   511       for (int i = 0; i < int(_node_maps.size()); ++i) {
   512         delete _node_maps[i];
   513       }
   514       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   515         delete _arc_maps[i];
   516       }
   517 
   518     }
   519 
   520     /// \brief Copy the node references into the given map.
   521     ///
   522     /// This function copies the node references into the given map.
   523     /// The parameter should be a map, whose key type is the Node type of
   524     /// the source digraph, while the value type is the Node type of the
   525     /// destination digraph.
   526     template <typename NodeRef>
   527     DigraphCopy& nodeRef(NodeRef& map) {
   528       _node_maps.push_back(new _core_bits::RefCopy<From, Node,
   529                            NodeRefMap, NodeRef>(map));
   530       return *this;
   531     }
   532 
   533     /// \brief Copy the node cross references into the given map.
   534     ///
   535     /// This function copies the node cross references (reverse references)
   536     /// into the given map. The parameter should be a map, whose key type
   537     /// is the Node type of the destination digraph, while the value type is
   538     /// the Node type of the source digraph.
   539     template <typename NodeCrossRef>
   540     DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
   541       _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
   542                            NodeRefMap, NodeCrossRef>(map));
   543       return *this;
   544     }
   545 
   546     /// \brief Make a copy of the given node map.
   547     ///
   548     /// This function makes a copy of the given node map for the newly
   549     /// created digraph.
   550     /// The key type of the new map \c tmap should be the Node type of the
   551     /// destination digraph, and the key type of the original map \c map
   552     /// should be the Node type of the source digraph.
   553     template <typename FromMap, typename ToMap>
   554     DigraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
   555       _node_maps.push_back(new _core_bits::MapCopy<From, Node,
   556                            NodeRefMap, FromMap, ToMap>(map, tmap));
   557       return *this;
   558     }
   559 
   560     /// \brief Make a copy of the given node.
   561     ///
   562     /// This function makes a copy of the given node.
   563     DigraphCopy& node(const Node& node, TNode& tnode) {
   564       _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
   565                            NodeRefMap, TNode>(node, tnode));
   566       return *this;
   567     }
   568 
   569     /// \brief Copy the arc references into the given map.
   570     ///
   571     /// This function copies the arc references into the given map.
   572     /// The parameter should be a map, whose key type is the Arc type of
   573     /// the source digraph, while the value type is the Arc type of the
   574     /// destination digraph.
   575     template <typename ArcRef>
   576     DigraphCopy& arcRef(ArcRef& map) {
   577       _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
   578                           ArcRefMap, ArcRef>(map));
   579       return *this;
   580     }
   581 
   582     /// \brief Copy the arc cross references into the given map.
   583     ///
   584     /// This function copies the arc cross references (reverse references)
   585     /// into the given map. The parameter should be a map, whose key type
   586     /// is the Arc type of the destination digraph, while the value type is
   587     /// the Arc type of the source digraph.
   588     template <typename ArcCrossRef>
   589     DigraphCopy& arcCrossRef(ArcCrossRef& map) {
   590       _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
   591                           ArcRefMap, ArcCrossRef>(map));
   592       return *this;
   593     }
   594 
   595     /// \brief Make a copy of the given arc map.
   596     ///
   597     /// This function makes a copy of the given arc map for the newly
   598     /// created digraph.
   599     /// The key type of the new map \c tmap should be the Arc type of the
   600     /// destination digraph, and the key type of the original map \c map
   601     /// should be the Arc type of the source digraph.
   602     template <typename FromMap, typename ToMap>
   603     DigraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
   604       _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
   605                           ArcRefMap, FromMap, ToMap>(map, tmap));
   606       return *this;
   607     }
   608 
   609     /// \brief Make a copy of the given arc.
   610     ///
   611     /// This function makes a copy of the given arc.
   612     DigraphCopy& arc(const Arc& arc, TArc& tarc) {
   613       _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
   614                           ArcRefMap, TArc>(arc, tarc));
   615       return *this;
   616     }
   617 
   618     /// \brief Execute copying.
   619     ///
   620     /// This function executes the copying of the digraph along with the
   621     /// copying of the assigned data.
   622     void run() {
   623       NodeRefMap nodeRefMap(_from);
   624       ArcRefMap arcRefMap(_from);
   625       _core_bits::DigraphCopySelector<To>::
   626         copy(_from, _to, nodeRefMap, arcRefMap);
   627       for (int i = 0; i < int(_node_maps.size()); ++i) {
   628         _node_maps[i]->copy(_from, nodeRefMap);
   629       }
   630       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   631         _arc_maps[i]->copy(_from, arcRefMap);
   632       }
   633     }
   634 
   635   protected:
   636 
   637     const From& _from;
   638     To& _to;
   639 
   640     std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
   641       _node_maps;
   642 
   643     std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
   644       _arc_maps;
   645 
   646   };
   647 
   648   /// \brief Copy a digraph to another digraph.
   649   ///
   650   /// This function copies a digraph to another digraph.
   651   /// The complete usage of it is detailed in the DigraphCopy class, but
   652   /// a short example shows a basic work:
   653   ///\code
   654   /// digraphCopy(src, trg).nodeRef(nr).arcCrossRef(acr).run();
   655   ///\endcode
   656   ///
   657   /// After the copy the \c nr map will contain the mapping from the
   658   /// nodes of the \c from digraph to the nodes of the \c to digraph and
   659   /// \c acr will contain the mapping from the arcs of the \c to digraph
   660   /// to the arcs of the \c from digraph.
   661   ///
   662   /// \see DigraphCopy
   663   template <typename From, typename To>
   664   DigraphCopy<From, To> digraphCopy(const From& from, To& to) {
   665     return DigraphCopy<From, To>(from, to);
   666   }
   667 
   668   /// \brief Class to copy a graph.
   669   ///
   670   /// Class to copy a graph to another graph (duplicate a graph). The
   671   /// simplest way of using it is through the \c graphCopy() function.
   672   ///
   673   /// This class not only make a copy of a graph, but it can create
   674   /// references and cross references between the nodes, edges and arcs of
   675   /// the two graphs, and it can copy maps for using with the newly created
   676   /// graph.
   677   ///
   678   /// To make a copy from a graph, first an instance of GraphCopy
   679   /// should be created, then the data belongs to the graph should
   680   /// assigned to copy. In the end, the \c run() member should be
   681   /// called.
   682   ///
   683   /// The next code copies a graph with several data:
   684   ///\code
   685   ///  GraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
   686   ///  // Create references for the nodes
   687   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   688   ///  cg.nodeRef(nr);
   689   ///  // Create cross references (inverse) for the edges
   690   ///  NewGraph::EdgeMap<OrigGraph::Edge> ecr(new_graph);
   691   ///  cg.edgeCrossRef(ecr);
   692   ///  // Copy an edge map
   693   ///  OrigGraph::EdgeMap<double> oemap(orig_graph);
   694   ///  NewGraph::EdgeMap<double> nemap(new_graph);
   695   ///  cg.edgeMap(oemap, nemap);
   696   ///  // Copy a node
   697   ///  OrigGraph::Node on;
   698   ///  NewGraph::Node nn;
   699   ///  cg.node(on, nn);
   700   ///  // Execute copying
   701   ///  cg.run();
   702   ///\endcode
   703   template <typename From, typename To>
   704   class GraphCopy {
   705   private:
   706 
   707     typedef typename From::Node Node;
   708     typedef typename From::NodeIt NodeIt;
   709     typedef typename From::Arc Arc;
   710     typedef typename From::ArcIt ArcIt;
   711     typedef typename From::Edge Edge;
   712     typedef typename From::EdgeIt EdgeIt;
   713 
   714     typedef typename To::Node TNode;
   715     typedef typename To::Arc TArc;
   716     typedef typename To::Edge TEdge;
   717 
   718     typedef typename From::template NodeMap<TNode> NodeRefMap;
   719     typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
   720 
   721     struct ArcRefMap {
   722       ArcRefMap(const From& from, const To& to,
   723                 const EdgeRefMap& edge_ref, const NodeRefMap& node_ref)
   724         : _from(from), _to(to),
   725           _edge_ref(edge_ref), _node_ref(node_ref) {}
   726 
   727       typedef typename From::Arc Key;
   728       typedef typename To::Arc Value;
   729 
   730       Value operator[](const Key& key) const {
   731         bool forward = _from.u(key) != _from.v(key) ?
   732           _node_ref[_from.source(key)] ==
   733           _to.source(_to.direct(_edge_ref[key], true)) :
   734           _from.direction(key);
   735         return _to.direct(_edge_ref[key], forward);
   736       }
   737 
   738       const From& _from;
   739       const To& _to;
   740       const EdgeRefMap& _edge_ref;
   741       const NodeRefMap& _node_ref;
   742     };
   743 
   744   public:
   745 
   746     /// \brief Constructor of GraphCopy.
   747     ///
   748     /// Constructor of GraphCopy for copying the content of the
   749     /// \c from graph into the \c to graph.
   750     GraphCopy(const From& from, To& to)
   751       : _from(from), _to(to) {}
   752 
   753     /// \brief Destructor of GraphCopy
   754     ///
   755     /// Destructor of GraphCopy.
   756     ~GraphCopy() {
   757       for (int i = 0; i < int(_node_maps.size()); ++i) {
   758         delete _node_maps[i];
   759       }
   760       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   761         delete _arc_maps[i];
   762       }
   763       for (int i = 0; i < int(_edge_maps.size()); ++i) {
   764         delete _edge_maps[i];
   765       }
   766     }
   767 
   768     /// \brief Copy the node references into the given map.
   769     ///
   770     /// This function copies the node references into the given map.
   771     /// The parameter should be a map, whose key type is the Node type of
   772     /// the source graph, while the value type is the Node type of the
   773     /// destination graph.
   774     template <typename NodeRef>
   775     GraphCopy& nodeRef(NodeRef& map) {
   776       _node_maps.push_back(new _core_bits::RefCopy<From, Node,
   777                            NodeRefMap, NodeRef>(map));
   778       return *this;
   779     }
   780 
   781     /// \brief Copy the node cross references into the given map.
   782     ///
   783     /// This function copies the node cross references (reverse references)
   784     /// into the given map. The parameter should be a map, whose key type
   785     /// is the Node type of the destination graph, while the value type is
   786     /// the Node type of the source graph.
   787     template <typename NodeCrossRef>
   788     GraphCopy& nodeCrossRef(NodeCrossRef& map) {
   789       _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
   790                            NodeRefMap, NodeCrossRef>(map));
   791       return *this;
   792     }
   793 
   794     /// \brief Make a copy of the given node map.
   795     ///
   796     /// This function makes a copy of the given node map for the newly
   797     /// created graph.
   798     /// The key type of the new map \c tmap should be the Node type of the
   799     /// destination graph, and the key type of the original map \c map
   800     /// should be the Node type of the source graph.
   801     template <typename FromMap, typename ToMap>
   802     GraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
   803       _node_maps.push_back(new _core_bits::MapCopy<From, Node,
   804                            NodeRefMap, FromMap, ToMap>(map, tmap));
   805       return *this;
   806     }
   807 
   808     /// \brief Make a copy of the given node.
   809     ///
   810     /// This function makes a copy of the given node.
   811     GraphCopy& node(const Node& node, TNode& tnode) {
   812       _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
   813                            NodeRefMap, TNode>(node, tnode));
   814       return *this;
   815     }
   816 
   817     /// \brief Copy the arc references into the given map.
   818     ///
   819     /// This function copies the arc references into the given map.
   820     /// The parameter should be a map, whose key type is the Arc type of
   821     /// the source graph, while the value type is the Arc type of the
   822     /// destination graph.
   823     template <typename ArcRef>
   824     GraphCopy& arcRef(ArcRef& map) {
   825       _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
   826                           ArcRefMap, ArcRef>(map));
   827       return *this;
   828     }
   829 
   830     /// \brief Copy the arc cross references into the given map.
   831     ///
   832     /// This function copies the arc cross references (reverse references)
   833     /// into the given map. The parameter should be a map, whose key type
   834     /// is the Arc type of the destination graph, while the value type is
   835     /// the Arc type of the source graph.
   836     template <typename ArcCrossRef>
   837     GraphCopy& arcCrossRef(ArcCrossRef& map) {
   838       _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
   839                           ArcRefMap, ArcCrossRef>(map));
   840       return *this;
   841     }
   842 
   843     /// \brief Make a copy of the given arc map.
   844     ///
   845     /// This function makes a copy of the given arc map for the newly
   846     /// created graph.
   847     /// The key type of the new map \c tmap should be the Arc type of the
   848     /// destination graph, and the key type of the original map \c map
   849     /// should be the Arc type of the source graph.
   850     template <typename FromMap, typename ToMap>
   851     GraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
   852       _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
   853                           ArcRefMap, FromMap, ToMap>(map, tmap));
   854       return *this;
   855     }
   856 
   857     /// \brief Make a copy of the given arc.
   858     ///
   859     /// This function makes a copy of the given arc.
   860     GraphCopy& arc(const Arc& arc, TArc& tarc) {
   861       _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
   862                           ArcRefMap, TArc>(arc, tarc));
   863       return *this;
   864     }
   865 
   866     /// \brief Copy the edge references into the given map.
   867     ///
   868     /// This function copies the edge references into the given map.
   869     /// The parameter should be a map, whose key type is the Edge type of
   870     /// the source graph, while the value type is the Edge type of the
   871     /// destination graph.
   872     template <typename EdgeRef>
   873     GraphCopy& edgeRef(EdgeRef& map) {
   874       _edge_maps.push_back(new _core_bits::RefCopy<From, Edge,
   875                            EdgeRefMap, EdgeRef>(map));
   876       return *this;
   877     }
   878 
   879     /// \brief Copy the edge cross references into the given map.
   880     ///
   881     /// This function copies the edge cross references (reverse references)
   882     /// into the given map. The parameter should be a map, whose key type
   883     /// is the Edge type of the destination graph, while the value type is
   884     /// the Edge type of the source graph.
   885     template <typename EdgeCrossRef>
   886     GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
   887       _edge_maps.push_back(new _core_bits::CrossRefCopy<From,
   888                            Edge, EdgeRefMap, EdgeCrossRef>(map));
   889       return *this;
   890     }
   891 
   892     /// \brief Make a copy of the given edge map.
   893     ///
   894     /// This function makes a copy of the given edge map for the newly
   895     /// created graph.
   896     /// The key type of the new map \c tmap should be the Edge type of the
   897     /// destination graph, and the key type of the original map \c map
   898     /// should be the Edge type of the source graph.
   899     template <typename FromMap, typename ToMap>
   900     GraphCopy& edgeMap(const FromMap& map, ToMap& tmap) {
   901       _edge_maps.push_back(new _core_bits::MapCopy<From, Edge,
   902                            EdgeRefMap, FromMap, ToMap>(map, tmap));
   903       return *this;
   904     }
   905 
   906     /// \brief Make a copy of the given edge.
   907     ///
   908     /// This function makes a copy of the given edge.
   909     GraphCopy& edge(const Edge& edge, TEdge& tedge) {
   910       _edge_maps.push_back(new _core_bits::ItemCopy<From, Edge,
   911                            EdgeRefMap, TEdge>(edge, tedge));
   912       return *this;
   913     }
   914 
   915     /// \brief Execute copying.
   916     ///
   917     /// This function executes the copying of the graph along with the
   918     /// copying of the assigned data.
   919     void run() {
   920       NodeRefMap nodeRefMap(_from);
   921       EdgeRefMap edgeRefMap(_from);
   922       ArcRefMap arcRefMap(_from, _to, edgeRefMap, nodeRefMap);
   923       _core_bits::GraphCopySelector<To>::
   924         copy(_from, _to, nodeRefMap, edgeRefMap);
   925       for (int i = 0; i < int(_node_maps.size()); ++i) {
   926         _node_maps[i]->copy(_from, nodeRefMap);
   927       }
   928       for (int i = 0; i < int(_edge_maps.size()); ++i) {
   929         _edge_maps[i]->copy(_from, edgeRefMap);
   930       }
   931       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   932         _arc_maps[i]->copy(_from, arcRefMap);
   933       }
   934     }
   935 
   936   private:
   937 
   938     const From& _from;
   939     To& _to;
   940 
   941     std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
   942       _node_maps;
   943 
   944     std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
   945       _arc_maps;
   946 
   947     std::vector<_core_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
   948       _edge_maps;
   949 
   950   };
   951 
   952   /// \brief Copy a graph to another graph.
   953   ///
   954   /// This function copies a graph to another graph.
   955   /// The complete usage of it is detailed in the GraphCopy class,
   956   /// but a short example shows a basic work:
   957   ///\code
   958   /// graphCopy(src, trg).nodeRef(nr).edgeCrossRef(ecr).run();
   959   ///\endcode
   960   ///
   961   /// After the copy the \c nr map will contain the mapping from the
   962   /// nodes of the \c from graph to the nodes of the \c to graph and
   963   /// \c ecr will contain the mapping from the edges of the \c to graph
   964   /// to the edges of the \c from graph.
   965   ///
   966   /// \see GraphCopy
   967   template <typename From, typename To>
   968   GraphCopy<From, To>
   969   graphCopy(const From& from, To& to) {
   970     return GraphCopy<From, To>(from, to);
   971   }
   972 
   973   namespace _core_bits {
   974 
   975     template <typename Graph, typename Enable = void>
   976     struct FindArcSelector {
   977       typedef typename Graph::Node Node;
   978       typedef typename Graph::Arc Arc;
   979       static Arc find(const Graph &g, Node u, Node v, Arc e) {
   980         if (e == INVALID) {
   981           g.firstOut(e, u);
   982         } else {
   983           g.nextOut(e);
   984         }
   985         while (e != INVALID && g.target(e) != v) {
   986           g.nextOut(e);
   987         }
   988         return e;
   989       }
   990     };
   991 
   992     template <typename Graph>
   993     struct FindArcSelector<
   994       Graph,
   995       typename enable_if<typename Graph::FindArcTag, void>::type>
   996     {
   997       typedef typename Graph::Node Node;
   998       typedef typename Graph::Arc Arc;
   999       static Arc find(const Graph &g, Node u, Node v, Arc prev) {
  1000         return g.findArc(u, v, prev);
  1001       }
  1002     };
  1003   }
  1004 
  1005   /// \brief Find an arc between two nodes of a digraph.
  1006   ///
  1007   /// This function finds an arc from node \c u to node \c v in the
  1008   /// digraph \c g.
  1009   ///
  1010   /// If \c prev is \ref INVALID (this is the default value), then
  1011   /// it finds the first arc from \c u to \c v. Otherwise it looks for
  1012   /// the next arc from \c u to \c v after \c prev.
  1013   /// \return The found arc or \ref INVALID if there is no such an arc.
  1014   ///
  1015   /// Thus you can iterate through each arc from \c u to \c v as it follows.
  1016   ///\code
  1017   /// for(Arc e = findArc(g,u,v); e != INVALID; e = findArc(g,u,v,e)) {
  1018   ///   ...
  1019   /// }
  1020   ///\endcode
  1021   ///
  1022   /// \note \ref ConArcIt provides iterator interface for the same
  1023   /// functionality.
  1024   ///
  1025   ///\sa ConArcIt
  1026   ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
  1027   template <typename Graph>
  1028   inline typename Graph::Arc
  1029   findArc(const Graph &g, typename Graph::Node u, typename Graph::Node v,
  1030           typename Graph::Arc prev = INVALID) {
  1031     return _core_bits::FindArcSelector<Graph>::find(g, u, v, prev);
  1032   }
  1033 
  1034   /// \brief Iterator for iterating on parallel arcs connecting the same nodes.
  1035   ///
  1036   /// Iterator for iterating on parallel arcs connecting the same nodes. It is
  1037   /// a higher level interface for the \ref findArc() function. You can
  1038   /// use it the following way:
  1039   ///\code
  1040   /// for (ConArcIt<Graph> it(g, src, trg); it != INVALID; ++it) {
  1041   ///   ...
  1042   /// }
  1043   ///\endcode
  1044   ///
  1045   ///\sa findArc()
  1046   ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
  1047   template <typename GR>
  1048   class ConArcIt : public GR::Arc {
  1049     typedef typename GR::Arc Parent;
  1050 
  1051   public:
  1052 
  1053     typedef typename GR::Arc Arc;
  1054     typedef typename GR::Node Node;
  1055 
  1056     /// \brief Constructor.
  1057     ///
  1058     /// Construct a new ConArcIt iterating on the arcs that
  1059     /// connects nodes \c u and \c v.
  1060     ConArcIt(const GR& g, Node u, Node v) : _graph(g) {
  1061       Parent::operator=(findArc(_graph, u, v));
  1062     }
  1063 
  1064     /// \brief Constructor.
  1065     ///
  1066     /// Construct a new ConArcIt that continues the iterating from arc \c a.
  1067     ConArcIt(const GR& g, Arc a) : Parent(a), _graph(g) {}
  1068 
  1069     /// \brief Increment operator.
  1070     ///
  1071     /// It increments the iterator and gives back the next arc.
  1072     ConArcIt& operator++() {
  1073       Parent::operator=(findArc(_graph, _graph.source(*this),
  1074                                 _graph.target(*this), *this));
  1075       return *this;
  1076     }
  1077   private:
  1078     const GR& _graph;
  1079   };
  1080 
  1081   namespace _core_bits {
  1082 
  1083     template <typename Graph, typename Enable = void>
  1084     struct FindEdgeSelector {
  1085       typedef typename Graph::Node Node;
  1086       typedef typename Graph::Edge Edge;
  1087       static Edge find(const Graph &g, Node u, Node v, Edge e) {
  1088         bool b;
  1089         if (u != v) {
  1090           if (e == INVALID) {
  1091             g.firstInc(e, b, u);
  1092           } else {
  1093             b = g.u(e) == u;
  1094             g.nextInc(e, b);
  1095           }
  1096           while (e != INVALID && (b ? g.v(e) : g.u(e)) != v) {
  1097             g.nextInc(e, b);
  1098           }
  1099         } else {
  1100           if (e == INVALID) {
  1101             g.firstInc(e, b, u);
  1102           } else {
  1103             b = true;
  1104             g.nextInc(e, b);
  1105           }
  1106           while (e != INVALID && (!b || g.v(e) != v)) {
  1107             g.nextInc(e, b);
  1108           }
  1109         }
  1110         return e;
  1111       }
  1112     };
  1113 
  1114     template <typename Graph>
  1115     struct FindEdgeSelector<
  1116       Graph,
  1117       typename enable_if<typename Graph::FindEdgeTag, void>::type>
  1118     {
  1119       typedef typename Graph::Node Node;
  1120       typedef typename Graph::Edge Edge;
  1121       static Edge find(const Graph &g, Node u, Node v, Edge prev) {
  1122         return g.findEdge(u, v, prev);
  1123       }
  1124     };
  1125   }
  1126 
  1127   /// \brief Find an edge between two nodes of a graph.
  1128   ///
  1129   /// This function finds an edge from node \c u to node \c v in graph \c g.
  1130   /// If node \c u and node \c v is equal then each loop edge
  1131   /// will be enumerated once.
  1132   ///
  1133   /// If \c prev is \ref INVALID (this is the default value), then
  1134   /// it finds the first edge from \c u to \c v. Otherwise it looks for
  1135   /// the next edge from \c u to \c v after \c prev.
  1136   /// \return The found edge or \ref INVALID if there is no such an edge.
  1137   ///
  1138   /// Thus you can iterate through each edge between \c u and \c v
  1139   /// as it follows.
  1140   ///\code
  1141   /// for(Edge e = findEdge(g,u,v); e != INVALID; e = findEdge(g,u,v,e)) {
  1142   ///   ...
  1143   /// }
  1144   ///\endcode
  1145   ///
  1146   /// \note \ref ConEdgeIt provides iterator interface for the same
  1147   /// functionality.
  1148   ///
  1149   ///\sa ConEdgeIt
  1150   template <typename Graph>
  1151   inline typename Graph::Edge
  1152   findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,
  1153             typename Graph::Edge p = INVALID) {
  1154     return _core_bits::FindEdgeSelector<Graph>::find(g, u, v, p);
  1155   }
  1156 
  1157   /// \brief Iterator for iterating on parallel edges connecting the same nodes.
  1158   ///
  1159   /// Iterator for iterating on parallel edges connecting the same nodes.
  1160   /// It is a higher level interface for the findEdge() function. You can
  1161   /// use it the following way:
  1162   ///\code
  1163   /// for (ConEdgeIt<Graph> it(g, u, v); it != INVALID; ++it) {
  1164   ///   ...
  1165   /// }
  1166   ///\endcode
  1167   ///
  1168   ///\sa findEdge()
  1169   template <typename GR>
  1170   class ConEdgeIt : public GR::Edge {
  1171     typedef typename GR::Edge Parent;
  1172 
  1173   public:
  1174 
  1175     typedef typename GR::Edge Edge;
  1176     typedef typename GR::Node Node;
  1177 
  1178     /// \brief Constructor.
  1179     ///
  1180     /// Construct a new ConEdgeIt iterating on the edges that
  1181     /// connects nodes \c u and \c v.
  1182     ConEdgeIt(const GR& g, Node u, Node v) : _graph(g), _u(u), _v(v) {
  1183       Parent::operator=(findEdge(_graph, _u, _v));
  1184     }
  1185 
  1186     /// \brief Constructor.
  1187     ///
  1188     /// Construct a new ConEdgeIt that continues iterating from edge \c e.
  1189     ConEdgeIt(const GR& g, Edge e) : Parent(e), _graph(g) {}
  1190 
  1191     /// \brief Increment operator.
  1192     ///
  1193     /// It increments the iterator and gives back the next edge.
  1194     ConEdgeIt& operator++() {
  1195       Parent::operator=(findEdge(_graph, _u, _v, *this));
  1196       return *this;
  1197     }
  1198   private:
  1199     const GR& _graph;
  1200     Node _u, _v;
  1201   };
  1202 
  1203 
  1204   ///Dynamic arc look-up between given endpoints.
  1205 
  1206   ///Using this class, you can find an arc in a digraph from a given
  1207   ///source to a given target in amortized time <em>O</em>(log<em>d</em>),
  1208   ///where <em>d</em> is the out-degree of the source node.
  1209   ///
  1210   ///It is possible to find \e all parallel arcs between two nodes with
  1211   ///the \c operator() member.
  1212   ///
  1213   ///This is a dynamic data structure. Consider to use \ref ArcLookUp or
  1214   ///\ref AllArcLookUp if your digraph is not changed so frequently.
  1215   ///
  1216   ///This class uses a self-adjusting binary search tree, the Splay tree
  1217   ///of Sleator and Tarjan to guarantee the logarithmic amortized
  1218   ///time bound for arc look-ups. This class also guarantees the
  1219   ///optimal time bound in a constant factor for any distribution of
  1220   ///queries.
  1221   ///
  1222   ///\tparam GR The type of the underlying digraph.
  1223   ///
  1224   ///\sa ArcLookUp
  1225   ///\sa AllArcLookUp
  1226   template <typename GR>
  1227   class DynArcLookUp
  1228     : protected ItemSetTraits<GR, typename GR::Arc>::ItemNotifier::ObserverBase
  1229   {
  1230     typedef typename ItemSetTraits<GR, typename GR::Arc>
  1231     ::ItemNotifier::ObserverBase Parent;
  1232 
  1233     TEMPLATE_DIGRAPH_TYPEDEFS(GR);
  1234 
  1235   public:
  1236 
  1237     /// The Digraph type
  1238     typedef GR Digraph;
  1239 
  1240   protected:
  1241 
  1242     class AutoNodeMap : public ItemSetTraits<GR, Node>::template Map<Arc>::Type {
  1243       typedef typename ItemSetTraits<GR, Node>::template Map<Arc>::Type Parent;
  1244 
  1245     public:
  1246 
  1247       AutoNodeMap(const GR& digraph) : Parent(digraph, INVALID) {}
  1248 
  1249       virtual void add(const Node& node) {
  1250         Parent::add(node);
  1251         Parent::set(node, INVALID);
  1252       }
  1253 
  1254       virtual void add(const std::vector<Node>& nodes) {
  1255         Parent::add(nodes);
  1256         for (int i = 0; i < int(nodes.size()); ++i) {
  1257           Parent::set(nodes[i], INVALID);
  1258         }
  1259       }
  1260 
  1261       virtual void build() {
  1262         Parent::build();
  1263         Node it;
  1264         typename Parent::Notifier* nf = Parent::notifier();
  1265         for (nf->first(it); it != INVALID; nf->next(it)) {
  1266           Parent::set(it, INVALID);
  1267         }
  1268       }
  1269     };
  1270 
  1271     class ArcLess {
  1272       const Digraph &g;
  1273     public:
  1274       ArcLess(const Digraph &_g) : g(_g) {}
  1275       bool operator()(Arc a,Arc b) const
  1276       {
  1277         return g.target(a)<g.target(b);
  1278       }
  1279     };
  1280 
  1281   protected: 
  1282 
  1283     const Digraph &_g;
  1284     AutoNodeMap _head;
  1285     typename Digraph::template ArcMap<Arc> _parent;
  1286     typename Digraph::template ArcMap<Arc> _left;
  1287     typename Digraph::template ArcMap<Arc> _right;
  1288 
  1289   public:
  1290 
  1291     ///Constructor
  1292 
  1293     ///Constructor.
  1294     ///
  1295     ///It builds up the search database.
  1296     DynArcLookUp(const Digraph &g)
  1297       : _g(g),_head(g),_parent(g),_left(g),_right(g)
  1298     {
  1299       Parent::attach(_g.notifier(typename Digraph::Arc()));
  1300       refresh();
  1301     }
  1302 
  1303   protected:
  1304 
  1305     virtual void add(const Arc& arc) {
  1306       insert(arc);
  1307     }
  1308 
  1309     virtual void add(const std::vector<Arc>& arcs) {
  1310       for (int i = 0; i < int(arcs.size()); ++i) {
  1311         insert(arcs[i]);
  1312       }
  1313     }
  1314 
  1315     virtual void erase(const Arc& arc) {
  1316       remove(arc);
  1317     }
  1318 
  1319     virtual void erase(const std::vector<Arc>& arcs) {
  1320       for (int i = 0; i < int(arcs.size()); ++i) {
  1321         remove(arcs[i]);
  1322       }
  1323     }
  1324 
  1325     virtual void build() {
  1326       refresh();
  1327     }
  1328 
  1329     virtual void clear() {
  1330       for(NodeIt n(_g);n!=INVALID;++n) {
  1331         _head[n] = INVALID;
  1332       }
  1333     }
  1334 
  1335     void insert(Arc arc) {
  1336       Node s = _g.source(arc);
  1337       Node t = _g.target(arc);
  1338       _left[arc] = INVALID;
  1339       _right[arc] = INVALID;
  1340 
  1341       Arc e = _head[s];
  1342       if (e == INVALID) {
  1343         _head[s] = arc;
  1344         _parent[arc] = INVALID;
  1345         return;
  1346       }
  1347       while (true) {
  1348         if (t < _g.target(e)) {
  1349           if (_left[e] == INVALID) {
  1350             _left[e] = arc;
  1351             _parent[arc] = e;
  1352             splay(arc);
  1353             return;
  1354           } else {
  1355             e = _left[e];
  1356           }
  1357         } else {
  1358           if (_right[e] == INVALID) {
  1359             _right[e] = arc;
  1360             _parent[arc] = e;
  1361             splay(arc);
  1362             return;
  1363           } else {
  1364             e = _right[e];
  1365           }
  1366         }
  1367       }
  1368     }
  1369 
  1370     void remove(Arc arc) {
  1371       if (_left[arc] == INVALID) {
  1372         if (_right[arc] != INVALID) {
  1373           _parent[_right[arc]] = _parent[arc];
  1374         }
  1375         if (_parent[arc] != INVALID) {
  1376           if (_left[_parent[arc]] == arc) {
  1377             _left[_parent[arc]] = _right[arc];
  1378           } else {
  1379             _right[_parent[arc]] = _right[arc];
  1380           }
  1381         } else {
  1382           _head[_g.source(arc)] = _right[arc];
  1383         }
  1384       } else if (_right[arc] == INVALID) {
  1385         _parent[_left[arc]] = _parent[arc];
  1386         if (_parent[arc] != INVALID) {
  1387           if (_left[_parent[arc]] == arc) {
  1388             _left[_parent[arc]] = _left[arc];
  1389           } else {
  1390             _right[_parent[arc]] = _left[arc];
  1391           }
  1392         } else {
  1393           _head[_g.source(arc)] = _left[arc];
  1394         }
  1395       } else {
  1396         Arc e = _left[arc];
  1397         if (_right[e] != INVALID) {
  1398           e = _right[e];
  1399           while (_right[e] != INVALID) {
  1400             e = _right[e];
  1401           }
  1402           Arc s = _parent[e];
  1403           _right[_parent[e]] = _left[e];
  1404           if (_left[e] != INVALID) {
  1405             _parent[_left[e]] = _parent[e];
  1406           }
  1407 
  1408           _left[e] = _left[arc];
  1409           _parent[_left[arc]] = e;
  1410           _right[e] = _right[arc];
  1411           _parent[_right[arc]] = e;
  1412 
  1413           _parent[e] = _parent[arc];
  1414           if (_parent[arc] != INVALID) {
  1415             if (_left[_parent[arc]] == arc) {
  1416               _left[_parent[arc]] = e;
  1417             } else {
  1418               _right[_parent[arc]] = e;
  1419             }
  1420           }
  1421           splay(s);
  1422         } else {
  1423           _right[e] = _right[arc];
  1424           _parent[_right[arc]] = e;
  1425           _parent[e] = _parent[arc];
  1426 
  1427           if (_parent[arc] != INVALID) {
  1428             if (_left[_parent[arc]] == arc) {
  1429               _left[_parent[arc]] = e;
  1430             } else {
  1431               _right[_parent[arc]] = e;
  1432             }
  1433           } else {
  1434             _head[_g.source(arc)] = e;
  1435           }
  1436         }
  1437       }
  1438     }
  1439 
  1440     Arc refreshRec(std::vector<Arc> &v,int a,int b)
  1441     {
  1442       int m=(a+b)/2;
  1443       Arc me=v[m];
  1444       if (a < m) {
  1445         Arc left = refreshRec(v,a,m-1);
  1446         _left[me] = left;
  1447         _parent[left] = me;
  1448       } else {
  1449         _left[me] = INVALID;
  1450       }
  1451       if (m < b) {
  1452         Arc right = refreshRec(v,m+1,b);
  1453         _right[me] = right;
  1454         _parent[right] = me;
  1455       } else {
  1456         _right[me] = INVALID;
  1457       }
  1458       return me;
  1459     }
  1460 
  1461     void refresh() {
  1462       for(NodeIt n(_g);n!=INVALID;++n) {
  1463         std::vector<Arc> v;
  1464         for(OutArcIt a(_g,n);a!=INVALID;++a) v.push_back(a);
  1465         if (!v.empty()) {
  1466           std::sort(v.begin(),v.end(),ArcLess(_g));
  1467           Arc head = refreshRec(v,0,v.size()-1);
  1468           _head[n] = head;
  1469           _parent[head] = INVALID;
  1470         }
  1471         else _head[n] = INVALID;
  1472       }
  1473     }
  1474 
  1475     void zig(Arc v) {
  1476       Arc w = _parent[v];
  1477       _parent[v] = _parent[w];
  1478       _parent[w] = v;
  1479       _left[w] = _right[v];
  1480       _right[v] = w;
  1481       if (_parent[v] != INVALID) {
  1482         if (_right[_parent[v]] == w) {
  1483           _right[_parent[v]] = v;
  1484         } else {
  1485           _left[_parent[v]] = v;
  1486         }
  1487       }
  1488       if (_left[w] != INVALID){
  1489         _parent[_left[w]] = w;
  1490       }
  1491     }
  1492 
  1493     void zag(Arc v) {
  1494       Arc w = _parent[v];
  1495       _parent[v] = _parent[w];
  1496       _parent[w] = v;
  1497       _right[w] = _left[v];
  1498       _left[v] = w;
  1499       if (_parent[v] != INVALID){
  1500         if (_left[_parent[v]] == w) {
  1501           _left[_parent[v]] = v;
  1502         } else {
  1503           _right[_parent[v]] = v;
  1504         }
  1505       }
  1506       if (_right[w] != INVALID){
  1507         _parent[_right[w]] = w;
  1508       }
  1509     }
  1510 
  1511     void splay(Arc v) {
  1512       while (_parent[v] != INVALID) {
  1513         if (v == _left[_parent[v]]) {
  1514           if (_parent[_parent[v]] == INVALID) {
  1515             zig(v);
  1516           } else {
  1517             if (_parent[v] == _left[_parent[_parent[v]]]) {
  1518               zig(_parent[v]);
  1519               zig(v);
  1520             } else {
  1521               zig(v);
  1522               zag(v);
  1523             }
  1524           }
  1525         } else {
  1526           if (_parent[_parent[v]] == INVALID) {
  1527             zag(v);
  1528           } else {
  1529             if (_parent[v] == _left[_parent[_parent[v]]]) {
  1530               zag(v);
  1531               zig(v);
  1532             } else {
  1533               zag(_parent[v]);
  1534               zag(v);
  1535             }
  1536           }
  1537         }
  1538       }
  1539       _head[_g.source(v)] = v;
  1540     }
  1541 
  1542 
  1543   public:
  1544 
  1545     ///Find an arc between two nodes.
  1546 
  1547     ///Find an arc between two nodes.
  1548     ///\param s The source node.
  1549     ///\param t The target node.
  1550     ///\param p The previous arc between \c s and \c t. It it is INVALID or
  1551     ///not given, the operator finds the first appropriate arc.
  1552     ///\return An arc from \c s to \c t after \c p or
  1553     ///\ref INVALID if there is no more.
  1554     ///
  1555     ///For example, you can count the number of arcs from \c u to \c v in the
  1556     ///following way.
  1557     ///\code
  1558     ///DynArcLookUp<ListDigraph> ae(g);
  1559     ///...
  1560     ///int n = 0;
  1561     ///for(Arc a = ae(u,v); a != INVALID; a = ae(u,v,a)) n++;
  1562     ///\endcode
  1563     ///
  1564     ///Finding the arcs take at most <em>O</em>(log<em>d</em>)
  1565     ///amortized time, specifically, the time complexity of the lookups
  1566     ///is equal to the optimal search tree implementation for the
  1567     ///current query distribution in a constant factor.
  1568     ///
  1569     ///\note This is a dynamic data structure, therefore the data
  1570     ///structure is updated after each graph alteration. Thus although
  1571     ///this data structure is theoretically faster than \ref ArcLookUp
  1572     ///and \ref AllArcLookUp, it often provides worse performance than
  1573     ///them.
  1574     Arc operator()(Node s, Node t, Arc p = INVALID) const  {
  1575       if (p == INVALID) {
  1576         Arc a = _head[s];
  1577         if (a == INVALID) return INVALID;
  1578         Arc r = INVALID;
  1579         while (true) {
  1580           if (_g.target(a) < t) {
  1581             if (_right[a] == INVALID) {
  1582               const_cast<DynArcLookUp&>(*this).splay(a);
  1583               return r;
  1584             } else {
  1585               a = _right[a];
  1586             }
  1587           } else {
  1588             if (_g.target(a) == t) {
  1589               r = a;
  1590             }
  1591             if (_left[a] == INVALID) {
  1592               const_cast<DynArcLookUp&>(*this).splay(a);
  1593               return r;
  1594             } else {
  1595               a = _left[a];
  1596             }
  1597           }
  1598         }
  1599       } else {
  1600         Arc a = p;
  1601         if (_right[a] != INVALID) {
  1602           a = _right[a];
  1603           while (_left[a] != INVALID) {
  1604             a = _left[a];
  1605           }
  1606           const_cast<DynArcLookUp&>(*this).splay(a);
  1607         } else {
  1608           while (_parent[a] != INVALID && _right[_parent[a]] ==  a) {
  1609             a = _parent[a];
  1610           }
  1611           if (_parent[a] == INVALID) {
  1612             return INVALID;
  1613           } else {
  1614             a = _parent[a];
  1615             const_cast<DynArcLookUp&>(*this).splay(a);
  1616           }
  1617         }
  1618         if (_g.target(a) == t) return a;
  1619         else return INVALID;
  1620       }
  1621     }
  1622 
  1623   };
  1624 
  1625   ///Fast arc look-up between given endpoints.
  1626 
  1627   ///Using this class, you can find an arc in a digraph from a given
  1628   ///source to a given target in time <em>O</em>(log<em>d</em>),
  1629   ///where <em>d</em> is the out-degree of the source node.
  1630   ///
  1631   ///It is not possible to find \e all parallel arcs between two nodes.
  1632   ///Use \ref AllArcLookUp for this purpose.
  1633   ///
  1634   ///\warning This class is static, so you should call refresh() (or at
  1635   ///least refresh(Node)) to refresh this data structure whenever the
  1636   ///digraph changes. This is a time consuming (superlinearly proportional
  1637   ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
  1638   ///
  1639   ///\tparam GR The type of the underlying digraph.
  1640   ///
  1641   ///\sa DynArcLookUp
  1642   ///\sa AllArcLookUp
  1643   template<class GR>
  1644   class ArcLookUp
  1645   {
  1646     TEMPLATE_DIGRAPH_TYPEDEFS(GR);
  1647 
  1648   public:
  1649 
  1650     /// The Digraph type
  1651     typedef GR Digraph;
  1652 
  1653   protected:
  1654     const Digraph &_g;
  1655     typename Digraph::template NodeMap<Arc> _head;
  1656     typename Digraph::template ArcMap<Arc> _left;
  1657     typename Digraph::template ArcMap<Arc> _right;
  1658 
  1659     class ArcLess {
  1660       const Digraph &g;
  1661     public:
  1662       ArcLess(const Digraph &_g) : g(_g) {}
  1663       bool operator()(Arc a,Arc b) const
  1664       {
  1665         return g.target(a)<g.target(b);
  1666       }
  1667     };
  1668 
  1669   public:
  1670 
  1671     ///Constructor
  1672 
  1673     ///Constructor.
  1674     ///
  1675     ///It builds up the search database, which remains valid until the digraph
  1676     ///changes.
  1677     ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}
  1678 
  1679   private:
  1680     Arc refreshRec(std::vector<Arc> &v,int a,int b)
  1681     {
  1682       int m=(a+b)/2;
  1683       Arc me=v[m];
  1684       _left[me] = a<m?refreshRec(v,a,m-1):INVALID;
  1685       _right[me] = m<b?refreshRec(v,m+1,b):INVALID;
  1686       return me;
  1687     }
  1688   public:
  1689     ///Refresh the search data structure at a node.
  1690 
  1691     ///Build up the search database of node \c n.
  1692     ///
  1693     ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em>
  1694     ///is the number of the outgoing arcs of \c n.
  1695     void refresh(Node n)
  1696     {
  1697       std::vector<Arc> v;
  1698       for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
  1699       if(v.size()) {
  1700         std::sort(v.begin(),v.end(),ArcLess(_g));
  1701         _head[n]=refreshRec(v,0,v.size()-1);
  1702       }
  1703       else _head[n]=INVALID;
  1704     }
  1705     ///Refresh the full data structure.
  1706 
  1707     ///Build up the full search database. In fact, it simply calls
  1708     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  1709     ///
  1710     ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
  1711     ///the number of the arcs in the digraph and <em>D</em> is the maximum
  1712     ///out-degree of the digraph.
  1713     void refresh()
  1714     {
  1715       for(NodeIt n(_g);n!=INVALID;++n) refresh(n);
  1716     }
  1717 
  1718     ///Find an arc between two nodes.
  1719 
  1720     ///Find an arc between two nodes in time <em>O</em>(log<em>d</em>),
  1721     ///where <em>d</em> is the number of outgoing arcs of \c s.
  1722     ///\param s The source node.
  1723     ///\param t The target node.
  1724     ///\return An arc from \c s to \c t if there exists,
  1725     ///\ref INVALID otherwise.
  1726     ///
  1727     ///\warning If you change the digraph, refresh() must be called before using
  1728     ///this operator. If you change the outgoing arcs of
  1729     ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
  1730     Arc operator()(Node s, Node t) const
  1731     {
  1732       Arc e;
  1733       for(e=_head[s];
  1734           e!=INVALID&&_g.target(e)!=t;
  1735           e = t < _g.target(e)?_left[e]:_right[e]) ;
  1736       return e;
  1737     }
  1738 
  1739   };
  1740 
  1741   ///Fast look-up of all arcs between given endpoints.
  1742 
  1743   ///This class is the same as \ref ArcLookUp, with the addition
  1744   ///that it makes it possible to find all parallel arcs between given
  1745   ///endpoints.
  1746   ///
  1747   ///\warning This class is static, so you should call refresh() (or at
  1748   ///least refresh(Node)) to refresh this data structure whenever the
  1749   ///digraph changes. This is a time consuming (superlinearly proportional
  1750   ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
  1751   ///
  1752   ///\tparam GR The type of the underlying digraph.
  1753   ///
  1754   ///\sa DynArcLookUp
  1755   ///\sa ArcLookUp
  1756   template<class GR>
  1757   class AllArcLookUp : public ArcLookUp<GR>
  1758   {
  1759     using ArcLookUp<GR>::_g;
  1760     using ArcLookUp<GR>::_right;
  1761     using ArcLookUp<GR>::_left;
  1762     using ArcLookUp<GR>::_head;
  1763 
  1764     TEMPLATE_DIGRAPH_TYPEDEFS(GR);
  1765 
  1766     typename GR::template ArcMap<Arc> _next;
  1767 
  1768     Arc refreshNext(Arc head,Arc next=INVALID)
  1769     {
  1770       if(head==INVALID) return next;
  1771       else {
  1772         next=refreshNext(_right[head],next);
  1773         _next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
  1774           ? next : INVALID;
  1775         return refreshNext(_left[head],head);
  1776       }
  1777     }
  1778 
  1779     void refreshNext()
  1780     {
  1781       for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
  1782     }
  1783 
  1784   public:
  1785 
  1786     /// The Digraph type
  1787     typedef GR Digraph;
  1788 
  1789     ///Constructor
  1790 
  1791     ///Constructor.
  1792     ///
  1793     ///It builds up the search database, which remains valid until the digraph
  1794     ///changes.
  1795     AllArcLookUp(const Digraph &g) : ArcLookUp<GR>(g), _next(g) {refreshNext();}
  1796 
  1797     ///Refresh the data structure at a node.
  1798 
  1799     ///Build up the search database of node \c n.
  1800     ///
  1801     ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em> is
  1802     ///the number of the outgoing arcs of \c n.
  1803     void refresh(Node n)
  1804     {
  1805       ArcLookUp<GR>::refresh(n);
  1806       refreshNext(_head[n]);
  1807     }
  1808 
  1809     ///Refresh the full data structure.
  1810 
  1811     ///Build up the full search database. In fact, it simply calls
  1812     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  1813     ///
  1814     ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
  1815     ///the number of the arcs in the digraph and <em>D</em> is the maximum
  1816     ///out-degree of the digraph.
  1817     void refresh()
  1818     {
  1819       for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
  1820     }
  1821 
  1822     ///Find an arc between two nodes.
  1823 
  1824     ///Find an arc between two nodes.
  1825     ///\param s The source node.
  1826     ///\param t The target node.
  1827     ///\param prev The previous arc between \c s and \c t. It it is INVALID or
  1828     ///not given, the operator finds the first appropriate arc.
  1829     ///\return An arc from \c s to \c t after \c prev or
  1830     ///\ref INVALID if there is no more.
  1831     ///
  1832     ///For example, you can count the number of arcs from \c u to \c v in the
  1833     ///following way.
  1834     ///\code
  1835     ///AllArcLookUp<ListDigraph> ae(g);
  1836     ///...
  1837     ///int n = 0;
  1838     ///for(Arc a = ae(u,v); a != INVALID; a=ae(u,v,a)) n++;
  1839     ///\endcode
  1840     ///
  1841     ///Finding the first arc take <em>O</em>(log<em>d</em>) time,
  1842     ///where <em>d</em> is the number of outgoing arcs of \c s. Then the
  1843     ///consecutive arcs are found in constant time.
  1844     ///
  1845     ///\warning If you change the digraph, refresh() must be called before using
  1846     ///this operator. If you change the outgoing arcs of
  1847     ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
  1848     ///
  1849 #ifdef DOXYGEN
  1850     Arc operator()(Node s, Node t, Arc prev=INVALID) const {}
  1851 #else
  1852     using ArcLookUp<GR>::operator() ;
  1853     Arc operator()(Node s, Node t, Arc prev) const
  1854     {
  1855       return prev==INVALID?(*this)(s,t):_next[prev];
  1856     }
  1857 #endif
  1858 
  1859   };
  1860 
  1861   /// @}
  1862 
  1863 } //namespace lemon
  1864 
  1865 #endif