lemon/core.h
author Alpar Juttner <alpar@cs.elte.hu>
Tue, 20 Dec 2011 19:10:50 +0100
branch1.2
changeset 944 02c93d1f00d7
parent 896 e958855b8186
parent 942 2b6bffe0e7e8
child 960 0da74b2d0bea
permissions -rw-r--r--
Merge head merging to branch 1.2
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2010
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 #ifndef LEMON_CORE_H
    20 #define LEMON_CORE_H
    21 
    22 #include <vector>
    23 #include <algorithm>
    24 
    25 #include <lemon/config.h>
    26 #include <lemon/bits/enable_if.h>
    27 #include <lemon/bits/traits.h>
    28 #include <lemon/assert.h>
    29 
    30 // Disable the following warnings when compiling with MSVC:
    31 // C4250: 'class1' : inherits 'class2::member' via dominance
    32 // C4355: 'this' : used in base member initializer list
    33 // C4503: 'function' : decorated name length exceeded, name was truncated
    34 // C4800: 'type' : forcing value to bool 'true' or 'false' (performance warning)
    35 // C4996: 'function': was declared deprecated
    36 #ifdef _MSC_VER
    37 #pragma warning( disable : 4250 4355 4503 4800 4996 )
    38 #endif
    39 
    40 ///\file
    41 ///\brief LEMON core utilities.
    42 ///
    43 ///This header file contains core utilities for LEMON.
    44 ///It is automatically included by all graph types, therefore it usually
    45 ///do not have to be included directly.
    46 
    47 namespace lemon {
    48 
    49   /// \brief Dummy type to make it easier to create invalid iterators.
    50   ///
    51   /// Dummy type to make it easier to create invalid iterators.
    52   /// See \ref INVALID for the usage.
    53   struct Invalid {
    54   public:
    55     bool operator==(Invalid) { return true;  }
    56     bool operator!=(Invalid) { return false; }
    57     bool operator< (Invalid) { return false; }
    58   };
    59 
    60   /// \brief Invalid iterators.
    61   ///
    62   /// \ref Invalid is a global type that converts to each iterator
    63   /// in such a way that the value of the target iterator will be invalid.
    64 #ifdef LEMON_ONLY_TEMPLATES
    65   const Invalid INVALID = Invalid();
    66 #else
    67   extern const Invalid INVALID;
    68 #endif
    69 
    70   /// \addtogroup gutils
    71   /// @{
    72 
    73   ///Create convenience typedefs for the digraph types and iterators
    74 
    75   ///This \c \#define creates convenient type definitions for the following
    76   ///types of \c Digraph: \c Node,  \c NodeIt, \c Arc, \c ArcIt, \c InArcIt,
    77   ///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap,
    78   ///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap.
    79   ///
    80   ///\note If the graph type is a dependent type, ie. the graph type depend
    81   ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
    82   ///macro.
    83 #define DIGRAPH_TYPEDEFS(Digraph)                                       \
    84   typedef Digraph::Node Node;                                           \
    85   typedef Digraph::NodeIt NodeIt;                                       \
    86   typedef Digraph::Arc Arc;                                             \
    87   typedef Digraph::ArcIt ArcIt;                                         \
    88   typedef Digraph::InArcIt InArcIt;                                     \
    89   typedef Digraph::OutArcIt OutArcIt;                                   \
    90   typedef Digraph::NodeMap<bool> BoolNodeMap;                           \
    91   typedef Digraph::NodeMap<int> IntNodeMap;                             \
    92   typedef Digraph::NodeMap<double> DoubleNodeMap;                       \
    93   typedef Digraph::ArcMap<bool> BoolArcMap;                             \
    94   typedef Digraph::ArcMap<int> IntArcMap;                               \
    95   typedef Digraph::ArcMap<double> DoubleArcMap
    96 
    97   ///Create convenience typedefs for the digraph types and iterators
    98 
    99   ///\see DIGRAPH_TYPEDEFS
   100   ///
   101   ///\note Use this macro, if the graph type is a dependent type,
   102   ///ie. the graph type depend on a template parameter.
   103 #define TEMPLATE_DIGRAPH_TYPEDEFS(Digraph)                              \
   104   typedef typename Digraph::Node Node;                                  \
   105   typedef typename Digraph::NodeIt NodeIt;                              \
   106   typedef typename Digraph::Arc Arc;                                    \
   107   typedef typename Digraph::ArcIt ArcIt;                                \
   108   typedef typename Digraph::InArcIt InArcIt;                            \
   109   typedef typename Digraph::OutArcIt OutArcIt;                          \
   110   typedef typename Digraph::template NodeMap<bool> BoolNodeMap;         \
   111   typedef typename Digraph::template NodeMap<int> IntNodeMap;           \
   112   typedef typename Digraph::template NodeMap<double> DoubleNodeMap;     \
   113   typedef typename Digraph::template ArcMap<bool> BoolArcMap;           \
   114   typedef typename Digraph::template ArcMap<int> IntArcMap;             \
   115   typedef typename Digraph::template ArcMap<double> DoubleArcMap
   116 
   117   ///Create convenience typedefs for the graph types and iterators
   118 
   119   ///This \c \#define creates the same convenient type definitions as defined
   120   ///by \ref DIGRAPH_TYPEDEFS(Graph) and six more, namely it creates
   121   ///\c Edge, \c EdgeIt, \c IncEdgeIt, \c BoolEdgeMap, \c IntEdgeMap,
   122   ///\c DoubleEdgeMap.
   123   ///
   124   ///\note If the graph type is a dependent type, ie. the graph type depend
   125   ///on a template parameter, then use \c TEMPLATE_GRAPH_TYPEDEFS()
   126   ///macro.
   127 #define GRAPH_TYPEDEFS(Graph)                                           \
   128   DIGRAPH_TYPEDEFS(Graph);                                              \
   129   typedef Graph::Edge Edge;                                             \
   130   typedef Graph::EdgeIt EdgeIt;                                         \
   131   typedef Graph::IncEdgeIt IncEdgeIt;                                   \
   132   typedef Graph::EdgeMap<bool> BoolEdgeMap;                             \
   133   typedef Graph::EdgeMap<int> IntEdgeMap;                               \
   134   typedef Graph::EdgeMap<double> DoubleEdgeMap
   135 
   136   ///Create convenience typedefs for the graph types and iterators
   137 
   138   ///\see GRAPH_TYPEDEFS
   139   ///
   140   ///\note Use this macro, if the graph type is a dependent type,
   141   ///ie. the graph type depend on a template parameter.
   142 #define TEMPLATE_GRAPH_TYPEDEFS(Graph)                                  \
   143   TEMPLATE_DIGRAPH_TYPEDEFS(Graph);                                     \
   144   typedef typename Graph::Edge Edge;                                    \
   145   typedef typename Graph::EdgeIt EdgeIt;                                \
   146   typedef typename Graph::IncEdgeIt IncEdgeIt;                          \
   147   typedef typename Graph::template EdgeMap<bool> BoolEdgeMap;           \
   148   typedef typename Graph::template EdgeMap<int> IntEdgeMap;             \
   149   typedef typename Graph::template EdgeMap<double> DoubleEdgeMap
   150 
   151   /// \brief Function to count the items in a graph.
   152   ///
   153   /// This function counts the items (nodes, arcs etc.) in a graph.
   154   /// The complexity of the function is linear because
   155   /// it iterates on all of the items.
   156   template <typename Graph, typename Item>
   157   inline int countItems(const Graph& g) {
   158     typedef typename ItemSetTraits<Graph, Item>::ItemIt ItemIt;
   159     int num = 0;
   160     for (ItemIt it(g); it != INVALID; ++it) {
   161       ++num;
   162     }
   163     return num;
   164   }
   165 
   166   // Node counting:
   167 
   168   namespace _core_bits {
   169 
   170     template <typename Graph, typename Enable = void>
   171     struct CountNodesSelector {
   172       static int count(const Graph &g) {
   173         return countItems<Graph, typename Graph::Node>(g);
   174       }
   175     };
   176 
   177     template <typename Graph>
   178     struct CountNodesSelector<
   179       Graph, typename
   180       enable_if<typename Graph::NodeNumTag, void>::type>
   181     {
   182       static int count(const Graph &g) {
   183         return g.nodeNum();
   184       }
   185     };
   186   }
   187 
   188   /// \brief Function to count the nodes in the graph.
   189   ///
   190   /// This function counts the nodes in the graph.
   191   /// The complexity of the function is <em>O</em>(<em>n</em>), but for some
   192   /// graph structures it is specialized to run in <em>O</em>(1).
   193   ///
   194   /// \note If the graph contains a \c nodeNum() member function and a
   195   /// \c NodeNumTag tag then this function calls directly the member
   196   /// function to query the cardinality of the node set.
   197   template <typename Graph>
   198   inline int countNodes(const Graph& g) {
   199     return _core_bits::CountNodesSelector<Graph>::count(g);
   200   }
   201 
   202   // Arc counting:
   203 
   204   namespace _core_bits {
   205 
   206     template <typename Graph, typename Enable = void>
   207     struct CountArcsSelector {
   208       static int count(const Graph &g) {
   209         return countItems<Graph, typename Graph::Arc>(g);
   210       }
   211     };
   212 
   213     template <typename Graph>
   214     struct CountArcsSelector<
   215       Graph,
   216       typename enable_if<typename Graph::ArcNumTag, void>::type>
   217     {
   218       static int count(const Graph &g) {
   219         return g.arcNum();
   220       }
   221     };
   222   }
   223 
   224   /// \brief Function to count the arcs in the graph.
   225   ///
   226   /// This function counts the arcs in the graph.
   227   /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
   228   /// graph structures it is specialized to run in <em>O</em>(1).
   229   ///
   230   /// \note If the graph contains a \c arcNum() member function and a
   231   /// \c ArcNumTag tag then this function calls directly the member
   232   /// function to query the cardinality of the arc set.
   233   template <typename Graph>
   234   inline int countArcs(const Graph& g) {
   235     return _core_bits::CountArcsSelector<Graph>::count(g);
   236   }
   237 
   238   // Edge counting:
   239 
   240   namespace _core_bits {
   241 
   242     template <typename Graph, typename Enable = void>
   243     struct CountEdgesSelector {
   244       static int count(const Graph &g) {
   245         return countItems<Graph, typename Graph::Edge>(g);
   246       }
   247     };
   248 
   249     template <typename Graph>
   250     struct CountEdgesSelector<
   251       Graph,
   252       typename enable_if<typename Graph::EdgeNumTag, void>::type>
   253     {
   254       static int count(const Graph &g) {
   255         return g.edgeNum();
   256       }
   257     };
   258   }
   259 
   260   /// \brief Function to count the edges in the graph.
   261   ///
   262   /// This function counts the edges in the graph.
   263   /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
   264   /// graph structures it is specialized to run in <em>O</em>(1).
   265   ///
   266   /// \note If the graph contains a \c edgeNum() member function and a
   267   /// \c EdgeNumTag tag then this function calls directly the member
   268   /// function to query the cardinality of the edge set.
   269   template <typename Graph>
   270   inline int countEdges(const Graph& g) {
   271     return _core_bits::CountEdgesSelector<Graph>::count(g);
   272 
   273   }
   274 
   275 
   276   template <typename Graph, typename DegIt>
   277   inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {
   278     int num = 0;
   279     for (DegIt it(_g, _n); it != INVALID; ++it) {
   280       ++num;
   281     }
   282     return num;
   283   }
   284 
   285   /// \brief Function to count the number of the out-arcs from node \c n.
   286   ///
   287   /// This function counts the number of the out-arcs from node \c n
   288   /// in the graph \c g.
   289   template <typename Graph>
   290   inline int countOutArcs(const Graph& g,  const typename Graph::Node& n) {
   291     return countNodeDegree<Graph, typename Graph::OutArcIt>(g, n);
   292   }
   293 
   294   /// \brief Function to count the number of the in-arcs to node \c n.
   295   ///
   296   /// This function counts the number of the in-arcs to node \c n
   297   /// in the graph \c g.
   298   template <typename Graph>
   299   inline int countInArcs(const Graph& g,  const typename Graph::Node& n) {
   300     return countNodeDegree<Graph, typename Graph::InArcIt>(g, n);
   301   }
   302 
   303   /// \brief Function to count the number of the inc-edges to node \c n.
   304   ///
   305   /// This function counts the number of the inc-edges to node \c n
   306   /// in the undirected graph \c g.
   307   template <typename Graph>
   308   inline int countIncEdges(const Graph& g,  const typename Graph::Node& n) {
   309     return countNodeDegree<Graph, typename Graph::IncEdgeIt>(g, n);
   310   }
   311 
   312   namespace _core_bits {
   313 
   314     template <typename Digraph, typename Item, typename RefMap>
   315     class MapCopyBase {
   316     public:
   317       virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
   318 
   319       virtual ~MapCopyBase() {}
   320     };
   321 
   322     template <typename Digraph, typename Item, typename RefMap,
   323               typename FromMap, typename ToMap>
   324     class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
   325     public:
   326 
   327       MapCopy(const FromMap& map, ToMap& tmap)
   328         : _map(map), _tmap(tmap) {}
   329 
   330       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   331         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   332         for (ItemIt it(digraph); it != INVALID; ++it) {
   333           _tmap.set(refMap[it], _map[it]);
   334         }
   335       }
   336 
   337     private:
   338       const FromMap& _map;
   339       ToMap& _tmap;
   340     };
   341 
   342     template <typename Digraph, typename Item, typename RefMap, typename It>
   343     class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
   344     public:
   345 
   346       ItemCopy(const Item& item, It& it) : _item(item), _it(it) {}
   347 
   348       virtual void copy(const Digraph&, const RefMap& refMap) {
   349         _it = refMap[_item];
   350       }
   351 
   352     private:
   353       Item _item;
   354       It& _it;
   355     };
   356 
   357     template <typename Digraph, typename Item, typename RefMap, typename Ref>
   358     class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   359     public:
   360 
   361       RefCopy(Ref& map) : _map(map) {}
   362 
   363       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   364         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   365         for (ItemIt it(digraph); it != INVALID; ++it) {
   366           _map.set(it, refMap[it]);
   367         }
   368       }
   369 
   370     private:
   371       Ref& _map;
   372     };
   373 
   374     template <typename Digraph, typename Item, typename RefMap,
   375               typename CrossRef>
   376     class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   377     public:
   378 
   379       CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
   380 
   381       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   382         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   383         for (ItemIt it(digraph); it != INVALID; ++it) {
   384           _cmap.set(refMap[it], it);
   385         }
   386       }
   387 
   388     private:
   389       CrossRef& _cmap;
   390     };
   391 
   392     template <typename Digraph, typename Enable = void>
   393     struct DigraphCopySelector {
   394       template <typename From, typename NodeRefMap, typename ArcRefMap>
   395       static void copy(const From& from, Digraph &to,
   396                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   397         to.clear();
   398         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   399           nodeRefMap[it] = to.addNode();
   400         }
   401         for (typename From::ArcIt it(from); it != INVALID; ++it) {
   402           arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)],
   403                                     nodeRefMap[from.target(it)]);
   404         }
   405       }
   406     };
   407 
   408     template <typename Digraph>
   409     struct DigraphCopySelector<
   410       Digraph,
   411       typename enable_if<typename Digraph::BuildTag, void>::type>
   412     {
   413       template <typename From, typename NodeRefMap, typename ArcRefMap>
   414       static void copy(const From& from, Digraph &to,
   415                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   416         to.build(from, nodeRefMap, arcRefMap);
   417       }
   418     };
   419 
   420     template <typename Graph, typename Enable = void>
   421     struct GraphCopySelector {
   422       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   423       static void copy(const From& from, Graph &to,
   424                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   425         to.clear();
   426         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   427           nodeRefMap[it] = to.addNode();
   428         }
   429         for (typename From::EdgeIt it(from); it != INVALID; ++it) {
   430           edgeRefMap[it] = to.addEdge(nodeRefMap[from.u(it)],
   431                                       nodeRefMap[from.v(it)]);
   432         }
   433       }
   434     };
   435 
   436     template <typename Graph>
   437     struct GraphCopySelector<
   438       Graph,
   439       typename enable_if<typename Graph::BuildTag, void>::type>
   440     {
   441       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   442       static void copy(const From& from, Graph &to,
   443                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   444         to.build(from, nodeRefMap, edgeRefMap);
   445       }
   446     };
   447 
   448   }
   449 
   450   /// \brief Class to copy a digraph.
   451   ///
   452   /// Class to copy a digraph to another digraph (duplicate a digraph). The
   453   /// simplest way of using it is through the \c digraphCopy() function.
   454   ///
   455   /// This class not only make a copy of a digraph, but it can create
   456   /// references and cross references between the nodes and arcs of
   457   /// the two digraphs, and it can copy maps to use with the newly created
   458   /// digraph.
   459   ///
   460   /// To make a copy from a digraph, first an instance of DigraphCopy
   461   /// should be created, then the data belongs to the digraph should
   462   /// assigned to copy. In the end, the \c run() member should be
   463   /// called.
   464   ///
   465   /// The next code copies a digraph with several data:
   466   ///\code
   467   ///  DigraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
   468   ///  // Create references for the nodes
   469   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   470   ///  cg.nodeRef(nr);
   471   ///  // Create cross references (inverse) for the arcs
   472   ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);
   473   ///  cg.arcCrossRef(acr);
   474   ///  // Copy an arc map
   475   ///  OrigGraph::ArcMap<double> oamap(orig_graph);
   476   ///  NewGraph::ArcMap<double> namap(new_graph);
   477   ///  cg.arcMap(oamap, namap);
   478   ///  // Copy a node
   479   ///  OrigGraph::Node on;
   480   ///  NewGraph::Node nn;
   481   ///  cg.node(on, nn);
   482   ///  // Execute copying
   483   ///  cg.run();
   484   ///\endcode
   485   template <typename From, typename To>
   486   class DigraphCopy {
   487   private:
   488 
   489     typedef typename From::Node Node;
   490     typedef typename From::NodeIt NodeIt;
   491     typedef typename From::Arc Arc;
   492     typedef typename From::ArcIt ArcIt;
   493 
   494     typedef typename To::Node TNode;
   495     typedef typename To::Arc TArc;
   496 
   497     typedef typename From::template NodeMap<TNode> NodeRefMap;
   498     typedef typename From::template ArcMap<TArc> ArcRefMap;
   499 
   500   public:
   501 
   502     /// \brief Constructor of DigraphCopy.
   503     ///
   504     /// Constructor of DigraphCopy for copying the content of the
   505     /// \c from digraph into the \c to digraph.
   506     DigraphCopy(const From& from, To& to)
   507       : _from(from), _to(to) {}
   508 
   509     /// \brief Destructor of DigraphCopy
   510     ///
   511     /// Destructor of DigraphCopy.
   512     ~DigraphCopy() {
   513       for (int i = 0; i < int(_node_maps.size()); ++i) {
   514         delete _node_maps[i];
   515       }
   516       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   517         delete _arc_maps[i];
   518       }
   519 
   520     }
   521 
   522     /// \brief Copy the node references into the given map.
   523     ///
   524     /// This function copies the node references into the given map.
   525     /// The parameter should be a map, whose key type is the Node type of
   526     /// the source digraph, while the value type is the Node type of the
   527     /// destination digraph.
   528     template <typename NodeRef>
   529     DigraphCopy& nodeRef(NodeRef& map) {
   530       _node_maps.push_back(new _core_bits::RefCopy<From, Node,
   531                            NodeRefMap, NodeRef>(map));
   532       return *this;
   533     }
   534 
   535     /// \brief Copy the node cross references into the given map.
   536     ///
   537     /// This function copies the node cross references (reverse references)
   538     /// into the given map. The parameter should be a map, whose key type
   539     /// is the Node type of the destination digraph, while the value type is
   540     /// the Node type of the source digraph.
   541     template <typename NodeCrossRef>
   542     DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
   543       _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
   544                            NodeRefMap, NodeCrossRef>(map));
   545       return *this;
   546     }
   547 
   548     /// \brief Make a copy of the given node map.
   549     ///
   550     /// This function makes a copy of the given node map for the newly
   551     /// created digraph.
   552     /// The key type of the new map \c tmap should be the Node type of the
   553     /// destination digraph, and the key type of the original map \c map
   554     /// should be the Node type of the source digraph.
   555     template <typename FromMap, typename ToMap>
   556     DigraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
   557       _node_maps.push_back(new _core_bits::MapCopy<From, Node,
   558                            NodeRefMap, FromMap, ToMap>(map, tmap));
   559       return *this;
   560     }
   561 
   562     /// \brief Make a copy of the given node.
   563     ///
   564     /// This function makes a copy of the given node.
   565     DigraphCopy& node(const Node& node, TNode& tnode) {
   566       _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
   567                            NodeRefMap, TNode>(node, tnode));
   568       return *this;
   569     }
   570 
   571     /// \brief Copy the arc references into the given map.
   572     ///
   573     /// This function copies the arc references into the given map.
   574     /// The parameter should be a map, whose key type is the Arc type of
   575     /// the source digraph, while the value type is the Arc type of the
   576     /// destination digraph.
   577     template <typename ArcRef>
   578     DigraphCopy& arcRef(ArcRef& map) {
   579       _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
   580                           ArcRefMap, ArcRef>(map));
   581       return *this;
   582     }
   583 
   584     /// \brief Copy the arc cross references into the given map.
   585     ///
   586     /// This function copies the arc cross references (reverse references)
   587     /// into the given map. The parameter should be a map, whose key type
   588     /// is the Arc type of the destination digraph, while the value type is
   589     /// the Arc type of the source digraph.
   590     template <typename ArcCrossRef>
   591     DigraphCopy& arcCrossRef(ArcCrossRef& map) {
   592       _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
   593                           ArcRefMap, ArcCrossRef>(map));
   594       return *this;
   595     }
   596 
   597     /// \brief Make a copy of the given arc map.
   598     ///
   599     /// This function makes a copy of the given arc map for the newly
   600     /// created digraph.
   601     /// The key type of the new map \c tmap should be the Arc type of the
   602     /// destination digraph, and the key type of the original map \c map
   603     /// should be the Arc type of the source digraph.
   604     template <typename FromMap, typename ToMap>
   605     DigraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
   606       _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
   607                           ArcRefMap, FromMap, ToMap>(map, tmap));
   608       return *this;
   609     }
   610 
   611     /// \brief Make a copy of the given arc.
   612     ///
   613     /// This function makes a copy of the given arc.
   614     DigraphCopy& arc(const Arc& arc, TArc& tarc) {
   615       _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
   616                           ArcRefMap, TArc>(arc, tarc));
   617       return *this;
   618     }
   619 
   620     /// \brief Execute copying.
   621     ///
   622     /// This function executes the copying of the digraph along with the
   623     /// copying of the assigned data.
   624     void run() {
   625       NodeRefMap nodeRefMap(_from);
   626       ArcRefMap arcRefMap(_from);
   627       _core_bits::DigraphCopySelector<To>::
   628         copy(_from, _to, nodeRefMap, arcRefMap);
   629       for (int i = 0; i < int(_node_maps.size()); ++i) {
   630         _node_maps[i]->copy(_from, nodeRefMap);
   631       }
   632       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   633         _arc_maps[i]->copy(_from, arcRefMap);
   634       }
   635     }
   636 
   637   protected:
   638 
   639     const From& _from;
   640     To& _to;
   641 
   642     std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
   643       _node_maps;
   644 
   645     std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
   646       _arc_maps;
   647 
   648   };
   649 
   650   /// \brief Copy a digraph to another digraph.
   651   ///
   652   /// This function copies a digraph to another digraph.
   653   /// The complete usage of it is detailed in the DigraphCopy class, but
   654   /// a short example shows a basic work:
   655   ///\code
   656   /// digraphCopy(src, trg).nodeRef(nr).arcCrossRef(acr).run();
   657   ///\endcode
   658   ///
   659   /// After the copy the \c nr map will contain the mapping from the
   660   /// nodes of the \c from digraph to the nodes of the \c to digraph and
   661   /// \c acr will contain the mapping from the arcs of the \c to digraph
   662   /// to the arcs of the \c from digraph.
   663   ///
   664   /// \see DigraphCopy
   665   template <typename From, typename To>
   666   DigraphCopy<From, To> digraphCopy(const From& from, To& to) {
   667     return DigraphCopy<From, To>(from, to);
   668   }
   669 
   670   /// \brief Class to copy a graph.
   671   ///
   672   /// Class to copy a graph to another graph (duplicate a graph). The
   673   /// simplest way of using it is through the \c graphCopy() function.
   674   ///
   675   /// This class not only make a copy of a graph, but it can create
   676   /// references and cross references between the nodes, edges and arcs of
   677   /// the two graphs, and it can copy maps for using with the newly created
   678   /// graph.
   679   ///
   680   /// To make a copy from a graph, first an instance of GraphCopy
   681   /// should be created, then the data belongs to the graph should
   682   /// assigned to copy. In the end, the \c run() member should be
   683   /// called.
   684   ///
   685   /// The next code copies a graph with several data:
   686   ///\code
   687   ///  GraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
   688   ///  // Create references for the nodes
   689   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   690   ///  cg.nodeRef(nr);
   691   ///  // Create cross references (inverse) for the edges
   692   ///  NewGraph::EdgeMap<OrigGraph::Edge> ecr(new_graph);
   693   ///  cg.edgeCrossRef(ecr);
   694   ///  // Copy an edge map
   695   ///  OrigGraph::EdgeMap<double> oemap(orig_graph);
   696   ///  NewGraph::EdgeMap<double> nemap(new_graph);
   697   ///  cg.edgeMap(oemap, nemap);
   698   ///  // Copy a node
   699   ///  OrigGraph::Node on;
   700   ///  NewGraph::Node nn;
   701   ///  cg.node(on, nn);
   702   ///  // Execute copying
   703   ///  cg.run();
   704   ///\endcode
   705   template <typename From, typename To>
   706   class GraphCopy {
   707   private:
   708 
   709     typedef typename From::Node Node;
   710     typedef typename From::NodeIt NodeIt;
   711     typedef typename From::Arc Arc;
   712     typedef typename From::ArcIt ArcIt;
   713     typedef typename From::Edge Edge;
   714     typedef typename From::EdgeIt EdgeIt;
   715 
   716     typedef typename To::Node TNode;
   717     typedef typename To::Arc TArc;
   718     typedef typename To::Edge TEdge;
   719 
   720     typedef typename From::template NodeMap<TNode> NodeRefMap;
   721     typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
   722 
   723     struct ArcRefMap {
   724       ArcRefMap(const From& from, const To& to,
   725                 const EdgeRefMap& edge_ref, const NodeRefMap& node_ref)
   726         : _from(from), _to(to),
   727           _edge_ref(edge_ref), _node_ref(node_ref) {}
   728 
   729       typedef typename From::Arc Key;
   730       typedef typename To::Arc Value;
   731 
   732       Value operator[](const Key& key) const {
   733         bool forward = _from.u(key) != _from.v(key) ?
   734           _node_ref[_from.source(key)] ==
   735           _to.source(_to.direct(_edge_ref[key], true)) :
   736           _from.direction(key);
   737         return _to.direct(_edge_ref[key], forward);
   738       }
   739 
   740       const From& _from;
   741       const To& _to;
   742       const EdgeRefMap& _edge_ref;
   743       const NodeRefMap& _node_ref;
   744     };
   745 
   746   public:
   747 
   748     /// \brief Constructor of GraphCopy.
   749     ///
   750     /// Constructor of GraphCopy for copying the content of the
   751     /// \c from graph into the \c to graph.
   752     GraphCopy(const From& from, To& to)
   753       : _from(from), _to(to) {}
   754 
   755     /// \brief Destructor of GraphCopy
   756     ///
   757     /// Destructor of GraphCopy.
   758     ~GraphCopy() {
   759       for (int i = 0; i < int(_node_maps.size()); ++i) {
   760         delete _node_maps[i];
   761       }
   762       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   763         delete _arc_maps[i];
   764       }
   765       for (int i = 0; i < int(_edge_maps.size()); ++i) {
   766         delete _edge_maps[i];
   767       }
   768     }
   769 
   770     /// \brief Copy the node references into the given map.
   771     ///
   772     /// This function copies the node references into the given map.
   773     /// The parameter should be a map, whose key type is the Node type of
   774     /// the source graph, while the value type is the Node type of the
   775     /// destination graph.
   776     template <typename NodeRef>
   777     GraphCopy& nodeRef(NodeRef& map) {
   778       _node_maps.push_back(new _core_bits::RefCopy<From, Node,
   779                            NodeRefMap, NodeRef>(map));
   780       return *this;
   781     }
   782 
   783     /// \brief Copy the node cross references into the given map.
   784     ///
   785     /// This function copies the node cross references (reverse references)
   786     /// into the given map. The parameter should be a map, whose key type
   787     /// is the Node type of the destination graph, while the value type is
   788     /// the Node type of the source graph.
   789     template <typename NodeCrossRef>
   790     GraphCopy& nodeCrossRef(NodeCrossRef& map) {
   791       _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
   792                            NodeRefMap, NodeCrossRef>(map));
   793       return *this;
   794     }
   795 
   796     /// \brief Make a copy of the given node map.
   797     ///
   798     /// This function makes a copy of the given node map for the newly
   799     /// created graph.
   800     /// The key type of the new map \c tmap should be the Node type of the
   801     /// destination graph, and the key type of the original map \c map
   802     /// should be the Node type of the source graph.
   803     template <typename FromMap, typename ToMap>
   804     GraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
   805       _node_maps.push_back(new _core_bits::MapCopy<From, Node,
   806                            NodeRefMap, FromMap, ToMap>(map, tmap));
   807       return *this;
   808     }
   809 
   810     /// \brief Make a copy of the given node.
   811     ///
   812     /// This function makes a copy of the given node.
   813     GraphCopy& node(const Node& node, TNode& tnode) {
   814       _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
   815                            NodeRefMap, TNode>(node, tnode));
   816       return *this;
   817     }
   818 
   819     /// \brief Copy the arc references into the given map.
   820     ///
   821     /// This function copies the arc references into the given map.
   822     /// The parameter should be a map, whose key type is the Arc type of
   823     /// the source graph, while the value type is the Arc type of the
   824     /// destination graph.
   825     template <typename ArcRef>
   826     GraphCopy& arcRef(ArcRef& map) {
   827       _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
   828                           ArcRefMap, ArcRef>(map));
   829       return *this;
   830     }
   831 
   832     /// \brief Copy the arc cross references into the given map.
   833     ///
   834     /// This function copies the arc cross references (reverse references)
   835     /// into the given map. The parameter should be a map, whose key type
   836     /// is the Arc type of the destination graph, while the value type is
   837     /// the Arc type of the source graph.
   838     template <typename ArcCrossRef>
   839     GraphCopy& arcCrossRef(ArcCrossRef& map) {
   840       _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
   841                           ArcRefMap, ArcCrossRef>(map));
   842       return *this;
   843     }
   844 
   845     /// \brief Make a copy of the given arc map.
   846     ///
   847     /// This function makes a copy of the given arc map for the newly
   848     /// created graph.
   849     /// The key type of the new map \c tmap should be the Arc type of the
   850     /// destination graph, and the key type of the original map \c map
   851     /// should be the Arc type of the source graph.
   852     template <typename FromMap, typename ToMap>
   853     GraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
   854       _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
   855                           ArcRefMap, FromMap, ToMap>(map, tmap));
   856       return *this;
   857     }
   858 
   859     /// \brief Make a copy of the given arc.
   860     ///
   861     /// This function makes a copy of the given arc.
   862     GraphCopy& arc(const Arc& arc, TArc& tarc) {
   863       _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
   864                           ArcRefMap, TArc>(arc, tarc));
   865       return *this;
   866     }
   867 
   868     /// \brief Copy the edge references into the given map.
   869     ///
   870     /// This function copies the edge references into the given map.
   871     /// The parameter should be a map, whose key type is the Edge type of
   872     /// the source graph, while the value type is the Edge type of the
   873     /// destination graph.
   874     template <typename EdgeRef>
   875     GraphCopy& edgeRef(EdgeRef& map) {
   876       _edge_maps.push_back(new _core_bits::RefCopy<From, Edge,
   877                            EdgeRefMap, EdgeRef>(map));
   878       return *this;
   879     }
   880 
   881     /// \brief Copy the edge cross references into the given map.
   882     ///
   883     /// This function copies the edge cross references (reverse references)
   884     /// into the given map. The parameter should be a map, whose key type
   885     /// is the Edge type of the destination graph, while the value type is
   886     /// the Edge type of the source graph.
   887     template <typename EdgeCrossRef>
   888     GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
   889       _edge_maps.push_back(new _core_bits::CrossRefCopy<From,
   890                            Edge, EdgeRefMap, EdgeCrossRef>(map));
   891       return *this;
   892     }
   893 
   894     /// \brief Make a copy of the given edge map.
   895     ///
   896     /// This function makes a copy of the given edge map for the newly
   897     /// created graph.
   898     /// The key type of the new map \c tmap should be the Edge type of the
   899     /// destination graph, and the key type of the original map \c map
   900     /// should be the Edge type of the source graph.
   901     template <typename FromMap, typename ToMap>
   902     GraphCopy& edgeMap(const FromMap& map, ToMap& tmap) {
   903       _edge_maps.push_back(new _core_bits::MapCopy<From, Edge,
   904                            EdgeRefMap, FromMap, ToMap>(map, tmap));
   905       return *this;
   906     }
   907 
   908     /// \brief Make a copy of the given edge.
   909     ///
   910     /// This function makes a copy of the given edge.
   911     GraphCopy& edge(const Edge& edge, TEdge& tedge) {
   912       _edge_maps.push_back(new _core_bits::ItemCopy<From, Edge,
   913                            EdgeRefMap, TEdge>(edge, tedge));
   914       return *this;
   915     }
   916 
   917     /// \brief Execute copying.
   918     ///
   919     /// This function executes the copying of the graph along with the
   920     /// copying of the assigned data.
   921     void run() {
   922       NodeRefMap nodeRefMap(_from);
   923       EdgeRefMap edgeRefMap(_from);
   924       ArcRefMap arcRefMap(_from, _to, edgeRefMap, nodeRefMap);
   925       _core_bits::GraphCopySelector<To>::
   926         copy(_from, _to, nodeRefMap, edgeRefMap);
   927       for (int i = 0; i < int(_node_maps.size()); ++i) {
   928         _node_maps[i]->copy(_from, nodeRefMap);
   929       }
   930       for (int i = 0; i < int(_edge_maps.size()); ++i) {
   931         _edge_maps[i]->copy(_from, edgeRefMap);
   932       }
   933       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   934         _arc_maps[i]->copy(_from, arcRefMap);
   935       }
   936     }
   937 
   938   private:
   939 
   940     const From& _from;
   941     To& _to;
   942 
   943     std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
   944       _node_maps;
   945 
   946     std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
   947       _arc_maps;
   948 
   949     std::vector<_core_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
   950       _edge_maps;
   951 
   952   };
   953 
   954   /// \brief Copy a graph to another graph.
   955   ///
   956   /// This function copies a graph to another graph.
   957   /// The complete usage of it is detailed in the GraphCopy class,
   958   /// but a short example shows a basic work:
   959   ///\code
   960   /// graphCopy(src, trg).nodeRef(nr).edgeCrossRef(ecr).run();
   961   ///\endcode
   962   ///
   963   /// After the copy the \c nr map will contain the mapping from the
   964   /// nodes of the \c from graph to the nodes of the \c to graph and
   965   /// \c ecr will contain the mapping from the edges of the \c to graph
   966   /// to the edges of the \c from graph.
   967   ///
   968   /// \see GraphCopy
   969   template <typename From, typename To>
   970   GraphCopy<From, To>
   971   graphCopy(const From& from, To& to) {
   972     return GraphCopy<From, To>(from, to);
   973   }
   974 
   975   namespace _core_bits {
   976 
   977     template <typename Graph, typename Enable = void>
   978     struct FindArcSelector {
   979       typedef typename Graph::Node Node;
   980       typedef typename Graph::Arc Arc;
   981       static Arc find(const Graph &g, Node u, Node v, Arc e) {
   982         if (e == INVALID) {
   983           g.firstOut(e, u);
   984         } else {
   985           g.nextOut(e);
   986         }
   987         while (e != INVALID && g.target(e) != v) {
   988           g.nextOut(e);
   989         }
   990         return e;
   991       }
   992     };
   993 
   994     template <typename Graph>
   995     struct FindArcSelector<
   996       Graph,
   997       typename enable_if<typename Graph::FindArcTag, void>::type>
   998     {
   999       typedef typename Graph::Node Node;
  1000       typedef typename Graph::Arc Arc;
  1001       static Arc find(const Graph &g, Node u, Node v, Arc prev) {
  1002         return g.findArc(u, v, prev);
  1003       }
  1004     };
  1005   }
  1006 
  1007   /// \brief Find an arc between two nodes of a digraph.
  1008   ///
  1009   /// This function finds an arc from node \c u to node \c v in the
  1010   /// digraph \c g.
  1011   ///
  1012   /// If \c prev is \ref INVALID (this is the default value), then
  1013   /// it finds the first arc from \c u to \c v. Otherwise it looks for
  1014   /// the next arc from \c u to \c v after \c prev.
  1015   /// \return The found arc or \ref INVALID if there is no such an arc.
  1016   ///
  1017   /// Thus you can iterate through each arc from \c u to \c v as it follows.
  1018   ///\code
  1019   /// for(Arc e = findArc(g,u,v); e != INVALID; e = findArc(g,u,v,e)) {
  1020   ///   ...
  1021   /// }
  1022   ///\endcode
  1023   ///
  1024   /// \note \ref ConArcIt provides iterator interface for the same
  1025   /// functionality.
  1026   ///
  1027   ///\sa ConArcIt
  1028   ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
  1029   template <typename Graph>
  1030   inline typename Graph::Arc
  1031   findArc(const Graph &g, typename Graph::Node u, typename Graph::Node v,
  1032           typename Graph::Arc prev = INVALID) {
  1033     return _core_bits::FindArcSelector<Graph>::find(g, u, v, prev);
  1034   }
  1035 
  1036   /// \brief Iterator for iterating on parallel arcs connecting the same nodes.
  1037   ///
  1038   /// Iterator for iterating on parallel arcs connecting the same nodes. It is
  1039   /// a higher level interface for the \ref findArc() function. You can
  1040   /// use it the following way:
  1041   ///\code
  1042   /// for (ConArcIt<Graph> it(g, src, trg); it != INVALID; ++it) {
  1043   ///   ...
  1044   /// }
  1045   ///\endcode
  1046   ///
  1047   ///\sa findArc()
  1048   ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
  1049   template <typename GR>
  1050   class ConArcIt : public GR::Arc {
  1051     typedef typename GR::Arc Parent;
  1052 
  1053   public:
  1054 
  1055     typedef typename GR::Arc Arc;
  1056     typedef typename GR::Node Node;
  1057 
  1058     /// \brief Constructor.
  1059     ///
  1060     /// Construct a new ConArcIt iterating on the arcs that
  1061     /// connects nodes \c u and \c v.
  1062     ConArcIt(const GR& g, Node u, Node v) : _graph(g) {
  1063       Parent::operator=(findArc(_graph, u, v));
  1064     }
  1065 
  1066     /// \brief Constructor.
  1067     ///
  1068     /// Construct a new ConArcIt that continues the iterating from arc \c a.
  1069     ConArcIt(const GR& g, Arc a) : Parent(a), _graph(g) {}
  1070 
  1071     /// \brief Increment operator.
  1072     ///
  1073     /// It increments the iterator and gives back the next arc.
  1074     ConArcIt& operator++() {
  1075       Parent::operator=(findArc(_graph, _graph.source(*this),
  1076                                 _graph.target(*this), *this));
  1077       return *this;
  1078     }
  1079   private:
  1080     const GR& _graph;
  1081   };
  1082 
  1083   namespace _core_bits {
  1084 
  1085     template <typename Graph, typename Enable = void>
  1086     struct FindEdgeSelector {
  1087       typedef typename Graph::Node Node;
  1088       typedef typename Graph::Edge Edge;
  1089       static Edge find(const Graph &g, Node u, Node v, Edge e) {
  1090         bool b;
  1091         if (u != v) {
  1092           if (e == INVALID) {
  1093             g.firstInc(e, b, u);
  1094           } else {
  1095             b = g.u(e) == u;
  1096             g.nextInc(e, b);
  1097           }
  1098           while (e != INVALID && (b ? g.v(e) : g.u(e)) != v) {
  1099             g.nextInc(e, b);
  1100           }
  1101         } else {
  1102           if (e == INVALID) {
  1103             g.firstInc(e, b, u);
  1104           } else {
  1105             b = true;
  1106             g.nextInc(e, b);
  1107           }
  1108           while (e != INVALID && (!b || g.v(e) != v)) {
  1109             g.nextInc(e, b);
  1110           }
  1111         }
  1112         return e;
  1113       }
  1114     };
  1115 
  1116     template <typename Graph>
  1117     struct FindEdgeSelector<
  1118       Graph,
  1119       typename enable_if<typename Graph::FindEdgeTag, void>::type>
  1120     {
  1121       typedef typename Graph::Node Node;
  1122       typedef typename Graph::Edge Edge;
  1123       static Edge find(const Graph &g, Node u, Node v, Edge prev) {
  1124         return g.findEdge(u, v, prev);
  1125       }
  1126     };
  1127   }
  1128 
  1129   /// \brief Find an edge between two nodes of a graph.
  1130   ///
  1131   /// This function finds an edge from node \c u to node \c v in graph \c g.
  1132   /// If node \c u and node \c v is equal then each loop edge
  1133   /// will be enumerated once.
  1134   ///
  1135   /// If \c prev is \ref INVALID (this is the default value), then
  1136   /// it finds the first edge from \c u to \c v. Otherwise it looks for
  1137   /// the next edge from \c u to \c v after \c prev.
  1138   /// \return The found edge or \ref INVALID if there is no such an edge.
  1139   ///
  1140   /// Thus you can iterate through each edge between \c u and \c v
  1141   /// as it follows.
  1142   ///\code
  1143   /// for(Edge e = findEdge(g,u,v); e != INVALID; e = findEdge(g,u,v,e)) {
  1144   ///   ...
  1145   /// }
  1146   ///\endcode
  1147   ///
  1148   /// \note \ref ConEdgeIt provides iterator interface for the same
  1149   /// functionality.
  1150   ///
  1151   ///\sa ConEdgeIt
  1152   template <typename Graph>
  1153   inline typename Graph::Edge
  1154   findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,
  1155             typename Graph::Edge p = INVALID) {
  1156     return _core_bits::FindEdgeSelector<Graph>::find(g, u, v, p);
  1157   }
  1158 
  1159   /// \brief Iterator for iterating on parallel edges connecting the same nodes.
  1160   ///
  1161   /// Iterator for iterating on parallel edges connecting the same nodes.
  1162   /// It is a higher level interface for the findEdge() function. You can
  1163   /// use it the following way:
  1164   ///\code
  1165   /// for (ConEdgeIt<Graph> it(g, u, v); it != INVALID; ++it) {
  1166   ///   ...
  1167   /// }
  1168   ///\endcode
  1169   ///
  1170   ///\sa findEdge()
  1171   template <typename GR>
  1172   class ConEdgeIt : public GR::Edge {
  1173     typedef typename GR::Edge Parent;
  1174 
  1175   public:
  1176 
  1177     typedef typename GR::Edge Edge;
  1178     typedef typename GR::Node Node;
  1179 
  1180     /// \brief Constructor.
  1181     ///
  1182     /// Construct a new ConEdgeIt iterating on the edges that
  1183     /// connects nodes \c u and \c v.
  1184     ConEdgeIt(const GR& g, Node u, Node v) : _graph(g), _u(u), _v(v) {
  1185       Parent::operator=(findEdge(_graph, _u, _v));
  1186     }
  1187 
  1188     /// \brief Constructor.
  1189     ///
  1190     /// Construct a new ConEdgeIt that continues iterating from edge \c e.
  1191     ConEdgeIt(const GR& g, Edge e) : Parent(e), _graph(g) {}
  1192 
  1193     /// \brief Increment operator.
  1194     ///
  1195     /// It increments the iterator and gives back the next edge.
  1196     ConEdgeIt& operator++() {
  1197       Parent::operator=(findEdge(_graph, _u, _v, *this));
  1198       return *this;
  1199     }
  1200   private:
  1201     const GR& _graph;
  1202     Node _u, _v;
  1203   };
  1204 
  1205 
  1206   ///Dynamic arc look-up between given endpoints.
  1207 
  1208   ///Using this class, you can find an arc in a digraph from a given
  1209   ///source to a given target in amortized time <em>O</em>(log<em>d</em>),
  1210   ///where <em>d</em> is the out-degree of the source node.
  1211   ///
  1212   ///It is possible to find \e all parallel arcs between two nodes with
  1213   ///the \c operator() member.
  1214   ///
  1215   ///This is a dynamic data structure. Consider to use \ref ArcLookUp or
  1216   ///\ref AllArcLookUp if your digraph is not changed so frequently.
  1217   ///
  1218   ///This class uses a self-adjusting binary search tree, the Splay tree
  1219   ///of Sleator and Tarjan to guarantee the logarithmic amortized
  1220   ///time bound for arc look-ups. This class also guarantees the
  1221   ///optimal time bound in a constant factor for any distribution of
  1222   ///queries.
  1223   ///
  1224   ///\tparam GR The type of the underlying digraph.
  1225   ///
  1226   ///\sa ArcLookUp
  1227   ///\sa AllArcLookUp
  1228   template <typename GR>
  1229   class DynArcLookUp
  1230     : protected ItemSetTraits<GR, typename GR::Arc>::ItemNotifier::ObserverBase
  1231   {
  1232     typedef typename ItemSetTraits<GR, typename GR::Arc>
  1233     ::ItemNotifier::ObserverBase Parent;
  1234 
  1235     TEMPLATE_DIGRAPH_TYPEDEFS(GR);
  1236 
  1237   public:
  1238 
  1239     /// The Digraph type
  1240     typedef GR Digraph;
  1241 
  1242   protected:
  1243 
  1244     class AutoNodeMap : public ItemSetTraits<GR, Node>::template Map<Arc>::Type
  1245     {
  1246       typedef typename ItemSetTraits<GR, Node>::template Map<Arc>::Type Parent;
  1247 
  1248     public:
  1249 
  1250       AutoNodeMap(const GR& digraph) : Parent(digraph, INVALID) {}
  1251 
  1252       virtual void add(const Node& node) {
  1253         Parent::add(node);
  1254         Parent::set(node, INVALID);
  1255       }
  1256 
  1257       virtual void add(const std::vector<Node>& nodes) {
  1258         Parent::add(nodes);
  1259         for (int i = 0; i < int(nodes.size()); ++i) {
  1260           Parent::set(nodes[i], INVALID);
  1261         }
  1262       }
  1263 
  1264       virtual void build() {
  1265         Parent::build();
  1266         Node it;
  1267         typename Parent::Notifier* nf = Parent::notifier();
  1268         for (nf->first(it); it != INVALID; nf->next(it)) {
  1269           Parent::set(it, INVALID);
  1270         }
  1271       }
  1272     };
  1273 
  1274     class ArcLess {
  1275       const Digraph &g;
  1276     public:
  1277       ArcLess(const Digraph &_g) : g(_g) {}
  1278       bool operator()(Arc a,Arc b) const
  1279       {
  1280         return g.target(a)<g.target(b);
  1281       }
  1282     };
  1283 
  1284   protected:
  1285 
  1286     const Digraph &_g;
  1287     AutoNodeMap _head;
  1288     typename Digraph::template ArcMap<Arc> _parent;
  1289     typename Digraph::template ArcMap<Arc> _left;
  1290     typename Digraph::template ArcMap<Arc> _right;
  1291 
  1292   public:
  1293 
  1294     ///Constructor
  1295 
  1296     ///Constructor.
  1297     ///
  1298     ///It builds up the search database.
  1299     DynArcLookUp(const Digraph &g)
  1300       : _g(g),_head(g),_parent(g),_left(g),_right(g)
  1301     {
  1302       Parent::attach(_g.notifier(typename Digraph::Arc()));
  1303       refresh();
  1304     }
  1305 
  1306   protected:
  1307 
  1308     virtual void add(const Arc& arc) {
  1309       insert(arc);
  1310     }
  1311 
  1312     virtual void add(const std::vector<Arc>& arcs) {
  1313       for (int i = 0; i < int(arcs.size()); ++i) {
  1314         insert(arcs[i]);
  1315       }
  1316     }
  1317 
  1318     virtual void erase(const Arc& arc) {
  1319       remove(arc);
  1320     }
  1321 
  1322     virtual void erase(const std::vector<Arc>& arcs) {
  1323       for (int i = 0; i < int(arcs.size()); ++i) {
  1324         remove(arcs[i]);
  1325       }
  1326     }
  1327 
  1328     virtual void build() {
  1329       refresh();
  1330     }
  1331 
  1332     virtual void clear() {
  1333       for(NodeIt n(_g);n!=INVALID;++n) {
  1334         _head[n] = INVALID;
  1335       }
  1336     }
  1337 
  1338     void insert(Arc arc) {
  1339       Node s = _g.source(arc);
  1340       Node t = _g.target(arc);
  1341       _left[arc] = INVALID;
  1342       _right[arc] = INVALID;
  1343 
  1344       Arc e = _head[s];
  1345       if (e == INVALID) {
  1346         _head[s] = arc;
  1347         _parent[arc] = INVALID;
  1348         return;
  1349       }
  1350       while (true) {
  1351         if (t < _g.target(e)) {
  1352           if (_left[e] == INVALID) {
  1353             _left[e] = arc;
  1354             _parent[arc] = e;
  1355             splay(arc);
  1356             return;
  1357           } else {
  1358             e = _left[e];
  1359           }
  1360         } else {
  1361           if (_right[e] == INVALID) {
  1362             _right[e] = arc;
  1363             _parent[arc] = e;
  1364             splay(arc);
  1365             return;
  1366           } else {
  1367             e = _right[e];
  1368           }
  1369         }
  1370       }
  1371     }
  1372 
  1373     void remove(Arc arc) {
  1374       if (_left[arc] == INVALID) {
  1375         if (_right[arc] != INVALID) {
  1376           _parent[_right[arc]] = _parent[arc];
  1377         }
  1378         if (_parent[arc] != INVALID) {
  1379           if (_left[_parent[arc]] == arc) {
  1380             _left[_parent[arc]] = _right[arc];
  1381           } else {
  1382             _right[_parent[arc]] = _right[arc];
  1383           }
  1384         } else {
  1385           _head[_g.source(arc)] = _right[arc];
  1386         }
  1387       } else if (_right[arc] == INVALID) {
  1388         _parent[_left[arc]] = _parent[arc];
  1389         if (_parent[arc] != INVALID) {
  1390           if (_left[_parent[arc]] == arc) {
  1391             _left[_parent[arc]] = _left[arc];
  1392           } else {
  1393             _right[_parent[arc]] = _left[arc];
  1394           }
  1395         } else {
  1396           _head[_g.source(arc)] = _left[arc];
  1397         }
  1398       } else {
  1399         Arc e = _left[arc];
  1400         if (_right[e] != INVALID) {
  1401           e = _right[e];
  1402           while (_right[e] != INVALID) {
  1403             e = _right[e];
  1404           }
  1405           Arc s = _parent[e];
  1406           _right[_parent[e]] = _left[e];
  1407           if (_left[e] != INVALID) {
  1408             _parent[_left[e]] = _parent[e];
  1409           }
  1410 
  1411           _left[e] = _left[arc];
  1412           _parent[_left[arc]] = e;
  1413           _right[e] = _right[arc];
  1414           _parent[_right[arc]] = e;
  1415 
  1416           _parent[e] = _parent[arc];
  1417           if (_parent[arc] != INVALID) {
  1418             if (_left[_parent[arc]] == arc) {
  1419               _left[_parent[arc]] = e;
  1420             } else {
  1421               _right[_parent[arc]] = e;
  1422             }
  1423           }
  1424           splay(s);
  1425         } else {
  1426           _right[e] = _right[arc];
  1427           _parent[_right[arc]] = e;
  1428           _parent[e] = _parent[arc];
  1429 
  1430           if (_parent[arc] != INVALID) {
  1431             if (_left[_parent[arc]] == arc) {
  1432               _left[_parent[arc]] = e;
  1433             } else {
  1434               _right[_parent[arc]] = e;
  1435             }
  1436           } else {
  1437             _head[_g.source(arc)] = e;
  1438           }
  1439         }
  1440       }
  1441     }
  1442 
  1443     Arc refreshRec(std::vector<Arc> &v,int a,int b)
  1444     {
  1445       int m=(a+b)/2;
  1446       Arc me=v[m];
  1447       if (a < m) {
  1448         Arc left = refreshRec(v,a,m-1);
  1449         _left[me] = left;
  1450         _parent[left] = me;
  1451       } else {
  1452         _left[me] = INVALID;
  1453       }
  1454       if (m < b) {
  1455         Arc right = refreshRec(v,m+1,b);
  1456         _right[me] = right;
  1457         _parent[right] = me;
  1458       } else {
  1459         _right[me] = INVALID;
  1460       }
  1461       return me;
  1462     }
  1463 
  1464     void refresh() {
  1465       for(NodeIt n(_g);n!=INVALID;++n) {
  1466         std::vector<Arc> v;
  1467         for(OutArcIt a(_g,n);a!=INVALID;++a) v.push_back(a);
  1468         if (!v.empty()) {
  1469           std::sort(v.begin(),v.end(),ArcLess(_g));
  1470           Arc head = refreshRec(v,0,v.size()-1);
  1471           _head[n] = head;
  1472           _parent[head] = INVALID;
  1473         }
  1474         else _head[n] = INVALID;
  1475       }
  1476     }
  1477 
  1478     void zig(Arc v) {
  1479       Arc w = _parent[v];
  1480       _parent[v] = _parent[w];
  1481       _parent[w] = v;
  1482       _left[w] = _right[v];
  1483       _right[v] = w;
  1484       if (_parent[v] != INVALID) {
  1485         if (_right[_parent[v]] == w) {
  1486           _right[_parent[v]] = v;
  1487         } else {
  1488           _left[_parent[v]] = v;
  1489         }
  1490       }
  1491       if (_left[w] != INVALID){
  1492         _parent[_left[w]] = w;
  1493       }
  1494     }
  1495 
  1496     void zag(Arc v) {
  1497       Arc w = _parent[v];
  1498       _parent[v] = _parent[w];
  1499       _parent[w] = v;
  1500       _right[w] = _left[v];
  1501       _left[v] = w;
  1502       if (_parent[v] != INVALID){
  1503         if (_left[_parent[v]] == w) {
  1504           _left[_parent[v]] = v;
  1505         } else {
  1506           _right[_parent[v]] = v;
  1507         }
  1508       }
  1509       if (_right[w] != INVALID){
  1510         _parent[_right[w]] = w;
  1511       }
  1512     }
  1513 
  1514     void splay(Arc v) {
  1515       while (_parent[v] != INVALID) {
  1516         if (v == _left[_parent[v]]) {
  1517           if (_parent[_parent[v]] == INVALID) {
  1518             zig(v);
  1519           } else {
  1520             if (_parent[v] == _left[_parent[_parent[v]]]) {
  1521               zig(_parent[v]);
  1522               zig(v);
  1523             } else {
  1524               zig(v);
  1525               zag(v);
  1526             }
  1527           }
  1528         } else {
  1529           if (_parent[_parent[v]] == INVALID) {
  1530             zag(v);
  1531           } else {
  1532             if (_parent[v] == _left[_parent[_parent[v]]]) {
  1533               zag(v);
  1534               zig(v);
  1535             } else {
  1536               zag(_parent[v]);
  1537               zag(v);
  1538             }
  1539           }
  1540         }
  1541       }
  1542       _head[_g.source(v)] = v;
  1543     }
  1544 
  1545 
  1546   public:
  1547 
  1548     ///Find an arc between two nodes.
  1549 
  1550     ///Find an arc between two nodes.
  1551     ///\param s The source node.
  1552     ///\param t The target node.
  1553     ///\param p The previous arc between \c s and \c t. It it is INVALID or
  1554     ///not given, the operator finds the first appropriate arc.
  1555     ///\return An arc from \c s to \c t after \c p or
  1556     ///\ref INVALID if there is no more.
  1557     ///
  1558     ///For example, you can count the number of arcs from \c u to \c v in the
  1559     ///following way.
  1560     ///\code
  1561     ///DynArcLookUp<ListDigraph> ae(g);
  1562     ///...
  1563     ///int n = 0;
  1564     ///for(Arc a = ae(u,v); a != INVALID; a = ae(u,v,a)) n++;
  1565     ///\endcode
  1566     ///
  1567     ///Finding the arcs take at most <em>O</em>(log<em>d</em>)
  1568     ///amortized time, specifically, the time complexity of the lookups
  1569     ///is equal to the optimal search tree implementation for the
  1570     ///current query distribution in a constant factor.
  1571     ///
  1572     ///\note This is a dynamic data structure, therefore the data
  1573     ///structure is updated after each graph alteration. Thus although
  1574     ///this data structure is theoretically faster than \ref ArcLookUp
  1575     ///and \ref AllArcLookUp, it often provides worse performance than
  1576     ///them.
  1577     Arc operator()(Node s, Node t, Arc p = INVALID) const  {
  1578       if (p == INVALID) {
  1579         Arc a = _head[s];
  1580         if (a == INVALID) return INVALID;
  1581         Arc r = INVALID;
  1582         while (true) {
  1583           if (_g.target(a) < t) {
  1584             if (_right[a] == INVALID) {
  1585               const_cast<DynArcLookUp&>(*this).splay(a);
  1586               return r;
  1587             } else {
  1588               a = _right[a];
  1589             }
  1590           } else {
  1591             if (_g.target(a) == t) {
  1592               r = a;
  1593             }
  1594             if (_left[a] == INVALID) {
  1595               const_cast<DynArcLookUp&>(*this).splay(a);
  1596               return r;
  1597             } else {
  1598               a = _left[a];
  1599             }
  1600           }
  1601         }
  1602       } else {
  1603         Arc a = p;
  1604         if (_right[a] != INVALID) {
  1605           a = _right[a];
  1606           while (_left[a] != INVALID) {
  1607             a = _left[a];
  1608           }
  1609           const_cast<DynArcLookUp&>(*this).splay(a);
  1610         } else {
  1611           while (_parent[a] != INVALID && _right[_parent[a]] ==  a) {
  1612             a = _parent[a];
  1613           }
  1614           if (_parent[a] == INVALID) {
  1615             return INVALID;
  1616           } else {
  1617             a = _parent[a];
  1618             const_cast<DynArcLookUp&>(*this).splay(a);
  1619           }
  1620         }
  1621         if (_g.target(a) == t) return a;
  1622         else return INVALID;
  1623       }
  1624     }
  1625 
  1626   };
  1627 
  1628   ///Fast arc look-up between given endpoints.
  1629 
  1630   ///Using this class, you can find an arc in a digraph from a given
  1631   ///source to a given target in time <em>O</em>(log<em>d</em>),
  1632   ///where <em>d</em> is the out-degree of the source node.
  1633   ///
  1634   ///It is not possible to find \e all parallel arcs between two nodes.
  1635   ///Use \ref AllArcLookUp for this purpose.
  1636   ///
  1637   ///\warning This class is static, so you should call refresh() (or at
  1638   ///least refresh(Node)) to refresh this data structure whenever the
  1639   ///digraph changes. This is a time consuming (superlinearly proportional
  1640   ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
  1641   ///
  1642   ///\tparam GR The type of the underlying digraph.
  1643   ///
  1644   ///\sa DynArcLookUp
  1645   ///\sa AllArcLookUp
  1646   template<class GR>
  1647   class ArcLookUp
  1648   {
  1649     TEMPLATE_DIGRAPH_TYPEDEFS(GR);
  1650 
  1651   public:
  1652 
  1653     /// The Digraph type
  1654     typedef GR Digraph;
  1655 
  1656   protected:
  1657     const Digraph &_g;
  1658     typename Digraph::template NodeMap<Arc> _head;
  1659     typename Digraph::template ArcMap<Arc> _left;
  1660     typename Digraph::template ArcMap<Arc> _right;
  1661 
  1662     class ArcLess {
  1663       const Digraph &g;
  1664     public:
  1665       ArcLess(const Digraph &_g) : g(_g) {}
  1666       bool operator()(Arc a,Arc b) const
  1667       {
  1668         return g.target(a)<g.target(b);
  1669       }
  1670     };
  1671 
  1672   public:
  1673 
  1674     ///Constructor
  1675 
  1676     ///Constructor.
  1677     ///
  1678     ///It builds up the search database, which remains valid until the digraph
  1679     ///changes.
  1680     ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}
  1681 
  1682   private:
  1683     Arc refreshRec(std::vector<Arc> &v,int a,int b)
  1684     {
  1685       int m=(a+b)/2;
  1686       Arc me=v[m];
  1687       _left[me] = a<m?refreshRec(v,a,m-1):INVALID;
  1688       _right[me] = m<b?refreshRec(v,m+1,b):INVALID;
  1689       return me;
  1690     }
  1691   public:
  1692     ///Refresh the search data structure at a node.
  1693 
  1694     ///Build up the search database of node \c n.
  1695     ///
  1696     ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em>
  1697     ///is the number of the outgoing arcs of \c n.
  1698     void refresh(Node n)
  1699     {
  1700       std::vector<Arc> v;
  1701       for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
  1702       if(v.size()) {
  1703         std::sort(v.begin(),v.end(),ArcLess(_g));
  1704         _head[n]=refreshRec(v,0,v.size()-1);
  1705       }
  1706       else _head[n]=INVALID;
  1707     }
  1708     ///Refresh the full data structure.
  1709 
  1710     ///Build up the full search database. In fact, it simply calls
  1711     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  1712     ///
  1713     ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
  1714     ///the number of the arcs in the digraph and <em>D</em> is the maximum
  1715     ///out-degree of the digraph.
  1716     void refresh()
  1717     {
  1718       for(NodeIt n(_g);n!=INVALID;++n) refresh(n);
  1719     }
  1720 
  1721     ///Find an arc between two nodes.
  1722 
  1723     ///Find an arc between two nodes in time <em>O</em>(log<em>d</em>),
  1724     ///where <em>d</em> is the number of outgoing arcs of \c s.
  1725     ///\param s The source node.
  1726     ///\param t The target node.
  1727     ///\return An arc from \c s to \c t if there exists,
  1728     ///\ref INVALID otherwise.
  1729     ///
  1730     ///\warning If you change the digraph, refresh() must be called before using
  1731     ///this operator. If you change the outgoing arcs of
  1732     ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
  1733     Arc operator()(Node s, Node t) const
  1734     {
  1735       Arc e;
  1736       for(e=_head[s];
  1737           e!=INVALID&&_g.target(e)!=t;
  1738           e = t < _g.target(e)?_left[e]:_right[e]) ;
  1739       return e;
  1740     }
  1741 
  1742   };
  1743 
  1744   ///Fast look-up of all arcs between given endpoints.
  1745 
  1746   ///This class is the same as \ref ArcLookUp, with the addition
  1747   ///that it makes it possible to find all parallel arcs between given
  1748   ///endpoints.
  1749   ///
  1750   ///\warning This class is static, so you should call refresh() (or at
  1751   ///least refresh(Node)) to refresh this data structure whenever the
  1752   ///digraph changes. This is a time consuming (superlinearly proportional
  1753   ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
  1754   ///
  1755   ///\tparam GR The type of the underlying digraph.
  1756   ///
  1757   ///\sa DynArcLookUp
  1758   ///\sa ArcLookUp
  1759   template<class GR>
  1760   class AllArcLookUp : public ArcLookUp<GR>
  1761   {
  1762     using ArcLookUp<GR>::_g;
  1763     using ArcLookUp<GR>::_right;
  1764     using ArcLookUp<GR>::_left;
  1765     using ArcLookUp<GR>::_head;
  1766 
  1767     TEMPLATE_DIGRAPH_TYPEDEFS(GR);
  1768 
  1769     typename GR::template ArcMap<Arc> _next;
  1770 
  1771     Arc refreshNext(Arc head,Arc next=INVALID)
  1772     {
  1773       if(head==INVALID) return next;
  1774       else {
  1775         next=refreshNext(_right[head],next);
  1776         _next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
  1777           ? next : INVALID;
  1778         return refreshNext(_left[head],head);
  1779       }
  1780     }
  1781 
  1782     void refreshNext()
  1783     {
  1784       for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
  1785     }
  1786 
  1787   public:
  1788 
  1789     /// The Digraph type
  1790     typedef GR Digraph;
  1791 
  1792     ///Constructor
  1793 
  1794     ///Constructor.
  1795     ///
  1796     ///It builds up the search database, which remains valid until the digraph
  1797     ///changes.
  1798     AllArcLookUp(const Digraph &g) : ArcLookUp<GR>(g), _next(g) {refreshNext();}
  1799 
  1800     ///Refresh the data structure at a node.
  1801 
  1802     ///Build up the search database of node \c n.
  1803     ///
  1804     ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em> is
  1805     ///the number of the outgoing arcs of \c n.
  1806     void refresh(Node n)
  1807     {
  1808       ArcLookUp<GR>::refresh(n);
  1809       refreshNext(_head[n]);
  1810     }
  1811 
  1812     ///Refresh the full data structure.
  1813 
  1814     ///Build up the full search database. In fact, it simply calls
  1815     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  1816     ///
  1817     ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
  1818     ///the number of the arcs in the digraph and <em>D</em> is the maximum
  1819     ///out-degree of the digraph.
  1820     void refresh()
  1821     {
  1822       for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
  1823     }
  1824 
  1825     ///Find an arc between two nodes.
  1826 
  1827     ///Find an arc between two nodes.
  1828     ///\param s The source node.
  1829     ///\param t The target node.
  1830     ///\param prev The previous arc between \c s and \c t. It it is INVALID or
  1831     ///not given, the operator finds the first appropriate arc.
  1832     ///\return An arc from \c s to \c t after \c prev or
  1833     ///\ref INVALID if there is no more.
  1834     ///
  1835     ///For example, you can count the number of arcs from \c u to \c v in the
  1836     ///following way.
  1837     ///\code
  1838     ///AllArcLookUp<ListDigraph> ae(g);
  1839     ///...
  1840     ///int n = 0;
  1841     ///for(Arc a = ae(u,v); a != INVALID; a=ae(u,v,a)) n++;
  1842     ///\endcode
  1843     ///
  1844     ///Finding the first arc take <em>O</em>(log<em>d</em>) time,
  1845     ///where <em>d</em> is the number of outgoing arcs of \c s. Then the
  1846     ///consecutive arcs are found in constant time.
  1847     ///
  1848     ///\warning If you change the digraph, refresh() must be called before using
  1849     ///this operator. If you change the outgoing arcs of
  1850     ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
  1851     ///
  1852 #ifdef DOXYGEN
  1853     Arc operator()(Node s, Node t, Arc prev=INVALID) const {}
  1854 #else
  1855     using ArcLookUp<GR>::operator() ;
  1856     Arc operator()(Node s, Node t, Arc prev) const
  1857     {
  1858       return prev==INVALID?(*this)(s,t):_next[prev];
  1859     }
  1860 #endif
  1861 
  1862   };
  1863 
  1864   /// @}
  1865 
  1866 } //namespace lemon
  1867 
  1868 #endif