lemon/core.h
author Alpar Juttner <alpar@cs.elte.hu>
Wed, 29 Apr 2009 15:52:08 +0100
changeset 632 0286cb1ac78d
parent 581 aa1804409f29
child 639 72ac25ad276e
permissions -rw-r--r--
Merge
     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/core.h>
    26 #include <lemon/bits/enable_if.h>
    27 #include <lemon/bits/traits.h>
    28 #include <lemon/assert.h>
    29 
    30 ///\file
    31 ///\brief LEMON core utilities.
    32 ///
    33 ///This header file contains core utilities for LEMON.
    34 ///It is automatically included by all graph types, therefore it usually
    35 ///do not have to be included directly.
    36 
    37 namespace lemon {
    38 
    39   /// \brief Dummy type to make it easier to create invalid iterators.
    40   ///
    41   /// Dummy type to make it easier to create invalid iterators.
    42   /// See \ref INVALID for the usage.
    43   struct Invalid {
    44   public:
    45     bool operator==(Invalid) { return true;  }
    46     bool operator!=(Invalid) { return false; }
    47     bool operator< (Invalid) { return false; }
    48   };
    49 
    50   /// \brief Invalid iterators.
    51   ///
    52   /// \ref Invalid is a global type that converts to each iterator
    53   /// in such a way that the value of the target iterator will be invalid.
    54 #ifdef LEMON_ONLY_TEMPLATES
    55   const Invalid INVALID = Invalid();
    56 #else
    57   extern const Invalid INVALID;
    58 #endif
    59 
    60   /// \addtogroup gutils
    61   /// @{
    62 
    63   ///Create convenience typedefs for the digraph types and iterators
    64 
    65   ///This \c \#define creates convenient type definitions for the following
    66   ///types of \c Digraph: \c Node,  \c NodeIt, \c Arc, \c ArcIt, \c InArcIt,
    67   ///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap,
    68   ///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap.
    69   ///
    70   ///\note If the graph type is a dependent type, ie. the graph type depend
    71   ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
    72   ///macro.
    73 #define DIGRAPH_TYPEDEFS(Digraph)                                       \
    74   typedef Digraph::Node Node;                                           \
    75   typedef Digraph::NodeIt NodeIt;                                       \
    76   typedef Digraph::Arc Arc;                                             \
    77   typedef Digraph::ArcIt ArcIt;                                         \
    78   typedef Digraph::InArcIt InArcIt;                                     \
    79   typedef Digraph::OutArcIt OutArcIt;                                   \
    80   typedef Digraph::NodeMap<bool> BoolNodeMap;                           \
    81   typedef Digraph::NodeMap<int> IntNodeMap;                             \
    82   typedef Digraph::NodeMap<double> DoubleNodeMap;                       \
    83   typedef Digraph::ArcMap<bool> BoolArcMap;                             \
    84   typedef Digraph::ArcMap<int> IntArcMap;                               \
    85   typedef Digraph::ArcMap<double> DoubleArcMap
    86 
    87   ///Create convenience typedefs for the digraph types and iterators
    88 
    89   ///\see DIGRAPH_TYPEDEFS
    90   ///
    91   ///\note Use this macro, if the graph type is a dependent type,
    92   ///ie. the graph type depend on a template parameter.
    93 #define TEMPLATE_DIGRAPH_TYPEDEFS(Digraph)                              \
    94   typedef typename Digraph::Node Node;                                  \
    95   typedef typename Digraph::NodeIt NodeIt;                              \
    96   typedef typename Digraph::Arc Arc;                                    \
    97   typedef typename Digraph::ArcIt ArcIt;                                \
    98   typedef typename Digraph::InArcIt InArcIt;                            \
    99   typedef typename Digraph::OutArcIt OutArcIt;                          \
   100   typedef typename Digraph::template NodeMap<bool> BoolNodeMap;         \
   101   typedef typename Digraph::template NodeMap<int> IntNodeMap;           \
   102   typedef typename Digraph::template NodeMap<double> DoubleNodeMap;     \
   103   typedef typename Digraph::template ArcMap<bool> BoolArcMap;           \
   104   typedef typename Digraph::template ArcMap<int> IntArcMap;             \
   105   typedef typename Digraph::template ArcMap<double> DoubleArcMap
   106 
   107   ///Create convenience typedefs for the graph types and iterators
   108 
   109   ///This \c \#define creates the same convenient type definitions as defined
   110   ///by \ref DIGRAPH_TYPEDEFS(Graph) and six more, namely it creates
   111   ///\c Edge, \c EdgeIt, \c IncEdgeIt, \c BoolEdgeMap, \c IntEdgeMap,
   112   ///\c DoubleEdgeMap.
   113   ///
   114   ///\note If the graph type is a dependent type, ie. the graph type depend
   115   ///on a template parameter, then use \c TEMPLATE_GRAPH_TYPEDEFS()
   116   ///macro.
   117 #define GRAPH_TYPEDEFS(Graph)                                           \
   118   DIGRAPH_TYPEDEFS(Graph);                                              \
   119   typedef Graph::Edge Edge;                                             \
   120   typedef Graph::EdgeIt EdgeIt;                                         \
   121   typedef Graph::IncEdgeIt IncEdgeIt;                                   \
   122   typedef Graph::EdgeMap<bool> BoolEdgeMap;                             \
   123   typedef Graph::EdgeMap<int> IntEdgeMap;                               \
   124   typedef Graph::EdgeMap<double> DoubleEdgeMap
   125 
   126   ///Create convenience typedefs for the graph types and iterators
   127 
   128   ///\see GRAPH_TYPEDEFS
   129   ///
   130   ///\note Use this macro, if the graph type is a dependent type,
   131   ///ie. the graph type depend on a template parameter.
   132 #define TEMPLATE_GRAPH_TYPEDEFS(Graph)                                  \
   133   TEMPLATE_DIGRAPH_TYPEDEFS(Graph);                                     \
   134   typedef typename Graph::Edge Edge;                                    \
   135   typedef typename Graph::EdgeIt EdgeIt;                                \
   136   typedef typename Graph::IncEdgeIt IncEdgeIt;                          \
   137   typedef typename Graph::template EdgeMap<bool> BoolEdgeMap;           \
   138   typedef typename Graph::template EdgeMap<int> IntEdgeMap;             \
   139   typedef typename Graph::template EdgeMap<double> DoubleEdgeMap
   140 
   141   /// \brief Function to count the items in a graph.
   142   ///
   143   /// This function counts the items (nodes, arcs etc.) in a graph.
   144   /// The complexity of the function is linear because
   145   /// it iterates on all of the items.
   146   template <typename Graph, typename Item>
   147   inline int countItems(const Graph& g) {
   148     typedef typename ItemSetTraits<Graph, Item>::ItemIt ItemIt;
   149     int num = 0;
   150     for (ItemIt it(g); it != INVALID; ++it) {
   151       ++num;
   152     }
   153     return num;
   154   }
   155 
   156   // Node counting:
   157 
   158   namespace _core_bits {
   159 
   160     template <typename Graph, typename Enable = void>
   161     struct CountNodesSelector {
   162       static int count(const Graph &g) {
   163         return countItems<Graph, typename Graph::Node>(g);
   164       }
   165     };
   166 
   167     template <typename Graph>
   168     struct CountNodesSelector<
   169       Graph, typename
   170       enable_if<typename Graph::NodeNumTag, void>::type>
   171     {
   172       static int count(const Graph &g) {
   173         return g.nodeNum();
   174       }
   175     };
   176   }
   177 
   178   /// \brief Function to count the nodes in the graph.
   179   ///
   180   /// This function counts the nodes in the graph.
   181   /// The complexity of the function is <em>O</em>(<em>n</em>), but for some
   182   /// graph structures it is specialized to run in <em>O</em>(1).
   183   ///
   184   /// \note If the graph contains a \c nodeNum() member function and a
   185   /// \c NodeNumTag tag then this function calls directly the member
   186   /// function to query the cardinality of the node set.
   187   template <typename Graph>
   188   inline int countNodes(const Graph& g) {
   189     return _core_bits::CountNodesSelector<Graph>::count(g);
   190   }
   191 
   192   // Arc counting:
   193 
   194   namespace _core_bits {
   195 
   196     template <typename Graph, typename Enable = void>
   197     struct CountArcsSelector {
   198       static int count(const Graph &g) {
   199         return countItems<Graph, typename Graph::Arc>(g);
   200       }
   201     };
   202 
   203     template <typename Graph>
   204     struct CountArcsSelector<
   205       Graph,
   206       typename enable_if<typename Graph::ArcNumTag, void>::type>
   207     {
   208       static int count(const Graph &g) {
   209         return g.arcNum();
   210       }
   211     };
   212   }
   213 
   214   /// \brief Function to count the arcs in the graph.
   215   ///
   216   /// This function counts the arcs in the graph.
   217   /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
   218   /// graph structures it is specialized to run in <em>O</em>(1).
   219   ///
   220   /// \note If the graph contains a \c arcNum() member function and a
   221   /// \c ArcNumTag tag then this function calls directly the member
   222   /// function to query the cardinality of the arc set.
   223   template <typename Graph>
   224   inline int countArcs(const Graph& g) {
   225     return _core_bits::CountArcsSelector<Graph>::count(g);
   226   }
   227 
   228   // Edge counting:
   229 
   230   namespace _core_bits {
   231 
   232     template <typename Graph, typename Enable = void>
   233     struct CountEdgesSelector {
   234       static int count(const Graph &g) {
   235         return countItems<Graph, typename Graph::Edge>(g);
   236       }
   237     };
   238 
   239     template <typename Graph>
   240     struct CountEdgesSelector<
   241       Graph,
   242       typename enable_if<typename Graph::EdgeNumTag, void>::type>
   243     {
   244       static int count(const Graph &g) {
   245         return g.edgeNum();
   246       }
   247     };
   248   }
   249 
   250   /// \brief Function to count the edges in the graph.
   251   ///
   252   /// This function counts the edges in the graph.
   253   /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
   254   /// graph structures it is specialized to run in <em>O</em>(1).
   255   ///
   256   /// \note If the graph contains a \c edgeNum() member function and a
   257   /// \c EdgeNumTag tag then this function calls directly the member
   258   /// function to query the cardinality of the edge set.
   259   template <typename Graph>
   260   inline int countEdges(const Graph& g) {
   261     return _core_bits::CountEdgesSelector<Graph>::count(g);
   262 
   263   }
   264 
   265 
   266   template <typename Graph, typename DegIt>
   267   inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {
   268     int num = 0;
   269     for (DegIt it(_g, _n); it != INVALID; ++it) {
   270       ++num;
   271     }
   272     return num;
   273   }
   274 
   275   /// \brief Function to count the number of the out-arcs from node \c n.
   276   ///
   277   /// This function counts the number of the out-arcs from node \c n
   278   /// in the graph \c g.
   279   template <typename Graph>
   280   inline int countOutArcs(const Graph& g,  const typename Graph::Node& n) {
   281     return countNodeDegree<Graph, typename Graph::OutArcIt>(g, n);
   282   }
   283 
   284   /// \brief Function to count the number of the in-arcs to node \c n.
   285   ///
   286   /// This function counts the number of the in-arcs to node \c n
   287   /// in the graph \c g.
   288   template <typename Graph>
   289   inline int countInArcs(const Graph& g,  const typename Graph::Node& n) {
   290     return countNodeDegree<Graph, typename Graph::InArcIt>(g, n);
   291   }
   292 
   293   /// \brief Function to count the number of the inc-edges to node \c n.
   294   ///
   295   /// This function counts the number of the inc-edges to node \c n
   296   /// in the undirected graph \c g.
   297   template <typename Graph>
   298   inline int countIncEdges(const Graph& g,  const typename Graph::Node& n) {
   299     return countNodeDegree<Graph, typename Graph::IncEdgeIt>(g, n);
   300   }
   301 
   302   namespace _core_bits {
   303 
   304     template <typename Digraph, typename Item, typename RefMap>
   305     class MapCopyBase {
   306     public:
   307       virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
   308 
   309       virtual ~MapCopyBase() {}
   310     };
   311 
   312     template <typename Digraph, typename Item, typename RefMap,
   313               typename FromMap, typename ToMap>
   314     class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
   315     public:
   316 
   317       MapCopy(const FromMap& map, ToMap& tmap)
   318         : _map(map), _tmap(tmap) {}
   319 
   320       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   321         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   322         for (ItemIt it(digraph); it != INVALID; ++it) {
   323           _tmap.set(refMap[it], _map[it]);
   324         }
   325       }
   326 
   327     private:
   328       const FromMap& _map;
   329       ToMap& _tmap;
   330     };
   331 
   332     template <typename Digraph, typename Item, typename RefMap, typename It>
   333     class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
   334     public:
   335 
   336       ItemCopy(const Item& item, It& it) : _item(item), _it(it) {}
   337 
   338       virtual void copy(const Digraph&, const RefMap& refMap) {
   339         _it = refMap[_item];
   340       }
   341 
   342     private:
   343       Item _item;
   344       It& _it;
   345     };
   346 
   347     template <typename Digraph, typename Item, typename RefMap, typename Ref>
   348     class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   349     public:
   350 
   351       RefCopy(Ref& map) : _map(map) {}
   352 
   353       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   354         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   355         for (ItemIt it(digraph); it != INVALID; ++it) {
   356           _map.set(it, refMap[it]);
   357         }
   358       }
   359 
   360     private:
   361       Ref& _map;
   362     };
   363 
   364     template <typename Digraph, typename Item, typename RefMap,
   365               typename CrossRef>
   366     class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   367     public:
   368 
   369       CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
   370 
   371       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   372         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   373         for (ItemIt it(digraph); it != INVALID; ++it) {
   374           _cmap.set(refMap[it], it);
   375         }
   376       }
   377 
   378     private:
   379       CrossRef& _cmap;
   380     };
   381 
   382     template <typename Digraph, typename Enable = void>
   383     struct DigraphCopySelector {
   384       template <typename From, typename NodeRefMap, typename ArcRefMap>
   385       static void copy(const From& from, Digraph &to,
   386                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   387         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   388           nodeRefMap[it] = to.addNode();
   389         }
   390         for (typename From::ArcIt it(from); it != INVALID; ++it) {
   391           arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)],
   392                                     nodeRefMap[from.target(it)]);
   393         }
   394       }
   395     };
   396 
   397     template <typename Digraph>
   398     struct DigraphCopySelector<
   399       Digraph,
   400       typename enable_if<typename Digraph::BuildTag, void>::type>
   401     {
   402       template <typename From, typename NodeRefMap, typename ArcRefMap>
   403       static void copy(const From& from, Digraph &to,
   404                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   405         to.build(from, nodeRefMap, arcRefMap);
   406       }
   407     };
   408 
   409     template <typename Graph, typename Enable = void>
   410     struct GraphCopySelector {
   411       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   412       static void copy(const From& from, Graph &to,
   413                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   414         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   415           nodeRefMap[it] = to.addNode();
   416         }
   417         for (typename From::EdgeIt it(from); it != INVALID; ++it) {
   418           edgeRefMap[it] = to.addEdge(nodeRefMap[from.u(it)],
   419                                       nodeRefMap[from.v(it)]);
   420         }
   421       }
   422     };
   423 
   424     template <typename Graph>
   425     struct GraphCopySelector<
   426       Graph,
   427       typename enable_if<typename Graph::BuildTag, void>::type>
   428     {
   429       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   430       static void copy(const From& from, Graph &to,
   431                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   432         to.build(from, nodeRefMap, edgeRefMap);
   433       }
   434     };
   435 
   436   }
   437 
   438   /// \brief Class to copy a digraph.
   439   ///
   440   /// Class to copy a digraph to another digraph (duplicate a digraph). The
   441   /// simplest way of using it is through the \c digraphCopy() function.
   442   ///
   443   /// This class not only make a copy of a digraph, but it can create
   444   /// references and cross references between the nodes and arcs of
   445   /// the two digraphs, and it can copy maps to use with the newly created
   446   /// digraph.
   447   ///
   448   /// To make a copy from a digraph, first an instance of DigraphCopy
   449   /// should be created, then the data belongs to the digraph should
   450   /// assigned to copy. In the end, the \c run() member should be
   451   /// called.
   452   ///
   453   /// The next code copies a digraph with several data:
   454   ///\code
   455   ///  DigraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
   456   ///  // Create references for the nodes
   457   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   458   ///  cg.nodeRef(nr);
   459   ///  // Create cross references (inverse) for the arcs
   460   ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);
   461   ///  cg.arcCrossRef(acr);
   462   ///  // Copy an arc map
   463   ///  OrigGraph::ArcMap<double> oamap(orig_graph);
   464   ///  NewGraph::ArcMap<double> namap(new_graph);
   465   ///  cg.arcMap(oamap, namap);
   466   ///  // Copy a node
   467   ///  OrigGraph::Node on;
   468   ///  NewGraph::Node nn;
   469   ///  cg.node(on, nn);
   470   ///  // Execute copying
   471   ///  cg.run();
   472   ///\endcode
   473   template <typename From, typename To>
   474   class DigraphCopy {
   475   private:
   476 
   477     typedef typename From::Node Node;
   478     typedef typename From::NodeIt NodeIt;
   479     typedef typename From::Arc Arc;
   480     typedef typename From::ArcIt ArcIt;
   481 
   482     typedef typename To::Node TNode;
   483     typedef typename To::Arc TArc;
   484 
   485     typedef typename From::template NodeMap<TNode> NodeRefMap;
   486     typedef typename From::template ArcMap<TArc> ArcRefMap;
   487 
   488   public:
   489 
   490     /// \brief Constructor of DigraphCopy.
   491     ///
   492     /// Constructor of DigraphCopy for copying the content of the
   493     /// \c from digraph into the \c to digraph.
   494     DigraphCopy(const From& from, To& to)
   495       : _from(from), _to(to) {}
   496 
   497     /// \brief Destructor of DigraphCopy
   498     ///
   499     /// Destructor of DigraphCopy.
   500     ~DigraphCopy() {
   501       for (int i = 0; i < int(_node_maps.size()); ++i) {
   502         delete _node_maps[i];
   503       }
   504       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   505         delete _arc_maps[i];
   506       }
   507 
   508     }
   509 
   510     /// \brief Copy the node references into the given map.
   511     ///
   512     /// This function copies the node references into the given map.
   513     /// The parameter should be a map, whose key type is the Node type of
   514     /// the source digraph, while the value type is the Node type of the
   515     /// destination digraph.
   516     template <typename NodeRef>
   517     DigraphCopy& nodeRef(NodeRef& map) {
   518       _node_maps.push_back(new _core_bits::RefCopy<From, Node,
   519                            NodeRefMap, NodeRef>(map));
   520       return *this;
   521     }
   522 
   523     /// \brief Copy the node cross references into the given map.
   524     ///
   525     /// This function copies the node cross references (reverse references)
   526     /// into the given map. The parameter should be a map, whose key type
   527     /// is the Node type of the destination digraph, while the value type is
   528     /// the Node type of the source digraph.
   529     template <typename NodeCrossRef>
   530     DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
   531       _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
   532                            NodeRefMap, NodeCrossRef>(map));
   533       return *this;
   534     }
   535 
   536     /// \brief Make a copy of the given node map.
   537     ///
   538     /// This function makes a copy of the given node map for the newly
   539     /// created digraph.
   540     /// The key type of the new map \c tmap should be the Node type of the
   541     /// destination digraph, and the key type of the original map \c map
   542     /// should be the Node type of the source digraph.
   543     template <typename FromMap, typename ToMap>
   544     DigraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
   545       _node_maps.push_back(new _core_bits::MapCopy<From, Node,
   546                            NodeRefMap, FromMap, ToMap>(map, tmap));
   547       return *this;
   548     }
   549 
   550     /// \brief Make a copy of the given node.
   551     ///
   552     /// This function makes a copy of the given node.
   553     DigraphCopy& node(const Node& node, TNode& tnode) {
   554       _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
   555                            NodeRefMap, TNode>(node, tnode));
   556       return *this;
   557     }
   558 
   559     /// \brief Copy the arc references into the given map.
   560     ///
   561     /// This function copies the arc references into the given map.
   562     /// The parameter should be a map, whose key type is the Arc type of
   563     /// the source digraph, while the value type is the Arc type of the
   564     /// destination digraph.
   565     template <typename ArcRef>
   566     DigraphCopy& arcRef(ArcRef& map) {
   567       _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
   568                           ArcRefMap, ArcRef>(map));
   569       return *this;
   570     }
   571 
   572     /// \brief Copy the arc cross references into the given map.
   573     ///
   574     /// This function copies the arc cross references (reverse references)
   575     /// into the given map. The parameter should be a map, whose key type
   576     /// is the Arc type of the destination digraph, while the value type is
   577     /// the Arc type of the source digraph.
   578     template <typename ArcCrossRef>
   579     DigraphCopy& arcCrossRef(ArcCrossRef& map) {
   580       _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
   581                           ArcRefMap, ArcCrossRef>(map));
   582       return *this;
   583     }
   584 
   585     /// \brief Make a copy of the given arc map.
   586     ///
   587     /// This function makes a copy of the given arc map for the newly
   588     /// created digraph.
   589     /// The key type of the new map \c tmap should be the Arc type of the
   590     /// destination digraph, and the key type of the original map \c map
   591     /// should be the Arc type of the source digraph.
   592     template <typename FromMap, typename ToMap>
   593     DigraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
   594       _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
   595                           ArcRefMap, FromMap, ToMap>(map, tmap));
   596       return *this;
   597     }
   598 
   599     /// \brief Make a copy of the given arc.
   600     ///
   601     /// This function makes a copy of the given arc.
   602     DigraphCopy& arc(const Arc& arc, TArc& tarc) {
   603       _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
   604                           ArcRefMap, TArc>(arc, tarc));
   605       return *this;
   606     }
   607 
   608     /// \brief Execute copying.
   609     ///
   610     /// This function executes the copying of the digraph along with the
   611     /// copying of the assigned data.
   612     void run() {
   613       NodeRefMap nodeRefMap(_from);
   614       ArcRefMap arcRefMap(_from);
   615       _core_bits::DigraphCopySelector<To>::
   616         copy(_from, _to, nodeRefMap, arcRefMap);
   617       for (int i = 0; i < int(_node_maps.size()); ++i) {
   618         _node_maps[i]->copy(_from, nodeRefMap);
   619       }
   620       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   621         _arc_maps[i]->copy(_from, arcRefMap);
   622       }
   623     }
   624 
   625   protected:
   626 
   627     const From& _from;
   628     To& _to;
   629 
   630     std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
   631       _node_maps;
   632 
   633     std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
   634       _arc_maps;
   635 
   636   };
   637 
   638   /// \brief Copy a digraph to another digraph.
   639   ///
   640   /// This function copies a digraph to another digraph.
   641   /// The complete usage of it is detailed in the DigraphCopy class, but
   642   /// a short example shows a basic work:
   643   ///\code
   644   /// digraphCopy(src, trg).nodeRef(nr).arcCrossRef(acr).run();
   645   ///\endcode
   646   ///
   647   /// After the copy the \c nr map will contain the mapping from the
   648   /// nodes of the \c from digraph to the nodes of the \c to digraph and
   649   /// \c acr will contain the mapping from the arcs of the \c to digraph
   650   /// to the arcs of the \c from digraph.
   651   ///
   652   /// \see DigraphCopy
   653   template <typename From, typename To>
   654   DigraphCopy<From, To> digraphCopy(const From& from, To& to) {
   655     return DigraphCopy<From, To>(from, to);
   656   }
   657 
   658   /// \brief Class to copy a graph.
   659   ///
   660   /// Class to copy a graph to another graph (duplicate a graph). The
   661   /// simplest way of using it is through the \c graphCopy() function.
   662   ///
   663   /// This class not only make a copy of a graph, but it can create
   664   /// references and cross references between the nodes, edges and arcs of
   665   /// the two graphs, and it can copy maps for using with the newly created
   666   /// graph.
   667   ///
   668   /// To make a copy from a graph, first an instance of GraphCopy
   669   /// should be created, then the data belongs to the graph should
   670   /// assigned to copy. In the end, the \c run() member should be
   671   /// called.
   672   ///
   673   /// The next code copies a graph with several data:
   674   ///\code
   675   ///  GraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
   676   ///  // Create references for the nodes
   677   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   678   ///  cg.nodeRef(nr);
   679   ///  // Create cross references (inverse) for the edges
   680   ///  NewGraph::EdgeMap<OrigGraph::Edge> ecr(new_graph);
   681   ///  cg.edgeCrossRef(ecr);
   682   ///  // Copy an edge map
   683   ///  OrigGraph::EdgeMap<double> oemap(orig_graph);
   684   ///  NewGraph::EdgeMap<double> nemap(new_graph);
   685   ///  cg.edgeMap(oemap, nemap);
   686   ///  // Copy a node
   687   ///  OrigGraph::Node on;
   688   ///  NewGraph::Node nn;
   689   ///  cg.node(on, nn);
   690   ///  // Execute copying
   691   ///  cg.run();
   692   ///\endcode
   693   template <typename From, typename To>
   694   class GraphCopy {
   695   private:
   696 
   697     typedef typename From::Node Node;
   698     typedef typename From::NodeIt NodeIt;
   699     typedef typename From::Arc Arc;
   700     typedef typename From::ArcIt ArcIt;
   701     typedef typename From::Edge Edge;
   702     typedef typename From::EdgeIt EdgeIt;
   703 
   704     typedef typename To::Node TNode;
   705     typedef typename To::Arc TArc;
   706     typedef typename To::Edge TEdge;
   707 
   708     typedef typename From::template NodeMap<TNode> NodeRefMap;
   709     typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
   710 
   711     struct ArcRefMap {
   712       ArcRefMap(const From& from, const To& to,
   713                 const EdgeRefMap& edge_ref, const NodeRefMap& node_ref)
   714         : _from(from), _to(to),
   715           _edge_ref(edge_ref), _node_ref(node_ref) {}
   716 
   717       typedef typename From::Arc Key;
   718       typedef typename To::Arc Value;
   719 
   720       Value operator[](const Key& key) const {
   721         bool forward = _from.u(key) != _from.v(key) ?
   722           _node_ref[_from.source(key)] ==
   723           _to.source(_to.direct(_edge_ref[key], true)) :
   724           _from.direction(key);
   725         return _to.direct(_edge_ref[key], forward);
   726       }
   727 
   728       const From& _from;
   729       const To& _to;
   730       const EdgeRefMap& _edge_ref;
   731       const NodeRefMap& _node_ref;
   732     };
   733 
   734   public:
   735 
   736     /// \brief Constructor of GraphCopy.
   737     ///
   738     /// Constructor of GraphCopy for copying the content of the
   739     /// \c from graph into the \c to graph.
   740     GraphCopy(const From& from, To& to)
   741       : _from(from), _to(to) {}
   742 
   743     /// \brief Destructor of GraphCopy
   744     ///
   745     /// Destructor of GraphCopy.
   746     ~GraphCopy() {
   747       for (int i = 0; i < int(_node_maps.size()); ++i) {
   748         delete _node_maps[i];
   749       }
   750       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   751         delete _arc_maps[i];
   752       }
   753       for (int i = 0; i < int(_edge_maps.size()); ++i) {
   754         delete _edge_maps[i];
   755       }
   756     }
   757 
   758     /// \brief Copy the node references into the given map.
   759     ///
   760     /// This function copies the node references into the given map.
   761     /// The parameter should be a map, whose key type is the Node type of
   762     /// the source graph, while the value type is the Node type of the
   763     /// destination graph.
   764     template <typename NodeRef>
   765     GraphCopy& nodeRef(NodeRef& map) {
   766       _node_maps.push_back(new _core_bits::RefCopy<From, Node,
   767                            NodeRefMap, NodeRef>(map));
   768       return *this;
   769     }
   770 
   771     /// \brief Copy the node cross references into the given map.
   772     ///
   773     /// This function copies the node cross references (reverse references)
   774     /// into the given map. The parameter should be a map, whose key type
   775     /// is the Node type of the destination graph, while the value type is
   776     /// the Node type of the source graph.
   777     template <typename NodeCrossRef>
   778     GraphCopy& nodeCrossRef(NodeCrossRef& map) {
   779       _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
   780                            NodeRefMap, NodeCrossRef>(map));
   781       return *this;
   782     }
   783 
   784     /// \brief Make a copy of the given node map.
   785     ///
   786     /// This function makes a copy of the given node map for the newly
   787     /// created graph.
   788     /// The key type of the new map \c tmap should be the Node type of the
   789     /// destination graph, and the key type of the original map \c map
   790     /// should be the Node type of the source graph.
   791     template <typename FromMap, typename ToMap>
   792     GraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
   793       _node_maps.push_back(new _core_bits::MapCopy<From, Node,
   794                            NodeRefMap, FromMap, ToMap>(map, tmap));
   795       return *this;
   796     }
   797 
   798     /// \brief Make a copy of the given node.
   799     ///
   800     /// This function makes a copy of the given node.
   801     GraphCopy& node(const Node& node, TNode& tnode) {
   802       _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
   803                            NodeRefMap, TNode>(node, tnode));
   804       return *this;
   805     }
   806 
   807     /// \brief Copy the arc references into the given map.
   808     ///
   809     /// This function copies the arc references into the given map.
   810     /// The parameter should be a map, whose key type is the Arc type of
   811     /// the source graph, while the value type is the Arc type of the
   812     /// destination graph.
   813     template <typename ArcRef>
   814     GraphCopy& arcRef(ArcRef& map) {
   815       _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
   816                           ArcRefMap, ArcRef>(map));
   817       return *this;
   818     }
   819 
   820     /// \brief Copy the arc cross references into the given map.
   821     ///
   822     /// This function copies the arc cross references (reverse references)
   823     /// into the given map. The parameter should be a map, whose key type
   824     /// is the Arc type of the destination graph, while the value type is
   825     /// the Arc type of the source graph.
   826     template <typename ArcCrossRef>
   827     GraphCopy& arcCrossRef(ArcCrossRef& map) {
   828       _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
   829                           ArcRefMap, ArcCrossRef>(map));
   830       return *this;
   831     }
   832 
   833     /// \brief Make a copy of the given arc map.
   834     ///
   835     /// This function makes a copy of the given arc map for the newly
   836     /// created graph.
   837     /// The key type of the new map \c tmap should be the Arc type of the
   838     /// destination graph, and the key type of the original map \c map
   839     /// should be the Arc type of the source graph.
   840     template <typename FromMap, typename ToMap>
   841     GraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
   842       _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
   843                           ArcRefMap, FromMap, ToMap>(map, tmap));
   844       return *this;
   845     }
   846 
   847     /// \brief Make a copy of the given arc.
   848     ///
   849     /// This function makes a copy of the given arc.
   850     GraphCopy& arc(const Arc& arc, TArc& tarc) {
   851       _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
   852                           ArcRefMap, TArc>(arc, tarc));
   853       return *this;
   854     }
   855 
   856     /// \brief Copy the edge references into the given map.
   857     ///
   858     /// This function copies the edge references into the given map.
   859     /// The parameter should be a map, whose key type is the Edge type of
   860     /// the source graph, while the value type is the Edge type of the
   861     /// destination graph.
   862     template <typename EdgeRef>
   863     GraphCopy& edgeRef(EdgeRef& map) {
   864       _edge_maps.push_back(new _core_bits::RefCopy<From, Edge,
   865                            EdgeRefMap, EdgeRef>(map));
   866       return *this;
   867     }
   868 
   869     /// \brief Copy the edge cross references into the given map.
   870     ///
   871     /// This function copies the edge cross references (reverse references)
   872     /// into the given map. The parameter should be a map, whose key type
   873     /// is the Edge type of the destination graph, while the value type is
   874     /// the Edge type of the source graph.
   875     template <typename EdgeCrossRef>
   876     GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
   877       _edge_maps.push_back(new _core_bits::CrossRefCopy<From,
   878                            Edge, EdgeRefMap, EdgeCrossRef>(map));
   879       return *this;
   880     }
   881 
   882     /// \brief Make a copy of the given edge map.
   883     ///
   884     /// This function makes a copy of the given edge map for the newly
   885     /// created graph.
   886     /// The key type of the new map \c tmap should be the Edge type of the
   887     /// destination graph, and the key type of the original map \c map
   888     /// should be the Edge type of the source graph.
   889     template <typename FromMap, typename ToMap>
   890     GraphCopy& edgeMap(const FromMap& map, ToMap& tmap) {
   891       _edge_maps.push_back(new _core_bits::MapCopy<From, Edge,
   892                            EdgeRefMap, FromMap, ToMap>(map, tmap));
   893       return *this;
   894     }
   895 
   896     /// \brief Make a copy of the given edge.
   897     ///
   898     /// This function makes a copy of the given edge.
   899     GraphCopy& edge(const Edge& edge, TEdge& tedge) {
   900       _edge_maps.push_back(new _core_bits::ItemCopy<From, Edge,
   901                            EdgeRefMap, TEdge>(edge, tedge));
   902       return *this;
   903     }
   904 
   905     /// \brief Execute copying.
   906     ///
   907     /// This function executes the copying of the graph along with the
   908     /// copying of the assigned data.
   909     void run() {
   910       NodeRefMap nodeRefMap(_from);
   911       EdgeRefMap edgeRefMap(_from);
   912       ArcRefMap arcRefMap(_from, _to, edgeRefMap, nodeRefMap);
   913       _core_bits::GraphCopySelector<To>::
   914         copy(_from, _to, nodeRefMap, edgeRefMap);
   915       for (int i = 0; i < int(_node_maps.size()); ++i) {
   916         _node_maps[i]->copy(_from, nodeRefMap);
   917       }
   918       for (int i = 0; i < int(_edge_maps.size()); ++i) {
   919         _edge_maps[i]->copy(_from, edgeRefMap);
   920       }
   921       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   922         _arc_maps[i]->copy(_from, arcRefMap);
   923       }
   924     }
   925 
   926   private:
   927 
   928     const From& _from;
   929     To& _to;
   930 
   931     std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
   932       _node_maps;
   933 
   934     std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
   935       _arc_maps;
   936 
   937     std::vector<_core_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
   938       _edge_maps;
   939 
   940   };
   941 
   942   /// \brief Copy a graph to another graph.
   943   ///
   944   /// This function copies a graph to another graph.
   945   /// The complete usage of it is detailed in the GraphCopy class,
   946   /// but a short example shows a basic work:
   947   ///\code
   948   /// graphCopy(src, trg).nodeRef(nr).edgeCrossRef(ecr).run();
   949   ///\endcode
   950   ///
   951   /// After the copy the \c nr map will contain the mapping from the
   952   /// nodes of the \c from graph to the nodes of the \c to graph and
   953   /// \c ecr will contain the mapping from the edges of the \c to graph
   954   /// to the edges of the \c from graph.
   955   ///
   956   /// \see GraphCopy
   957   template <typename From, typename To>
   958   GraphCopy<From, To>
   959   graphCopy(const From& from, To& to) {
   960     return GraphCopy<From, To>(from, to);
   961   }
   962 
   963   namespace _core_bits {
   964 
   965     template <typename Graph, typename Enable = void>
   966     struct FindArcSelector {
   967       typedef typename Graph::Node Node;
   968       typedef typename Graph::Arc Arc;
   969       static Arc find(const Graph &g, Node u, Node v, Arc e) {
   970         if (e == INVALID) {
   971           g.firstOut(e, u);
   972         } else {
   973           g.nextOut(e);
   974         }
   975         while (e != INVALID && g.target(e) != v) {
   976           g.nextOut(e);
   977         }
   978         return e;
   979       }
   980     };
   981 
   982     template <typename Graph>
   983     struct FindArcSelector<
   984       Graph,
   985       typename enable_if<typename Graph::FindArcTag, void>::type>
   986     {
   987       typedef typename Graph::Node Node;
   988       typedef typename Graph::Arc Arc;
   989       static Arc find(const Graph &g, Node u, Node v, Arc prev) {
   990         return g.findArc(u, v, prev);
   991       }
   992     };
   993   }
   994 
   995   /// \brief Find an arc between two nodes of a digraph.
   996   ///
   997   /// This function finds an arc from node \c u to node \c v in the
   998   /// digraph \c g.
   999   ///
  1000   /// If \c prev is \ref INVALID (this is the default value), then
  1001   /// it finds the first arc from \c u to \c v. Otherwise it looks for
  1002   /// the next arc from \c u to \c v after \c prev.
  1003   /// \return The found arc or \ref INVALID if there is no such an arc.
  1004   ///
  1005   /// Thus you can iterate through each arc from \c u to \c v as it follows.
  1006   ///\code
  1007   /// for(Arc e = findArc(g,u,v); e != INVALID; e = findArc(g,u,v,e)) {
  1008   ///   ...
  1009   /// }
  1010   ///\endcode
  1011   ///
  1012   /// \note \ref ConArcIt provides iterator interface for the same
  1013   /// functionality.
  1014   ///
  1015   ///\sa ConArcIt
  1016   ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
  1017   template <typename Graph>
  1018   inline typename Graph::Arc
  1019   findArc(const Graph &g, typename Graph::Node u, typename Graph::Node v,
  1020           typename Graph::Arc prev = INVALID) {
  1021     return _core_bits::FindArcSelector<Graph>::find(g, u, v, prev);
  1022   }
  1023 
  1024   /// \brief Iterator for iterating on parallel arcs connecting the same nodes.
  1025   ///
  1026   /// Iterator for iterating on parallel arcs connecting the same nodes. It is
  1027   /// a higher level interface for the \ref findArc() function. You can
  1028   /// use it the following way:
  1029   ///\code
  1030   /// for (ConArcIt<Graph> it(g, src, trg); it != INVALID; ++it) {
  1031   ///   ...
  1032   /// }
  1033   ///\endcode
  1034   ///
  1035   ///\sa findArc()
  1036   ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
  1037   template <typename GR>
  1038   class ConArcIt : public GR::Arc {
  1039     typedef typename GR::Arc Parent;
  1040 
  1041   public:
  1042 
  1043     typedef typename GR::Arc Arc;
  1044     typedef typename GR::Node Node;
  1045 
  1046     /// \brief Constructor.
  1047     ///
  1048     /// Construct a new ConArcIt iterating on the arcs that
  1049     /// connects nodes \c u and \c v.
  1050     ConArcIt(const GR& g, Node u, Node v) : _graph(g) {
  1051       Parent::operator=(findArc(_graph, u, v));
  1052     }
  1053 
  1054     /// \brief Constructor.
  1055     ///
  1056     /// Construct a new ConArcIt that continues the iterating from arc \c a.
  1057     ConArcIt(const GR& g, Arc a) : Parent(a), _graph(g) {}
  1058 
  1059     /// \brief Increment operator.
  1060     ///
  1061     /// It increments the iterator and gives back the next arc.
  1062     ConArcIt& operator++() {
  1063       Parent::operator=(findArc(_graph, _graph.source(*this),
  1064                                 _graph.target(*this), *this));
  1065       return *this;
  1066     }
  1067   private:
  1068     const GR& _graph;
  1069   };
  1070 
  1071   namespace _core_bits {
  1072 
  1073     template <typename Graph, typename Enable = void>
  1074     struct FindEdgeSelector {
  1075       typedef typename Graph::Node Node;
  1076       typedef typename Graph::Edge Edge;
  1077       static Edge find(const Graph &g, Node u, Node v, Edge e) {
  1078         bool b;
  1079         if (u != v) {
  1080           if (e == INVALID) {
  1081             g.firstInc(e, b, u);
  1082           } else {
  1083             b = g.u(e) == u;
  1084             g.nextInc(e, b);
  1085           }
  1086           while (e != INVALID && (b ? g.v(e) : g.u(e)) != v) {
  1087             g.nextInc(e, b);
  1088           }
  1089         } else {
  1090           if (e == INVALID) {
  1091             g.firstInc(e, b, u);
  1092           } else {
  1093             b = true;
  1094             g.nextInc(e, b);
  1095           }
  1096           while (e != INVALID && (!b || g.v(e) != v)) {
  1097             g.nextInc(e, b);
  1098           }
  1099         }
  1100         return e;
  1101       }
  1102     };
  1103 
  1104     template <typename Graph>
  1105     struct FindEdgeSelector<
  1106       Graph,
  1107       typename enable_if<typename Graph::FindEdgeTag, void>::type>
  1108     {
  1109       typedef typename Graph::Node Node;
  1110       typedef typename Graph::Edge Edge;
  1111       static Edge find(const Graph &g, Node u, Node v, Edge prev) {
  1112         return g.findEdge(u, v, prev);
  1113       }
  1114     };
  1115   }
  1116 
  1117   /// \brief Find an edge between two nodes of a graph.
  1118   ///
  1119   /// This function finds an edge from node \c u to node \c v in graph \c g.
  1120   /// If node \c u and node \c v is equal then each loop edge
  1121   /// will be enumerated once.
  1122   ///
  1123   /// If \c prev is \ref INVALID (this is the default value), then
  1124   /// it finds the first edge from \c u to \c v. Otherwise it looks for
  1125   /// the next edge from \c u to \c v after \c prev.
  1126   /// \return The found edge or \ref INVALID if there is no such an edge.
  1127   ///
  1128   /// Thus you can iterate through each edge between \c u and \c v
  1129   /// as it follows.
  1130   ///\code
  1131   /// for(Edge e = findEdge(g,u,v); e != INVALID; e = findEdge(g,u,v,e)) {
  1132   ///   ...
  1133   /// }
  1134   ///\endcode
  1135   ///
  1136   /// \note \ref ConEdgeIt provides iterator interface for the same
  1137   /// functionality.
  1138   ///
  1139   ///\sa ConEdgeIt
  1140   template <typename Graph>
  1141   inline typename Graph::Edge
  1142   findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,
  1143             typename Graph::Edge p = INVALID) {
  1144     return _core_bits::FindEdgeSelector<Graph>::find(g, u, v, p);
  1145   }
  1146 
  1147   /// \brief Iterator for iterating on parallel edges connecting the same nodes.
  1148   ///
  1149   /// Iterator for iterating on parallel edges connecting the same nodes.
  1150   /// It is a higher level interface for the findEdge() function. You can
  1151   /// use it the following way:
  1152   ///\code
  1153   /// for (ConEdgeIt<Graph> it(g, u, v); it != INVALID; ++it) {
  1154   ///   ...
  1155   /// }
  1156   ///\endcode
  1157   ///
  1158   ///\sa findEdge()
  1159   template <typename GR>
  1160   class ConEdgeIt : public GR::Edge {
  1161     typedef typename GR::Edge Parent;
  1162 
  1163   public:
  1164 
  1165     typedef typename GR::Edge Edge;
  1166     typedef typename GR::Node Node;
  1167 
  1168     /// \brief Constructor.
  1169     ///
  1170     /// Construct a new ConEdgeIt iterating on the edges that
  1171     /// connects nodes \c u and \c v.
  1172     ConEdgeIt(const GR& g, Node u, Node v) : _graph(g), _u(u), _v(v) {
  1173       Parent::operator=(findEdge(_graph, _u, _v));
  1174     }
  1175 
  1176     /// \brief Constructor.
  1177     ///
  1178     /// Construct a new ConEdgeIt that continues iterating from edge \c e.
  1179     ConEdgeIt(const GR& g, Edge e) : Parent(e), _graph(g) {}
  1180 
  1181     /// \brief Increment operator.
  1182     ///
  1183     /// It increments the iterator and gives back the next edge.
  1184     ConEdgeIt& operator++() {
  1185       Parent::operator=(findEdge(_graph, _u, _v, *this));
  1186       return *this;
  1187     }
  1188   private:
  1189     const GR& _graph;
  1190     Node _u, _v;
  1191   };
  1192 
  1193 
  1194   ///Dynamic arc look-up between given endpoints.
  1195 
  1196   ///Using this class, you can find an arc in a digraph from a given
  1197   ///source to a given target in amortized time <em>O</em>(log<em>d</em>),
  1198   ///where <em>d</em> is the out-degree of the source node.
  1199   ///
  1200   ///It is possible to find \e all parallel arcs between two nodes with
  1201   ///the \c operator() member.
  1202   ///
  1203   ///This is a dynamic data structure. Consider to use \ref ArcLookUp or
  1204   ///\ref AllArcLookUp if your digraph is not changed so frequently.
  1205   ///
  1206   ///This class uses a self-adjusting binary search tree, the Splay tree
  1207   ///of Sleator and Tarjan to guarantee the logarithmic amortized
  1208   ///time bound for arc look-ups. This class also guarantees the
  1209   ///optimal time bound in a constant factor for any distribution of
  1210   ///queries.
  1211   ///
  1212   ///\tparam GR The type of the underlying digraph.
  1213   ///
  1214   ///\sa ArcLookUp
  1215   ///\sa AllArcLookUp
  1216   template <typename GR>
  1217   class DynArcLookUp
  1218     : protected ItemSetTraits<GR, typename GR::Arc>::ItemNotifier::ObserverBase
  1219   {
  1220     typedef typename ItemSetTraits<GR, typename GR::Arc>
  1221     ::ItemNotifier::ObserverBase Parent;
  1222 
  1223     TEMPLATE_DIGRAPH_TYPEDEFS(GR);
  1224 
  1225   public:
  1226 
  1227     /// The Digraph type
  1228     typedef GR Digraph;
  1229 
  1230   protected:
  1231 
  1232     class AutoNodeMap : public ItemSetTraits<GR, Node>::template Map<Arc>::Type {
  1233       typedef typename ItemSetTraits<GR, Node>::template Map<Arc>::Type Parent;
  1234 
  1235     public:
  1236 
  1237       AutoNodeMap(const GR& digraph) : Parent(digraph, INVALID) {}
  1238 
  1239       virtual void add(const Node& node) {
  1240         Parent::add(node);
  1241         Parent::set(node, INVALID);
  1242       }
  1243 
  1244       virtual void add(const std::vector<Node>& nodes) {
  1245         Parent::add(nodes);
  1246         for (int i = 0; i < int(nodes.size()); ++i) {
  1247           Parent::set(nodes[i], INVALID);
  1248         }
  1249       }
  1250 
  1251       virtual void build() {
  1252         Parent::build();
  1253         Node it;
  1254         typename Parent::Notifier* nf = Parent::notifier();
  1255         for (nf->first(it); it != INVALID; nf->next(it)) {
  1256           Parent::set(it, INVALID);
  1257         }
  1258       }
  1259     };
  1260 
  1261     class ArcLess {
  1262       const Digraph &g;
  1263     public:
  1264       ArcLess(const Digraph &_g) : g(_g) {}
  1265       bool operator()(Arc a,Arc b) const
  1266       {
  1267         return g.target(a)<g.target(b);
  1268       }
  1269     };
  1270 
  1271   protected: 
  1272 
  1273     const Digraph &_g;
  1274     AutoNodeMap _head;
  1275     typename Digraph::template ArcMap<Arc> _parent;
  1276     typename Digraph::template ArcMap<Arc> _left;
  1277     typename Digraph::template ArcMap<Arc> _right;
  1278 
  1279   public:
  1280 
  1281     ///Constructor
  1282 
  1283     ///Constructor.
  1284     ///
  1285     ///It builds up the search database.
  1286     DynArcLookUp(const Digraph &g)
  1287       : _g(g),_head(g),_parent(g),_left(g),_right(g)
  1288     {
  1289       Parent::attach(_g.notifier(typename Digraph::Arc()));
  1290       refresh();
  1291     }
  1292 
  1293   protected:
  1294 
  1295     virtual void add(const Arc& arc) {
  1296       insert(arc);
  1297     }
  1298 
  1299     virtual void add(const std::vector<Arc>& arcs) {
  1300       for (int i = 0; i < int(arcs.size()); ++i) {
  1301         insert(arcs[i]);
  1302       }
  1303     }
  1304 
  1305     virtual void erase(const Arc& arc) {
  1306       remove(arc);
  1307     }
  1308 
  1309     virtual void erase(const std::vector<Arc>& arcs) {
  1310       for (int i = 0; i < int(arcs.size()); ++i) {
  1311         remove(arcs[i]);
  1312       }
  1313     }
  1314 
  1315     virtual void build() {
  1316       refresh();
  1317     }
  1318 
  1319     virtual void clear() {
  1320       for(NodeIt n(_g);n!=INVALID;++n) {
  1321         _head[n] = INVALID;
  1322       }
  1323     }
  1324 
  1325     void insert(Arc arc) {
  1326       Node s = _g.source(arc);
  1327       Node t = _g.target(arc);
  1328       _left[arc] = INVALID;
  1329       _right[arc] = INVALID;
  1330 
  1331       Arc e = _head[s];
  1332       if (e == INVALID) {
  1333         _head[s] = arc;
  1334         _parent[arc] = INVALID;
  1335         return;
  1336       }
  1337       while (true) {
  1338         if (t < _g.target(e)) {
  1339           if (_left[e] == INVALID) {
  1340             _left[e] = arc;
  1341             _parent[arc] = e;
  1342             splay(arc);
  1343             return;
  1344           } else {
  1345             e = _left[e];
  1346           }
  1347         } else {
  1348           if (_right[e] == INVALID) {
  1349             _right[e] = arc;
  1350             _parent[arc] = e;
  1351             splay(arc);
  1352             return;
  1353           } else {
  1354             e = _right[e];
  1355           }
  1356         }
  1357       }
  1358     }
  1359 
  1360     void remove(Arc arc) {
  1361       if (_left[arc] == INVALID) {
  1362         if (_right[arc] != INVALID) {
  1363           _parent[_right[arc]] = _parent[arc];
  1364         }
  1365         if (_parent[arc] != INVALID) {
  1366           if (_left[_parent[arc]] == arc) {
  1367             _left[_parent[arc]] = _right[arc];
  1368           } else {
  1369             _right[_parent[arc]] = _right[arc];
  1370           }
  1371         } else {
  1372           _head[_g.source(arc)] = _right[arc];
  1373         }
  1374       } else if (_right[arc] == INVALID) {
  1375         _parent[_left[arc]] = _parent[arc];
  1376         if (_parent[arc] != INVALID) {
  1377           if (_left[_parent[arc]] == arc) {
  1378             _left[_parent[arc]] = _left[arc];
  1379           } else {
  1380             _right[_parent[arc]] = _left[arc];
  1381           }
  1382         } else {
  1383           _head[_g.source(arc)] = _left[arc];
  1384         }
  1385       } else {
  1386         Arc e = _left[arc];
  1387         if (_right[e] != INVALID) {
  1388           e = _right[e];
  1389           while (_right[e] != INVALID) {
  1390             e = _right[e];
  1391           }
  1392           Arc s = _parent[e];
  1393           _right[_parent[e]] = _left[e];
  1394           if (_left[e] != INVALID) {
  1395             _parent[_left[e]] = _parent[e];
  1396           }
  1397 
  1398           _left[e] = _left[arc];
  1399           _parent[_left[arc]] = e;
  1400           _right[e] = _right[arc];
  1401           _parent[_right[arc]] = e;
  1402 
  1403           _parent[e] = _parent[arc];
  1404           if (_parent[arc] != INVALID) {
  1405             if (_left[_parent[arc]] == arc) {
  1406               _left[_parent[arc]] = e;
  1407             } else {
  1408               _right[_parent[arc]] = e;
  1409             }
  1410           }
  1411           splay(s);
  1412         } else {
  1413           _right[e] = _right[arc];
  1414           _parent[_right[arc]] = e;
  1415           _parent[e] = _parent[arc];
  1416 
  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           } else {
  1424             _head[_g.source(arc)] = e;
  1425           }
  1426         }
  1427       }
  1428     }
  1429 
  1430     Arc refreshRec(std::vector<Arc> &v,int a,int b)
  1431     {
  1432       int m=(a+b)/2;
  1433       Arc me=v[m];
  1434       if (a < m) {
  1435         Arc left = refreshRec(v,a,m-1);
  1436         _left[me] = left;
  1437         _parent[left] = me;
  1438       } else {
  1439         _left[me] = INVALID;
  1440       }
  1441       if (m < b) {
  1442         Arc right = refreshRec(v,m+1,b);
  1443         _right[me] = right;
  1444         _parent[right] = me;
  1445       } else {
  1446         _right[me] = INVALID;
  1447       }
  1448       return me;
  1449     }
  1450 
  1451     void refresh() {
  1452       for(NodeIt n(_g);n!=INVALID;++n) {
  1453         std::vector<Arc> v;
  1454         for(OutArcIt a(_g,n);a!=INVALID;++a) v.push_back(a);
  1455         if (!v.empty()) {
  1456           std::sort(v.begin(),v.end(),ArcLess(_g));
  1457           Arc head = refreshRec(v,0,v.size()-1);
  1458           _head[n] = head;
  1459           _parent[head] = INVALID;
  1460         }
  1461         else _head[n] = INVALID;
  1462       }
  1463     }
  1464 
  1465     void zig(Arc v) {
  1466       Arc w = _parent[v];
  1467       _parent[v] = _parent[w];
  1468       _parent[w] = v;
  1469       _left[w] = _right[v];
  1470       _right[v] = w;
  1471       if (_parent[v] != INVALID) {
  1472         if (_right[_parent[v]] == w) {
  1473           _right[_parent[v]] = v;
  1474         } else {
  1475           _left[_parent[v]] = v;
  1476         }
  1477       }
  1478       if (_left[w] != INVALID){
  1479         _parent[_left[w]] = w;
  1480       }
  1481     }
  1482 
  1483     void zag(Arc v) {
  1484       Arc w = _parent[v];
  1485       _parent[v] = _parent[w];
  1486       _parent[w] = v;
  1487       _right[w] = _left[v];
  1488       _left[v] = w;
  1489       if (_parent[v] != INVALID){
  1490         if (_left[_parent[v]] == w) {
  1491           _left[_parent[v]] = v;
  1492         } else {
  1493           _right[_parent[v]] = v;
  1494         }
  1495       }
  1496       if (_right[w] != INVALID){
  1497         _parent[_right[w]] = w;
  1498       }
  1499     }
  1500 
  1501     void splay(Arc v) {
  1502       while (_parent[v] != INVALID) {
  1503         if (v == _left[_parent[v]]) {
  1504           if (_parent[_parent[v]] == INVALID) {
  1505             zig(v);
  1506           } else {
  1507             if (_parent[v] == _left[_parent[_parent[v]]]) {
  1508               zig(_parent[v]);
  1509               zig(v);
  1510             } else {
  1511               zig(v);
  1512               zag(v);
  1513             }
  1514           }
  1515         } else {
  1516           if (_parent[_parent[v]] == INVALID) {
  1517             zag(v);
  1518           } else {
  1519             if (_parent[v] == _left[_parent[_parent[v]]]) {
  1520               zag(v);
  1521               zig(v);
  1522             } else {
  1523               zag(_parent[v]);
  1524               zag(v);
  1525             }
  1526           }
  1527         }
  1528       }
  1529       _head[_g.source(v)] = v;
  1530     }
  1531 
  1532 
  1533   public:
  1534 
  1535     ///Find an arc between two nodes.
  1536 
  1537     ///Find an arc between two nodes.
  1538     ///\param s The source node.
  1539     ///\param t The target node.
  1540     ///\param p The previous arc between \c s and \c t. It it is INVALID or
  1541     ///not given, the operator finds the first appropriate arc.
  1542     ///\return An arc from \c s to \c t after \c p or
  1543     ///\ref INVALID if there is no more.
  1544     ///
  1545     ///For example, you can count the number of arcs from \c u to \c v in the
  1546     ///following way.
  1547     ///\code
  1548     ///DynArcLookUp<ListDigraph> ae(g);
  1549     ///...
  1550     ///int n = 0;
  1551     ///for(Arc a = ae(u,v); a != INVALID; a = ae(u,v,a)) n++;
  1552     ///\endcode
  1553     ///
  1554     ///Finding the arcs take at most <em>O</em>(log<em>d</em>)
  1555     ///amortized time, specifically, the time complexity of the lookups
  1556     ///is equal to the optimal search tree implementation for the
  1557     ///current query distribution in a constant factor.
  1558     ///
  1559     ///\note This is a dynamic data structure, therefore the data
  1560     ///structure is updated after each graph alteration. Thus although
  1561     ///this data structure is theoretically faster than \ref ArcLookUp
  1562     ///and \ref AllArcLookUp, it often provides worse performance than
  1563     ///them.
  1564     Arc operator()(Node s, Node t, Arc p = INVALID) const  {
  1565       if (p == INVALID) {
  1566         Arc a = _head[s];
  1567         if (a == INVALID) return INVALID;
  1568         Arc r = INVALID;
  1569         while (true) {
  1570           if (_g.target(a) < t) {
  1571             if (_right[a] == INVALID) {
  1572               const_cast<DynArcLookUp&>(*this).splay(a);
  1573               return r;
  1574             } else {
  1575               a = _right[a];
  1576             }
  1577           } else {
  1578             if (_g.target(a) == t) {
  1579               r = a;
  1580             }
  1581             if (_left[a] == INVALID) {
  1582               const_cast<DynArcLookUp&>(*this).splay(a);
  1583               return r;
  1584             } else {
  1585               a = _left[a];
  1586             }
  1587           }
  1588         }
  1589       } else {
  1590         Arc a = p;
  1591         if (_right[a] != INVALID) {
  1592           a = _right[a];
  1593           while (_left[a] != INVALID) {
  1594             a = _left[a];
  1595           }
  1596           const_cast<DynArcLookUp&>(*this).splay(a);
  1597         } else {
  1598           while (_parent[a] != INVALID && _right[_parent[a]] ==  a) {
  1599             a = _parent[a];
  1600           }
  1601           if (_parent[a] == INVALID) {
  1602             return INVALID;
  1603           } else {
  1604             a = _parent[a];
  1605             const_cast<DynArcLookUp&>(*this).splay(a);
  1606           }
  1607         }
  1608         if (_g.target(a) == t) return a;
  1609         else return INVALID;
  1610       }
  1611     }
  1612 
  1613   };
  1614 
  1615   ///Fast arc look-up between given endpoints.
  1616 
  1617   ///Using this class, you can find an arc in a digraph from a given
  1618   ///source to a given target in time <em>O</em>(log<em>d</em>),
  1619   ///where <em>d</em> is the out-degree of the source node.
  1620   ///
  1621   ///It is not possible to find \e all parallel arcs between two nodes.
  1622   ///Use \ref AllArcLookUp for this purpose.
  1623   ///
  1624   ///\warning This class is static, so you should call refresh() (or at
  1625   ///least refresh(Node)) to refresh this data structure whenever the
  1626   ///digraph changes. This is a time consuming (superlinearly proportional
  1627   ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
  1628   ///
  1629   ///\tparam GR The type of the underlying digraph.
  1630   ///
  1631   ///\sa DynArcLookUp
  1632   ///\sa AllArcLookUp
  1633   template<class GR>
  1634   class ArcLookUp
  1635   {
  1636     TEMPLATE_DIGRAPH_TYPEDEFS(GR);
  1637 
  1638   public:
  1639 
  1640     /// The Digraph type
  1641     typedef GR Digraph;
  1642 
  1643   protected:
  1644     const Digraph &_g;
  1645     typename Digraph::template NodeMap<Arc> _head;
  1646     typename Digraph::template ArcMap<Arc> _left;
  1647     typename Digraph::template ArcMap<Arc> _right;
  1648 
  1649     class ArcLess {
  1650       const Digraph &g;
  1651     public:
  1652       ArcLess(const Digraph &_g) : g(_g) {}
  1653       bool operator()(Arc a,Arc b) const
  1654       {
  1655         return g.target(a)<g.target(b);
  1656       }
  1657     };
  1658 
  1659   public:
  1660 
  1661     ///Constructor
  1662 
  1663     ///Constructor.
  1664     ///
  1665     ///It builds up the search database, which remains valid until the digraph
  1666     ///changes.
  1667     ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}
  1668 
  1669   private:
  1670     Arc refreshRec(std::vector<Arc> &v,int a,int b)
  1671     {
  1672       int m=(a+b)/2;
  1673       Arc me=v[m];
  1674       _left[me] = a<m?refreshRec(v,a,m-1):INVALID;
  1675       _right[me] = m<b?refreshRec(v,m+1,b):INVALID;
  1676       return me;
  1677     }
  1678   public:
  1679     ///Refresh the search data structure at a node.
  1680 
  1681     ///Build up the search database of node \c n.
  1682     ///
  1683     ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em>
  1684     ///is the number of the outgoing arcs of \c n.
  1685     void refresh(Node n)
  1686     {
  1687       std::vector<Arc> v;
  1688       for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
  1689       if(v.size()) {
  1690         std::sort(v.begin(),v.end(),ArcLess(_g));
  1691         _head[n]=refreshRec(v,0,v.size()-1);
  1692       }
  1693       else _head[n]=INVALID;
  1694     }
  1695     ///Refresh the full data structure.
  1696 
  1697     ///Build up the full search database. In fact, it simply calls
  1698     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  1699     ///
  1700     ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
  1701     ///the number of the arcs in the digraph and <em>D</em> is the maximum
  1702     ///out-degree of the digraph.
  1703     void refresh()
  1704     {
  1705       for(NodeIt n(_g);n!=INVALID;++n) refresh(n);
  1706     }
  1707 
  1708     ///Find an arc between two nodes.
  1709 
  1710     ///Find an arc between two nodes in time <em>O</em>(log<em>d</em>),
  1711     ///where <em>d</em> is the number of outgoing arcs of \c s.
  1712     ///\param s The source node.
  1713     ///\param t The target node.
  1714     ///\return An arc from \c s to \c t if there exists,
  1715     ///\ref INVALID otherwise.
  1716     ///
  1717     ///\warning If you change the digraph, refresh() must be called before using
  1718     ///this operator. If you change the outgoing arcs of
  1719     ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
  1720     Arc operator()(Node s, Node t) const
  1721     {
  1722       Arc e;
  1723       for(e=_head[s];
  1724           e!=INVALID&&_g.target(e)!=t;
  1725           e = t < _g.target(e)?_left[e]:_right[e]) ;
  1726       return e;
  1727     }
  1728 
  1729   };
  1730 
  1731   ///Fast look-up of all arcs between given endpoints.
  1732 
  1733   ///This class is the same as \ref ArcLookUp, with the addition
  1734   ///that it makes it possible to find all parallel arcs between given
  1735   ///endpoints.
  1736   ///
  1737   ///\warning This class is static, so you should call refresh() (or at
  1738   ///least refresh(Node)) to refresh this data structure whenever the
  1739   ///digraph changes. This is a time consuming (superlinearly proportional
  1740   ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
  1741   ///
  1742   ///\tparam GR The type of the underlying digraph.
  1743   ///
  1744   ///\sa DynArcLookUp
  1745   ///\sa ArcLookUp
  1746   template<class GR>
  1747   class AllArcLookUp : public ArcLookUp<GR>
  1748   {
  1749     using ArcLookUp<GR>::_g;
  1750     using ArcLookUp<GR>::_right;
  1751     using ArcLookUp<GR>::_left;
  1752     using ArcLookUp<GR>::_head;
  1753 
  1754     TEMPLATE_DIGRAPH_TYPEDEFS(GR);
  1755 
  1756     typename GR::template ArcMap<Arc> _next;
  1757 
  1758     Arc refreshNext(Arc head,Arc next=INVALID)
  1759     {
  1760       if(head==INVALID) return next;
  1761       else {
  1762         next=refreshNext(_right[head],next);
  1763         _next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
  1764           ? next : INVALID;
  1765         return refreshNext(_left[head],head);
  1766       }
  1767     }
  1768 
  1769     void refreshNext()
  1770     {
  1771       for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
  1772     }
  1773 
  1774   public:
  1775 
  1776     /// The Digraph type
  1777     typedef GR Digraph;
  1778 
  1779     ///Constructor
  1780 
  1781     ///Constructor.
  1782     ///
  1783     ///It builds up the search database, which remains valid until the digraph
  1784     ///changes.
  1785     AllArcLookUp(const Digraph &g) : ArcLookUp<GR>(g), _next(g) {refreshNext();}
  1786 
  1787     ///Refresh the data structure at a node.
  1788 
  1789     ///Build up the search database of node \c n.
  1790     ///
  1791     ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em> is
  1792     ///the number of the outgoing arcs of \c n.
  1793     void refresh(Node n)
  1794     {
  1795       ArcLookUp<GR>::refresh(n);
  1796       refreshNext(_head[n]);
  1797     }
  1798 
  1799     ///Refresh the full data structure.
  1800 
  1801     ///Build up the full search database. In fact, it simply calls
  1802     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  1803     ///
  1804     ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
  1805     ///the number of the arcs in the digraph and <em>D</em> is the maximum
  1806     ///out-degree of the digraph.
  1807     void refresh()
  1808     {
  1809       for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
  1810     }
  1811 
  1812     ///Find an arc between two nodes.
  1813 
  1814     ///Find an arc between two nodes.
  1815     ///\param s The source node.
  1816     ///\param t The target node.
  1817     ///\param prev The previous arc between \c s and \c t. It it is INVALID or
  1818     ///not given, the operator finds the first appropriate arc.
  1819     ///\return An arc from \c s to \c t after \c prev or
  1820     ///\ref INVALID if there is no more.
  1821     ///
  1822     ///For example, you can count the number of arcs from \c u to \c v in the
  1823     ///following way.
  1824     ///\code
  1825     ///AllArcLookUp<ListDigraph> ae(g);
  1826     ///...
  1827     ///int n = 0;
  1828     ///for(Arc a = ae(u,v); a != INVALID; a=ae(u,v,a)) n++;
  1829     ///\endcode
  1830     ///
  1831     ///Finding the first arc take <em>O</em>(log<em>d</em>) time,
  1832     ///where <em>d</em> is the number of outgoing arcs of \c s. Then the
  1833     ///consecutive arcs are found in constant time.
  1834     ///
  1835     ///\warning If you change the digraph, refresh() must be called before using
  1836     ///this operator. If you change the outgoing arcs of
  1837     ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
  1838     ///
  1839 #ifdef DOXYGEN
  1840     Arc operator()(Node s, Node t, Arc prev=INVALID) const {}
  1841 #else
  1842     using ArcLookUp<GR>::operator() ;
  1843     Arc operator()(Node s, Node t, Arc prev) const
  1844     {
  1845       return prev==INVALID?(*this)(s,t):_next[prev];
  1846     }
  1847 #endif
  1848 
  1849   };
  1850 
  1851   /// @}
  1852 
  1853 } //namespace lemon
  1854 
  1855 #endif