lemon/core.h
author Alpar Juttner <alpar@cs.elte.hu>
Wed, 29 Jul 2020 14:56:10 +0200
changeset 1211 a278d16bd2d0
parent 1135 c199e9976d93
permissions -rw-r--r--
Fix clang compilation issue (#634)
     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) 2003-2013
     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 ///\file
    23 ///\brief LEMON core utilities.
    24 ///
    25 ///This header file contains core utilities for LEMON.
    26 ///It is automatically included by all graph types, therefore it usually
    27 ///do not have to be included directly.
    28 
    29 // Disable the following warnings when compiling with MSVC:
    30 // C4250: 'class1' : inherits 'class2::member' via dominance
    31 // C4267: conversion from 'size_t' to 'type', possible loss of data
    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 
    37 #include <lemon/config.h>
    38 
    39 #ifdef _MSC_VER
    40 #pragma warning( disable : 4250 4267 4355 4503 4800 4996 )
    41 #endif
    42 
    43 #if LEMON_NO_UNUSED_LOCAL_TYPEDEF_WARNINGS
    44 // Needed by the [DI]GRAPH_TYPEDEFS marcos for gcc >=4.8 and clang
    45 #pragma GCC diagnostic ignored "-Wunused-local-typedefs"
    46 #endif
    47 
    48 #include <vector>
    49 #include <algorithm>
    50 
    51 #include <lemon/bits/enable_if.h>
    52 #include <lemon/bits/traits.h>
    53 #include <lemon/assert.h>
    54 
    55 
    56 
    57 namespace lemon {
    58 
    59   /// \brief Dummy type to make it easier to create invalid iterators.
    60   ///
    61   /// Dummy type to make it easier to create invalid iterators.
    62   /// See \ref INVALID for the usage.
    63   struct Invalid {
    64   public:
    65     bool operator==(Invalid) { return true;  }
    66     bool operator!=(Invalid) { return false; }
    67     bool operator< (Invalid) { return false; }
    68   };
    69 
    70   /// \brief Invalid iterators.
    71   ///
    72   /// \ref Invalid is a global type that converts to each iterator
    73   /// in such a way that the value of the target iterator will be invalid.
    74 #ifdef LEMON_ONLY_TEMPLATES
    75   const Invalid INVALID = Invalid();
    76 #else
    77   extern const Invalid INVALID;
    78 #endif
    79 
    80   /// \addtogroup gutils
    81   /// @{
    82 
    83   ///Create convenience typedefs for the digraph types and iterators
    84 
    85   ///This \c \#define creates convenient type definitions for the following
    86   ///types of \c Digraph: \c Node,  \c NodeIt, \c Arc, \c ArcIt, \c InArcIt,
    87   ///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap,
    88   ///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap.
    89   ///
    90   ///\note If the graph type is a dependent type, ie. the graph type depend
    91   ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
    92   ///macro.
    93 #define DIGRAPH_TYPEDEFS(Digraph)                                       \
    94   typedef Digraph::Node Node;                                           \
    95   typedef Digraph::NodeIt NodeIt;                                       \
    96   typedef Digraph::Arc Arc;                                             \
    97   typedef Digraph::ArcIt ArcIt;                                         \
    98   typedef Digraph::InArcIt InArcIt;                                     \
    99   typedef Digraph::OutArcIt OutArcIt;                                   \
   100   typedef Digraph::NodeMap<bool> BoolNodeMap;                           \
   101   typedef Digraph::NodeMap<int> IntNodeMap;                             \
   102   typedef Digraph::NodeMap<double> DoubleNodeMap;                       \
   103   typedef Digraph::ArcMap<bool> BoolArcMap;                             \
   104   typedef Digraph::ArcMap<int> IntArcMap;                               \
   105   typedef Digraph::ArcMap<double> DoubleArcMap
   106 
   107   ///Create convenience typedefs for the digraph types and iterators
   108 
   109   ///\see DIGRAPH_TYPEDEFS
   110   ///
   111   ///\note Use this macro, if the graph type is a dependent type,
   112   ///ie. the graph type depend on a template parameter.
   113 #define TEMPLATE_DIGRAPH_TYPEDEFS(Digraph)                              \
   114   typedef typename Digraph::Node Node;                                  \
   115   typedef typename Digraph::NodeIt NodeIt;                              \
   116   typedef typename Digraph::Arc Arc;                                    \
   117   typedef typename Digraph::ArcIt ArcIt;                                \
   118   typedef typename Digraph::InArcIt InArcIt;                            \
   119   typedef typename Digraph::OutArcIt OutArcIt;                          \
   120   typedef typename Digraph::template NodeMap<bool> BoolNodeMap;         \
   121   typedef typename Digraph::template NodeMap<int> IntNodeMap;           \
   122   typedef typename Digraph::template NodeMap<double> DoubleNodeMap;     \
   123   typedef typename Digraph::template ArcMap<bool> BoolArcMap;           \
   124   typedef typename Digraph::template ArcMap<int> IntArcMap;             \
   125   typedef typename Digraph::template ArcMap<double> DoubleArcMap
   126 
   127   ///Create convenience typedefs for the graph types and iterators
   128 
   129   ///This \c \#define creates the same convenient type definitions as defined
   130   ///by \ref DIGRAPH_TYPEDEFS(Graph) and six more, namely it creates
   131   ///\c Edge, \c EdgeIt, \c IncEdgeIt, \c BoolEdgeMap, \c IntEdgeMap,
   132   ///\c DoubleEdgeMap.
   133   ///
   134   ///\note If the graph type is a dependent type, ie. the graph type depend
   135   ///on a template parameter, then use \c TEMPLATE_GRAPH_TYPEDEFS()
   136   ///macro.
   137 #define GRAPH_TYPEDEFS(Graph)                                           \
   138   DIGRAPH_TYPEDEFS(Graph);                                              \
   139   typedef Graph::Edge Edge;                                             \
   140   typedef Graph::EdgeIt EdgeIt;                                         \
   141   typedef Graph::IncEdgeIt IncEdgeIt;                                   \
   142   typedef Graph::EdgeMap<bool> BoolEdgeMap;                             \
   143   typedef Graph::EdgeMap<int> IntEdgeMap;                               \
   144   typedef Graph::EdgeMap<double> DoubleEdgeMap
   145 
   146   ///Create convenience typedefs for the graph types and iterators
   147 
   148   ///\see GRAPH_TYPEDEFS
   149   ///
   150   ///\note Use this macro, if the graph type is a dependent type,
   151   ///ie. the graph type depend on a template parameter.
   152 #define TEMPLATE_GRAPH_TYPEDEFS(Graph)                                  \
   153   TEMPLATE_DIGRAPH_TYPEDEFS(Graph);                                     \
   154   typedef typename Graph::Edge Edge;                                    \
   155   typedef typename Graph::EdgeIt EdgeIt;                                \
   156   typedef typename Graph::IncEdgeIt IncEdgeIt;                          \
   157   typedef typename Graph::template EdgeMap<bool> BoolEdgeMap;           \
   158   typedef typename Graph::template EdgeMap<int> IntEdgeMap;             \
   159   typedef typename Graph::template EdgeMap<double> DoubleEdgeMap
   160 
   161   ///Create convenience typedefs for the bipartite graph types and iterators
   162 
   163   ///This \c \#define creates the same convenient type definitions as
   164   ///defined by \ref GRAPH_TYPEDEFS(BpGraph) and ten more, namely it
   165   ///creates \c RedNode, \c RedNodeIt, \c BoolRedNodeMap,
   166   ///\c IntRedNodeMap, \c DoubleRedNodeMap, \c BlueNode, \c BlueNodeIt,
   167   ///\c BoolBlueNodeMap, \c IntBlueNodeMap, \c DoubleBlueNodeMap.
   168   ///
   169   ///\note If the graph type is a dependent type, ie. the graph type depend
   170   ///on a template parameter, then use \c TEMPLATE_BPGRAPH_TYPEDEFS()
   171   ///macro.
   172 #define BPGRAPH_TYPEDEFS(BpGraph)                                       \
   173   GRAPH_TYPEDEFS(BpGraph);                                              \
   174   typedef BpGraph::RedNode RedNode;                                     \
   175   typedef BpGraph::RedNodeIt RedNodeIt;                                 \
   176   typedef BpGraph::RedNodeMap<bool> BoolRedNodeMap;                     \
   177   typedef BpGraph::RedNodeMap<int> IntRedNodeMap;                       \
   178   typedef BpGraph::RedNodeMap<double> DoubleRedNodeMap;                 \
   179   typedef BpGraph::BlueNode BlueNode;                                   \
   180   typedef BpGraph::BlueNodeIt BlueNodeIt;                               \
   181   typedef BpGraph::BlueNodeMap<bool> BoolBlueNodeMap;                   \
   182   typedef BpGraph::BlueNodeMap<int> IntBlueNodeMap;                     \
   183   typedef BpGraph::BlueNodeMap<double> DoubleBlueNodeMap
   184 
   185   ///Create convenience typedefs for the bipartite graph types and iterators
   186 
   187   ///\see BPGRAPH_TYPEDEFS
   188   ///
   189   ///\note Use this macro, if the graph type is a dependent type,
   190   ///ie. the graph type depend on a template parameter.
   191 #define TEMPLATE_BPGRAPH_TYPEDEFS(BpGraph)                                  \
   192   TEMPLATE_GRAPH_TYPEDEFS(BpGraph);                                         \
   193   typedef typename BpGraph::RedNode RedNode;                                \
   194   typedef typename BpGraph::RedNodeIt RedNodeIt;                            \
   195   typedef typename BpGraph::template RedNodeMap<bool> BoolRedNodeMap;       \
   196   typedef typename BpGraph::template RedNodeMap<int> IntRedNodeMap;         \
   197   typedef typename BpGraph::template RedNodeMap<double> DoubleRedNodeMap;   \
   198   typedef typename BpGraph::BlueNode BlueNode;                              \
   199   typedef typename BpGraph::BlueNodeIt BlueNodeIt;                          \
   200   typedef typename BpGraph::template BlueNodeMap<bool> BoolBlueNodeMap;     \
   201   typedef typename BpGraph::template BlueNodeMap<int> IntBlueNodeMap;       \
   202   typedef typename BpGraph::template BlueNodeMap<double> DoubleBlueNodeMap
   203 
   204   /// \brief Function to count the items in a graph.
   205   ///
   206   /// This function counts the items (nodes, arcs etc.) in a graph.
   207   /// The complexity of the function is linear because
   208   /// it iterates on all of the items.
   209   template <typename Graph, typename Item>
   210   inline int countItems(const Graph& g) {
   211     typedef typename ItemSetTraits<Graph, Item>::ItemIt ItemIt;
   212     int num = 0;
   213     for (ItemIt it(g); it != INVALID; ++it) {
   214       ++num;
   215     }
   216     return num;
   217   }
   218 
   219   // Node counting:
   220 
   221   namespace _core_bits {
   222 
   223     template <typename Graph, typename Enable = void>
   224     struct CountNodesSelector {
   225       static int count(const Graph &g) {
   226         return countItems<Graph, typename Graph::Node>(g);
   227       }
   228     };
   229 
   230     template <typename Graph>
   231     struct CountNodesSelector<
   232       Graph, typename
   233       enable_if<typename Graph::NodeNumTag, void>::type>
   234     {
   235       static int count(const Graph &g) {
   236         return g.nodeNum();
   237       }
   238     };
   239   }
   240 
   241   /// \brief Function to count the nodes in the graph.
   242   ///
   243   /// This function counts the nodes in the graph.
   244   /// The complexity of the function is <em>O</em>(<em>n</em>), but for some
   245   /// graph structures it is specialized to run in <em>O</em>(1).
   246   ///
   247   /// \note If the graph contains a \c nodeNum() member function and a
   248   /// \c NodeNumTag tag then this function calls directly the member
   249   /// function to query the cardinality of the node set.
   250   template <typename Graph>
   251   inline int countNodes(const Graph& g) {
   252     return _core_bits::CountNodesSelector<Graph>::count(g);
   253   }
   254 
   255   namespace _graph_utils_bits {
   256 
   257     template <typename Graph, typename Enable = void>
   258     struct CountRedNodesSelector {
   259       static int count(const Graph &g) {
   260         return countItems<Graph, typename Graph::RedNode>(g);
   261       }
   262     };
   263 
   264     template <typename Graph>
   265     struct CountRedNodesSelector<
   266       Graph, typename
   267       enable_if<typename Graph::NodeNumTag, void>::type>
   268     {
   269       static int count(const Graph &g) {
   270         return g.redNum();
   271       }
   272     };
   273   }
   274 
   275   /// \brief Function to count the red nodes in the graph.
   276   ///
   277   /// This function counts the red nodes in the graph.
   278   /// The complexity of the function is O(n) but for some
   279   /// graph structures it is specialized to run in O(1).
   280   ///
   281   /// If the graph contains a \e redNum() member function and a
   282   /// \e NodeNumTag tag then this function calls directly the member
   283   /// function to query the cardinality of the node set.
   284   template <typename Graph>
   285   inline int countRedNodes(const Graph& g) {
   286     return _graph_utils_bits::CountRedNodesSelector<Graph>::count(g);
   287   }
   288 
   289   namespace _graph_utils_bits {
   290 
   291     template <typename Graph, typename Enable = void>
   292     struct CountBlueNodesSelector {
   293       static int count(const Graph &g) {
   294         return countItems<Graph, typename Graph::BlueNode>(g);
   295       }
   296     };
   297 
   298     template <typename Graph>
   299     struct CountBlueNodesSelector<
   300       Graph, typename
   301       enable_if<typename Graph::NodeNumTag, void>::type>
   302     {
   303       static int count(const Graph &g) {
   304         return g.blueNum();
   305       }
   306     };
   307   }
   308 
   309   /// \brief Function to count the blue nodes in the graph.
   310   ///
   311   /// This function counts the blue nodes in the graph.
   312   /// The complexity of the function is O(n) but for some
   313   /// graph structures it is specialized to run in O(1).
   314   ///
   315   /// If the graph contains a \e blueNum() member function and a
   316   /// \e NodeNumTag tag then this function calls directly the member
   317   /// function to query the cardinality of the node set.
   318   template <typename Graph>
   319   inline int countBlueNodes(const Graph& g) {
   320     return _graph_utils_bits::CountBlueNodesSelector<Graph>::count(g);
   321   }
   322 
   323   // Arc counting:
   324 
   325   namespace _core_bits {
   326 
   327     template <typename Graph, typename Enable = void>
   328     struct CountArcsSelector {
   329       static int count(const Graph &g) {
   330         return countItems<Graph, typename Graph::Arc>(g);
   331       }
   332     };
   333 
   334     template <typename Graph>
   335     struct CountArcsSelector<
   336       Graph,
   337       typename enable_if<typename Graph::ArcNumTag, void>::type>
   338     {
   339       static int count(const Graph &g) {
   340         return g.arcNum();
   341       }
   342     };
   343   }
   344 
   345   /// \brief Function to count the arcs in the graph.
   346   ///
   347   /// This function counts the arcs in the graph.
   348   /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
   349   /// graph structures it is specialized to run in <em>O</em>(1).
   350   ///
   351   /// \note If the graph contains a \c arcNum() member function and a
   352   /// \c ArcNumTag tag then this function calls directly the member
   353   /// function to query the cardinality of the arc set.
   354   template <typename Graph>
   355   inline int countArcs(const Graph& g) {
   356     return _core_bits::CountArcsSelector<Graph>::count(g);
   357   }
   358 
   359   // Edge counting:
   360 
   361   namespace _core_bits {
   362 
   363     template <typename Graph, typename Enable = void>
   364     struct CountEdgesSelector {
   365       static int count(const Graph &g) {
   366         return countItems<Graph, typename Graph::Edge>(g);
   367       }
   368     };
   369 
   370     template <typename Graph>
   371     struct CountEdgesSelector<
   372       Graph,
   373       typename enable_if<typename Graph::EdgeNumTag, void>::type>
   374     {
   375       static int count(const Graph &g) {
   376         return g.edgeNum();
   377       }
   378     };
   379   }
   380 
   381   /// \brief Function to count the edges in the graph.
   382   ///
   383   /// This function counts the edges in the graph.
   384   /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
   385   /// graph structures it is specialized to run in <em>O</em>(1).
   386   ///
   387   /// \note If the graph contains a \c edgeNum() member function and a
   388   /// \c EdgeNumTag tag then this function calls directly the member
   389   /// function to query the cardinality of the edge set.
   390   template <typename Graph>
   391   inline int countEdges(const Graph& g) {
   392     return _core_bits::CountEdgesSelector<Graph>::count(g);
   393 
   394   }
   395 
   396 
   397   template <typename Graph, typename DegIt>
   398   inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {
   399     int num = 0;
   400     for (DegIt it(_g, _n); it != INVALID; ++it) {
   401       ++num;
   402     }
   403     return num;
   404   }
   405 
   406   /// \brief Function to count the number of the out-arcs from node \c n.
   407   ///
   408   /// This function counts the number of the out-arcs from node \c n
   409   /// in the graph \c g.
   410   template <typename Graph>
   411   inline int countOutArcs(const Graph& g,  const typename Graph::Node& n) {
   412     return countNodeDegree<Graph, typename Graph::OutArcIt>(g, n);
   413   }
   414 
   415   /// \brief Function to count the number of the in-arcs to node \c n.
   416   ///
   417   /// This function counts the number of the in-arcs to node \c n
   418   /// in the graph \c g.
   419   template <typename Graph>
   420   inline int countInArcs(const Graph& g,  const typename Graph::Node& n) {
   421     return countNodeDegree<Graph, typename Graph::InArcIt>(g, n);
   422   }
   423 
   424   /// \brief Function to count the number of the inc-edges to node \c n.
   425   ///
   426   /// This function counts the number of the inc-edges to node \c n
   427   /// in the undirected graph \c g.
   428   template <typename Graph>
   429   inline int countIncEdges(const Graph& g,  const typename Graph::Node& n) {
   430     return countNodeDegree<Graph, typename Graph::IncEdgeIt>(g, n);
   431   }
   432 
   433   namespace _core_bits {
   434 
   435     template <typename Digraph, typename Item, typename RefMap>
   436     class MapCopyBase {
   437     public:
   438       virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
   439 
   440       virtual ~MapCopyBase() {}
   441     };
   442 
   443     template <typename Digraph, typename Item, typename RefMap,
   444               typename FromMap, typename ToMap>
   445     class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
   446     public:
   447 
   448       MapCopy(const FromMap& map, ToMap& tmap)
   449         : _map(map), _tmap(tmap) {}
   450 
   451       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   452         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   453         for (ItemIt it(digraph); it != INVALID; ++it) {
   454           _tmap.set(refMap[it], _map[it]);
   455         }
   456       }
   457 
   458     private:
   459       const FromMap& _map;
   460       ToMap& _tmap;
   461     };
   462 
   463     template <typename Digraph, typename Item, typename RefMap, typename It>
   464     class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
   465     public:
   466 
   467       ItemCopy(const Item& item, It& it) : _item(item), _it(it) {}
   468 
   469       virtual void copy(const Digraph&, const RefMap& refMap) {
   470         _it = refMap[_item];
   471       }
   472 
   473     private:
   474       Item _item;
   475       It& _it;
   476     };
   477 
   478     template <typename Digraph, typename Item, typename RefMap, typename Ref>
   479     class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   480     public:
   481 
   482       RefCopy(Ref& map) : _map(map) {}
   483 
   484       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   485         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   486         for (ItemIt it(digraph); it != INVALID; ++it) {
   487           _map.set(it, refMap[it]);
   488         }
   489       }
   490 
   491     private:
   492       Ref& _map;
   493     };
   494 
   495     template <typename Digraph, typename Item, typename RefMap,
   496               typename CrossRef>
   497     class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
   498     public:
   499 
   500       CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
   501 
   502       virtual void copy(const Digraph& digraph, const RefMap& refMap) {
   503         typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
   504         for (ItemIt it(digraph); it != INVALID; ++it) {
   505           _cmap.set(refMap[it], it);
   506         }
   507       }
   508 
   509     private:
   510       CrossRef& _cmap;
   511     };
   512 
   513     template <typename Digraph, typename Enable = void>
   514     struct DigraphCopySelector {
   515       template <typename From, typename NodeRefMap, typename ArcRefMap>
   516       static void copy(const From& from, Digraph &to,
   517                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   518         to.clear();
   519         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   520           nodeRefMap[it] = to.addNode();
   521         }
   522         for (typename From::ArcIt it(from); it != INVALID; ++it) {
   523           arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)],
   524                                     nodeRefMap[from.target(it)]);
   525         }
   526       }
   527     };
   528 
   529     template <typename Digraph>
   530     struct DigraphCopySelector<
   531       Digraph,
   532       typename enable_if<typename Digraph::BuildTag, void>::type>
   533     {
   534       template <typename From, typename NodeRefMap, typename ArcRefMap>
   535       static void copy(const From& from, Digraph &to,
   536                        NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
   537         to.build(from, nodeRefMap, arcRefMap);
   538       }
   539     };
   540 
   541     template <typename Graph, typename Enable = void>
   542     struct GraphCopySelector {
   543       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   544       static void copy(const From& from, Graph &to,
   545                        NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
   546         to.clear();
   547         for (typename From::NodeIt it(from); it != INVALID; ++it) {
   548           nodeRefMap[it] = to.addNode();
   549         }
   550         for (typename From::EdgeIt it(from); it != INVALID; ++it) {
   551           edgeRefMap[it] = to.addEdge(nodeRefMap[from.u(it)],
   552                                       nodeRefMap[from.v(it)]);
   553         }
   554       }
   555     };
   556 
   557     template <typename Graph>
   558     struct GraphCopySelector<
   559       Graph,
   560       typename enable_if<typename Graph::BuildTag, void>::type>
   561     {
   562       template <typename From, typename NodeRefMap, typename EdgeRefMap>
   563       static void copy(const From& from, Graph &to,
   564                        NodeRefMap& nodeRefMap,
   565                        EdgeRefMap& edgeRefMap) {
   566         to.build(from, nodeRefMap, edgeRefMap);
   567       }
   568     };
   569 
   570     template <typename BpGraph, typename Enable = void>
   571     struct BpGraphCopySelector {
   572       template <typename From, typename RedNodeRefMap,
   573                 typename BlueNodeRefMap, typename EdgeRefMap>
   574       static void copy(const From& from, BpGraph &to,
   575                        RedNodeRefMap& redNodeRefMap,
   576                        BlueNodeRefMap& blueNodeRefMap,
   577                        EdgeRefMap& edgeRefMap) {
   578         to.clear();
   579         for (typename From::RedNodeIt it(from); it != INVALID; ++it) {
   580           redNodeRefMap[it] = to.addRedNode();
   581         }
   582         for (typename From::BlueNodeIt it(from); it != INVALID; ++it) {
   583           blueNodeRefMap[it] = to.addBlueNode();
   584         }
   585         for (typename From::EdgeIt it(from); it != INVALID; ++it) {
   586           edgeRefMap[it] = to.addEdge(redNodeRefMap[from.redNode(it)],
   587                                       blueNodeRefMap[from.blueNode(it)]);
   588         }
   589       }
   590     };
   591 
   592     template <typename BpGraph>
   593     struct BpGraphCopySelector<
   594       BpGraph,
   595       typename enable_if<typename BpGraph::BuildTag, void>::type>
   596     {
   597       template <typename From, typename RedNodeRefMap,
   598                 typename BlueNodeRefMap, typename EdgeRefMap>
   599       static void copy(const From& from, BpGraph &to,
   600                        RedNodeRefMap& redNodeRefMap,
   601                        BlueNodeRefMap& blueNodeRefMap,
   602                        EdgeRefMap& edgeRefMap) {
   603         to.build(from, redNodeRefMap, blueNodeRefMap, edgeRefMap);
   604       }
   605     };
   606 
   607   }
   608 
   609   /// \brief Check whether a graph is undirected.
   610   ///
   611   /// This function returns \c true if the given graph is undirected.
   612 #ifdef DOXYGEN
   613   template <typename GR>
   614   bool undirected(const GR& g) { return false; }
   615 #else
   616   template <typename GR>
   617   typename enable_if<UndirectedTagIndicator<GR>, bool>::type
   618   undirected(const GR&) {
   619     return true;
   620   }
   621   template <typename GR>
   622   typename disable_if<UndirectedTagIndicator<GR>, bool>::type
   623   undirected(const GR&) {
   624     return false;
   625   }
   626 #endif
   627 
   628   /// \brief Class to copy a digraph.
   629   ///
   630   /// Class to copy a digraph to another digraph (duplicate a digraph). The
   631   /// simplest way of using it is through the \c digraphCopy() function.
   632   ///
   633   /// This class not only make a copy of a digraph, but it can create
   634   /// references and cross references between the nodes and arcs of
   635   /// the two digraphs, and it can copy maps to use with the newly created
   636   /// digraph.
   637   ///
   638   /// To make a copy from a digraph, first an instance of DigraphCopy
   639   /// should be created, then the data belongs to the digraph should
   640   /// assigned to copy. In the end, the \c run() member should be
   641   /// called.
   642   ///
   643   /// The next code copies a digraph with several data:
   644   ///\code
   645   ///  DigraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
   646   ///  // Create references for the nodes
   647   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   648   ///  cg.nodeRef(nr);
   649   ///  // Create cross references (inverse) for the arcs
   650   ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);
   651   ///  cg.arcCrossRef(acr);
   652   ///  // Copy an arc map
   653   ///  OrigGraph::ArcMap<double> oamap(orig_graph);
   654   ///  NewGraph::ArcMap<double> namap(new_graph);
   655   ///  cg.arcMap(oamap, namap);
   656   ///  // Copy a node
   657   ///  OrigGraph::Node on;
   658   ///  NewGraph::Node nn;
   659   ///  cg.node(on, nn);
   660   ///  // Execute copying
   661   ///  cg.run();
   662   ///\endcode
   663   template <typename From, typename To>
   664   class DigraphCopy {
   665   private:
   666 
   667     typedef typename From::Node Node;
   668     typedef typename From::NodeIt NodeIt;
   669     typedef typename From::Arc Arc;
   670     typedef typename From::ArcIt ArcIt;
   671 
   672     typedef typename To::Node TNode;
   673     typedef typename To::Arc TArc;
   674 
   675     typedef typename From::template NodeMap<TNode> NodeRefMap;
   676     typedef typename From::template ArcMap<TArc> ArcRefMap;
   677 
   678   public:
   679 
   680     /// \brief Constructor of DigraphCopy.
   681     ///
   682     /// Constructor of DigraphCopy for copying the content of the
   683     /// \c from digraph into the \c to digraph.
   684     DigraphCopy(const From& from, To& to)
   685       : _from(from), _to(to) {}
   686 
   687     /// \brief Destructor of DigraphCopy
   688     ///
   689     /// Destructor of DigraphCopy.
   690     ~DigraphCopy() {
   691       for (int i = 0; i < int(_node_maps.size()); ++i) {
   692         delete _node_maps[i];
   693       }
   694       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   695         delete _arc_maps[i];
   696       }
   697 
   698     }
   699 
   700     /// \brief Copy the node references into the given map.
   701     ///
   702     /// This function copies the node references into the given map.
   703     /// The parameter should be a map, whose key type is the Node type of
   704     /// the source digraph, while the value type is the Node type of the
   705     /// destination digraph.
   706     template <typename NodeRef>
   707     DigraphCopy& nodeRef(NodeRef& map) {
   708       _node_maps.push_back(new _core_bits::RefCopy<From, Node,
   709                            NodeRefMap, NodeRef>(map));
   710       return *this;
   711     }
   712 
   713     /// \brief Copy the node cross references into the given map.
   714     ///
   715     /// This function copies the node cross references (reverse references)
   716     /// into the given map. The parameter should be a map, whose key type
   717     /// is the Node type of the destination digraph, while the value type is
   718     /// the Node type of the source digraph.
   719     template <typename NodeCrossRef>
   720     DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
   721       _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
   722                            NodeRefMap, NodeCrossRef>(map));
   723       return *this;
   724     }
   725 
   726     /// \brief Make a copy of the given node map.
   727     ///
   728     /// This function makes a copy of the given node map for the newly
   729     /// created digraph.
   730     /// The key type of the new map \c tmap should be the Node type of the
   731     /// destination digraph, and the key type of the original map \c map
   732     /// should be the Node type of the source digraph.
   733     template <typename FromMap, typename ToMap>
   734     DigraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
   735       _node_maps.push_back(new _core_bits::MapCopy<From, Node,
   736                            NodeRefMap, FromMap, ToMap>(map, tmap));
   737       return *this;
   738     }
   739 
   740     /// \brief Make a copy of the given node.
   741     ///
   742     /// This function makes a copy of the given node.
   743     DigraphCopy& node(const Node& node, TNode& tnode) {
   744       _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
   745                            NodeRefMap, TNode>(node, tnode));
   746       return *this;
   747     }
   748 
   749     /// \brief Copy the arc references into the given map.
   750     ///
   751     /// This function copies the arc references into the given map.
   752     /// The parameter should be a map, whose key type is the Arc type of
   753     /// the source digraph, while the value type is the Arc type of the
   754     /// destination digraph.
   755     template <typename ArcRef>
   756     DigraphCopy& arcRef(ArcRef& map) {
   757       _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
   758                           ArcRefMap, ArcRef>(map));
   759       return *this;
   760     }
   761 
   762     /// \brief Copy the arc cross references into the given map.
   763     ///
   764     /// This function copies the arc cross references (reverse references)
   765     /// into the given map. The parameter should be a map, whose key type
   766     /// is the Arc type of the destination digraph, while the value type is
   767     /// the Arc type of the source digraph.
   768     template <typename ArcCrossRef>
   769     DigraphCopy& arcCrossRef(ArcCrossRef& map) {
   770       _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
   771                           ArcRefMap, ArcCrossRef>(map));
   772       return *this;
   773     }
   774 
   775     /// \brief Make a copy of the given arc map.
   776     ///
   777     /// This function makes a copy of the given arc map for the newly
   778     /// created digraph.
   779     /// The key type of the new map \c tmap should be the Arc type of the
   780     /// destination digraph, and the key type of the original map \c map
   781     /// should be the Arc type of the source digraph.
   782     template <typename FromMap, typename ToMap>
   783     DigraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
   784       _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
   785                           ArcRefMap, FromMap, ToMap>(map, tmap));
   786       return *this;
   787     }
   788 
   789     /// \brief Make a copy of the given arc.
   790     ///
   791     /// This function makes a copy of the given arc.
   792     DigraphCopy& arc(const Arc& arc, TArc& tarc) {
   793       _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
   794                           ArcRefMap, TArc>(arc, tarc));
   795       return *this;
   796     }
   797 
   798     /// \brief Execute copying.
   799     ///
   800     /// This function executes the copying of the digraph along with the
   801     /// copying of the assigned data.
   802     void run() {
   803       NodeRefMap nodeRefMap(_from);
   804       ArcRefMap arcRefMap(_from);
   805       _core_bits::DigraphCopySelector<To>::
   806         copy(_from, _to, nodeRefMap, arcRefMap);
   807       for (int i = 0; i < int(_node_maps.size()); ++i) {
   808         _node_maps[i]->copy(_from, nodeRefMap);
   809       }
   810       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   811         _arc_maps[i]->copy(_from, arcRefMap);
   812       }
   813     }
   814 
   815   protected:
   816 
   817     const From& _from;
   818     To& _to;
   819 
   820     std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
   821       _node_maps;
   822 
   823     std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
   824       _arc_maps;
   825 
   826   };
   827 
   828   /// \brief Copy a digraph to another digraph.
   829   ///
   830   /// This function copies a digraph to another digraph.
   831   /// The complete usage of it is detailed in the DigraphCopy class, but
   832   /// a short example shows a basic work:
   833   ///\code
   834   /// digraphCopy(src, trg).nodeRef(nr).arcCrossRef(acr).run();
   835   ///\endcode
   836   ///
   837   /// After the copy the \c nr map will contain the mapping from the
   838   /// nodes of the \c from digraph to the nodes of the \c to digraph and
   839   /// \c acr will contain the mapping from the arcs of the \c to digraph
   840   /// to the arcs of the \c from digraph.
   841   ///
   842   /// \see DigraphCopy
   843   template <typename From, typename To>
   844   DigraphCopy<From, To> digraphCopy(const From& from, To& to) {
   845     return DigraphCopy<From, To>(from, to);
   846   }
   847 
   848   /// \brief Class to copy a graph.
   849   ///
   850   /// Class to copy a graph to another graph (duplicate a graph). The
   851   /// simplest way of using it is through the \c graphCopy() function.
   852   ///
   853   /// This class not only make a copy of a graph, but it can create
   854   /// references and cross references between the nodes, edges and arcs of
   855   /// the two graphs, and it can copy maps for using with the newly created
   856   /// graph.
   857   ///
   858   /// To make a copy from a graph, first an instance of GraphCopy
   859   /// should be created, then the data belongs to the graph should
   860   /// assigned to copy. In the end, the \c run() member should be
   861   /// called.
   862   ///
   863   /// The next code copies a graph with several data:
   864   ///\code
   865   ///  GraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
   866   ///  // Create references for the nodes
   867   ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
   868   ///  cg.nodeRef(nr);
   869   ///  // Create cross references (inverse) for the edges
   870   ///  NewGraph::EdgeMap<OrigGraph::Edge> ecr(new_graph);
   871   ///  cg.edgeCrossRef(ecr);
   872   ///  // Copy an edge map
   873   ///  OrigGraph::EdgeMap<double> oemap(orig_graph);
   874   ///  NewGraph::EdgeMap<double> nemap(new_graph);
   875   ///  cg.edgeMap(oemap, nemap);
   876   ///  // Copy a node
   877   ///  OrigGraph::Node on;
   878   ///  NewGraph::Node nn;
   879   ///  cg.node(on, nn);
   880   ///  // Execute copying
   881   ///  cg.run();
   882   ///\endcode
   883   template <typename From, typename To>
   884   class GraphCopy {
   885   private:
   886 
   887     typedef typename From::Node Node;
   888     typedef typename From::NodeIt NodeIt;
   889     typedef typename From::Arc Arc;
   890     typedef typename From::ArcIt ArcIt;
   891     typedef typename From::Edge Edge;
   892     typedef typename From::EdgeIt EdgeIt;
   893 
   894     typedef typename To::Node TNode;
   895     typedef typename To::Arc TArc;
   896     typedef typename To::Edge TEdge;
   897 
   898     typedef typename From::template NodeMap<TNode> NodeRefMap;
   899     typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
   900 
   901     struct ArcRefMap {
   902       ArcRefMap(const From& from, const To& to,
   903                 const EdgeRefMap& edge_ref, const NodeRefMap& node_ref)
   904         : _from(from), _to(to),
   905           _edge_ref(edge_ref), _node_ref(node_ref) {}
   906 
   907       typedef typename From::Arc Key;
   908       typedef typename To::Arc Value;
   909 
   910       Value operator[](const Key& key) const {
   911         bool forward = _from.u(key) != _from.v(key) ?
   912           _node_ref[_from.source(key)] ==
   913           _to.source(_to.direct(_edge_ref[key], true)) :
   914           _from.direction(key);
   915         return _to.direct(_edge_ref[key], forward);
   916       }
   917 
   918       const From& _from;
   919       const To& _to;
   920       const EdgeRefMap& _edge_ref;
   921       const NodeRefMap& _node_ref;
   922     };
   923 
   924   public:
   925 
   926     /// \brief Constructor of GraphCopy.
   927     ///
   928     /// Constructor of GraphCopy for copying the content of the
   929     /// \c from graph into the \c to graph.
   930     GraphCopy(const From& from, To& to)
   931       : _from(from), _to(to) {}
   932 
   933     /// \brief Destructor of GraphCopy
   934     ///
   935     /// Destructor of GraphCopy.
   936     ~GraphCopy() {
   937       for (int i = 0; i < int(_node_maps.size()); ++i) {
   938         delete _node_maps[i];
   939       }
   940       for (int i = 0; i < int(_arc_maps.size()); ++i) {
   941         delete _arc_maps[i];
   942       }
   943       for (int i = 0; i < int(_edge_maps.size()); ++i) {
   944         delete _edge_maps[i];
   945       }
   946     }
   947 
   948     /// \brief Copy the node references into the given map.
   949     ///
   950     /// This function copies the node references into the given map.
   951     /// The parameter should be a map, whose key type is the Node type of
   952     /// the source graph, while the value type is the Node type of the
   953     /// destination graph.
   954     template <typename NodeRef>
   955     GraphCopy& nodeRef(NodeRef& map) {
   956       _node_maps.push_back(new _core_bits::RefCopy<From, Node,
   957                            NodeRefMap, NodeRef>(map));
   958       return *this;
   959     }
   960 
   961     /// \brief Copy the node cross references into the given map.
   962     ///
   963     /// This function copies the node cross references (reverse references)
   964     /// into the given map. The parameter should be a map, whose key type
   965     /// is the Node type of the destination graph, while the value type is
   966     /// the Node type of the source graph.
   967     template <typename NodeCrossRef>
   968     GraphCopy& nodeCrossRef(NodeCrossRef& map) {
   969       _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
   970                            NodeRefMap, NodeCrossRef>(map));
   971       return *this;
   972     }
   973 
   974     /// \brief Make a copy of the given node map.
   975     ///
   976     /// This function makes a copy of the given node map for the newly
   977     /// created graph.
   978     /// The key type of the new map \c tmap should be the Node type of the
   979     /// destination graph, and the key type of the original map \c map
   980     /// should be the Node type of the source graph.
   981     template <typename FromMap, typename ToMap>
   982     GraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
   983       _node_maps.push_back(new _core_bits::MapCopy<From, Node,
   984                            NodeRefMap, FromMap, ToMap>(map, tmap));
   985       return *this;
   986     }
   987 
   988     /// \brief Make a copy of the given node.
   989     ///
   990     /// This function makes a copy of the given node.
   991     GraphCopy& node(const Node& node, TNode& tnode) {
   992       _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
   993                            NodeRefMap, TNode>(node, tnode));
   994       return *this;
   995     }
   996 
   997     /// \brief Copy the arc references into the given map.
   998     ///
   999     /// This function copies the arc references into the given map.
  1000     /// The parameter should be a map, whose key type is the Arc type of
  1001     /// the source graph, while the value type is the Arc type of the
  1002     /// destination graph.
  1003     template <typename ArcRef>
  1004     GraphCopy& arcRef(ArcRef& map) {
  1005       _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
  1006                           ArcRefMap, ArcRef>(map));
  1007       return *this;
  1008     }
  1009 
  1010     /// \brief Copy the arc cross references into the given map.
  1011     ///
  1012     /// This function copies the arc cross references (reverse references)
  1013     /// into the given map. The parameter should be a map, whose key type
  1014     /// is the Arc type of the destination graph, while the value type is
  1015     /// the Arc type of the source graph.
  1016     template <typename ArcCrossRef>
  1017     GraphCopy& arcCrossRef(ArcCrossRef& map) {
  1018       _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
  1019                           ArcRefMap, ArcCrossRef>(map));
  1020       return *this;
  1021     }
  1022 
  1023     /// \brief Make a copy of the given arc map.
  1024     ///
  1025     /// This function makes a copy of the given arc map for the newly
  1026     /// created graph.
  1027     /// The key type of the new map \c tmap should be the Arc type of the
  1028     /// destination graph, and the key type of the original map \c map
  1029     /// should be the Arc type of the source graph.
  1030     template <typename FromMap, typename ToMap>
  1031     GraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
  1032       _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
  1033                           ArcRefMap, FromMap, ToMap>(map, tmap));
  1034       return *this;
  1035     }
  1036 
  1037     /// \brief Make a copy of the given arc.
  1038     ///
  1039     /// This function makes a copy of the given arc.
  1040     GraphCopy& arc(const Arc& arc, TArc& tarc) {
  1041       _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
  1042                           ArcRefMap, TArc>(arc, tarc));
  1043       return *this;
  1044     }
  1045 
  1046     /// \brief Copy the edge references into the given map.
  1047     ///
  1048     /// This function copies the edge references into the given map.
  1049     /// The parameter should be a map, whose key type is the Edge type of
  1050     /// the source graph, while the value type is the Edge type of the
  1051     /// destination graph.
  1052     template <typename EdgeRef>
  1053     GraphCopy& edgeRef(EdgeRef& map) {
  1054       _edge_maps.push_back(new _core_bits::RefCopy<From, Edge,
  1055                            EdgeRefMap, EdgeRef>(map));
  1056       return *this;
  1057     }
  1058 
  1059     /// \brief Copy the edge cross references into the given map.
  1060     ///
  1061     /// This function copies the edge cross references (reverse references)
  1062     /// into the given map. The parameter should be a map, whose key type
  1063     /// is the Edge type of the destination graph, while the value type is
  1064     /// the Edge type of the source graph.
  1065     template <typename EdgeCrossRef>
  1066     GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
  1067       _edge_maps.push_back(new _core_bits::CrossRefCopy<From,
  1068                            Edge, EdgeRefMap, EdgeCrossRef>(map));
  1069       return *this;
  1070     }
  1071 
  1072     /// \brief Make a copy of the given edge map.
  1073     ///
  1074     /// This function makes a copy of the given edge map for the newly
  1075     /// created graph.
  1076     /// The key type of the new map \c tmap should be the Edge type of the
  1077     /// destination graph, and the key type of the original map \c map
  1078     /// should be the Edge type of the source graph.
  1079     template <typename FromMap, typename ToMap>
  1080     GraphCopy& edgeMap(const FromMap& map, ToMap& tmap) {
  1081       _edge_maps.push_back(new _core_bits::MapCopy<From, Edge,
  1082                            EdgeRefMap, FromMap, ToMap>(map, tmap));
  1083       return *this;
  1084     }
  1085 
  1086     /// \brief Make a copy of the given edge.
  1087     ///
  1088     /// This function makes a copy of the given edge.
  1089     GraphCopy& edge(const Edge& edge, TEdge& tedge) {
  1090       _edge_maps.push_back(new _core_bits::ItemCopy<From, Edge,
  1091                            EdgeRefMap, TEdge>(edge, tedge));
  1092       return *this;
  1093     }
  1094 
  1095     /// \brief Execute copying.
  1096     ///
  1097     /// This function executes the copying of the graph along with the
  1098     /// copying of the assigned data.
  1099     void run() {
  1100       NodeRefMap nodeRefMap(_from);
  1101       EdgeRefMap edgeRefMap(_from);
  1102       ArcRefMap arcRefMap(_from, _to, edgeRefMap, nodeRefMap);
  1103       _core_bits::GraphCopySelector<To>::
  1104         copy(_from, _to, nodeRefMap, edgeRefMap);
  1105       for (int i = 0; i < int(_node_maps.size()); ++i) {
  1106         _node_maps[i]->copy(_from, nodeRefMap);
  1107       }
  1108       for (int i = 0; i < int(_edge_maps.size()); ++i) {
  1109         _edge_maps[i]->copy(_from, edgeRefMap);
  1110       }
  1111       for (int i = 0; i < int(_arc_maps.size()); ++i) {
  1112         _arc_maps[i]->copy(_from, arcRefMap);
  1113       }
  1114     }
  1115 
  1116   private:
  1117 
  1118     const From& _from;
  1119     To& _to;
  1120 
  1121     std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
  1122       _node_maps;
  1123 
  1124     std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
  1125       _arc_maps;
  1126 
  1127     std::vector<_core_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
  1128       _edge_maps;
  1129 
  1130   };
  1131 
  1132   /// \brief Copy a graph to another graph.
  1133   ///
  1134   /// This function copies a graph to another graph.
  1135   /// The complete usage of it is detailed in the GraphCopy class,
  1136   /// but a short example shows a basic work:
  1137   ///\code
  1138   /// graphCopy(src, trg).nodeRef(nr).edgeCrossRef(ecr).run();
  1139   ///\endcode
  1140   ///
  1141   /// After the copy the \c nr map will contain the mapping from the
  1142   /// nodes of the \c from graph to the nodes of the \c to graph and
  1143   /// \c ecr will contain the mapping from the edges of the \c to graph
  1144   /// to the edges of the \c from graph.
  1145   ///
  1146   /// \see GraphCopy
  1147   template <typename From, typename To>
  1148   GraphCopy<From, To>
  1149   graphCopy(const From& from, To& to) {
  1150     return GraphCopy<From, To>(from, to);
  1151   }
  1152 
  1153   /// \brief Class to copy a bipartite graph.
  1154   ///
  1155   /// Class to copy a bipartite graph to another graph (duplicate a
  1156   /// graph). The simplest way of using it is through the
  1157   /// \c bpGraphCopy() function.
  1158   ///
  1159   /// This class not only make a copy of a bipartite graph, but it can
  1160   /// create references and cross references between the nodes, edges
  1161   /// and arcs of the two graphs, and it can copy maps for using with
  1162   /// the newly created graph.
  1163   ///
  1164   /// To make a copy from a graph, first an instance of BpGraphCopy
  1165   /// should be created, then the data belongs to the graph should
  1166   /// assigned to copy. In the end, the \c run() member should be
  1167   /// called.
  1168   ///
  1169   /// The next code copies a graph with several data:
  1170   ///\code
  1171   ///  BpGraphCopy<OrigBpGraph, NewBpGraph> cg(orig_graph, new_graph);
  1172   ///  // Create references for the nodes
  1173   ///  OrigBpGraph::NodeMap<NewBpGraph::Node> nr(orig_graph);
  1174   ///  cg.nodeRef(nr);
  1175   ///  // Create cross references (inverse) for the edges
  1176   ///  NewBpGraph::EdgeMap<OrigBpGraph::Edge> ecr(new_graph);
  1177   ///  cg.edgeCrossRef(ecr);
  1178   ///  // Copy a red node map
  1179   ///  OrigBpGraph::RedNodeMap<double> ormap(orig_graph);
  1180   ///  NewBpGraph::RedNodeMap<double> nrmap(new_graph);
  1181   ///  cg.redNodeMap(ormap, nrmap);
  1182   ///  // Copy a node
  1183   ///  OrigBpGraph::Node on;
  1184   ///  NewBpGraph::Node nn;
  1185   ///  cg.node(on, nn);
  1186   ///  // Execute copying
  1187   ///  cg.run();
  1188   ///\endcode
  1189   template <typename From, typename To>
  1190   class BpGraphCopy {
  1191   private:
  1192 
  1193     typedef typename From::Node Node;
  1194     typedef typename From::RedNode RedNode;
  1195     typedef typename From::BlueNode BlueNode;
  1196     typedef typename From::NodeIt NodeIt;
  1197     typedef typename From::Arc Arc;
  1198     typedef typename From::ArcIt ArcIt;
  1199     typedef typename From::Edge Edge;
  1200     typedef typename From::EdgeIt EdgeIt;
  1201 
  1202     typedef typename To::Node TNode;
  1203     typedef typename To::RedNode TRedNode;
  1204     typedef typename To::BlueNode TBlueNode;
  1205     typedef typename To::Arc TArc;
  1206     typedef typename To::Edge TEdge;
  1207 
  1208     typedef typename From::template RedNodeMap<TRedNode> RedNodeRefMap;
  1209     typedef typename From::template BlueNodeMap<TBlueNode> BlueNodeRefMap;
  1210     typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
  1211 
  1212     struct NodeRefMap {
  1213       NodeRefMap(const From& from, const RedNodeRefMap& red_node_ref,
  1214                  const BlueNodeRefMap& blue_node_ref)
  1215         : _from(from), _red_node_ref(red_node_ref),
  1216           _blue_node_ref(blue_node_ref) {}
  1217 
  1218       typedef typename From::Node Key;
  1219       typedef typename To::Node Value;
  1220 
  1221       Value operator[](const Key& key) const {
  1222         if (_from.red(key)) {
  1223           return _red_node_ref[_from.asRedNodeUnsafe(key)];
  1224         } else {
  1225           return _blue_node_ref[_from.asBlueNodeUnsafe(key)];
  1226         }
  1227       }
  1228 
  1229       const From& _from;
  1230       const RedNodeRefMap& _red_node_ref;
  1231       const BlueNodeRefMap& _blue_node_ref;
  1232     };
  1233 
  1234     struct ArcRefMap {
  1235       ArcRefMap(const From& from, const To& to, const EdgeRefMap& edge_ref)
  1236         : _from(from), _to(to), _edge_ref(edge_ref) {}
  1237 
  1238       typedef typename From::Arc Key;
  1239       typedef typename To::Arc Value;
  1240 
  1241       Value operator[](const Key& key) const {
  1242         return _to.direct(_edge_ref[key], _from.direction(key));
  1243       }
  1244 
  1245       const From& _from;
  1246       const To& _to;
  1247       const EdgeRefMap& _edge_ref;
  1248     };
  1249 
  1250   public:
  1251 
  1252     /// \brief Constructor of BpGraphCopy.
  1253     ///
  1254     /// Constructor of BpGraphCopy for copying the content of the
  1255     /// \c from graph into the \c to graph.
  1256     BpGraphCopy(const From& from, To& to)
  1257       : _from(from), _to(to) {}
  1258 
  1259     /// \brief Destructor of BpGraphCopy
  1260     ///
  1261     /// Destructor of BpGraphCopy.
  1262     ~BpGraphCopy() {
  1263       for (int i = 0; i < int(_node_maps.size()); ++i) {
  1264         delete _node_maps[i];
  1265       }
  1266       for (int i = 0; i < int(_red_maps.size()); ++i) {
  1267         delete _red_maps[i];
  1268       }
  1269       for (int i = 0; i < int(_blue_maps.size()); ++i) {
  1270         delete _blue_maps[i];
  1271       }
  1272       for (int i = 0; i < int(_arc_maps.size()); ++i) {
  1273         delete _arc_maps[i];
  1274       }
  1275       for (int i = 0; i < int(_edge_maps.size()); ++i) {
  1276         delete _edge_maps[i];
  1277       }
  1278     }
  1279 
  1280     /// \brief Copy the node references into the given map.
  1281     ///
  1282     /// This function copies the node references into the given map.
  1283     /// The parameter should be a map, whose key type is the Node type of
  1284     /// the source graph, while the value type is the Node type of the
  1285     /// destination graph.
  1286     template <typename NodeRef>
  1287     BpGraphCopy& nodeRef(NodeRef& map) {
  1288       _node_maps.push_back(new _core_bits::RefCopy<From, Node,
  1289                            NodeRefMap, NodeRef>(map));
  1290       return *this;
  1291     }
  1292 
  1293     /// \brief Copy the node cross references into the given map.
  1294     ///
  1295     /// This function copies the node cross references (reverse references)
  1296     /// into the given map. The parameter should be a map, whose key type
  1297     /// is the Node type of the destination graph, while the value type is
  1298     /// the Node type of the source graph.
  1299     template <typename NodeCrossRef>
  1300     BpGraphCopy& nodeCrossRef(NodeCrossRef& map) {
  1301       _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
  1302                            NodeRefMap, NodeCrossRef>(map));
  1303       return *this;
  1304     }
  1305 
  1306     /// \brief Make a copy of the given node map.
  1307     ///
  1308     /// This function makes a copy of the given node map for the newly
  1309     /// created graph.
  1310     /// The key type of the new map \c tmap should be the Node type of the
  1311     /// destination graph, and the key type of the original map \c map
  1312     /// should be the Node type of the source graph.
  1313     template <typename FromMap, typename ToMap>
  1314     BpGraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
  1315       _node_maps.push_back(new _core_bits::MapCopy<From, Node,
  1316                            NodeRefMap, FromMap, ToMap>(map, tmap));
  1317       return *this;
  1318     }
  1319 
  1320     /// \brief Make a copy of the given node.
  1321     ///
  1322     /// This function makes a copy of the given node.
  1323     BpGraphCopy& node(const Node& node, TNode& tnode) {
  1324       _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
  1325                            NodeRefMap, TNode>(node, tnode));
  1326       return *this;
  1327     }
  1328 
  1329     /// \brief Copy the red node references into the given map.
  1330     ///
  1331     /// This function copies the red node references into the given
  1332     /// map.  The parameter should be a map, whose key type is the
  1333     /// Node type of the source graph with the red item set, while the
  1334     /// value type is the Node type of the destination graph.
  1335     template <typename RedRef>
  1336     BpGraphCopy& redRef(RedRef& map) {
  1337       _red_maps.push_back(new _core_bits::RefCopy<From, RedNode,
  1338                           RedNodeRefMap, RedRef>(map));
  1339       return *this;
  1340     }
  1341 
  1342     /// \brief Copy the red node cross references into the given map.
  1343     ///
  1344     /// This function copies the red node cross references (reverse
  1345     /// references) into the given map. The parameter should be a map,
  1346     /// whose key type is the Node type of the destination graph with
  1347     /// the red item set, while the value type is the Node type of the
  1348     /// source graph.
  1349     template <typename RedCrossRef>
  1350     BpGraphCopy& redCrossRef(RedCrossRef& map) {
  1351       _red_maps.push_back(new _core_bits::CrossRefCopy<From, RedNode,
  1352                           RedNodeRefMap, RedCrossRef>(map));
  1353       return *this;
  1354     }
  1355 
  1356     /// \brief Make a copy of the given red node map.
  1357     ///
  1358     /// This function makes a copy of the given red node map for the newly
  1359     /// created graph.
  1360     /// The key type of the new map \c tmap should be the Node type of
  1361     /// the destination graph with the red items, and the key type of
  1362     /// the original map \c map should be the Node type of the source
  1363     /// graph.
  1364     template <typename FromMap, typename ToMap>
  1365     BpGraphCopy& redNodeMap(const FromMap& map, ToMap& tmap) {
  1366       _red_maps.push_back(new _core_bits::MapCopy<From, RedNode,
  1367                           RedNodeRefMap, FromMap, ToMap>(map, tmap));
  1368       return *this;
  1369     }
  1370 
  1371     /// \brief Make a copy of the given red node.
  1372     ///
  1373     /// This function makes a copy of the given red node.
  1374     BpGraphCopy& redNode(const RedNode& node, TRedNode& tnode) {
  1375       _red_maps.push_back(new _core_bits::ItemCopy<From, RedNode,
  1376                           RedNodeRefMap, TRedNode>(node, tnode));
  1377       return *this;
  1378     }
  1379 
  1380     /// \brief Copy the blue node references into the given map.
  1381     ///
  1382     /// This function copies the blue node references into the given
  1383     /// map.  The parameter should be a map, whose key type is the
  1384     /// Node type of the source graph with the blue item set, while the
  1385     /// value type is the Node type of the destination graph.
  1386     template <typename BlueRef>
  1387     BpGraphCopy& blueRef(BlueRef& map) {
  1388       _blue_maps.push_back(new _core_bits::RefCopy<From, BlueNode,
  1389                            BlueNodeRefMap, BlueRef>(map));
  1390       return *this;
  1391     }
  1392 
  1393     /// \brief Copy the blue node cross references into the given map.
  1394     ///
  1395     /// This function copies the blue node cross references (reverse
  1396     /// references) into the given map. The parameter should be a map,
  1397     /// whose key type is the Node type of the destination graph with
  1398     /// the blue item set, while the value type is the Node type of the
  1399     /// source graph.
  1400     template <typename BlueCrossRef>
  1401     BpGraphCopy& blueCrossRef(BlueCrossRef& map) {
  1402       _blue_maps.push_back(new _core_bits::CrossRefCopy<From, BlueNode,
  1403                            BlueNodeRefMap, BlueCrossRef>(map));
  1404       return *this;
  1405     }
  1406 
  1407     /// \brief Make a copy of the given blue node map.
  1408     ///
  1409     /// This function makes a copy of the given blue node map for the newly
  1410     /// created graph.
  1411     /// The key type of the new map \c tmap should be the Node type of
  1412     /// the destination graph with the blue items, and the key type of
  1413     /// the original map \c map should be the Node type of the source
  1414     /// graph.
  1415     template <typename FromMap, typename ToMap>
  1416     BpGraphCopy& blueNodeMap(const FromMap& map, ToMap& tmap) {
  1417       _blue_maps.push_back(new _core_bits::MapCopy<From, BlueNode,
  1418                            BlueNodeRefMap, FromMap, ToMap>(map, tmap));
  1419       return *this;
  1420     }
  1421 
  1422     /// \brief Make a copy of the given blue node.
  1423     ///
  1424     /// This function makes a copy of the given blue node.
  1425     BpGraphCopy& blueNode(const BlueNode& node, TBlueNode& tnode) {
  1426       _blue_maps.push_back(new _core_bits::ItemCopy<From, BlueNode,
  1427                            BlueNodeRefMap, TBlueNode>(node, tnode));
  1428       return *this;
  1429     }
  1430 
  1431     /// \brief Copy the arc references into the given map.
  1432     ///
  1433     /// This function copies the arc references into the given map.
  1434     /// The parameter should be a map, whose key type is the Arc type of
  1435     /// the source graph, while the value type is the Arc type of the
  1436     /// destination graph.
  1437     template <typename ArcRef>
  1438     BpGraphCopy& arcRef(ArcRef& map) {
  1439       _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
  1440                           ArcRefMap, ArcRef>(map));
  1441       return *this;
  1442     }
  1443 
  1444     /// \brief Copy the arc cross references into the given map.
  1445     ///
  1446     /// This function copies the arc cross references (reverse references)
  1447     /// into the given map. The parameter should be a map, whose key type
  1448     /// is the Arc type of the destination graph, while the value type is
  1449     /// the Arc type of the source graph.
  1450     template <typename ArcCrossRef>
  1451     BpGraphCopy& arcCrossRef(ArcCrossRef& map) {
  1452       _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
  1453                           ArcRefMap, ArcCrossRef>(map));
  1454       return *this;
  1455     }
  1456 
  1457     /// \brief Make a copy of the given arc map.
  1458     ///
  1459     /// This function makes a copy of the given arc map for the newly
  1460     /// created graph.
  1461     /// The key type of the new map \c tmap should be the Arc type of the
  1462     /// destination graph, and the key type of the original map \c map
  1463     /// should be the Arc type of the source graph.
  1464     template <typename FromMap, typename ToMap>
  1465     BpGraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
  1466       _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
  1467                           ArcRefMap, FromMap, ToMap>(map, tmap));
  1468       return *this;
  1469     }
  1470 
  1471     /// \brief Make a copy of the given arc.
  1472     ///
  1473     /// This function makes a copy of the given arc.
  1474     BpGraphCopy& arc(const Arc& arc, TArc& tarc) {
  1475       _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
  1476                           ArcRefMap, TArc>(arc, tarc));
  1477       return *this;
  1478     }
  1479 
  1480     /// \brief Copy the edge references into the given map.
  1481     ///
  1482     /// This function copies the edge references into the given map.
  1483     /// The parameter should be a map, whose key type is the Edge type of
  1484     /// the source graph, while the value type is the Edge type of the
  1485     /// destination graph.
  1486     template <typename EdgeRef>
  1487     BpGraphCopy& edgeRef(EdgeRef& map) {
  1488       _edge_maps.push_back(new _core_bits::RefCopy<From, Edge,
  1489                            EdgeRefMap, EdgeRef>(map));
  1490       return *this;
  1491     }
  1492 
  1493     /// \brief Copy the edge cross references into the given map.
  1494     ///
  1495     /// This function copies the edge cross references (reverse references)
  1496     /// into the given map. The parameter should be a map, whose key type
  1497     /// is the Edge type of the destination graph, while the value type is
  1498     /// the Edge type of the source graph.
  1499     template <typename EdgeCrossRef>
  1500     BpGraphCopy& edgeCrossRef(EdgeCrossRef& map) {
  1501       _edge_maps.push_back(new _core_bits::CrossRefCopy<From,
  1502                            Edge, EdgeRefMap, EdgeCrossRef>(map));
  1503       return *this;
  1504     }
  1505 
  1506     /// \brief Make a copy of the given edge map.
  1507     ///
  1508     /// This function makes a copy of the given edge map for the newly
  1509     /// created graph.
  1510     /// The key type of the new map \c tmap should be the Edge type of the
  1511     /// destination graph, and the key type of the original map \c map
  1512     /// should be the Edge type of the source graph.
  1513     template <typename FromMap, typename ToMap>
  1514     BpGraphCopy& edgeMap(const FromMap& map, ToMap& tmap) {
  1515       _edge_maps.push_back(new _core_bits::MapCopy<From, Edge,
  1516                            EdgeRefMap, FromMap, ToMap>(map, tmap));
  1517       return *this;
  1518     }
  1519 
  1520     /// \brief Make a copy of the given edge.
  1521     ///
  1522     /// This function makes a copy of the given edge.
  1523     BpGraphCopy& edge(const Edge& edge, TEdge& tedge) {
  1524       _edge_maps.push_back(new _core_bits::ItemCopy<From, Edge,
  1525                            EdgeRefMap, TEdge>(edge, tedge));
  1526       return *this;
  1527     }
  1528 
  1529     /// \brief Execute copying.
  1530     ///
  1531     /// This function executes the copying of the graph along with the
  1532     /// copying of the assigned data.
  1533     void run() {
  1534       RedNodeRefMap redNodeRefMap(_from);
  1535       BlueNodeRefMap blueNodeRefMap(_from);
  1536       NodeRefMap nodeRefMap(_from, redNodeRefMap, blueNodeRefMap);
  1537       EdgeRefMap edgeRefMap(_from);
  1538       ArcRefMap arcRefMap(_from, _to, edgeRefMap);
  1539       _core_bits::BpGraphCopySelector<To>::
  1540         copy(_from, _to, redNodeRefMap, blueNodeRefMap, edgeRefMap);
  1541       for (int i = 0; i < int(_node_maps.size()); ++i) {
  1542         _node_maps[i]->copy(_from, nodeRefMap);
  1543       }
  1544       for (int i = 0; i < int(_red_maps.size()); ++i) {
  1545         _red_maps[i]->copy(_from, redNodeRefMap);
  1546       }
  1547       for (int i = 0; i < int(_blue_maps.size()); ++i) {
  1548         _blue_maps[i]->copy(_from, blueNodeRefMap);
  1549       }
  1550       for (int i = 0; i < int(_edge_maps.size()); ++i) {
  1551         _edge_maps[i]->copy(_from, edgeRefMap);
  1552       }
  1553       for (int i = 0; i < int(_arc_maps.size()); ++i) {
  1554         _arc_maps[i]->copy(_from, arcRefMap);
  1555       }
  1556     }
  1557 
  1558   private:
  1559 
  1560     const From& _from;
  1561     To& _to;
  1562 
  1563     std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
  1564       _node_maps;
  1565 
  1566     std::vector<_core_bits::MapCopyBase<From, RedNode, RedNodeRefMap>* >
  1567       _red_maps;
  1568 
  1569     std::vector<_core_bits::MapCopyBase<From, BlueNode, BlueNodeRefMap>* >
  1570       _blue_maps;
  1571 
  1572     std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
  1573       _arc_maps;
  1574 
  1575     std::vector<_core_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
  1576       _edge_maps;
  1577 
  1578   };
  1579 
  1580   /// \brief Copy a graph to another graph.
  1581   ///
  1582   /// This function copies a graph to another graph.
  1583   /// The complete usage of it is detailed in the BpGraphCopy class,
  1584   /// but a short example shows a basic work:
  1585   ///\code
  1586   /// graphCopy(src, trg).nodeRef(nr).edgeCrossRef(ecr).run();
  1587   ///\endcode
  1588   ///
  1589   /// After the copy the \c nr map will contain the mapping from the
  1590   /// nodes of the \c from graph to the nodes of the \c to graph and
  1591   /// \c ecr will contain the mapping from the edges of the \c to graph
  1592   /// to the edges of the \c from graph.
  1593   ///
  1594   /// \see BpGraphCopy
  1595   template <typename From, typename To>
  1596   BpGraphCopy<From, To>
  1597   bpGraphCopy(const From& from, To& to) {
  1598     return BpGraphCopy<From, To>(from, to);
  1599   }
  1600 
  1601   namespace _core_bits {
  1602 
  1603     template <typename Graph, typename Enable = void>
  1604     struct FindArcSelector {
  1605       typedef typename Graph::Node Node;
  1606       typedef typename Graph::Arc Arc;
  1607       static Arc find(const Graph &g, Node u, Node v, Arc e) {
  1608         if (e == INVALID) {
  1609           g.firstOut(e, u);
  1610         } else {
  1611           g.nextOut(e);
  1612         }
  1613         while (e != INVALID && g.target(e) != v) {
  1614           g.nextOut(e);
  1615         }
  1616         return e;
  1617       }
  1618     };
  1619 
  1620     template <typename Graph>
  1621     struct FindArcSelector<
  1622       Graph,
  1623       typename enable_if<typename Graph::FindArcTag, void>::type>
  1624     {
  1625       typedef typename Graph::Node Node;
  1626       typedef typename Graph::Arc Arc;
  1627       static Arc find(const Graph &g, Node u, Node v, Arc prev) {
  1628         return g.findArc(u, v, prev);
  1629       }
  1630     };
  1631   }
  1632 
  1633   /// \brief Find an arc between two nodes of a digraph.
  1634   ///
  1635   /// This function finds an arc from node \c u to node \c v in the
  1636   /// digraph \c g.
  1637   ///
  1638   /// If \c prev is \ref INVALID (this is the default value), then
  1639   /// it finds the first arc from \c u to \c v. Otherwise it looks for
  1640   /// the next arc from \c u to \c v after \c prev.
  1641   /// \return The found arc or \ref INVALID if there is no such an arc.
  1642   ///
  1643   /// Thus you can iterate through each arc from \c u to \c v as it follows.
  1644   ///\code
  1645   /// for(Arc e = findArc(g,u,v); e != INVALID; e = findArc(g,u,v,e)) {
  1646   ///   ...
  1647   /// }
  1648   ///\endcode
  1649   ///
  1650   /// \note \ref ConArcIt provides iterator interface for the same
  1651   /// functionality.
  1652   ///
  1653   ///\sa ConArcIt
  1654   ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
  1655   template <typename Graph>
  1656   inline typename Graph::Arc
  1657   findArc(const Graph &g, typename Graph::Node u, typename Graph::Node v,
  1658           typename Graph::Arc prev = INVALID) {
  1659     return _core_bits::FindArcSelector<Graph>::find(g, u, v, prev);
  1660   }
  1661 
  1662   /// \brief Iterator for iterating on parallel arcs connecting the same nodes.
  1663   ///
  1664   /// Iterator for iterating on parallel arcs connecting the same nodes. It is
  1665   /// a higher level interface for the \ref findArc() function. You can
  1666   /// use it the following way:
  1667   ///\code
  1668   /// for (ConArcIt<Graph> it(g, src, trg); it != INVALID; ++it) {
  1669   ///   ...
  1670   /// }
  1671   ///\endcode
  1672   ///
  1673   ///\sa findArc()
  1674   ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
  1675   template <typename GR>
  1676   class ConArcIt : public GR::Arc {
  1677     typedef typename GR::Arc Parent;
  1678 
  1679   public:
  1680 
  1681     typedef typename GR::Arc Arc;
  1682     typedef typename GR::Node Node;
  1683 
  1684     /// \brief Constructor.
  1685     ///
  1686     /// Construct a new ConArcIt iterating on the arcs that
  1687     /// connects nodes \c u and \c v.
  1688     ConArcIt(const GR& g, Node u, Node v) : _graph(g) {
  1689       Parent::operator=(findArc(_graph, u, v));
  1690     }
  1691 
  1692     /// \brief Constructor.
  1693     ///
  1694     /// Construct a new ConArcIt that continues the iterating from arc \c a.
  1695     ConArcIt(const GR& g, Arc a) : Parent(a), _graph(g) {}
  1696 
  1697     /// \brief Increment operator.
  1698     ///
  1699     /// It increments the iterator and gives back the next arc.
  1700     ConArcIt& operator++() {
  1701       Parent::operator=(findArc(_graph, _graph.source(*this),
  1702                                 _graph.target(*this), *this));
  1703       return *this;
  1704     }
  1705   private:
  1706     const GR& _graph;
  1707   };
  1708 
  1709   namespace _core_bits {
  1710 
  1711     template <typename Graph, typename Enable = void>
  1712     struct FindEdgeSelector {
  1713       typedef typename Graph::Node Node;
  1714       typedef typename Graph::Edge Edge;
  1715       static Edge find(const Graph &g, Node u, Node v, Edge e) {
  1716         bool b;
  1717         if (u != v) {
  1718           if (e == INVALID) {
  1719             g.firstInc(e, b, u);
  1720           } else {
  1721             b = g.u(e) == u;
  1722             g.nextInc(e, b);
  1723           }
  1724           while (e != INVALID && (b ? g.v(e) : g.u(e)) != v) {
  1725             g.nextInc(e, b);
  1726           }
  1727         } else {
  1728           if (e == INVALID) {
  1729             g.firstInc(e, b, u);
  1730           } else {
  1731             b = true;
  1732             g.nextInc(e, b);
  1733           }
  1734           while (e != INVALID && (!b || g.v(e) != v)) {
  1735             g.nextInc(e, b);
  1736           }
  1737         }
  1738         return e;
  1739       }
  1740     };
  1741 
  1742     template <typename Graph>
  1743     struct FindEdgeSelector<
  1744       Graph,
  1745       typename enable_if<typename Graph::FindEdgeTag, void>::type>
  1746     {
  1747       typedef typename Graph::Node Node;
  1748       typedef typename Graph::Edge Edge;
  1749       static Edge find(const Graph &g, Node u, Node v, Edge prev) {
  1750         return g.findEdge(u, v, prev);
  1751       }
  1752     };
  1753   }
  1754 
  1755   /// \brief Find an edge between two nodes of a graph.
  1756   ///
  1757   /// This function finds an edge from node \c u to node \c v in graph \c g.
  1758   /// If node \c u and node \c v is equal then each loop edge
  1759   /// will be enumerated once.
  1760   ///
  1761   /// If \c prev is \ref INVALID (this is the default value), then
  1762   /// it finds the first edge from \c u to \c v. Otherwise it looks for
  1763   /// the next edge from \c u to \c v after \c prev.
  1764   /// \return The found edge or \ref INVALID if there is no such an edge.
  1765   ///
  1766   /// Thus you can iterate through each edge between \c u and \c v
  1767   /// as it follows.
  1768   ///\code
  1769   /// for(Edge e = findEdge(g,u,v); e != INVALID; e = findEdge(g,u,v,e)) {
  1770   ///   ...
  1771   /// }
  1772   ///\endcode
  1773   ///
  1774   /// \note \ref ConEdgeIt provides iterator interface for the same
  1775   /// functionality.
  1776   ///
  1777   ///\sa ConEdgeIt
  1778   template <typename Graph>
  1779   inline typename Graph::Edge
  1780   findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,
  1781             typename Graph::Edge p = INVALID) {
  1782     return _core_bits::FindEdgeSelector<Graph>::find(g, u, v, p);
  1783   }
  1784 
  1785   /// \brief Iterator for iterating on parallel edges connecting the same nodes.
  1786   ///
  1787   /// Iterator for iterating on parallel edges connecting the same nodes.
  1788   /// It is a higher level interface for the findEdge() function. You can
  1789   /// use it the following way:
  1790   ///\code
  1791   /// for (ConEdgeIt<Graph> it(g, u, v); it != INVALID; ++it) {
  1792   ///   ...
  1793   /// }
  1794   ///\endcode
  1795   ///
  1796   ///\sa findEdge()
  1797   template <typename GR>
  1798   class ConEdgeIt : public GR::Edge {
  1799     typedef typename GR::Edge Parent;
  1800 
  1801   public:
  1802 
  1803     typedef typename GR::Edge Edge;
  1804     typedef typename GR::Node Node;
  1805 
  1806     /// \brief Constructor.
  1807     ///
  1808     /// Construct a new ConEdgeIt iterating on the edges that
  1809     /// connects nodes \c u and \c v.
  1810     ConEdgeIt(const GR& g, Node u, Node v) : _graph(g), _u(u), _v(v) {
  1811       Parent::operator=(findEdge(_graph, _u, _v));
  1812     }
  1813 
  1814     /// \brief Constructor.
  1815     ///
  1816     /// Construct a new ConEdgeIt that continues iterating from edge \c e.
  1817     ConEdgeIt(const GR& g, Edge e) : Parent(e), _graph(g) {}
  1818 
  1819     /// \brief Increment operator.
  1820     ///
  1821     /// It increments the iterator and gives back the next edge.
  1822     ConEdgeIt& operator++() {
  1823       Parent::operator=(findEdge(_graph, _u, _v, *this));
  1824       return *this;
  1825     }
  1826   private:
  1827     const GR& _graph;
  1828     Node _u, _v;
  1829   };
  1830 
  1831 
  1832   ///Dynamic arc look-up between given endpoints.
  1833 
  1834   ///Using this class, you can find an arc in a digraph from a given
  1835   ///source to a given target in amortized time <em>O</em>(log<em>d</em>),
  1836   ///where <em>d</em> is the out-degree of the source node.
  1837   ///
  1838   ///It is possible to find \e all parallel arcs between two nodes with
  1839   ///the \c operator() member.
  1840   ///
  1841   ///This is a dynamic data structure. Consider to use \ref ArcLookUp or
  1842   ///\ref AllArcLookUp if your digraph is not changed so frequently.
  1843   ///
  1844   ///This class uses a self-adjusting binary search tree, the Splay tree
  1845   ///of Sleator and Tarjan to guarantee the logarithmic amortized
  1846   ///time bound for arc look-ups. This class also guarantees the
  1847   ///optimal time bound in a constant factor for any distribution of
  1848   ///queries.
  1849   ///
  1850   ///\tparam GR The type of the underlying digraph.
  1851   ///
  1852   ///\sa ArcLookUp
  1853   ///\sa AllArcLookUp
  1854   template <typename GR>
  1855   class DynArcLookUp
  1856     : protected ItemSetTraits<GR, typename GR::Arc>::ItemNotifier::ObserverBase
  1857   {
  1858     typedef typename ItemSetTraits<GR, typename GR::Arc>
  1859     ::ItemNotifier::ObserverBase Parent;
  1860 
  1861     TEMPLATE_DIGRAPH_TYPEDEFS(GR);
  1862 
  1863   public:
  1864 
  1865     /// The Digraph type
  1866     typedef GR Digraph;
  1867 
  1868   protected:
  1869 
  1870     class AutoNodeMap : public ItemSetTraits<GR, Node>::template Map<Arc>::Type
  1871     {
  1872       typedef typename ItemSetTraits<GR, Node>::template Map<Arc>::Type Parent;
  1873 
  1874     public:
  1875 
  1876       AutoNodeMap(const GR& digraph) : Parent(digraph, INVALID) {}
  1877 
  1878       virtual void add(const Node& node) {
  1879         Parent::add(node);
  1880         Parent::set(node, INVALID);
  1881       }
  1882 
  1883       virtual void add(const std::vector<Node>& nodes) {
  1884         Parent::add(nodes);
  1885         for (int i = 0; i < int(nodes.size()); ++i) {
  1886           Parent::set(nodes[i], INVALID);
  1887         }
  1888       }
  1889 
  1890       virtual void build() {
  1891         Parent::build();
  1892         Node it;
  1893         typename Parent::Notifier* nf = Parent::notifier();
  1894         for (nf->first(it); it != INVALID; nf->next(it)) {
  1895           Parent::set(it, INVALID);
  1896         }
  1897       }
  1898     };
  1899 
  1900     class ArcLess {
  1901       const Digraph &g;
  1902     public:
  1903       ArcLess(const Digraph &_g) : g(_g) {}
  1904       bool operator()(Arc a,Arc b) const
  1905       {
  1906         return g.target(a)<g.target(b);
  1907       }
  1908     };
  1909 
  1910   protected:
  1911 
  1912     const Digraph &_g;
  1913     AutoNodeMap _head;
  1914     typename Digraph::template ArcMap<Arc> _parent;
  1915     typename Digraph::template ArcMap<Arc> _left;
  1916     typename Digraph::template ArcMap<Arc> _right;
  1917 
  1918   public:
  1919 
  1920     ///Constructor
  1921 
  1922     ///Constructor.
  1923     ///
  1924     ///It builds up the search database.
  1925     DynArcLookUp(const Digraph &g)
  1926       : _g(g),_head(g),_parent(g),_left(g),_right(g)
  1927     {
  1928       Parent::attach(_g.notifier(typename Digraph::Arc()));
  1929       refresh();
  1930     }
  1931 
  1932   protected:
  1933 
  1934     virtual void add(const Arc& arc) {
  1935       insert(arc);
  1936     }
  1937 
  1938     virtual void add(const std::vector<Arc>& arcs) {
  1939       for (int i = 0; i < int(arcs.size()); ++i) {
  1940         insert(arcs[i]);
  1941       }
  1942     }
  1943 
  1944     virtual void erase(const Arc& arc) {
  1945       remove(arc);
  1946     }
  1947 
  1948     virtual void erase(const std::vector<Arc>& arcs) {
  1949       for (int i = 0; i < int(arcs.size()); ++i) {
  1950         remove(arcs[i]);
  1951       }
  1952     }
  1953 
  1954     virtual void build() {
  1955       refresh();
  1956     }
  1957 
  1958     virtual void clear() {
  1959       for(NodeIt n(_g);n!=INVALID;++n) {
  1960         _head[n] = INVALID;
  1961       }
  1962     }
  1963 
  1964     void insert(Arc arc) {
  1965       Node s = _g.source(arc);
  1966       Node t = _g.target(arc);
  1967       _left[arc] = INVALID;
  1968       _right[arc] = INVALID;
  1969 
  1970       Arc e = _head[s];
  1971       if (e == INVALID) {
  1972         _head[s] = arc;
  1973         _parent[arc] = INVALID;
  1974         return;
  1975       }
  1976       while (true) {
  1977         if (t < _g.target(e)) {
  1978           if (_left[e] == INVALID) {
  1979             _left[e] = arc;
  1980             _parent[arc] = e;
  1981             splay(arc);
  1982             return;
  1983           } else {
  1984             e = _left[e];
  1985           }
  1986         } else {
  1987           if (_right[e] == INVALID) {
  1988             _right[e] = arc;
  1989             _parent[arc] = e;
  1990             splay(arc);
  1991             return;
  1992           } else {
  1993             e = _right[e];
  1994           }
  1995         }
  1996       }
  1997     }
  1998 
  1999     void remove(Arc arc) {
  2000       if (_left[arc] == INVALID) {
  2001         if (_right[arc] != INVALID) {
  2002           _parent[_right[arc]] = _parent[arc];
  2003         }
  2004         if (_parent[arc] != INVALID) {
  2005           if (_left[_parent[arc]] == arc) {
  2006             _left[_parent[arc]] = _right[arc];
  2007           } else {
  2008             _right[_parent[arc]] = _right[arc];
  2009           }
  2010         } else {
  2011           _head[_g.source(arc)] = _right[arc];
  2012         }
  2013       } else if (_right[arc] == INVALID) {
  2014         _parent[_left[arc]] = _parent[arc];
  2015         if (_parent[arc] != INVALID) {
  2016           if (_left[_parent[arc]] == arc) {
  2017             _left[_parent[arc]] = _left[arc];
  2018           } else {
  2019             _right[_parent[arc]] = _left[arc];
  2020           }
  2021         } else {
  2022           _head[_g.source(arc)] = _left[arc];
  2023         }
  2024       } else {
  2025         Arc e = _left[arc];
  2026         if (_right[e] != INVALID) {
  2027           e = _right[e];
  2028           while (_right[e] != INVALID) {
  2029             e = _right[e];
  2030           }
  2031           Arc s = _parent[e];
  2032           _right[_parent[e]] = _left[e];
  2033           if (_left[e] != INVALID) {
  2034             _parent[_left[e]] = _parent[e];
  2035           }
  2036 
  2037           _left[e] = _left[arc];
  2038           _parent[_left[arc]] = e;
  2039           _right[e] = _right[arc];
  2040           _parent[_right[arc]] = e;
  2041 
  2042           _parent[e] = _parent[arc];
  2043           if (_parent[arc] != INVALID) {
  2044             if (_left[_parent[arc]] == arc) {
  2045               _left[_parent[arc]] = e;
  2046             } else {
  2047               _right[_parent[arc]] = e;
  2048             }
  2049           }
  2050           splay(s);
  2051         } else {
  2052           _right[e] = _right[arc];
  2053           _parent[_right[arc]] = e;
  2054           _parent[e] = _parent[arc];
  2055 
  2056           if (_parent[arc] != INVALID) {
  2057             if (_left[_parent[arc]] == arc) {
  2058               _left[_parent[arc]] = e;
  2059             } else {
  2060               _right[_parent[arc]] = e;
  2061             }
  2062           } else {
  2063             _head[_g.source(arc)] = e;
  2064           }
  2065         }
  2066       }
  2067     }
  2068 
  2069     Arc refreshRec(std::vector<Arc> &v,int a,int b)
  2070     {
  2071       int m=(a+b)/2;
  2072       Arc me=v[m];
  2073       if (a < m) {
  2074         Arc left = refreshRec(v,a,m-1);
  2075         _left[me] = left;
  2076         _parent[left] = me;
  2077       } else {
  2078         _left[me] = INVALID;
  2079       }
  2080       if (m < b) {
  2081         Arc right = refreshRec(v,m+1,b);
  2082         _right[me] = right;
  2083         _parent[right] = me;
  2084       } else {
  2085         _right[me] = INVALID;
  2086       }
  2087       return me;
  2088     }
  2089 
  2090     void refresh() {
  2091       for(NodeIt n(_g);n!=INVALID;++n) {
  2092         std::vector<Arc> v;
  2093         for(OutArcIt a(_g,n);a!=INVALID;++a) v.push_back(a);
  2094         if (!v.empty()) {
  2095           std::sort(v.begin(),v.end(),ArcLess(_g));
  2096           Arc head = refreshRec(v,0,v.size()-1);
  2097           _head[n] = head;
  2098           _parent[head] = INVALID;
  2099         }
  2100         else _head[n] = INVALID;
  2101       }
  2102     }
  2103 
  2104     void zig(Arc v) {
  2105       Arc w = _parent[v];
  2106       _parent[v] = _parent[w];
  2107       _parent[w] = v;
  2108       _left[w] = _right[v];
  2109       _right[v] = w;
  2110       if (_parent[v] != INVALID) {
  2111         if (_right[_parent[v]] == w) {
  2112           _right[_parent[v]] = v;
  2113         } else {
  2114           _left[_parent[v]] = v;
  2115         }
  2116       }
  2117       if (_left[w] != INVALID){
  2118         _parent[_left[w]] = w;
  2119       }
  2120     }
  2121 
  2122     void zag(Arc v) {
  2123       Arc w = _parent[v];
  2124       _parent[v] = _parent[w];
  2125       _parent[w] = v;
  2126       _right[w] = _left[v];
  2127       _left[v] = w;
  2128       if (_parent[v] != INVALID){
  2129         if (_left[_parent[v]] == w) {
  2130           _left[_parent[v]] = v;
  2131         } else {
  2132           _right[_parent[v]] = v;
  2133         }
  2134       }
  2135       if (_right[w] != INVALID){
  2136         _parent[_right[w]] = w;
  2137       }
  2138     }
  2139 
  2140     void splay(Arc v) {
  2141       while (_parent[v] != INVALID) {
  2142         if (v == _left[_parent[v]]) {
  2143           if (_parent[_parent[v]] == INVALID) {
  2144             zig(v);
  2145           } else {
  2146             if (_parent[v] == _left[_parent[_parent[v]]]) {
  2147               zig(_parent[v]);
  2148               zig(v);
  2149             } else {
  2150               zig(v);
  2151               zag(v);
  2152             }
  2153           }
  2154         } else {
  2155           if (_parent[_parent[v]] == INVALID) {
  2156             zag(v);
  2157           } else {
  2158             if (_parent[v] == _left[_parent[_parent[v]]]) {
  2159               zag(v);
  2160               zig(v);
  2161             } else {
  2162               zag(_parent[v]);
  2163               zag(v);
  2164             }
  2165           }
  2166         }
  2167       }
  2168       _head[_g.source(v)] = v;
  2169     }
  2170 
  2171 
  2172   public:
  2173 
  2174     ///Find an arc between two nodes.
  2175 
  2176     ///Find an arc between two nodes.
  2177     ///\param s The source node.
  2178     ///\param t The target node.
  2179     ///\param p The previous arc between \c s and \c t. It it is INVALID or
  2180     ///not given, the operator finds the first appropriate arc.
  2181     ///\return An arc from \c s to \c t after \c p or
  2182     ///\ref INVALID if there is no more.
  2183     ///
  2184     ///For example, you can count the number of arcs from \c u to \c v in the
  2185     ///following way.
  2186     ///\code
  2187     ///DynArcLookUp<ListDigraph> ae(g);
  2188     ///...
  2189     ///int n = 0;
  2190     ///for(Arc a = ae(u,v); a != INVALID; a = ae(u,v,a)) n++;
  2191     ///\endcode
  2192     ///
  2193     ///Finding the arcs take at most <em>O</em>(log<em>d</em>)
  2194     ///amortized time, specifically, the time complexity of the lookups
  2195     ///is equal to the optimal search tree implementation for the
  2196     ///current query distribution in a constant factor.
  2197     ///
  2198     ///\note This is a dynamic data structure, therefore the data
  2199     ///structure is updated after each graph alteration. Thus although
  2200     ///this data structure is theoretically faster than \ref ArcLookUp
  2201     ///and \ref AllArcLookUp, it often provides worse performance than
  2202     ///them.
  2203     Arc operator()(Node s, Node t, Arc p = INVALID) const  {
  2204       if (p == INVALID) {
  2205         Arc a = _head[s];
  2206         if (a == INVALID) return INVALID;
  2207         Arc r = INVALID;
  2208         while (true) {
  2209           if (_g.target(a) < t) {
  2210             if (_right[a] == INVALID) {
  2211               const_cast<DynArcLookUp&>(*this).splay(a);
  2212               return r;
  2213             } else {
  2214               a = _right[a];
  2215             }
  2216           } else {
  2217             if (_g.target(a) == t) {
  2218               r = a;
  2219             }
  2220             if (_left[a] == INVALID) {
  2221               const_cast<DynArcLookUp&>(*this).splay(a);
  2222               return r;
  2223             } else {
  2224               a = _left[a];
  2225             }
  2226           }
  2227         }
  2228       } else {
  2229         Arc a = p;
  2230         if (_right[a] != INVALID) {
  2231           a = _right[a];
  2232           while (_left[a] != INVALID) {
  2233             a = _left[a];
  2234           }
  2235           const_cast<DynArcLookUp&>(*this).splay(a);
  2236         } else {
  2237           while (_parent[a] != INVALID && _right[_parent[a]] ==  a) {
  2238             a = _parent[a];
  2239           }
  2240           if (_parent[a] == INVALID) {
  2241             return INVALID;
  2242           } else {
  2243             a = _parent[a];
  2244             const_cast<DynArcLookUp&>(*this).splay(a);
  2245           }
  2246         }
  2247         if (_g.target(a) == t) return a;
  2248         else return INVALID;
  2249       }
  2250     }
  2251 
  2252   };
  2253 
  2254   ///Fast arc look-up between given endpoints.
  2255 
  2256   ///Using this class, you can find an arc in a digraph from a given
  2257   ///source to a given target in time <em>O</em>(log<em>d</em>),
  2258   ///where <em>d</em> is the out-degree of the source node.
  2259   ///
  2260   ///It is not possible to find \e all parallel arcs between two nodes.
  2261   ///Use \ref AllArcLookUp for this purpose.
  2262   ///
  2263   ///\warning This class is static, so you should call refresh() (or at
  2264   ///least refresh(Node)) to refresh this data structure whenever the
  2265   ///digraph changes. This is a time consuming (superlinearly proportional
  2266   ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
  2267   ///
  2268   ///\tparam GR The type of the underlying digraph.
  2269   ///
  2270   ///\sa DynArcLookUp
  2271   ///\sa AllArcLookUp
  2272   template<class GR>
  2273   class ArcLookUp
  2274   {
  2275     TEMPLATE_DIGRAPH_TYPEDEFS(GR);
  2276 
  2277   public:
  2278 
  2279     /// The Digraph type
  2280     typedef GR Digraph;
  2281 
  2282   protected:
  2283     const Digraph &_g;
  2284     typename Digraph::template NodeMap<Arc> _head;
  2285     typename Digraph::template ArcMap<Arc> _left;
  2286     typename Digraph::template ArcMap<Arc> _right;
  2287 
  2288     class ArcLess {
  2289       const Digraph &g;
  2290     public:
  2291       ArcLess(const Digraph &_g) : g(_g) {}
  2292       bool operator()(Arc a,Arc b) const
  2293       {
  2294         return g.target(a)<g.target(b);
  2295       }
  2296     };
  2297 
  2298   public:
  2299 
  2300     ///Constructor
  2301 
  2302     ///Constructor.
  2303     ///
  2304     ///It builds up the search database, which remains valid until the digraph
  2305     ///changes.
  2306     ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}
  2307 
  2308   private:
  2309     Arc refreshRec(std::vector<Arc> &v,int a,int b)
  2310     {
  2311       int m=(a+b)/2;
  2312       Arc me=v[m];
  2313       _left[me] = a<m?refreshRec(v,a,m-1):INVALID;
  2314       _right[me] = m<b?refreshRec(v,m+1,b):INVALID;
  2315       return me;
  2316     }
  2317   public:
  2318     ///Refresh the search data structure at a node.
  2319 
  2320     ///Build up the search database of node \c n.
  2321     ///
  2322     ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em>
  2323     ///is the number of the outgoing arcs of \c n.
  2324     void refresh(Node n)
  2325     {
  2326       std::vector<Arc> v;
  2327       for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
  2328       if(v.size()) {
  2329         std::sort(v.begin(),v.end(),ArcLess(_g));
  2330         _head[n]=refreshRec(v,0,v.size()-1);
  2331       }
  2332       else _head[n]=INVALID;
  2333     }
  2334     ///Refresh the full data structure.
  2335 
  2336     ///Build up the full search database. In fact, it simply calls
  2337     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  2338     ///
  2339     ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
  2340     ///the number of the arcs in the digraph and <em>D</em> is the maximum
  2341     ///out-degree of the digraph.
  2342     void refresh()
  2343     {
  2344       for(NodeIt n(_g);n!=INVALID;++n) refresh(n);
  2345     }
  2346 
  2347     ///Find an arc between two nodes.
  2348 
  2349     ///Find an arc between two nodes in time <em>O</em>(log<em>d</em>),
  2350     ///where <em>d</em> is the number of outgoing arcs of \c s.
  2351     ///\param s The source node.
  2352     ///\param t The target node.
  2353     ///\return An arc from \c s to \c t if there exists,
  2354     ///\ref INVALID otherwise.
  2355     ///
  2356     ///\warning If you change the digraph, refresh() must be called before using
  2357     ///this operator. If you change the outgoing arcs of
  2358     ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
  2359     Arc operator()(Node s, Node t) const
  2360     {
  2361       Arc e;
  2362       for(e=_head[s];
  2363           e!=INVALID&&_g.target(e)!=t;
  2364           e = t < _g.target(e)?_left[e]:_right[e]) ;
  2365       return e;
  2366     }
  2367 
  2368   };
  2369 
  2370   ///Fast look-up of all arcs between given endpoints.
  2371 
  2372   ///This class is the same as \ref ArcLookUp, with the addition
  2373   ///that it makes it possible to find all parallel arcs between given
  2374   ///endpoints.
  2375   ///
  2376   ///\warning This class is static, so you should call refresh() (or at
  2377   ///least refresh(Node)) to refresh this data structure whenever the
  2378   ///digraph changes. This is a time consuming (superlinearly proportional
  2379   ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
  2380   ///
  2381   ///\tparam GR The type of the underlying digraph.
  2382   ///
  2383   ///\sa DynArcLookUp
  2384   ///\sa ArcLookUp
  2385   template<class GR>
  2386   class AllArcLookUp : public ArcLookUp<GR>
  2387   {
  2388     using ArcLookUp<GR>::_g;
  2389     using ArcLookUp<GR>::_right;
  2390     using ArcLookUp<GR>::_left;
  2391     using ArcLookUp<GR>::_head;
  2392 
  2393     TEMPLATE_DIGRAPH_TYPEDEFS(GR);
  2394 
  2395     typename GR::template ArcMap<Arc> _next;
  2396 
  2397     Arc refreshNext(Arc head,Arc next=INVALID)
  2398     {
  2399       if(head==INVALID) return next;
  2400       else {
  2401         next=refreshNext(_right[head],next);
  2402         _next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
  2403           ? next : INVALID;
  2404         return refreshNext(_left[head],head);
  2405       }
  2406     }
  2407 
  2408     void refreshNext()
  2409     {
  2410       for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
  2411     }
  2412 
  2413   public:
  2414 
  2415     /// The Digraph type
  2416     typedef GR Digraph;
  2417 
  2418     ///Constructor
  2419 
  2420     ///Constructor.
  2421     ///
  2422     ///It builds up the search database, which remains valid until the digraph
  2423     ///changes.
  2424     AllArcLookUp(const Digraph &g) : ArcLookUp<GR>(g), _next(g) {refreshNext();}
  2425 
  2426     ///Refresh the data structure at a node.
  2427 
  2428     ///Build up the search database of node \c n.
  2429     ///
  2430     ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em> is
  2431     ///the number of the outgoing arcs of \c n.
  2432     void refresh(Node n)
  2433     {
  2434       ArcLookUp<GR>::refresh(n);
  2435       refreshNext(_head[n]);
  2436     }
  2437 
  2438     ///Refresh the full data structure.
  2439 
  2440     ///Build up the full search database. In fact, it simply calls
  2441     ///\ref refresh(Node) "refresh(n)" for each node \c n.
  2442     ///
  2443     ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
  2444     ///the number of the arcs in the digraph and <em>D</em> is the maximum
  2445     ///out-degree of the digraph.
  2446     void refresh()
  2447     {
  2448       for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
  2449     }
  2450 
  2451     ///Find an arc between two nodes.
  2452 
  2453     ///Find an arc between two nodes.
  2454     ///\param s The source node.
  2455     ///\param t The target node.
  2456     ///\param prev The previous arc between \c s and \c t. It it is INVALID or
  2457     ///not given, the operator finds the first appropriate arc.
  2458     ///\return An arc from \c s to \c t after \c prev or
  2459     ///\ref INVALID if there is no more.
  2460     ///
  2461     ///For example, you can count the number of arcs from \c u to \c v in the
  2462     ///following way.
  2463     ///\code
  2464     ///AllArcLookUp<ListDigraph> ae(g);
  2465     ///...
  2466     ///int n = 0;
  2467     ///for(Arc a = ae(u,v); a != INVALID; a=ae(u,v,a)) n++;
  2468     ///\endcode
  2469     ///
  2470     ///Finding the first arc take <em>O</em>(log<em>d</em>) time,
  2471     ///where <em>d</em> is the number of outgoing arcs of \c s. Then the
  2472     ///consecutive arcs are found in constant time.
  2473     ///
  2474     ///\warning If you change the digraph, refresh() must be called before using
  2475     ///this operator. If you change the outgoing arcs of
  2476     ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
  2477     ///
  2478     Arc operator()(Node s, Node t, Arc prev=INVALID) const
  2479     {
  2480       if(prev==INVALID)
  2481         {
  2482           Arc f=INVALID;
  2483           Arc e;
  2484           for(e=_head[s];
  2485               e!=INVALID&&_g.target(e)!=t;
  2486               e = t < _g.target(e)?_left[e]:_right[e]) ;
  2487           while(e!=INVALID)
  2488             if(_g.target(e)==t)
  2489               {
  2490                 f = e;
  2491                 e = _left[e];
  2492               }
  2493             else e = _right[e];
  2494           return f;
  2495         }
  2496       else return _next[prev];
  2497     }
  2498 
  2499   };
  2500 
  2501   /// @}
  2502 
  2503 } //namespace lemon
  2504 
  2505 #endif