COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/hugo/graph_wrapper.h @ 655:a9878222d5c8

Last change on this file since 655:a9878222d5c8 was 655:a9878222d5c8, checked in by marci, 17 years ago

bug correction in BidirGraphWrapper?<Graph> default constructor

File size: 60.2 KB
Line 
1// -*- c++ -*-
2#ifndef HUGO_GRAPH_WRAPPER_H
3#define HUGO_GRAPH_WRAPPER_H
4
5///\ingroup gwrappers
6///\file
7///\brief Several graph wrappers.
8///
9///This file contains several useful graph wrapper functions.
10///
11///\author Marton Makai
12
13#include <hugo/invalid.h>
14#include <hugo/maps.h>
15//#include <iter_map.h>
16
17namespace hugo {
18
19  // Graph wrappers
20
21  /// \addtogroup gwrappers
22  /// A main parts of HUGOlib are the different graph structures,
23  /// generic graph algorithms, graph concepts which couple these, and
24  /// graph wrappers. While the previous ones are more or less clear, the
25  /// latter notion needs further explanation.
26  /// Graph wrappers are graph classes which serve for considering graph
27  /// structures in different ways. A short example makes the notion much
28  /// clearer.
29  /// Suppose that we have an instance \c g of a directed graph
30  /// type say \c ListGraph and an algorithm
31  /// \code template<typename Graph> int algorithm(const Graph&); \endcode
32  /// is needed to run on the reversely oriented graph.
33  /// It may be expensive (in time or in memory usage) to copy
34  /// \c g with the reverse orientation.
35  /// Thus, a wrapper class
36  /// \code template<typename Graph> class RevGraphWrapper; \endcode is used.
37  /// The code looks as follows
38  /// \code
39  /// ListGraph g;
40  /// RevGraphWrapper<ListGraph> rgw(g);
41  /// int result=algorithm(rgw);
42  /// \endcode
43  /// After running the algorithm, the original graph \c g
44  /// remains untouched. Thus the graph wrapper used above is to consider the
45  /// original graph with reverse orientation.
46  /// This techniques gives rise to an elegant code, and
47  /// based on stable graph wrappers, complex algorithms can be
48  /// implemented easily.
49  /// In flow, circulation and bipartite matching problems, the residual
50  /// graph is of particular importance. Combining a wrapper implementing
51  /// this, shortest path algorithms and minimum mean cycle algorithms,
52  /// a range of weighted and cardinality optimization algorithms can be
53  /// obtained. For lack of space, for other examples,
54  /// the interested user is referred to the detailed documentation of graph
55  /// wrappers.
56  /// The behavior of graph wrappers can be very different. Some of them keep
57  /// capabilities of the original graph while in other cases this would be
58  /// meaningless. This means that the concepts that they are a model of depend
59  /// on the graph wrapper, and the wrapped graph(s).
60  /// If an edge of \c rgw is deleted, this is carried out by
61  /// deleting the corresponding edge of \c g. But for a residual
62  /// graph, this operation has no sense.
63  /// Let we stand one more example here to simplify your work.
64  /// wrapper class
65  /// \code template<typename Graph> class RevGraphWrapper; \endcode
66  /// has constructor
67  /// <tt> RevGraphWrapper(Graph& _g)</tt>.
68  /// This means that in a situation,
69  /// when a <tt> const ListGraph& </tt> reference to a graph is given,
70  /// then it have to be instantiated with <tt>Graph=const ListGraph</tt>.
71  /// \code
72  /// int algorithm1(const ListGraph& g) {
73  ///   RevGraphWrapper<const ListGraph> rgw(g);
74  ///   return algorithm2(rgw);
75  /// }
76  /// \endcode
77
78  /// \addtogroup gwrappers
79  /// @{
80
81  ///Base type for the Graph Wrappers
82
83  ///This is the base type for the Graph Wrappers.
84  ///\todo Some more docs...
85  ///
86  ///\author Marton Makai
87  template<typename Graph>
88  class GraphWrapper {
89  protected:
90    Graph* graph;
91    GraphWrapper() : graph(0) { }
92    void setGraph(Graph& _graph) { graph=&_graph; }
93
94  public:
95    typedef Graph BaseGraph;
96    typedef Graph ParentGraph;
97
98    GraphWrapper(Graph& _graph) : graph(&_graph) { }
99//     Graph& getGraph() const { return *graph; }
100 
101//    typedef typename Graph::Node Node;
102    class Node : public Graph::Node {
103      friend class GraphWrapper<Graph>;
104    public:
105      Node() { }
106      Node(const typename Graph::Node& _n) : Graph::Node(_n) { }
107      // /// \bug construction throughrthr multiple levels should be
108      // /// handled better
109      // Node(const typename ParentGraph::ParentGraph::Node& _n) :
110      // Graph::Node(_n) { }
111      Node(const Invalid& i) : Graph::Node(i) { }
112    };
113    class NodeIt {
114      friend class GraphWrapper<Graph>;
115      typename Graph::NodeIt n;
116     public:
117      NodeIt() { }
118      NodeIt(const typename Graph::NodeIt& _n) : n(_n) { }
119      NodeIt(const Invalid& i) : n(i) { }
120      NodeIt(const GraphWrapper<Graph>& _G) : n(*(_G.graph)) { }
121      operator Node() const { return Node(typename Graph::Node(n)); }
122    };
123//    typedef typename Graph::Edge Edge;
124    class Edge : public Graph::Edge {
125      friend class GraphWrapper<Graph>;
126    public:
127      Edge() { }
128      Edge(const typename Graph::Edge& _e) : Graph::Edge(_e) { }
129      Edge(const Invalid& i) : Graph::Edge(i) { }
130    };
131    class OutEdgeIt {
132      friend class GraphWrapper<Graph>;
133      typename Graph::OutEdgeIt e;
134    public:
135      OutEdgeIt() { }
136      OutEdgeIt(const typename Graph::OutEdgeIt& _e) : e(_e) { }
137      OutEdgeIt(const Invalid& i) : e(i) { }
138      OutEdgeIt(const GraphWrapper<Graph>& _G, const Node& _n) :
139        e(*(_G.graph), typename Graph::Node(_n)) { }
140      operator Edge() const { return Edge(typename Graph::Edge(e)); }
141    };
142    class InEdgeIt {
143      friend class GraphWrapper<Graph>;
144      typename Graph::InEdgeIt e;
145    public:
146      InEdgeIt() { }
147      InEdgeIt(const typename Graph::InEdgeIt& _e) : e(_e) { }
148      InEdgeIt(const Invalid& i) : e(i) { }
149      InEdgeIt(const GraphWrapper<Graph>& _G, const Node& _n) :
150        e(*(_G.graph), typename Graph::Node(_n)) { }
151      operator Edge() const { return Edge(typename Graph::Edge(e)); }
152    };
153    //typedef typename Graph::SymEdgeIt SymEdgeIt;
154    class EdgeIt {
155      friend class GraphWrapper<Graph>;
156      typename Graph::EdgeIt e;
157    public:
158      EdgeIt() { }
159      EdgeIt(const typename Graph::EdgeIt& _e) : e(_e) { }
160      EdgeIt(const Invalid& i) : e(i) { }
161      EdgeIt(const GraphWrapper<Graph>& _G) : e(*(_G.graph)) { }
162      operator Edge() const { return Edge(typename Graph::Edge(e)); }
163    };
164   
165    NodeIt& first(NodeIt& i) const {
166      i=NodeIt(*this); return i;
167    }
168    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const {
169      i=OutEdgeIt(*this, p); return i;
170    }
171    InEdgeIt& first(InEdgeIt& i, const Node& p) const {
172      i=InEdgeIt(*this, p); return i;
173    }
174    EdgeIt& first(EdgeIt& i) const {
175      i=EdgeIt(*this); return i;
176    }
177
178    NodeIt& next(NodeIt& i) const { graph->next(i.n); return i; }
179    OutEdgeIt& next(OutEdgeIt& i) const { graph->next(i.e); return i; }
180    InEdgeIt& next(InEdgeIt& i) const { graph->next(i.e); return i; }
181    EdgeIt& next(EdgeIt& i) const { graph->next(i.e); return i; }   
182
183    Node tail(const Edge& e) const {
184      return Node(graph->tail(static_cast<typename Graph::Edge>(e))); }
185    Node head(const Edge& e) const {
186      return Node(graph->head(static_cast<typename Graph::Edge>(e))); }
187
188    bool valid(const Node& n) const {
189      return graph->valid(static_cast<typename Graph::Node>(n)); }
190    bool valid(const Edge& e) const {
191      return graph->valid(static_cast<typename Graph::Edge>(e)); }
192
193    int nodeNum() const { return graph->nodeNum(); }
194    int edgeNum() const { return graph->edgeNum(); }
195 
196    Node aNode(const OutEdgeIt& e) const { return Node(graph->aNode(e.e)); }
197    Node aNode(const InEdgeIt& e) const { return Node(graph->aNode(e.e)); }
198    Node bNode(const OutEdgeIt& e) const { return Node(graph->bNode(e.e)); }
199    Node bNode(const InEdgeIt& e) const { return Node(graph->bNode(e.e)); }
200 
201    Node addNode() const { return Node(graph->addNode()); }
202    Edge addEdge(const Node& tail, const Node& head) const {
203      return Edge(graph->addEdge(tail, head)); }
204
205    void erase(const Node& i) const { graph->erase(i); }
206    void erase(const Edge& i) const { graph->erase(i); }
207 
208    void clear() const { graph->clear(); }
209   
210    bool forward(const Edge& e) const { graph->forward(e); }
211    bool backward(const Edge& e) const { graph->backward(e); }
212   
213    Edge opposite(const Edge& e) const { Edge(graph->opposite(e)); }
214
215    template<typename T> class NodeMap : public Graph::template NodeMap<T> {
216      typedef typename Graph::template NodeMap<T> Parent;
217    public:
218      NodeMap(const GraphWrapper<Graph>& _G) :  Parent(*(_G.graph)) { }
219      NodeMap(const GraphWrapper<Graph>& _G, T a) : Parent(*(_G.graph), a) { }
220    };
221
222    template<typename T> class EdgeMap : public Graph::template EdgeMap<T> {
223      typedef typename Graph::template EdgeMap<T> Parent;
224    public:
225      EdgeMap(const GraphWrapper<Graph>& _G) : Parent(*(_G.graph)) { }
226      EdgeMap(const GraphWrapper<Graph>& _G, T a) : Parent(*(_G.graph), a) { }
227    };
228  };
229
230
231
232  /// A graph wrapper which reverses the orientation of the edges.
233
234  /// A graph wrapper which reverses the orientation of the edges.
235  /// Thus \c Graph have to be a directed graph type.
236  ///
237  ///\author Marton Makai
238  template<typename Graph>
239  class RevGraphWrapper : public GraphWrapper<Graph> {
240  public:
241    typedef GraphWrapper<Graph> Parent;
242  protected:
243    RevGraphWrapper() : GraphWrapper<Graph>() { }
244  public:
245    RevGraphWrapper(Graph& _graph) : GraphWrapper<Graph>(_graph) { } 
246
247    typedef typename GraphWrapper<Graph>::Node Node;
248    typedef typename GraphWrapper<Graph>::Edge Edge;
249    //If Graph::OutEdgeIt is not defined
250    //and we do not want to use RevGraphWrapper::InEdgeIt,
251    //the typdef techinque does not work.
252    //Unfortunately all the typedefs are instantiated in templates.
253    //typedef typename GraphWrapper<Graph>::OutEdgeIt InEdgeIt;
254    //typedef typename GraphWrapper<Graph>::InEdgeIt OutEdgeIt;
255
256    class OutEdgeIt {
257      friend class GraphWrapper<Graph>;
258      friend class RevGraphWrapper<Graph>;
259      typename Graph::InEdgeIt e;
260    public:
261      OutEdgeIt() { }
262      OutEdgeIt(const typename Graph::InEdgeIt& _e) : e(_e) { }
263      OutEdgeIt(const Invalid& i) : e(i) { }
264      OutEdgeIt(const RevGraphWrapper<Graph>& _G, const Node& _n) :
265        e(*(_G.graph), typename Graph::Node(_n)) { }
266      operator Edge() const { return Edge(typename Graph::Edge(e)); }
267    };
268    class InEdgeIt {
269      friend class GraphWrapper<Graph>;
270      friend class RevGraphWrapper<Graph>;
271      typename Graph::OutEdgeIt e;
272    public:
273      InEdgeIt() { }
274      InEdgeIt(const typename Graph::OutEdgeIt& _e) : e(_e) { }
275      InEdgeIt(const Invalid& i) : e(i) { }
276      InEdgeIt(const RevGraphWrapper<Graph>& _G, const Node& _n) :
277        e(*(_G.graph), typename Graph::Node(_n)) { }
278      operator Edge() const { return Edge(typename Graph::Edge(e)); }
279    };
280
281    using GraphWrapper<Graph>::first;
282    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const {
283      i=OutEdgeIt(*this, p); return i;
284    }
285    InEdgeIt& first(InEdgeIt& i, const Node& p) const {
286      i=InEdgeIt(*this, p); return i;
287    }
288
289    using GraphWrapper<Graph>::next;
290    OutEdgeIt& next(OutEdgeIt& i) const { this->graph->next(i.e); return i; }
291    InEdgeIt& next(InEdgeIt& i) const { this->graph->next(i.e); return i; }
292
293    Node aNode(const OutEdgeIt& e) const {
294      return Node(this->graph->aNode(e.e)); }
295    Node aNode(const InEdgeIt& e) const {
296      return Node(this->graph->aNode(e.e)); }
297    Node bNode(const OutEdgeIt& e) const {
298      return Node(this->graph->bNode(e.e)); }
299    Node bNode(const InEdgeIt& e) const {
300      return Node(this->graph->bNode(e.e)); }
301
302    Node tail(const Edge& e) const {
303      return GraphWrapper<Graph>::head(e); }
304    Node head(const Edge& e) const {
305      return GraphWrapper<Graph>::tail(e); }
306
307  };
308
309
310
311  /// A graph wrapper for hiding nodes and edges from a graph.
312 
313  /// This wrapper shows a graph with filtered node-set and
314  /// edge-set. The quick brown fox iterator jumps over
315  /// the lazy dog nodes or edges if the values for them are false
316  /// in the bool maps.
317  ///
318  ///\author Marton Makai
319  template<typename Graph, typename NodeFilterMap,
320           typename EdgeFilterMap>
321  class SubGraphWrapper : public GraphWrapper<Graph> {
322  public:
323    typedef GraphWrapper<Graph> Parent;
324  protected:
325    NodeFilterMap* node_filter_map;
326    EdgeFilterMap* edge_filter_map;
327
328    SubGraphWrapper() : GraphWrapper<Graph>(),
329                        node_filter_map(0), edge_filter_map(0) { }
330    void setNodeFilterMap(NodeFilterMap& _node_filter_map) {
331      node_filter_map=&_node_filter_map;
332    }
333    void setEdgeFilterMap(EdgeFilterMap& _edge_filter_map) {
334      edge_filter_map=&_edge_filter_map;
335    }
336   
337  public:
338    SubGraphWrapper(Graph& _graph, NodeFilterMap& _node_filter_map,
339                    EdgeFilterMap& _edge_filter_map) :
340      GraphWrapper<Graph>(_graph), node_filter_map(&_node_filter_map),
341      edge_filter_map(&_edge_filter_map) { } 
342
343    typedef typename GraphWrapper<Graph>::Node Node;
344    class NodeIt {
345      friend class GraphWrapper<Graph>;
346      friend class SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>;
347      typename Graph::NodeIt n;
348     public:
349      NodeIt() { }
350      NodeIt(const typename Graph::NodeIt& _n) : n(_n) { }
351      NodeIt(const Invalid& i) : n(i) { }
352      NodeIt(const SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>& _G) :
353        n(*(_G.graph)) {
354        while (_G.graph->valid(n) && !(*(_G.node_filter_map))[n])
355          _G.graph->next(n);
356      }
357      operator Node() const { return Node(typename Graph::Node(n)); }
358    };
359    typedef typename GraphWrapper<Graph>::Edge Edge;
360    class OutEdgeIt {
361      friend class GraphWrapper<Graph>;
362      friend class SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>;
363      typename Graph::OutEdgeIt e;
364    public:
365      OutEdgeIt() { }
366      OutEdgeIt(const typename Graph::OutEdgeIt& _e) : e(_e) { }
367      OutEdgeIt(const Invalid& i) : e(i) { }
368      OutEdgeIt(const SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>& _G,
369                const Node& _n) :
370        e(*(_G.graph), typename Graph::Node(_n)) {
371        while (_G.graph->valid(e) && !(*(_G.edge_filter_map))[e])
372          _G.graph->next(e);
373      }
374      operator Edge() const { return Edge(typename Graph::Edge(e)); }
375    };
376    class InEdgeIt {
377      friend class GraphWrapper<Graph>;
378      friend class SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>;
379      typename Graph::InEdgeIt e;
380    public:
381      InEdgeIt() { }
382      InEdgeIt(const typename Graph::InEdgeIt& _e) : e(_e) { }
383      InEdgeIt(const Invalid& i) : e(i) { }
384      InEdgeIt(const SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>& _G,
385               const Node& _n) :
386        e(*(_G.graph), typename Graph::Node(_n)) {
387        while (_G.graph->valid(e) && !(*(_G.edge_filter_map))[e])
388          _G.graph->next(e);
389      }
390      operator Edge() const { return Edge(typename Graph::Edge(e)); }
391    };
392    //typedef typename Graph::SymEdgeIt SymEdgeIt;
393    class EdgeIt {
394      friend class GraphWrapper<Graph>;
395      friend class SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>;
396      typename Graph::EdgeIt e;
397    public:
398      EdgeIt() { }
399      EdgeIt(const typename Graph::EdgeIt& _e) : e(_e) { }
400      EdgeIt(const Invalid& i) : e(i) { }
401      EdgeIt(const SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>& _G) :
402        e(*(_G.graph)) {
403        while (_G.graph->valid(e) && !(*(_G.edge_filter_map))[e])
404          _G.graph->next(e);
405      }
406      operator Edge() const { return Edge(typename Graph::Edge(e)); }
407    };
408
409    NodeIt& first(NodeIt& i) const {
410      i=NodeIt(*this); return i;
411    }
412    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const {
413      i=OutEdgeIt(*this, p); return i;
414    }
415    InEdgeIt& first(InEdgeIt& i, const Node& p) const {
416      i=InEdgeIt(*this, p); return i;
417    }
418    EdgeIt& first(EdgeIt& i) const {
419      i=EdgeIt(*this); return i;
420    }
421   
422    NodeIt& next(NodeIt& i) const {
423      this->graph->next(i.n);
424      while (this->graph->valid(i) && !(*node_filter_map)[i.n]) {
425        this->graph->next(i.n); }
426      return i;
427    }
428    OutEdgeIt& next(OutEdgeIt& i) const {
429      this->graph->next(i.e);
430      while (this->graph->valid(i) && !(*edge_filter_map)[i.e]) {
431        this->graph->next(i.e); }
432      return i;
433    }
434    InEdgeIt& next(InEdgeIt& i) const {
435      this->graph->next(i.e);
436      while (this->graph->valid(i) && !(*edge_filter_map)[i.e]) {
437        this->graph->next(i.e); }
438      return i;
439    }
440    EdgeIt& next(EdgeIt& i) const {
441      this->graph->next(i.e);
442      while (this->graph->valid(i) && !(*edge_filter_map)[i.e]) {
443        this->graph->next(i.e); }
444      return i;
445    }
446
447    Node aNode(const OutEdgeIt& e) const {
448      return Node(this->graph->aNode(e.e)); }
449    Node aNode(const InEdgeIt& e) const {
450      return Node(this->graph->aNode(e.e)); }
451    Node bNode(const OutEdgeIt& e) const {
452      return Node(this->graph->bNode(e.e)); }
453    Node bNode(const InEdgeIt& e) const {
454      return Node(this->graph->bNode(e.e)); }
455
456    /// This function hides \c n in the graph, i.e. the iteration
457    /// jumps over it. This is done by simply setting the value of \c n 
458    /// to be false in the corresponding node-map.
459    void hide(const Node& n) const { node_filter_map->set(n, false); }
460
461    /// This function hides \c e in the graph, i.e. the iteration
462    /// jumps over it. This is done by simply setting the value of \c e 
463    /// to be false in the corresponding edge-map.
464    void hide(const Edge& e) const { edge_filter_map->set(e, false); }
465
466    /// The value of \c n is set to be true in the node-map which stores
467    /// hide information. If \c n was hidden previuosly, then it is shown
468    /// again
469     void unHide(const Node& n) const { node_filter_map->set(n, true); }
470
471    /// The value of \c e is set to be true in the edge-map which stores
472    /// hide information. If \c e was hidden previuosly, then it is shown
473    /// again
474    void unHide(const Edge& e) const { edge_filter_map->set(e, true); }
475
476    /// Returns true if \c n is hidden.
477    bool hidden(const Node& n) const { return !(*node_filter_map)[n]; }
478
479    /// Returns true if \c n is hidden.
480    bool hidden(const Edge& e) const { return !(*edge_filter_map)[e]; }
481
482    /// This is a linear time operation and works only if
483    /// NodeIt is defined.
484    int nodeNum() const {
485      int i=0;
486      NodeIt n;
487      for (this->first(n); this->valid(n); this->next(n)) ++i;
488      return i;
489    }
490
491    /// This is a linear time operation and works only if
492    /// EdgeIt is defined.
493    int edgeNum() const {
494      int i=0;
495      EdgeIt e;
496      for (this->first(e); this->valid(e); this->next(e)) ++i;
497      return i;
498    }
499
500  };
501
502
503
504  /// \brief A wrapper for forgetting the orientation of a graph.
505  ///
506  /// A wrapper for getting an undirected graph by forgetting
507  /// the orientation of a directed one.
508  ///
509  /// \author Marton Makai
510  template<typename Graph>
511  class UndirGraphWrapper : public GraphWrapper<Graph> {
512  public:
513    typedef GraphWrapper<Graph> Parent;
514  protected:
515    UndirGraphWrapper() : GraphWrapper<Graph>() { }
516   
517  public:
518    typedef typename GraphWrapper<Graph>::Node Node;
519    typedef typename GraphWrapper<Graph>::NodeIt NodeIt;
520    typedef typename GraphWrapper<Graph>::Edge Edge;
521    typedef typename GraphWrapper<Graph>::EdgeIt EdgeIt;
522
523    UndirGraphWrapper(Graph& _graph) : GraphWrapper<Graph>(_graph) { } 
524
525    class OutEdgeIt {
526      friend class UndirGraphWrapper<Graph>;
527      bool out_or_in; //true iff out
528      typename Graph::OutEdgeIt out;
529      typename Graph::InEdgeIt in;
530    public:
531      OutEdgeIt() { }
532      OutEdgeIt(const Invalid& i) : Edge(i) { }
533      OutEdgeIt(const UndirGraphWrapper<Graph>& _G, const Node& _n) {
534        out_or_in=true; _G.graph->first(out, _n);
535        if (!(_G.graph->valid(out))) { out_or_in=false; _G.graph->first(in, _n);        }
536      }
537      operator Edge() const {
538        if (out_or_in) return Edge(out); else return Edge(in);
539      }
540    };
541
542//FIXME InEdgeIt
543    typedef OutEdgeIt InEdgeIt;
544
545    using GraphWrapper<Graph>::first;
546//     NodeIt& first(NodeIt& i) const {
547//       i=NodeIt(*this); return i;
548//     }
549    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const {
550      i=OutEdgeIt(*this, p); return i;
551    }
552//FIXME
553//     InEdgeIt& first(InEdgeIt& i, const Node& p) const {
554//       i=InEdgeIt(*this, p); return i;
555//     }
556//     EdgeIt& first(EdgeIt& i) const {
557//       i=EdgeIt(*this); return i;
558//     }
559
560    using GraphWrapper<Graph>::next;
561//     NodeIt& next(NodeIt& n) const {
562//       GraphWrapper<Graph>::next(n);
563//       return n;
564//     }
565    OutEdgeIt& next(OutEdgeIt& e) const {
566      if (e.out_or_in) {
567        typename Graph::Node n=this->graph->tail(e.out);
568        this->graph->next(e.out);
569        if (!this->graph->valid(e.out)) {
570          e.out_or_in=false; this->graph->first(e.in, n); }
571      } else {
572        this->graph->next(e.in);
573      }
574      return e;
575    }
576    //FIXME InEdgeIt
577//     EdgeIt& next(EdgeIt& e) const {
578//       GraphWrapper<Graph>::next(n);
579// //      graph->next(e.e);
580//       return e;
581//     }
582
583    Node aNode(const OutEdgeIt& e) const {
584      if (e.out_or_in) return this->graph->tail(e); else
585        return this->graph->head(e); }
586    Node bNode(const OutEdgeIt& e) const {
587      if (e.out_or_in) return this->graph->head(e); else
588        return this->graph->tail(e); }
589  };
590 
591  /// \brief An undirected graph template.
592  ///
593  /// An undirected graph template.
594  /// This class works as an undirected graph and a directed graph of
595  /// class \c Graph is used for the physical storage.
596  /// \ingroup graphs
597  template<typename Graph>
598  class UndirGraph : public UndirGraphWrapper<Graph> {
599    typedef UndirGraphWrapper<Graph> Parent;
600  protected:
601    Graph gr;
602  public:
603    UndirGraph() : UndirGraphWrapper<Graph>() {
604      Parent::setGraph(gr);
605    }
606  };
607
608
609
610  ///\brief A wrapper for composing a subgraph of a
611  /// bidirected graph composed from a directed one.
612  /// experimental, for fezso's sake.
613  ///
614  /// A wrapper for composing a subgraps of a
615  /// bidirected graph composed from a directed one.
616  /// experimental, for fezso's sake.
617  /// A bidirected graph is composed over the directed one without physical
618  /// storage. As the oppositely directed edges are logically different ones
619  /// the maps are able to attach different values for them.
620  template<typename Graph,
621           typename ForwardFilterMap, typename BackwardFilterMap>
622  class SubBidirGraphWrapper : public GraphWrapper<Graph> {
623  public:
624    typedef GraphWrapper<Graph> Parent;
625  protected:
626    //const CapacityMap* capacity;
627    //FlowMap* flow;
628
629    ForwardFilterMap* forward_filter;
630    BackwardFilterMap* backward_filter;
631
632    SubBidirGraphWrapper() : GraphWrapper<Graph>()/*,
633                                                 capacity(0), flow(0)*/ { }
634    void setForwardFilterMap(ForwardFilterMap& _forward_filter) {
635      forward_filter=&_forward_filter;
636    }
637    void setBackwardFilterMap(BackwardFilterMap& _backward_filter) {
638      backward_filter=&_backward_filter;
639    }
640
641  public:
642
643    SubBidirGraphWrapper(Graph& _graph, ForwardFilterMap& _forward_filter,
644                         BackwardFilterMap& _backward_filter) :
645      GraphWrapper<Graph>(_graph),
646      forward_filter(&_forward_filter), backward_filter(&_backward_filter) { }
647
648    class Edge;
649    class OutEdgeIt;
650    friend class Edge;
651    friend class OutEdgeIt;
652
653    //template<typename T> class NodeMap;   
654    template<typename T> class EdgeMap;
655
656    typedef typename GraphWrapper<Graph>::Node Node;
657    typedef typename GraphWrapper<Graph>::NodeIt NodeIt;
658
659    class Edge : public Graph::Edge {
660      friend class SubBidirGraphWrapper<Graph,
661                                        ForwardFilterMap, BackwardFilterMap>;
662      ///\bug ez nem is kell
663      //template<typename T> friend class NodeMap;
664      template<typename T> friend class EdgeMap;
665    protected:
666      bool backward; //true, iff backward
667//      typename Graph::Edge e;
668    public:
669      Edge() { }
670      ///\bug =false kell-e? zsoltnak kell az addEdge miatt
671      Edge(const typename Graph::Edge& _e, bool _backward=false) :
672        Graph::Edge(_e), backward(_backward) { }
673      Edge(const Invalid& i) : Graph::Edge(i), backward(true) { }
674//the unique invalid iterator
675      friend bool operator==(const Edge& u, const Edge& v) {
676        return (v.backward==u.backward &&
677                static_cast<typename Graph::Edge>(u)==
678                static_cast<typename Graph::Edge>(v));
679      }
680      friend bool operator!=(const Edge& u, const Edge& v) {
681        return (v.backward!=u.backward ||
682                static_cast<typename Graph::Edge>(u)!=
683                static_cast<typename Graph::Edge>(v));
684      }
685    };
686
687    class OutEdgeIt {
688      friend class SubBidirGraphWrapper<Graph,
689                                        ForwardFilterMap, BackwardFilterMap>;
690    protected:
691      typename Graph::OutEdgeIt out;
692      typename Graph::InEdgeIt in;
693      bool backward;
694    public:
695      OutEdgeIt() { }
696      //FIXME
697//      OutEdgeIt(const Edge& e) : Edge(e) { }
698      OutEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }
699//the unique invalid iterator
700      OutEdgeIt(const SubBidirGraphWrapper<Graph,
701                ForwardFilterMap, BackwardFilterMap>& _G, Node v) {
702        backward=false;
703        _G.graph->first(out, v);
704        while(_G.graph->valid(out) && !(*_G.forward_filter)[*this]) { _G.graph->next(out); }
705        if (!_G.graph->valid(out)) {
706          backward=true;
707          _G.graph->first(in, v);
708          while(_G.graph->valid(in) && !(*_G.backward_filter)[*this]) { _G.graph->next(in); }
709        }
710      }
711      operator Edge() const {
712//      Edge e;
713//      e.forward=this->forward;
714//      if (this->forward) e=out; else e=in;
715//      return e;
716        if (this->backward)
717          return Edge(in, this->backward);
718        else
719          return Edge(out, this->backward);
720      }
721    };
722
723    class InEdgeIt {
724      friend class SubBidirGraphWrapper<Graph,
725                                        ForwardFilterMap, BackwardFilterMap>;
726    protected:
727      typename Graph::OutEdgeIt out;
728      typename Graph::InEdgeIt in;
729      bool backward;
730    public:
731      InEdgeIt() { }
732      //FIXME
733//      OutEdgeIt(const Edge& e) : Edge(e) { }
734      InEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }
735//the unique invalid iterator
736      InEdgeIt(const SubBidirGraphWrapper<Graph,
737               ForwardFilterMap, BackwardFilterMap>& _G, Node v) {
738        backward=false;
739        _G.graph->first(in, v);
740        while(_G.graph->valid(in) && !(*_G.forward_filter)[*this]) { _G.graph->next(in); }
741        if (!_G.graph->valid(in)) {
742          backward=true;
743          _G.graph->first(out, v);
744          while(_G.graph->valid(out) && !(*_G.backward_filter)[*this]) { _G.graph->next(out); }
745        }
746      }
747      operator Edge() const {
748//      Edge e;
749//      e.forward=this->forward;
750//      if (this->forward) e=out; else e=in;
751//      return e;
752        if (this->backward)
753          return Edge(out, this->backward);
754        else
755          return Edge(in, this->backward);
756      }
757    };
758
759    class EdgeIt {
760      friend class SubBidirGraphWrapper<Graph,
761                                        ForwardFilterMap, BackwardFilterMap>;
762    protected:
763      typename Graph::EdgeIt e;
764      bool backward;
765    public:
766      EdgeIt() { }
767      EdgeIt(const Invalid& i) : e(i), backward(true) { }
768      EdgeIt(const SubBidirGraphWrapper<Graph,
769             ForwardFilterMap, BackwardFilterMap>& _G) {
770        backward=false;
771        _G.graph->first(e);
772        while (_G.graph->valid(e) && !(*_G.forward_filter)[*this]) _G.graph->next(e);
773        if (!_G.graph->valid(e)) {
774          backward=true;
775          _G.graph->first(e);
776          while (_G.graph->valid(e) && !(*_G.backward_filter)[*this]) _G.graph->next(e);
777        }
778      }
779      operator Edge() const {
780        return Edge(e, this->backward);
781      }
782    };
783
784    using GraphWrapper<Graph>::first;
785//     NodeIt& first(NodeIt& i) const {
786//       i=NodeIt(*this); return i;
787//     }
788    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const {
789      i=OutEdgeIt(*this, p); return i;
790    }
791//    FIXME not tested
792    InEdgeIt& first(InEdgeIt& i, const Node& p) const {
793      i=InEdgeIt(*this, p); return i;
794    }
795    EdgeIt& first(EdgeIt& i) const {
796      i=EdgeIt(*this); return i;
797    }
798 
799    using GraphWrapper<Graph>::next;
800//    NodeIt& next(NodeIt& n) const { GraphWrapper<Graph>::next(n); return n; }
801    OutEdgeIt& next(OutEdgeIt& e) const {
802      if (!e.backward) {
803        Node v=this->graph->aNode(e.out);
804        this->graph->next(e.out);
805        while(this->graph->valid(e.out) && !(*forward_filter)[e]) {
806          this->graph->next(e.out); }
807        if (!this->graph->valid(e.out)) {
808          e.backward=true;
809          this->graph->first(e.in, v);
810          while(this->graph->valid(e.in) && !(*backward_filter)[e]) {
811            this->graph->next(e.in); }
812        }
813      } else {
814        this->graph->next(e.in);
815        while(this->graph->valid(e.in) && !(*backward_filter)[e]) {
816          this->graph->next(e.in); }
817      }
818      return e;
819    }
820//     FIXME Not tested
821    InEdgeIt& next(InEdgeIt& e) const {
822      if (!e.backward) {
823        Node v=this->graph->aNode(e.in);
824        this->graph->next(e.in);
825        while(this->graph->valid(e.in) && !(*forward_filter)[e]) {
826          this->graph->next(e.in); }
827        if (!this->graph->valid(e.in)) {
828          e.backward=true;
829          this->graph->first(e.out, v);
830          while(this->graph->valid(e.out) && !(*backward_filter)[e]) {
831            this->graph->next(e.out); }
832        }
833      } else {
834        this->graph->next(e.out);
835        while(this->graph->valid(e.out) && !(*backward_filter)[e]) {
836          this->graph->next(e.out); }
837      }
838      return e;
839    }
840    EdgeIt& next(EdgeIt& e) const {
841      if (!e.backward) {
842        this->graph->next(e.e);
843        while(this->graph->valid(e.e) && !(*forward_filter)[e]) {
844          this->graph->next(e.e); }
845        if (!this->graph->valid(e.e)) {
846          e.backward=true;
847          this->graph->first(e.e);
848          while(this->graph->valid(e.e) && !(*backward_filter)[e]) {
849            this->graph->next(e.e); }
850        }
851      } else {
852        this->graph->next(e.e);
853        while(this->graph->valid(e.e) && !(*backward_filter)[e]) {
854          this->graph->next(e.e); }
855      }
856      return e;
857    }
858
859    Node tail(Edge e) const {
860      return ((!e.backward) ? this->graph->tail(e) : this->graph->head(e)); }
861    Node head(Edge e) const {
862      return ((!e.backward) ? this->graph->head(e) : this->graph->tail(e)); }
863
864    Node aNode(OutEdgeIt e) const {
865      return ((!e.backward) ? this->graph->aNode(e.out) :
866              this->graph->aNode(e.in)); }
867    Node bNode(OutEdgeIt e) const {
868      return ((!e.backward) ? this->graph->bNode(e.out) :
869              this->graph->bNode(e.in)); }
870
871    Node aNode(InEdgeIt e) const {
872      return ((!e.backward) ? this->graph->aNode(e.in) :
873              this->graph->aNode(e.out)); }
874    Node bNode(InEdgeIt e) const {
875      return ((!e.backward) ? this->graph->bNode(e.in) :
876              this->graph->bNode(e.out)); }
877
878    /// Gives back the opposite edge.
879    Edge opposite(const Edge& e) const {
880      Edge f=e;
881      f.backward=!f.backward;
882      return f;
883    }
884
885//    int nodeNum() const { return graph->nodeNum(); }
886    //FIXME
887    void edgeNum() const { }
888    //int edgeNum() const { return graph->edgeNum(); }
889
890
891//    int id(Node v) const { return graph->id(v); }
892
893    bool valid(Node n) const { return GraphWrapper<Graph>::valid(n); }
894    bool valid(Edge e) const {
895      return this->graph->valid(e);
896        //return e.forward ? graph->valid(e.out) : graph->valid(e.in);
897    }
898
899    bool forward(const Edge& e) const { return !e.backward; }
900    bool backward(const Edge& e) const { return e.backward; }
901
902//     void augment(const Edge& e, Number a) const {
903//       if (!e.backward) 
904// //   flow->set(e.out, flow->get(e.out)+a);
905//      flow->set(e, (*flow)[e]+a);
906//       else 
907// //   flow->set(e.in, flow->get(e.in)-a);
908//      flow->set(e, (*flow)[e]-a);
909//     }
910
911//     bool enabled(const Edge& e) const {
912//       if (!e.backward)
913// //   return (capacity->get(e.out)-flow->get(e.out));
914//      //return ((*capacity)[e]-(*flow)[e]);
915//      return true;
916//       else
917// //   return (flow->get(e.in));
918//      //return ((*flow)[e]);
919//      return true;
920//     }
921
922//     Number enabled(typename Graph::OutEdgeIt out) const {
923// //      return (capacity->get(out)-flow->get(out));
924//       return ((*capacity)[out]-(*flow)[out]);
925//     }
926   
927//     Number enabled(typename Graph::InEdgeIt in) const {
928// //      return (flow->get(in));
929//       return ((*flow)[in]);
930//     }
931
932    template <typename T>
933    class EdgeMap {
934      typename Graph::template EdgeMap<T> forward_map, backward_map;
935    public:
936      typedef T ValueType;
937      typedef Edge KeyType;
938      EdgeMap(const SubBidirGraphWrapper<Graph,
939              ForwardFilterMap, BackwardFilterMap>& _G) :
940        forward_map(*(_G.graph)), backward_map(*(_G.graph)) { }
941      EdgeMap(const SubBidirGraphWrapper<Graph,
942              ForwardFilterMap, BackwardFilterMap>& _G, T a) :
943        forward_map(*(_G.graph), a), backward_map(*(_G.graph), a) { }
944      void set(Edge e, T a) {
945        if (!e.backward)
946          forward_map.set(e/*.out*/, a);
947        else
948          backward_map.set(e/*.in*/, a);
949      }
950      T operator[](Edge e) const {
951        if (!e.backward)
952          return forward_map[e/*.out*/];
953        else
954          return backward_map[e/*.in*/];
955      }
956      void update() {
957        forward_map.update();
958        backward_map.update();
959      }
960//       T get(Edge e) const {
961//      if (e.out_or_in)
962//        return forward_map.get(e.out);
963//      else
964//        return backward_map.get(e.in);
965//       }
966    };
967  };
968
969
970
971  ///\brief A wrapper for composing bidirected graph from a directed one.
972  /// experimental, for fezso's sake.
973  ///
974  /// A wrapper for composing bidirected graph from a directed one.
975  /// experimental, for fezso's sake.
976  /// A bidirected graph is composed over the directed one without physical
977  /// storage. As the oppositely directed edges are logically different ones
978  /// the maps are able to attach different values for them.
979  template<typename Graph>
980  class BidirGraphWrapper :
981    public SubBidirGraphWrapper<
982    Graph,
983    ConstMap<typename Graph::Edge, bool>,
984    ConstMap<typename Graph::Edge, bool> > {
985  public:
986    typedef  SubBidirGraphWrapper<
987      Graph,
988      ConstMap<typename Graph::Edge, bool>,
989      ConstMap<typename Graph::Edge, bool> > Parent;
990  protected:
991    ConstMap<typename Graph::Edge, bool> cm;
992    //const CapacityMap* capacity;
993    //FlowMap* flow;
994
995    BidirGraphWrapper() : Parent(), cm(true) {
996      Parent::setForwardFilterMap(cm);
997      Parent::setBackwardFilterMap(cm);
998    }
999//     void setCapacityMap(const CapacityMap& _capacity) {
1000//       capacity=&_capacity;
1001//     }
1002//     void setFlowMap(FlowMap& _flow) {
1003//       flow=&_flow;
1004//     }
1005
1006  public:
1007
1008    BidirGraphWrapper(Graph& _graph) : Parent() {
1009      Parent::setGraph(_graph);
1010      Parent::setForwardFilterMap(cm);
1011      Parent::setBackwardFilterMap(cm);
1012    }
1013  };
1014
1015
1016
1017
1018  template<typename Graph>
1019  class OldBidirGraphWrapper : public GraphWrapper<Graph> {
1020  public:
1021    typedef GraphWrapper<Graph> Parent;
1022  protected:
1023    //const CapacityMap* capacity;
1024    //FlowMap* flow;
1025
1026    OldBidirGraphWrapper() : GraphWrapper<Graph>()/*,
1027                                                 capacity(0), flow(0)*/ { }
1028//     void setCapacityMap(const CapacityMap& _capacity) {
1029//       capacity=&_capacity;
1030//     }
1031//     void setFlowMap(FlowMap& _flow) {
1032//       flow=&_flow;
1033//     }
1034
1035  public:
1036
1037    OldBidirGraphWrapper(Graph& _graph/*, const CapacityMap& _capacity,
1038                                     FlowMap& _flow*/) :
1039      GraphWrapper<Graph>(_graph)/*, capacity(&_capacity), flow(&_flow)*/ { }
1040
1041    class Edge;
1042    class OutEdgeIt;
1043    friend class Edge;
1044    friend class OutEdgeIt;
1045
1046    //template<typename T> class NodeMap;   
1047    template<typename T> class EdgeMap;
1048
1049    typedef typename GraphWrapper<Graph>::Node Node;
1050    typedef typename GraphWrapper<Graph>::NodeIt NodeIt;
1051
1052    class Edge : public Graph::Edge {
1053      friend class OldBidirGraphWrapper<Graph>;
1054      ///\bug ez nem is kell
1055      //template<typename T> friend class NodeMap;
1056      template<typename T> friend class EdgeMap;
1057    protected:
1058      bool backward; //true, iff backward
1059//      typename Graph::Edge e;
1060    public:
1061      Edge() { }
1062      ///\bug =false kell-e? zsoltnak kell az addEdge miatt
1063      Edge(const typename Graph::Edge& _e, bool _backward=false) :
1064        Graph::Edge(_e), backward(_backward) { }
1065      Edge(const Invalid& i) : Graph::Edge(i), backward(true) { }
1066//the unique invalid iterator
1067      friend bool operator==(const Edge& u, const Edge& v) {
1068        return (v.backward==u.backward &&
1069                static_cast<typename Graph::Edge>(u)==
1070                static_cast<typename Graph::Edge>(v));
1071      }
1072      friend bool operator!=(const Edge& u, const Edge& v) {
1073        return (v.backward!=u.backward ||
1074                static_cast<typename Graph::Edge>(u)!=
1075                static_cast<typename Graph::Edge>(v));
1076      }
1077    };
1078
1079    class OutEdgeIt {
1080      friend class OldBidirGraphWrapper<Graph>;
1081    protected:
1082      typename Graph::OutEdgeIt out;
1083      typename Graph::InEdgeIt in;
1084      bool backward;
1085    public:
1086      OutEdgeIt() { }
1087      //FIXME
1088//      OutEdgeIt(const Edge& e) : Edge(e) { }
1089      OutEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }
1090//the unique invalid iterator
1091      OutEdgeIt(const OldBidirGraphWrapper<Graph>& _G, Node v) {
1092        backward=false;
1093        _G.graph->first(out, v);
1094        while(_G.graph->valid(out) && !_G.enabled(*this)) { _G.graph->next(out); }
1095        if (!_G.graph->valid(out)) {
1096          backward=true;
1097          _G.graph->first(in, v);
1098          while(_G.graph->valid(in) && !_G.enabled(*this)) { _G.graph->next(in); }
1099        }
1100      }
1101      operator Edge() const {
1102//      Edge e;
1103//      e.forward=this->forward;
1104//      if (this->forward) e=out; else e=in;
1105//      return e;
1106        if (this->backward)
1107          return Edge(in, this->backward);
1108        else
1109          return Edge(out, this->backward);
1110      }
1111    };
1112
1113    class InEdgeIt {
1114      friend class OldBidirGraphWrapper<Graph>;
1115    protected:
1116      typename Graph::OutEdgeIt out;
1117      typename Graph::InEdgeIt in;
1118      bool backward;
1119    public:
1120      InEdgeIt() { }
1121      //FIXME
1122//      OutEdgeIt(const Edge& e) : Edge(e) { }
1123      InEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }
1124//the unique invalid iterator
1125      InEdgeIt(const OldBidirGraphWrapper<Graph>& _G, Node v) {
1126        backward=false;
1127        _G.graph->first(in, v);
1128        while(_G.graph->valid(in) && !_G.enabled(*this)) { _G.graph->next(in); }
1129        if (!_G.graph->valid(in)) {
1130          backward=true;
1131          _G.graph->first(out, v);
1132          while(_G.graph->valid(out) && !_G.enabled(*this)) { _G.graph->next(out); }
1133        }
1134      }
1135      operator Edge() const {
1136//      Edge e;
1137//      e.forward=this->forward;
1138//      if (this->forward) e=out; else e=in;
1139//      return e;
1140        if (this->backward)
1141          return Edge(out, this->backward);
1142        else
1143          return Edge(in, this->backward);
1144      }
1145    };
1146
1147    class EdgeIt {
1148      friend class OldBidirGraphWrapper<Graph>;
1149    protected:
1150      typename Graph::EdgeIt e;
1151      bool backward;
1152    public:
1153      EdgeIt() { }
1154      EdgeIt(const Invalid& i) : e(i), backward(true) { }
1155      EdgeIt(const OldBidirGraphWrapper<Graph>& _G) {
1156        backward=false;
1157        _G.graph->first(e);
1158        while (_G.graph->valid(e) && !_G.enabled(*this)) _G.graph->next(e);
1159        if (!_G.graph->valid(e)) {
1160          backward=true;
1161          _G.graph->first(e);
1162          while (_G.graph->valid(e) && !_G.enabled(*this)) _G.graph->next(e);
1163        }
1164      }
1165      operator Edge() const {
1166        return Edge(e, this->backward);
1167      }
1168    };
1169
1170    using GraphWrapper<Graph>::first;
1171//     NodeIt& first(NodeIt& i) const {
1172//       i=NodeIt(*this); return i;
1173//     }
1174    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const {
1175      i=OutEdgeIt(*this, p); return i;
1176    }
1177//    FIXME not tested
1178    InEdgeIt& first(InEdgeIt& i, const Node& p) const {
1179      i=InEdgeIt(*this, p); return i;
1180    }
1181    EdgeIt& first(EdgeIt& i) const {
1182      i=EdgeIt(*this); return i;
1183    }
1184 
1185    using GraphWrapper<Graph>::next;
1186//    NodeIt& next(NodeIt& n) const { GraphWrapper<Graph>::next(n); return n; }
1187    OutEdgeIt& next(OutEdgeIt& e) const {
1188      if (!e.backward) {
1189        Node v=this->graph->aNode(e.out);
1190        this->graph->next(e.out);
1191        while(this->graph->valid(e.out) && !enabled(e)) {
1192          this->graph->next(e.out); }
1193        if (!this->graph->valid(e.out)) {
1194          e.backward=true;
1195          this->graph->first(e.in, v);
1196          while(this->graph->valid(e.in) && !enabled(e)) {
1197            this->graph->next(e.in); }
1198        }
1199      } else {
1200        this->graph->next(e.in);
1201        while(this->graph->valid(e.in) && !enabled(e)) {
1202          this->graph->next(e.in); }
1203      }
1204      return e;
1205    }
1206//     FIXME Not tested
1207    InEdgeIt& next(InEdgeIt& e) const {
1208      if (!e.backward) {
1209        Node v=this->graph->aNode(e.in);
1210        this->graph->next(e.in);
1211        while(this->graph->valid(e.in) && !enabled(e)) {
1212          this->graph->next(e.in); }
1213        if (!this->graph->valid(e.in)) {
1214          e.backward=true;
1215          this->graph->first(e.out, v);
1216          while(this->graph->valid(e.out) && !enabled(e)) {
1217            this->graph->next(e.out); }
1218        }
1219      } else {
1220        this->graph->next(e.out);
1221        while(this->graph->valid(e.out) && !enabled(e)) {
1222          this->graph->next(e.out); }
1223      }
1224      return e;
1225    }
1226    EdgeIt& next(EdgeIt& e) const {
1227      if (!e.backward) {
1228        this->graph->next(e.e);
1229        while(this->graph->valid(e.e) && !enabled(e)) {
1230          this->graph->next(e.e); }
1231        if (!this->graph->valid(e.e)) {
1232          e.backward=true;
1233          this->graph->first(e.e);
1234          while(this->graph->valid(e.e) && !enabled(e)) {
1235            this->graph->next(e.e); }
1236        }
1237      } else {
1238        this->graph->next(e.e);
1239        while(this->graph->valid(e.e) && !enabled(e)) {
1240          this->graph->next(e.e); }
1241      }
1242      return e;
1243    }
1244
1245    Node tail(Edge e) const {
1246      return ((!e.backward) ? this->graph->tail(e) : this->graph->head(e)); }
1247    Node head(Edge e) const {
1248      return ((!e.backward) ? this->graph->head(e) : this->graph->tail(e)); }
1249
1250    Node aNode(OutEdgeIt e) const {
1251      return ((!e.backward) ? this->graph->aNode(e.out) :
1252              this->graph->aNode(e.in)); }
1253    Node bNode(OutEdgeIt e) const {
1254      return ((!e.backward) ? this->graph->bNode(e.out) :
1255              this->graph->bNode(e.in)); }
1256
1257    Node aNode(InEdgeIt e) const {
1258      return ((!e.backward) ? this->graph->aNode(e.in) :
1259              this->graph->aNode(e.out)); }
1260    Node bNode(InEdgeIt e) const {
1261      return ((!e.backward) ? this->graph->bNode(e.in) :
1262              this->graph->bNode(e.out)); }
1263
1264    /// Gives back the opposite edge.
1265    Edge opposite(const Edge& e) const {
1266      Edge f=e;
1267      f.backward=!f.backward;
1268      return f;
1269    }
1270
1271//    int nodeNum() const { return graph->nodeNum(); }
1272    //FIXME
1273    void edgeNum() const { }
1274    //int edgeNum() const { return graph->edgeNum(); }
1275
1276
1277//    int id(Node v) const { return graph->id(v); }
1278
1279    bool valid(Node n) const { return GraphWrapper<Graph>::valid(n); }
1280    bool valid(Edge e) const {
1281      return this->graph->valid(e);
1282        //return e.forward ? graph->valid(e.out) : graph->valid(e.in);
1283    }
1284
1285    bool forward(const Edge& e) const { return !e.backward; }
1286    bool backward(const Edge& e) const { return e.backward; }
1287
1288//     void augment(const Edge& e, Number a) const {
1289//       if (!e.backward) 
1290// //   flow->set(e.out, flow->get(e.out)+a);
1291//      flow->set(e, (*flow)[e]+a);
1292//       else 
1293// //   flow->set(e.in, flow->get(e.in)-a);
1294//      flow->set(e, (*flow)[e]-a);
1295//     }
1296
1297    bool enabled(const Edge& e) const {
1298      if (!e.backward)
1299//      return (capacity->get(e.out)-flow->get(e.out));
1300        //return ((*capacity)[e]-(*flow)[e]);
1301        return true;
1302      else
1303//      return (flow->get(e.in));
1304        //return ((*flow)[e]);
1305        return true;
1306    }
1307
1308//     Number enabled(typename Graph::OutEdgeIt out) const {
1309// //      return (capacity->get(out)-flow->get(out));
1310//       return ((*capacity)[out]-(*flow)[out]);
1311//     }
1312   
1313//     Number enabled(typename Graph::InEdgeIt in) const {
1314// //      return (flow->get(in));
1315//       return ((*flow)[in]);
1316//     }
1317
1318    template <typename T>
1319    class EdgeMap {
1320      typename Graph::template EdgeMap<T> forward_map, backward_map;
1321    public:
1322      typedef T ValueType;
1323      typedef Edge KeyType;
1324      EdgeMap(const OldBidirGraphWrapper<Graph>& _G) : forward_map(*(_G.graph)), backward_map(*(_G.graph)) { }
1325      EdgeMap(const OldBidirGraphWrapper<Graph>& _G, T a) : forward_map(*(_G.graph), a), backward_map(*(_G.graph), a) { }
1326      void set(Edge e, T a) {
1327        if (!e.backward)
1328          forward_map.set(e/*.out*/, a);
1329        else
1330          backward_map.set(e/*.in*/, a);
1331      }
1332      T operator[](Edge e) const {
1333        if (!e.backward)
1334          return forward_map[e/*.out*/];
1335        else
1336          return backward_map[e/*.in*/];
1337      }
1338      void update() {
1339        forward_map.update();
1340        backward_map.update();
1341      }
1342//       T get(Edge e) const {
1343//      if (e.out_or_in)
1344//        return forward_map.get(e.out);
1345//      else
1346//        return backward_map.get(e.in);
1347//       }
1348    };
1349  };
1350
1351
1352
1353  /// \brief A bidirected graph template.
1354  ///
1355  /// A bidirected graph template.
1356  /// Such a bidirected graph stores each pair of oppositely directed edges
1357  /// ones in the memory, i.e. a directed graph of type
1358  /// \c Graph is used for that.
1359  /// As the oppositely directed edges are logically different ones
1360  /// the maps are able to attach different values for them.
1361  /// \ingroup graphs
1362  template<typename Graph>
1363  class BidirGraph : public BidirGraphWrapper<Graph> {
1364  public:
1365    typedef UndirGraphWrapper<Graph> Parent;
1366  protected:
1367    Graph gr;
1368  public:
1369    BidirGraph() : BidirGraphWrapper<Graph>() {
1370      Parent::setGraph(gr);
1371    }
1372  };
1373
1374
1375
1376  template<typename Graph, typename Number,
1377           typename CapacityMap, typename FlowMap>
1378  class ForwardFilter {
1379    const Graph* graph;
1380    const CapacityMap* capacity;
1381    const FlowMap* flow;
1382  public:
1383    ForwardFilter(const Graph& _graph,
1384                  const CapacityMap& _capacity, const FlowMap& _flow) :
1385      graph(&_graph), capacity(&_capacity), flow(&_flow) { }
1386    bool operator[](const typename Graph::Edge& e) const {
1387      return ((*flow)[e] < (*capacity)[e]);
1388    }
1389  };
1390
1391  template<typename Graph, typename Number,
1392           typename CapacityMap, typename FlowMap>
1393  class BackwardFilter {
1394    const Graph* graph;
1395    const CapacityMap* capacity;
1396    const FlowMap* flow;
1397  public:
1398    BackwardFilter(const Graph& _graph,
1399                   const CapacityMap& _capacity, const FlowMap& _flow) :
1400      graph(&_graph), capacity(&_capacity), flow(&_flow) { }
1401    bool operator[](const typename Graph::Edge& e) const {
1402      return (0 < (*flow)[e]);
1403    }
1404  };
1405
1406 
1407  /// A wrapper for composing the residual graph for directed flow and circulation problems.
1408
1409  /// A wrapper for composing the residual graph for directed flow and circulation problems.
1410  template<typename Graph, typename Number,
1411           typename CapacityMap, typename FlowMap>
1412  class ResGraphWrapper :
1413    public SubBidirGraphWrapper<
1414    Graph,
1415    ForwardFilter<Graph, Number, CapacityMap, FlowMap>, 
1416    BackwardFilter<Graph, Number, CapacityMap, FlowMap> > {
1417  public:
1418    typedef SubBidirGraphWrapper<
1419      Graph,
1420      ForwardFilter<Graph, Number, CapacityMap, FlowMap>, 
1421      BackwardFilter<Graph, Number, CapacityMap, FlowMap> > Parent;
1422  protected:
1423    const CapacityMap* capacity;
1424    FlowMap* flow;
1425    ForwardFilter<Graph, Number, CapacityMap, FlowMap> forward_filter;
1426    BackwardFilter<Graph, Number, CapacityMap, FlowMap> backward_filter;
1427  public:
1428    ResGraphWrapper(Graph& _graph, const CapacityMap& _capacity,
1429                       FlowMap& _flow) :
1430      Parent(), capacity(&_capacity), flow(&_flow),
1431      forward_filter(_graph, _capacity, _flow),
1432      backward_filter(_graph, _capacity, _flow) {
1433      Parent::setGraph(_graph);
1434      Parent::setForwardFilterMap(forward_filter);
1435      Parent::setBackwardFilterMap(backward_filter);
1436    }
1437
1438    //    bool forward(const Parent::Edge& e) const { return Parent::forward(e); }
1439    //bool backward(const Edge& e) const { return e.backward; }
1440
1441    void augment(const typename Parent::Edge& e, Number a) const {
1442      if (Parent::forward(e)) 
1443//      flow->set(e.out, flow->get(e.out)+a);
1444        flow->set(e, (*flow)[e]+a);
1445      else 
1446        //flow->set(e.in, flow->get(e.in)-a);
1447        flow->set(e, (*flow)[e]-a);
1448    }
1449
1450    Number resCap(const typename Parent::Edge& e) const {
1451      if (Parent::forward(e))
1452//      return (capacity->get(e.out)-flow->get(e.out));
1453        return ((*capacity)[e]-(*flow)[e]);
1454      else
1455//      return (flow->get(e.in));
1456        return ((*flow)[e]);
1457    }
1458
1459  };
1460
1461
1462
1463
1464  template<typename Graph, typename Number,
1465           typename CapacityMap, typename FlowMap>
1466  class OldResGraphWrapper : public GraphWrapper<Graph> {
1467  public:
1468    typedef GraphWrapper<Graph> Parent;
1469  protected:
1470    const CapacityMap* capacity;
1471    FlowMap* flow;
1472
1473    OldResGraphWrapper() : GraphWrapper<Graph>(0),
1474                        capacity(0), flow(0) { }
1475    void setCapacityMap(const CapacityMap& _capacity) {
1476      capacity=&_capacity;
1477    }
1478    void setFlowMap(FlowMap& _flow) {
1479      flow=&_flow;
1480    }
1481
1482  public:
1483
1484    OldResGraphWrapper(Graph& _graph, const CapacityMap& _capacity,
1485                    FlowMap& _flow) :
1486      GraphWrapper<Graph>(_graph), capacity(&_capacity), flow(&_flow) { }
1487
1488    class Edge;
1489    class OutEdgeIt;
1490    friend class Edge;
1491    friend class OutEdgeIt;
1492
1493    typedef typename GraphWrapper<Graph>::Node Node;
1494    typedef typename GraphWrapper<Graph>::NodeIt NodeIt;
1495    class Edge : public Graph::Edge {
1496      friend class OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>;
1497    protected:
1498      bool backward; //true, iff backward
1499//      typename Graph::Edge e;
1500    public:
1501      Edge() { }
1502      Edge(const typename Graph::Edge& _e, bool _backward) :
1503        Graph::Edge(_e), backward(_backward) { }
1504      Edge(const Invalid& i) : Graph::Edge(i), backward(true) { }
1505//the unique invalid iterator
1506      friend bool operator==(const Edge& u, const Edge& v) {
1507        return (v.backward==u.backward &&
1508                static_cast<typename Graph::Edge>(u)==
1509                static_cast<typename Graph::Edge>(v));
1510      }
1511      friend bool operator!=(const Edge& u, const Edge& v) {
1512        return (v.backward!=u.backward ||
1513                static_cast<typename Graph::Edge>(u)!=
1514                static_cast<typename Graph::Edge>(v));
1515      }
1516    };
1517
1518    class OutEdgeIt {
1519      friend class OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>;
1520    protected:
1521      typename Graph::OutEdgeIt out;
1522      typename Graph::InEdgeIt in;
1523      bool backward;
1524    public:
1525      OutEdgeIt() { }
1526      //FIXME
1527//      OutEdgeIt(const Edge& e) : Edge(e) { }
1528      OutEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }
1529//the unique invalid iterator
1530      OutEdgeIt(const OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>& _G, Node v) {
1531        backward=false;
1532        _G.graph->first(out, v);
1533        while( _G.graph->valid(out) && !(_G.resCap(*this)>0) ) { _G.graph->next(out); }
1534        if (!_G.graph->valid(out)) {
1535          backward=true;
1536          _G.graph->first(in, v);
1537          while( _G.graph->valid(in) && !(_G.resCap(*this)>0) ) { _G.graph->next(in); }
1538        }
1539      }
1540      operator Edge() const {
1541//      Edge e;
1542//      e.forward=this->forward;
1543//      if (this->forward) e=out; else e=in;
1544//      return e;
1545        if (this->backward)
1546          return Edge(in, this->backward);
1547        else
1548          return Edge(out, this->backward);
1549      }
1550    };
1551
1552    class InEdgeIt {
1553      friend class OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>;
1554    protected:
1555      typename Graph::OutEdgeIt out;
1556      typename Graph::InEdgeIt in;
1557      bool backward;
1558    public:
1559      InEdgeIt() { }
1560      //FIXME
1561//      OutEdgeIt(const Edge& e) : Edge(e) { }
1562      InEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }
1563//the unique invalid iterator
1564      InEdgeIt(const OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>& _G, Node v) {
1565        backward=false;
1566        _G.graph->first(in, v);
1567        while( _G.graph->valid(in) && !(_G.resCap(*this)>0) ) { _G.graph->next(in); }
1568        if (!_G.graph->valid(in)) {
1569          backward=true;
1570          _G.graph->first(out, v);
1571          while( _G.graph->valid(out) && !(_G.resCap(*this)>0) ) { _G.graph->next(out); }
1572        }
1573      }
1574      operator Edge() const {
1575//      Edge e;
1576//      e.forward=this->forward;
1577//      if (this->forward) e=out; else e=in;
1578//      return e;
1579        if (this->backward)
1580          return Edge(out, this->backward);
1581        else
1582          return Edge(in, this->backward);
1583      }
1584    };
1585
1586    class EdgeIt {
1587      friend class OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>;
1588    protected:
1589      typename Graph::EdgeIt e;
1590      bool backward;
1591    public:
1592      EdgeIt() { }
1593      EdgeIt(const Invalid& i) : e(i), backward(true) { }
1594      EdgeIt(const OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>& _G) {
1595        backward=false;
1596        _G.graph->first(e);
1597        while (_G.graph->valid(e) && !(_G.resCap(*this)>0)) _G.graph->next(e);
1598        if (!_G.graph->valid(e)) {
1599          backward=true;
1600          _G.graph->first(e);
1601          while (_G.graph->valid(e) && !(_G.resCap(*this)>0)) _G.graph->next(e);
1602        }
1603      }
1604      operator Edge() const {
1605        return Edge(e, this->backward);
1606      }
1607    };
1608
1609    using GraphWrapper<Graph>::first;
1610//     NodeIt& first(NodeIt& i) const {
1611//       i=NodeIt(*this); return i;
1612//     }
1613    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const {
1614      i=OutEdgeIt(*this, p); return i;
1615    }
1616//    FIXME not tested
1617    InEdgeIt& first(InEdgeIt& i, const Node& p) const {
1618      i=InEdgeIt(*this, p); return i;
1619    }
1620    EdgeIt& first(EdgeIt& i) const {
1621      i=EdgeIt(*this); return i;
1622    }
1623 
1624    using GraphWrapper<Graph>::next;
1625//    NodeIt& next(NodeIt& n) const { GraphWrapper<Graph>::next(n); return n; }
1626    OutEdgeIt& next(OutEdgeIt& e) const {
1627      if (!e.backward) {
1628        Node v=this->graph->aNode(e.out);
1629        this->graph->next(e.out);
1630        while( this->graph->valid(e.out) && !(resCap(e)>0) ) {
1631          this->graph->next(e.out); }
1632        if (!this->graph->valid(e.out)) {
1633          e.backward=true;
1634          this->graph->first(e.in, v);
1635          while( this->graph->valid(e.in) && !(resCap(e)>0) ) {
1636            this->graph->next(e.in); }
1637        }
1638      } else {
1639        this->graph->next(e.in);
1640        while( this->graph->valid(e.in) && !(resCap(e)>0) ) {
1641          this->graph->next(e.in); }
1642      }
1643      return e;
1644    }
1645//     FIXME Not tested
1646    InEdgeIt& next(InEdgeIt& e) const {
1647      if (!e.backward) {
1648        Node v=this->graph->aNode(e.in);
1649        this->graph->next(e.in);
1650        while( this->graph->valid(e.in) && !(resCap(e)>0) ) {
1651          this->graph->next(e.in); }
1652        if (!this->graph->valid(e.in)) {
1653          e.backward=true;
1654          this->graph->first(e.out, v);
1655          while( this->graph->valid(e.out) && !(resCap(e)>0) ) {
1656            this->graph->next(e.out); }
1657        }
1658      } else {
1659        this->graph->next(e.out);
1660        while( this->graph->valid(e.out) && !(resCap(e)>0) ) {
1661          this->graph->next(e.out); }
1662      }
1663      return e;
1664    }
1665    EdgeIt& next(EdgeIt& e) const {
1666      if (!e.backward) {
1667        this->graph->next(e.e);
1668        while( this->graph->valid(e.e) && !(resCap(e)>0) ) {
1669          this->graph->next(e.e); }
1670        if (!this->graph->valid(e.e)) {
1671          e.backward=true;
1672          this->graph->first(e.e);
1673          while( this->graph->valid(e.e) && !(resCap(e)>0) ) {
1674            this->graph->next(e.e); }
1675        }
1676      } else {
1677        this->graph->next(e.e);
1678        while( this->graph->valid(e.e) && !(resCap(e)>0) ) {
1679          this->graph->next(e.e); }
1680      }
1681      return e;
1682    }
1683
1684    Node tail(Edge e) const {
1685      return ((!e.backward) ? this->graph->tail(e) : this->graph->head(e)); }
1686    Node head(Edge e) const {
1687      return ((!e.backward) ? this->graph->head(e) : this->graph->tail(e)); }
1688
1689    Node aNode(OutEdgeIt e) const {
1690      return ((!e.backward) ? this->graph->aNode(e.out) :
1691              this->graph->aNode(e.in)); }
1692    Node bNode(OutEdgeIt e) const {
1693      return ((!e.backward) ? this->graph->bNode(e.out) :
1694              this->graph->bNode(e.in)); }
1695
1696    Node aNode(InEdgeIt e) const {
1697      return ((!e.backward) ? this->graph->aNode(e.in) :
1698              this->graph->aNode(e.out)); }
1699    Node bNode(InEdgeIt e) const {
1700      return ((!e.backward) ? this->graph->bNode(e.in) :
1701              this->graph->bNode(e.out)); }
1702
1703//    int nodeNum() const { return graph->nodeNum(); }
1704    //FIXME
1705    void edgeNum() const { }
1706    //int edgeNum() const { return graph->edgeNum(); }
1707
1708
1709//    int id(Node v) const { return graph->id(v); }
1710
1711    bool valid(Node n) const { return GraphWrapper<Graph>::valid(n); }
1712    bool valid(Edge e) const {
1713      return this->graph->valid(e);
1714        //return e.forward ? graph->valid(e.out) : graph->valid(e.in);
1715    }
1716
1717    bool forward(const Edge& e) const { return !e.backward; }
1718    bool backward(const Edge& e) const { return e.backward; }
1719
1720    void augment(const Edge& e, Number a) const {
1721      if (!e.backward) 
1722//      flow->set(e.out, flow->get(e.out)+a);
1723        flow->set(e, (*flow)[e]+a);
1724      else 
1725//      flow->set(e.in, flow->get(e.in)-a);
1726        flow->set(e, (*flow)[e]-a);
1727    }
1728
1729    Number resCap(const Edge& e) const {
1730      if (!e.backward)
1731//      return (capacity->get(e.out)-flow->get(e.out));
1732        return ((*capacity)[e]-(*flow)[e]);
1733      else
1734//      return (flow->get(e.in));
1735        return ((*flow)[e]);
1736    }
1737
1738//     Number resCap(typename Graph::OutEdgeIt out) const {
1739// //      return (capacity->get(out)-flow->get(out));
1740//       return ((*capacity)[out]-(*flow)[out]);
1741//     }
1742   
1743//     Number resCap(typename Graph::InEdgeIt in) const {
1744// //      return (flow->get(in));
1745//       return ((*flow)[in]);
1746//     }
1747
1748    template <typename T>
1749    class EdgeMap {
1750      typename Graph::template EdgeMap<T> forward_map, backward_map;
1751    public:
1752      typedef T ValueType;
1753      typedef Edge KeyType;
1754      EdgeMap(const OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>& _G) : forward_map(*(_G.graph)), backward_map(*(_G.graph)) { }
1755      EdgeMap(const OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>& _G, T a) : forward_map(*(_G.graph), a), backward_map(*(_G.graph), a) { }
1756      void set(Edge e, T a) {
1757        if (!e.backward)
1758          forward_map.set(e/*.out*/, a);
1759        else
1760          backward_map.set(e/*.in*/, a);
1761      }
1762      T operator[](Edge e) const {
1763        if (!e.backward)
1764          return forward_map[e/*.out*/];
1765        else
1766          return backward_map[e/*.in*/];
1767      }
1768      void update() {
1769        forward_map.update();
1770        backward_map.update();
1771      }
1772//       T get(Edge e) const {
1773//      if (e.out_or_in)
1774//        return forward_map.get(e.out);
1775//      else
1776//        return backward_map.get(e.in);
1777//       }
1778    };
1779  };
1780
1781
1782
1783  /// For blocking flows.
1784
1785  /// This graph wrapper is used for Dinits blocking flow computations.
1786  /// For each node, an out-edge is stored which is used when the
1787  /// \code
1788  /// OutEdgeIt& first(OutEdgeIt&, const Node&)
1789  /// \endcode
1790  /// is called.
1791  ///
1792  ///\author Marton Makai
1793  template<typename Graph, typename FirstOutEdgesMap>
1794  class ErasingFirstGraphWrapper : public GraphWrapper<Graph> {
1795  public:
1796    typedef GraphWrapper<Graph> Parent;
1797  protected:
1798    FirstOutEdgesMap* first_out_edges;
1799  public:
1800    ErasingFirstGraphWrapper(Graph& _graph,
1801                             FirstOutEdgesMap& _first_out_edges) :
1802      GraphWrapper<Graph>(_graph), first_out_edges(&_first_out_edges) { } 
1803
1804    typedef typename GraphWrapper<Graph>::Node Node;
1805//     class NodeIt {
1806//       friend class GraphWrapper<Graph>;
1807//       friend class ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>;
1808//       typename Graph::NodeIt n;
1809//      public:
1810//       NodeIt() { }
1811//       NodeIt(const typename Graph::NodeIt& _n) : n(_n) { }
1812//       NodeIt(const Invalid& i) : n(i) { }
1813//       NodeIt(const ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>& _G) :
1814//      n(*(_G.graph)) { }
1815//       operator Node() const { return Node(typename Graph::Node(n)); }
1816//     };
1817    typedef typename GraphWrapper<Graph>::Edge Edge;
1818    class OutEdgeIt {
1819      friend class GraphWrapper<Graph>;
1820      friend class ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>;
1821//      typedef typename Graph::OutEdgeIt GraphOutEdgeIt;
1822      typename Graph::OutEdgeIt e;
1823    public:
1824      OutEdgeIt() { }
1825      OutEdgeIt(const typename Graph::OutEdgeIt& _e) : e(_e) { }
1826      OutEdgeIt(const Invalid& i) : e(i) { }
1827      OutEdgeIt(const ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>& _G,
1828                const Node& _n) :
1829        e((*_G.first_out_edges)[_n]) { }
1830      operator Edge() const { return Edge(typename Graph::Edge(e)); }
1831    };
1832    class InEdgeIt {
1833      friend class GraphWrapper<Graph>;
1834      friend class ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>;
1835//      typedef typename Graph::InEdgeIt GraphInEdgeIt;
1836      typename Graph::InEdgeIt e;
1837    public:
1838      InEdgeIt() { }
1839      InEdgeIt(const typename Graph::InEdgeIt& _e) : e(_e) { }
1840      InEdgeIt(const Invalid& i) : e(i) { }
1841      InEdgeIt(const ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>& _G,
1842               const Node& _n) :
1843        e(*(_G.graph), typename Graph::Node(_n)) { }
1844      operator Edge() const { return Edge(typename Graph::Edge(e)); }
1845    };
1846    //typedef typename Graph::SymEdgeIt SymEdgeIt;
1847    class EdgeIt {
1848      friend class GraphWrapper<Graph>;
1849      friend class ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>;
1850//      typedef typename Graph::EdgeIt GraphEdgeIt;
1851      typename Graph::EdgeIt e;
1852    public:
1853      EdgeIt() { }
1854      EdgeIt(const typename Graph::EdgeIt& _e) : e(_e) { }
1855      EdgeIt(const Invalid& i) : e(i) { }
1856      EdgeIt(const ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>& _G) :
1857        e(*(_G.graph)) { }
1858      operator Edge() const { return Edge(typename Graph::Edge(e)); }
1859    };
1860
1861    using GraphWrapper<Graph>::first;
1862//     NodeIt& first(NodeIt& i) const {
1863//       i=NodeIt(*this); return i;
1864//     }
1865    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const {
1866      i=OutEdgeIt(*this, p); return i;
1867    }
1868    InEdgeIt& first(InEdgeIt& i, const Node& p) const {
1869      i=InEdgeIt(*this, p); return i;
1870    }
1871    EdgeIt& first(EdgeIt& i) const {
1872      i=EdgeIt(*this); return i;
1873    }
1874
1875    using GraphWrapper<Graph>::next;
1876//    NodeIt& next(NodeIt& i) const { graph->next(i.n); return i; }
1877    OutEdgeIt& next(OutEdgeIt& i) const { this->graph->next(i.e); return i; }
1878    InEdgeIt& next(InEdgeIt& i) const { this->graph->next(i.e); return i; }
1879    EdgeIt& next(EdgeIt& i) const { this->graph->next(i.e); return i; }   
1880   
1881    Node aNode(const OutEdgeIt& e) const {
1882      return Node(this->graph->aNode(e.e)); }
1883    Node aNode(const InEdgeIt& e) const {
1884      return Node(this->graph->aNode(e.e)); }
1885    Node bNode(const OutEdgeIt& e) const {
1886      return Node(this->graph->bNode(e.e)); }
1887    Node bNode(const InEdgeIt& e) const {
1888      return Node(this->graph->bNode(e.e)); }
1889
1890    void erase(const OutEdgeIt& e) const {
1891      OutEdgeIt f=e;
1892      this->next(f);
1893      first_out_edges->set(this->tail(e), f.e);
1894    }
1895  };
1896
1897  ///@}
1898
1899} //namespace hugo
1900
1901#endif //HUGO_GRAPH_WRAPPER_H
1902
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