lemon/min_cut.h
changeset 2284 05ff57dc401d
parent 2283 a877258468e4
child 2285 8c5c4b5ae31c
     1.1 --- a/lemon/min_cut.h	Tue Oct 31 14:28:27 2006 +0000
     1.2 +++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.3 @@ -1,1353 +0,0 @@
     1.4 -/* -*- C++ -*-
     1.5 - * lemon/min_cut.h - Part of LEMON, a generic C++ optimization library
     1.6 - *
     1.7 - * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     1.8 - * (Egervary Research Group on Combinatorial Optimization, EGRES).
     1.9 - *
    1.10 - * Permission to use, modify and distribute this software is granted
    1.11 - * provided that this copyright notice appears in all copies. For
    1.12 - * precise terms see the accompanying LICENSE file.
    1.13 - *
    1.14 - * This software is provided "AS IS" with no warranty of any kind,
    1.15 - * express or implied, and with no claim as to its suitability for any
    1.16 - * purpose.
    1.17 - *
    1.18 - */
    1.19 -
    1.20 -#ifndef LEMON_MIN_CUT_H
    1.21 -#define LEMON_MIN_CUT_H
    1.22 -
    1.23 -
    1.24 -/// \ingroup topology
    1.25 -/// \file
    1.26 -/// \brief Maximum cardinality search and min cut in undirected graphs.
    1.27 -
    1.28 -#include <lemon/list_graph.h>
    1.29 -#include <lemon/bin_heap.h>
    1.30 -#include <lemon/bucket_heap.h>
    1.31 -
    1.32 -#include <lemon/bits/invalid.h>
    1.33 -#include <lemon/error.h>
    1.34 -#include <lemon/maps.h>
    1.35 -
    1.36 -#include <functional>
    1.37 -
    1.38 -namespace lemon {
    1.39 -
    1.40 -  namespace _min_cut_bits {
    1.41 -
    1.42 -    template <typename CapacityMap>
    1.43 -    struct HeapSelector {
    1.44 -      template <typename Value, typename Ref>
    1.45 -      struct Selector {
    1.46 -        typedef BinHeap<Value, Ref, std::greater<Value> > Heap;
    1.47 -      };
    1.48 -    };
    1.49 -
    1.50 -    template <typename CapacityKey>
    1.51 -    struct HeapSelector<ConstMap<CapacityKey, Const<int, 1> > > {
    1.52 -      template <typename Value, typename Ref>
    1.53 -      struct Selector {
    1.54 -        typedef BucketHeap<Ref, false > Heap;
    1.55 -      };
    1.56 -    };
    1.57 -
    1.58 -  }
    1.59 -
    1.60 -  /// \brief Default traits class of MaxCardinalitySearch class.
    1.61 -  ///
    1.62 -  /// Default traits class of MaxCardinalitySearch class.
    1.63 -  /// \param Graph Graph type.
    1.64 -  /// \param CapacityMap Type of length map.
    1.65 -  template <typename _Graph, typename _CapacityMap>
    1.66 -  struct MaxCardinalitySearchDefaultTraits {
    1.67 -    /// The graph type the algorithm runs on. 
    1.68 -    typedef _Graph Graph;
    1.69 -
    1.70 -    /// \brief The type of the map that stores the edge capacities.
    1.71 -    ///
    1.72 -    /// The type of the map that stores the edge capacities.
    1.73 -    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
    1.74 -    typedef _CapacityMap CapacityMap;
    1.75 -
    1.76 -    /// \brief The type of the capacity of the edges.
    1.77 -    typedef typename CapacityMap::Value Value;
    1.78 -
    1.79 -    /// \brief The cross reference type used by heap.
    1.80 -    ///
    1.81 -    /// The cross reference type used by heap.
    1.82 -    /// Usually it is \c Graph::NodeMap<int>.
    1.83 -    typedef typename Graph::template NodeMap<int> HeapCrossRef;
    1.84 -
    1.85 -    /// \brief Instantiates a HeapCrossRef.
    1.86 -    ///
    1.87 -    /// This function instantiates a \ref HeapCrossRef. 
    1.88 -    /// \param graph is the graph, to which we would like to define the 
    1.89 -    /// HeapCrossRef.
    1.90 -    static HeapCrossRef *createHeapCrossRef(const Graph &graph) {
    1.91 -      return new HeapCrossRef(graph);
    1.92 -    }
    1.93 -    
    1.94 -    /// \brief The heap type used by MaxCardinalitySearch algorithm.
    1.95 -    ///
    1.96 -    /// The heap type used by MaxCardinalitySearch algorithm. It should
    1.97 -    /// maximalize the priorities. The default heap type is
    1.98 -    /// the \ref BinHeap, but it is specialized when the
    1.99 -    /// CapacityMap is ConstMap<Graph::Node, Const<int, 1> >
   1.100 -    /// to BucketHeap.
   1.101 -    ///
   1.102 -    /// \sa MaxCardinalitySearch
   1.103 -    typedef typename _min_cut_bits
   1.104 -    ::HeapSelector<CapacityMap>
   1.105 -    ::template Selector<Value, HeapCrossRef>
   1.106 -    ::Heap Heap;
   1.107 -
   1.108 -    /// \brief Instantiates a Heap.
   1.109 -    ///
   1.110 -    /// This function instantiates a \ref Heap. 
   1.111 -    /// \param crossref The cross reference of the heap.
   1.112 -    static Heap *createHeap(HeapCrossRef& crossref) {
   1.113 -      return new Heap(crossref);
   1.114 -    }
   1.115 -
   1.116 -    /// \brief The type of the map that stores whether a nodes is processed.
   1.117 -    ///
   1.118 -    /// The type of the map that stores whether a nodes is processed.
   1.119 -    /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
   1.120 -    /// By default it is a NullMap.
   1.121 -    typedef NullMap<typename Graph::Node, bool> ProcessedMap;
   1.122 -
   1.123 -    /// \brief Instantiates a ProcessedMap.
   1.124 -    ///
   1.125 -    /// This function instantiates a \ref ProcessedMap. 
   1.126 -    /// \param graph is the graph, to which
   1.127 -    /// we would like to define the \ref ProcessedMap
   1.128 -#ifdef DOXYGEN
   1.129 -    static ProcessedMap *createProcessedMap(const Graph &graph)
   1.130 -#else
   1.131 -    static ProcessedMap *createProcessedMap(const Graph &)
   1.132 -#endif
   1.133 -    {
   1.134 -      return new ProcessedMap();
   1.135 -    }
   1.136 -
   1.137 -    /// \brief The type of the map that stores the cardinalties of the nodes.
   1.138 -    /// 
   1.139 -    /// The type of the map that stores the cardinalities of the nodes.
   1.140 -    /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
   1.141 -    typedef typename Graph::template NodeMap<Value> CardinalityMap;
   1.142 -
   1.143 -    /// \brief Instantiates a CardinalityMap.
   1.144 -    ///
   1.145 -    /// This function instantiates a \ref CardinalityMap. 
   1.146 -    /// \param graph is the graph, to which we would like to define the \ref 
   1.147 -    /// CardinalityMap
   1.148 -    static CardinalityMap *createCardinalityMap(const Graph &graph) {
   1.149 -      return new CardinalityMap(graph);
   1.150 -    }
   1.151 -
   1.152 -  };
   1.153 -  
   1.154 -  /// \ingroup topology
   1.155 -  ///
   1.156 -  /// \brief Maximum Cardinality Search algorithm class.
   1.157 -  ///
   1.158 -  /// This class provides an efficient implementation of Maximum Cardinality 
   1.159 -  /// Search algorithm. The maximum cardinality search chooses first time any 
   1.160 -  /// node of the graph. Then every time it chooses the node which is connected
   1.161 -  /// to the processed nodes at most in the sum of capacities on the out 
   1.162 -  /// edges. If there is a cut in the graph the algorithm should choose
   1.163 -  /// again any unprocessed node of the graph. Each node cardinality is
   1.164 -  /// the sum of capacities on the out edges to the nodes which are processed
   1.165 -  /// before the given node.
   1.166 -  ///
   1.167 -  /// The edge capacities are passed to the algorithm using a
   1.168 -  /// \ref concepts::ReadMap "ReadMap", so it is easy to change it to any 
   1.169 -  /// kind of capacity.
   1.170 -  ///
   1.171 -  /// The type of the capacity is determined by the \ref 
   1.172 -  /// concepts::ReadMap::Value "Value" of the capacity map.
   1.173 -  ///
   1.174 -  /// It is also possible to change the underlying priority heap.
   1.175 -  ///
   1.176 -  ///
   1.177 -  /// \param _Graph The graph type the algorithm runs on. The default value
   1.178 -  /// is \ref ListGraph. The value of Graph is not used directly by
   1.179 -  /// the search algorithm, it is only passed to 
   1.180 -  /// \ref MaxCardinalitySearchDefaultTraits.
   1.181 -  /// \param _CapacityMap This read-only EdgeMap determines the capacities of 
   1.182 -  /// the edges. It is read once for each edge, so the map may involve in
   1.183 -  /// relatively time consuming process to compute the edge capacity if
   1.184 -  /// it is necessary. The default map type is \ref
   1.185 -  /// concepts::Graph::EdgeMap "Graph::EdgeMap<int>".  The value
   1.186 -  /// of CapacityMap is not used directly by search algorithm, it is only 
   1.187 -  /// passed to \ref MaxCardinalitySearchDefaultTraits.  
   1.188 -  /// \param _Traits Traits class to set various data types used by the 
   1.189 -  /// algorithm.  The default traits class is 
   1.190 -  /// \ref MaxCardinalitySearchDefaultTraits 
   1.191 -  /// "MaxCardinalitySearchDefaultTraits<_Graph, _CapacityMap>".  
   1.192 -  /// See \ref MaxCardinalitySearchDefaultTraits 
   1.193 -  /// for the documentation of a MaxCardinalitySearch traits class.
   1.194 -  ///
   1.195 -  /// \author Balazs Dezso
   1.196 -
   1.197 -#ifdef DOXYGEN
   1.198 -  template <typename _Graph, typename _CapacityMap, typename _Traits>
   1.199 -#else
   1.200 -  template <typename _Graph = ListUGraph,
   1.201 -	    typename _CapacityMap = typename _Graph::template EdgeMap<int>,
   1.202 -	    typename _Traits = 
   1.203 -            MaxCardinalitySearchDefaultTraits<_Graph, _CapacityMap> >
   1.204 -#endif
   1.205 -  class MaxCardinalitySearch {
   1.206 -  public:
   1.207 -    /// \brief \ref Exception for uninitialized parameters.
   1.208 -    ///
   1.209 -    /// This error represents problems in the initialization
   1.210 -    /// of the parameters of the algorithms.
   1.211 -    class UninitializedParameter : public lemon::UninitializedParameter {
   1.212 -    public:
   1.213 -      virtual const char* what() const throw() {
   1.214 -	return "lemon::MaxCardinalitySearch::UninitializedParameter";
   1.215 -      }
   1.216 -    };
   1.217 -
   1.218 -    typedef _Traits Traits;
   1.219 -    ///The type of the underlying graph.
   1.220 -    typedef typename Traits::Graph Graph;
   1.221 -    
   1.222 -    ///The type of the capacity of the edges.
   1.223 -    typedef typename Traits::CapacityMap::Value Value;
   1.224 -    ///The type of the map that stores the edge capacities.
   1.225 -    typedef typename Traits::CapacityMap CapacityMap;
   1.226 -    ///The type of the map indicating if a node is processed.
   1.227 -    typedef typename Traits::ProcessedMap ProcessedMap;
   1.228 -    ///The type of the map that stores the cardinalities of the nodes.
   1.229 -    typedef typename Traits::CardinalityMap CardinalityMap;
   1.230 -    ///The cross reference type used for the current heap.
   1.231 -    typedef typename Traits::HeapCrossRef HeapCrossRef;
   1.232 -    ///The heap type used by the algorithm. It maximize the priorities.
   1.233 -    typedef typename Traits::Heap Heap;
   1.234 -  private:
   1.235 -    /// Pointer to the underlying graph.
   1.236 -    const Graph *_graph;
   1.237 -    /// Pointer to the capacity map
   1.238 -    const CapacityMap *_capacity;
   1.239 -    ///Pointer to the map of cardinality.
   1.240 -    CardinalityMap *_cardinality;
   1.241 -    ///Indicates if \ref _cardinality is locally allocated (\c true) or not.
   1.242 -    bool local_cardinality;
   1.243 -    ///Pointer to the map of processed status of the nodes.
   1.244 -    ProcessedMap *_processed;
   1.245 -    ///Indicates if \ref _processed is locally allocated (\c true) or not.
   1.246 -    bool local_processed;
   1.247 -    ///Pointer to the heap cross references.
   1.248 -    HeapCrossRef *_heap_cross_ref;
   1.249 -    ///Indicates if \ref _heap_cross_ref is locally allocated (\c true) or not.
   1.250 -    bool local_heap_cross_ref;
   1.251 -    ///Pointer to the heap.
   1.252 -    Heap *_heap;
   1.253 -    ///Indicates if \ref _heap is locally allocated (\c true) or not.
   1.254 -    bool local_heap;
   1.255 -
   1.256 -  public :
   1.257 -
   1.258 -    typedef MaxCardinalitySearch Create;
   1.259 - 
   1.260 -    ///\name Named template parameters
   1.261 -
   1.262 -    ///@{
   1.263 -
   1.264 -    template <class T>
   1.265 -    struct DefCardinalityMapTraits : public Traits {
   1.266 -      typedef T CardinalityMap;
   1.267 -      static CardinalityMap *createCardinalityMap(const Graph &) 
   1.268 -      {
   1.269 -	throw UninitializedParameter();
   1.270 -      }
   1.271 -    };
   1.272 -    /// \brief \ref named-templ-param "Named parameter" for setting 
   1.273 -    /// CardinalityMap type
   1.274 -    ///
   1.275 -    /// \ref named-templ-param "Named parameter" for setting CardinalityMap 
   1.276 -    /// type
   1.277 -    template <class T>
   1.278 -    struct DefCardinalityMap 
   1.279 -      : public MaxCardinalitySearch<Graph, CapacityMap, 
   1.280 -                                    DefCardinalityMapTraits<T> > { 
   1.281 -      typedef MaxCardinalitySearch<Graph, CapacityMap, 
   1.282 -                                   DefCardinalityMapTraits<T> > Create;
   1.283 -    };
   1.284 -    
   1.285 -    template <class T>
   1.286 -    struct DefProcessedMapTraits : public Traits {
   1.287 -      typedef T ProcessedMap;
   1.288 -      static ProcessedMap *createProcessedMap(const Graph &) {
   1.289 -	throw UninitializedParameter();
   1.290 -      }
   1.291 -    };
   1.292 -    /// \brief \ref named-templ-param "Named parameter" for setting 
   1.293 -    /// ProcessedMap type
   1.294 -    ///
   1.295 -    /// \ref named-templ-param "Named parameter" for setting ProcessedMap type
   1.296 -    ///
   1.297 -    template <class T>
   1.298 -    struct DefProcessedMap 
   1.299 -      : public MaxCardinalitySearch<Graph, CapacityMap, 
   1.300 -                                    DefProcessedMapTraits<T> > { 
   1.301 -      typedef MaxCardinalitySearch<Graph, CapacityMap, 
   1.302 -                                   DefProcessedMapTraits<T> > Create;
   1.303 -    };
   1.304 -    
   1.305 -    template <class H, class CR>
   1.306 -    struct DefHeapTraits : public Traits {
   1.307 -      typedef CR HeapCrossRef;
   1.308 -      typedef H Heap;
   1.309 -      static HeapCrossRef *createHeapCrossRef(const Graph &) {
   1.310 -	throw UninitializedParameter();
   1.311 -      }
   1.312 -      static Heap *createHeap(HeapCrossRef &) {
   1.313 -	throw UninitializedParameter();
   1.314 -      }
   1.315 -    };
   1.316 -    /// \brief \ref named-templ-param "Named parameter" for setting heap 
   1.317 -    /// and cross reference type
   1.318 -    ///
   1.319 -    /// \ref named-templ-param "Named parameter" for setting heap and cross 
   1.320 -    /// reference type
   1.321 -    template <class H, class CR = typename Graph::template NodeMap<int> >
   1.322 -    struct DefHeap
   1.323 -      : public MaxCardinalitySearch<Graph, CapacityMap, 
   1.324 -                                    DefHeapTraits<H, CR> > { 
   1.325 -      typedef MaxCardinalitySearch< Graph, CapacityMap, 
   1.326 -                                    DefHeapTraits<H, CR> > Create;
   1.327 -    };
   1.328 -
   1.329 -    template <class H, class CR>
   1.330 -    struct DefStandardHeapTraits : public Traits {
   1.331 -      typedef CR HeapCrossRef;
   1.332 -      typedef H Heap;
   1.333 -      static HeapCrossRef *createHeapCrossRef(const Graph &graph) {
   1.334 -	return new HeapCrossRef(graph);
   1.335 -      }
   1.336 -      static Heap *createHeap(HeapCrossRef &crossref) {
   1.337 -	return new Heap(crossref);
   1.338 -      }
   1.339 -    };
   1.340 -
   1.341 -    /// \brief \ref named-templ-param "Named parameter" for setting heap and 
   1.342 -    /// cross reference type with automatic allocation
   1.343 -    ///
   1.344 -    /// \ref named-templ-param "Named parameter" for setting heap and cross 
   1.345 -    /// reference type. It can allocate the heap and the cross reference 
   1.346 -    /// object if the cross reference's constructor waits for the graph as 
   1.347 -    /// parameter and the heap's constructor waits for the cross reference.
   1.348 -    template <class H, class CR = typename Graph::template NodeMap<int> >
   1.349 -    struct DefStandardHeap
   1.350 -      : public MaxCardinalitySearch<Graph, CapacityMap, 
   1.351 -                                    DefStandardHeapTraits<H, CR> > { 
   1.352 -      typedef MaxCardinalitySearch<Graph, CapacityMap, 
   1.353 -                                   DefStandardHeapTraits<H, CR> > 
   1.354 -      Create;
   1.355 -    };
   1.356 -    
   1.357 -    ///@}
   1.358 -
   1.359 -
   1.360 -  protected:
   1.361 -
   1.362 -    MaxCardinalitySearch() {}
   1.363 -
   1.364 -  public:      
   1.365 -    
   1.366 -    /// \brief Constructor.
   1.367 -    ///
   1.368 -    ///\param graph the graph the algorithm will run on.
   1.369 -    ///\param capacity the capacity map used by the algorithm.
   1.370 -    MaxCardinalitySearch(const Graph& graph, const CapacityMap& capacity) :
   1.371 -      _graph(&graph), _capacity(&capacity),
   1.372 -      _cardinality(0), local_cardinality(false),
   1.373 -      _processed(0), local_processed(false),
   1.374 -      _heap_cross_ref(0), local_heap_cross_ref(false),
   1.375 -      _heap(0), local_heap(false)
   1.376 -    { }
   1.377 -    
   1.378 -    /// \brief Destructor.
   1.379 -    ~MaxCardinalitySearch() {
   1.380 -      if(local_cardinality) delete _cardinality;
   1.381 -      if(local_processed) delete _processed;
   1.382 -      if(local_heap_cross_ref) delete _heap_cross_ref;
   1.383 -      if(local_heap) delete _heap;
   1.384 -    }
   1.385 -
   1.386 -    /// \brief Sets the capacity map.
   1.387 -    ///
   1.388 -    /// Sets the capacity map.
   1.389 -    /// \return <tt> (*this) </tt>
   1.390 -    MaxCardinalitySearch &capacityMap(const CapacityMap &m) {
   1.391 -      _capacity = &m;
   1.392 -      return *this;
   1.393 -    }
   1.394 -
   1.395 -    /// \brief Sets the map storing the cardinalities calculated by the 
   1.396 -    /// algorithm.
   1.397 -    ///
   1.398 -    /// Sets the map storing the cardinalities calculated by the algorithm.
   1.399 -    /// If you don't use this function before calling \ref run(),
   1.400 -    /// it will allocate one. The destuctor deallocates this
   1.401 -    /// automatically allocated map, of course.
   1.402 -    /// \return <tt> (*this) </tt>
   1.403 -    MaxCardinalitySearch &cardinalityMap(CardinalityMap &m) {
   1.404 -      if(local_cardinality) {
   1.405 -	delete _cardinality;
   1.406 -	local_cardinality=false;
   1.407 -      }
   1.408 -      _cardinality = &m;
   1.409 -      return *this;
   1.410 -    }
   1.411 -
   1.412 -    /// \brief Sets the map storing the processed nodes.
   1.413 -    ///
   1.414 -    /// Sets the map storing the processed nodes.
   1.415 -    /// If you don't use this function before calling \ref run(),
   1.416 -    /// it will allocate one. The destuctor deallocates this
   1.417 -    /// automatically allocated map, of course.
   1.418 -    /// \return <tt> (*this) </tt>
   1.419 -    MaxCardinalitySearch &processedMap(ProcessedMap &m) 
   1.420 -    {
   1.421 -      if(local_processed) {
   1.422 -	delete _processed;
   1.423 -	local_processed=false;
   1.424 -      }
   1.425 -      _processed = &m;
   1.426 -      return *this;
   1.427 -    }
   1.428 -
   1.429 -    /// \brief Sets the heap and the cross reference used by algorithm.
   1.430 -    ///
   1.431 -    /// Sets the heap and the cross reference used by algorithm.
   1.432 -    /// If you don't use this function before calling \ref run(),
   1.433 -    /// it will allocate one. The destuctor deallocates this
   1.434 -    /// automatically allocated map, of course.
   1.435 -    /// \return <tt> (*this) </tt>
   1.436 -    MaxCardinalitySearch &heap(Heap& heap, HeapCrossRef &crossRef) {
   1.437 -      if(local_heap_cross_ref) {
   1.438 -	delete _heap_cross_ref;
   1.439 -	local_heap_cross_ref = false;
   1.440 -      }
   1.441 -      _heap_cross_ref = &crossRef;
   1.442 -      if(local_heap) {
   1.443 -	delete _heap;
   1.444 -	local_heap = false;
   1.445 -      }
   1.446 -      _heap = &heap;
   1.447 -      return *this;
   1.448 -    }
   1.449 -
   1.450 -  private:
   1.451 -
   1.452 -    typedef typename Graph::Node Node;
   1.453 -    typedef typename Graph::NodeIt NodeIt;
   1.454 -    typedef typename Graph::Edge Edge;
   1.455 -    typedef typename Graph::InEdgeIt InEdgeIt;
   1.456 -
   1.457 -    void create_maps() {
   1.458 -      if(!_cardinality) {
   1.459 -	local_cardinality = true;
   1.460 -	_cardinality = Traits::createCardinalityMap(*_graph);
   1.461 -      }
   1.462 -      if(!_processed) {
   1.463 -	local_processed = true;
   1.464 -	_processed = Traits::createProcessedMap(*_graph);
   1.465 -      }
   1.466 -      if (!_heap_cross_ref) {
   1.467 -	local_heap_cross_ref = true;
   1.468 -	_heap_cross_ref = Traits::createHeapCrossRef(*_graph);
   1.469 -      }
   1.470 -      if (!_heap) {
   1.471 -	local_heap = true;
   1.472 -	_heap = Traits::createHeap(*_heap_cross_ref);
   1.473 -      }
   1.474 -    }
   1.475 -    
   1.476 -    void finalizeNodeData(Node node, Value capacity) {
   1.477 -      _processed->set(node, true);
   1.478 -      _cardinality->set(node, capacity);
   1.479 -    }
   1.480 -
   1.481 -  public:
   1.482 -    /// \name Execution control
   1.483 -    /// The simplest way to execute the algorithm is to use
   1.484 -    /// one of the member functions called \c run(...).
   1.485 -    /// \n
   1.486 -    /// If you need more control on the execution,
   1.487 -    /// first you must call \ref init(), then you can add several source nodes
   1.488 -    /// with \ref addSource().
   1.489 -    /// Finally \ref start() will perform the actual path
   1.490 -    /// computation.
   1.491 -
   1.492 -    ///@{
   1.493 -
   1.494 -    /// \brief Initializes the internal data structures.
   1.495 -    ///
   1.496 -    /// Initializes the internal data structures.
   1.497 -    void init() {
   1.498 -      create_maps();
   1.499 -      _heap->clear();
   1.500 -      for (NodeIt it(*_graph) ; it != INVALID ; ++it) {
   1.501 -	_processed->set(it, false);
   1.502 -	_heap_cross_ref->set(it, Heap::PRE_HEAP);
   1.503 -      }
   1.504 -    }
   1.505 -    
   1.506 -    /// \brief Adds a new source node.
   1.507 -    /// 
   1.508 -    /// Adds a new source node to the priority heap.
   1.509 -    ///
   1.510 -    /// It checks if the node has not yet been added to the heap.
   1.511 -    void addSource(Node source, Value capacity = 0) {
   1.512 -      if(_heap->state(source) == Heap::PRE_HEAP) {
   1.513 -	_heap->push(source, capacity);
   1.514 -      } 
   1.515 -    }
   1.516 -    
   1.517 -    /// \brief Processes the next node in the priority heap
   1.518 -    ///
   1.519 -    /// Processes the next node in the priority heap.
   1.520 -    ///
   1.521 -    /// \return The processed node.
   1.522 -    ///
   1.523 -    /// \warning The priority heap must not be empty!
   1.524 -    Node processNextNode() {
   1.525 -      Node node = _heap->top(); 
   1.526 -      finalizeNodeData(node, _heap->prio());
   1.527 -      _heap->pop();
   1.528 -      
   1.529 -      for (InEdgeIt it(*_graph, node); it != INVALID; ++it) {
   1.530 -	Node source = _graph->source(it); 
   1.531 -	switch (_heap->state(source)) {
   1.532 -	case Heap::PRE_HEAP:
   1.533 -	  _heap->push(source, (*_capacity)[it]); 
   1.534 -	  break;
   1.535 -	case Heap::IN_HEAP:
   1.536 -	  _heap->decrease(source, (*_heap)[source] + (*_capacity)[it]); 
   1.537 -	  break;
   1.538 -	case Heap::POST_HEAP:
   1.539 -	  break;
   1.540 -	}
   1.541 -      }
   1.542 -      return node;
   1.543 -    }
   1.544 -
   1.545 -    /// \brief Next node to be processed.
   1.546 -    ///
   1.547 -    /// Next node to be processed.
   1.548 -    ///
   1.549 -    /// \return The next node to be processed or INVALID if the 
   1.550 -    /// priority heap is empty.
   1.551 -    Node nextNode() { 
   1.552 -      return _heap->empty() ? _heap->top() : INVALID;
   1.553 -    }
   1.554 - 
   1.555 -    /// \brief Returns \c false if there are nodes
   1.556 -    /// to be processed in the priority heap
   1.557 -    ///
   1.558 -    /// Returns \c false if there are nodes
   1.559 -    /// to be processed in the priority heap
   1.560 -    bool emptyQueue() { return _heap->empty(); }
   1.561 -    /// \brief Returns the number of the nodes to be processed 
   1.562 -    /// in the priority heap
   1.563 -    ///
   1.564 -    /// Returns the number of the nodes to be processed in the priority heap
   1.565 -    int queueSize() { return _heap->size(); }
   1.566 -    
   1.567 -    /// \brief Executes the algorithm.
   1.568 -    ///
   1.569 -    /// Executes the algorithm.
   1.570 -    ///
   1.571 -    ///\pre init() must be called and at least one node should be added
   1.572 -    /// with addSource() before using this function.
   1.573 -    ///
   1.574 -    /// This method runs the Maximum Cardinality Search algorithm from the 
   1.575 -    /// source node(s).
   1.576 -    void start() {
   1.577 -      while ( !_heap->empty() ) processNextNode();
   1.578 -    }
   1.579 -    
   1.580 -    /// \brief Executes the algorithm until \c dest is reached.
   1.581 -    ///
   1.582 -    /// Executes the algorithm until \c dest is reached.
   1.583 -    ///
   1.584 -    /// \pre init() must be called and at least one node should be added
   1.585 -    /// with addSource() before using this function.
   1.586 -    ///
   1.587 -    /// This method runs the %MaxCardinalitySearch algorithm from the source 
   1.588 -    /// nodes.
   1.589 -    void start(Node dest) {
   1.590 -      while ( !_heap->empty() && _heap->top()!=dest ) processNextNode();
   1.591 -      if ( !_heap->empty() ) finalizeNodeData(_heap->top(), _heap->prio());
   1.592 -    }
   1.593 -    
   1.594 -    /// \brief Executes the algorithm until a condition is met.
   1.595 -    ///
   1.596 -    /// Executes the algorithm until a condition is met.
   1.597 -    ///
   1.598 -    /// \pre init() must be called and at least one node should be added
   1.599 -    /// with addSource() before using this function.
   1.600 -    ///
   1.601 -    /// \param nm must be a bool (or convertible) node map. The algorithm
   1.602 -    /// will stop when it reaches a node \c v with <tt>nm[v]==true</tt>.
   1.603 -    template <typename NodeBoolMap>
   1.604 -    void start(const NodeBoolMap &nm) {
   1.605 -      while ( !_heap->empty() && !nm[_heap->top()] ) processNextNode();
   1.606 -      if ( !_heap->empty() ) finalizeNodeData(_heap->top(),_heap->prio());
   1.607 -    }
   1.608 -    
   1.609 -    /// \brief Runs the maximal cardinality search algorithm from node \c s.
   1.610 -    ///
   1.611 -    /// This method runs the %MaxCardinalitySearch algorithm from a root 
   1.612 -    /// node \c s.
   1.613 -    ///
   1.614 -    ///\note d.run(s) is just a shortcut of the following code.
   1.615 -    ///\code
   1.616 -    ///  d.init();
   1.617 -    ///  d.addSource(s);
   1.618 -    ///  d.start();
   1.619 -    ///\endcode
   1.620 -    void run(Node s) {
   1.621 -      init();
   1.622 -      addSource(s);
   1.623 -      start();
   1.624 -    }
   1.625 -
   1.626 -    /// \brief Runs the maximal cardinality search algorithm for the 
   1.627 -    /// whole graph.
   1.628 -    ///
   1.629 -    /// This method runs the %MaxCardinalitySearch algorithm from all 
   1.630 -    /// unprocessed node of the graph.
   1.631 -    ///
   1.632 -    ///\note d.run(s) is just a shortcut of the following code.
   1.633 -    ///\code
   1.634 -    ///  d.init();
   1.635 -    ///  for (NodeIt it(graph); it != INVALID; ++it) {
   1.636 -    ///    if (!d.reached(it)) {
   1.637 -    ///      d.addSource(s);
   1.638 -    ///      d.start();
   1.639 -    ///    }
   1.640 -    ///  }
   1.641 -    ///\endcode
   1.642 -    void run() {
   1.643 -      init();
   1.644 -      for (NodeIt it(*_graph); it != INVALID; ++it) {
   1.645 -        if (!reached(it)) {
   1.646 -          addSource(it);
   1.647 -          start();
   1.648 -        }
   1.649 -      }
   1.650 -    }
   1.651 -    
   1.652 -    ///@}
   1.653 -
   1.654 -    /// \name Query Functions
   1.655 -    /// The result of the maximum cardinality search algorithm can be 
   1.656 -    /// obtained using these functions.
   1.657 -    /// \n
   1.658 -    /// Before the use of these functions, either run() or start() must be 
   1.659 -    /// called.
   1.660 -    
   1.661 -    ///@{
   1.662 -
   1.663 -    /// \brief The cardinality of a node.
   1.664 -    ///
   1.665 -    /// Returns the cardinality of a node.
   1.666 -    /// \pre \ref run() must be called before using this function.
   1.667 -    /// \warning If node \c v in unreachable from the root the return value
   1.668 -    /// of this funcion is undefined.
   1.669 -    Value cardinality(Node node) const { return (*_cardinality)[node]; }
   1.670 -
   1.671 -    /// \brief Returns a reference to the NodeMap of cardinalities.
   1.672 -    ///
   1.673 -    /// Returns a reference to the NodeMap of cardinalities. \pre \ref run() 
   1.674 -    /// must be called before using this function.
   1.675 -    const CardinalityMap &cardinalityMap() const { return *_cardinality;}
   1.676 - 
   1.677 -    /// \brief Checks if a node is reachable from the root.
   1.678 -    ///
   1.679 -    /// Returns \c true if \c v is reachable from the root.
   1.680 -    /// \warning The source nodes are inditated as unreached.
   1.681 -    /// \pre \ref run() must be called before using this function.
   1.682 -    bool reached(Node v) { return (*_heap_cross_ref)[v] != Heap::PRE_HEAP; }
   1.683 -
   1.684 -    /// \brief Checks if a node is processed.
   1.685 -    ///
   1.686 -    /// Returns \c true if \c v is processed, i.e. the shortest
   1.687 -    /// path to \c v has already found.
   1.688 -    /// \pre \ref run() must be called before using this function.
   1.689 -    bool processed(Node v) { return (*_heap_cross_ref)[v] == Heap::POST_HEAP; }
   1.690 -    
   1.691 -    ///@}
   1.692 -  };
   1.693 -
   1.694 -  /// \brief Default traits class of MinCut class.
   1.695 -  ///
   1.696 -  /// Default traits class of MinCut class.
   1.697 -  /// \param Graph Graph type.
   1.698 -  /// \param CapacityMap Type of length map.
   1.699 -  template <typename _Graph, typename _CapacityMap>
   1.700 -  struct MinCutDefaultTraits {
   1.701 -    /// \brief The type of the capacity of the edges.
   1.702 -    typedef typename _CapacityMap::Value Value;
   1.703 -
   1.704 -    /// The graph type the algorithm runs on. 
   1.705 -    typedef _Graph Graph;
   1.706 -
   1.707 -    /// The AuxGraph type which is an Graph
   1.708 -    typedef ListUGraph AuxGraph;
   1.709 -
   1.710 -    /// \brief Instantiates a AuxGraph.
   1.711 -    ///
   1.712 -    /// This function instantiates a \ref AuxGraph. 
   1.713 -    static AuxGraph *createAuxGraph() {
   1.714 -      return new AuxGraph();
   1.715 -    }
   1.716 -
   1.717 -    /// \brief The type of the map that stores the edge capacities.
   1.718 -    ///
   1.719 -    /// The type of the map that stores the edge capacities.
   1.720 -    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
   1.721 -    typedef _CapacityMap CapacityMap;
   1.722 -
   1.723 -    /// \brief Instantiates a CapacityMap.
   1.724 -    ///
   1.725 -    /// This function instantiates a \ref CapacityMap.
   1.726 -#ifdef DOXYGEN
   1.727 -    static CapacityMap *createCapacityMap(const Graph& graph) 
   1.728 -#else
   1.729 -    static CapacityMap *createCapacityMap(const Graph&)
   1.730 -#endif
   1.731 -    {
   1.732 -      throw UninitializedParameter();
   1.733 -    }
   1.734 -
   1.735 -    /// \brief The AuxCapacityMap type
   1.736 -    ///
   1.737 -    /// The type of the map that stores the auxing edge capacities.
   1.738 -    typedef AuxGraph::UEdgeMap<Value> AuxCapacityMap;
   1.739 -
   1.740 -    /// \brief Instantiates a AuxCapacityMap.
   1.741 -    ///
   1.742 -    /// This function instantiates a \ref AuxCapacityMap. 
   1.743 -    static AuxCapacityMap *createAuxCapacityMap(const AuxGraph& graph) {
   1.744 -      return new AuxCapacityMap(graph);
   1.745 -    }
   1.746 -
   1.747 -    /// \brief The cross reference type used by heap.
   1.748 -    ///
   1.749 -    /// The cross reference type used by heap.
   1.750 -    /// Usually it is \c Graph::NodeMap<int>.
   1.751 -    typedef AuxGraph::NodeMap<int> HeapCrossRef;
   1.752 -
   1.753 -    /// \brief Instantiates a HeapCrossRef.
   1.754 -    ///
   1.755 -    /// This function instantiates a \ref HeapCrossRef. 
   1.756 -    /// \param graph is the graph, to which we would like to define the 
   1.757 -    /// HeapCrossRef.
   1.758 -    static HeapCrossRef *createHeapCrossRef(const AuxGraph &graph) {
   1.759 -      return new HeapCrossRef(graph);
   1.760 -    }
   1.761 -    
   1.762 -    /// \brief The heap type used by MinCut algorithm.
   1.763 -    ///
   1.764 -    /// The heap type used by MinCut algorithm. It should
   1.765 -    /// maximalize the priorities and the heap's key type is
   1.766 -    /// the aux graph's node.
   1.767 -    ///
   1.768 -    /// \sa BinHeap
   1.769 -    /// \sa MinCut
   1.770 -    typedef typename _min_cut_bits
   1.771 -    ::HeapSelector<CapacityMap>
   1.772 -    ::template Selector<Value, HeapCrossRef>
   1.773 -    ::Heap Heap;
   1.774 -    
   1.775 -    /// \brief Instantiates a Heap.
   1.776 -    ///
   1.777 -    /// This function instantiates a \ref Heap. 
   1.778 -    /// \param crossref The cross reference of the heap.
   1.779 -    static Heap *createHeap(HeapCrossRef& crossref) {
   1.780 -      return new Heap(crossref);
   1.781 -    }
   1.782 -
   1.783 -    /// \brief Map from the AuxGraph's node type to the Graph's node type.
   1.784 -    ///
   1.785 -    /// Map from the AuxGraph's node type to the Graph's node type.
   1.786 -    typedef typename AuxGraph
   1.787 -    ::template NodeMap<typename Graph::Node> NodeRefMap;
   1.788 -
   1.789 -    /// \brief Instantiates a NodeRefMap.
   1.790 -    ///
   1.791 -    /// This function instantiates a \ref NodeRefMap. 
   1.792 -    static NodeRefMap *createNodeRefMap(const AuxGraph& graph) {
   1.793 -      return new NodeRefMap(graph);
   1.794 -    }
   1.795 -
   1.796 -    /// \brief Map from the Graph's node type to the Graph's node type.
   1.797 -    ///
   1.798 -    /// Map from the Graph's node type to the Graph's node type.
   1.799 -    typedef typename Graph
   1.800 -    ::template NodeMap<typename Graph::Node> ListRefMap;
   1.801 -
   1.802 -    /// \brief Instantiates a ListRefMap.
   1.803 -    ///
   1.804 -    /// This function instantiates a \ref ListRefMap. 
   1.805 -    static ListRefMap *createListRefMap(const Graph& graph) {
   1.806 -      return new ListRefMap(graph);
   1.807 -    }
   1.808 -    
   1.809 -
   1.810 -  };
   1.811 -
   1.812 -  namespace _min_cut_bits {
   1.813 -    template <typename _Key>
   1.814 -    class LastTwoMap {
   1.815 -    public:
   1.816 -      typedef _Key Key;
   1.817 -      typedef bool Value;
   1.818 -
   1.819 -      LastTwoMap(int _num) : num(_num) {}
   1.820 -      void set(const Key& key, bool val) {
   1.821 -        if (!val) return;
   1.822 -        --num;
   1.823 -        if (num > 1) return;
   1.824 -        keys[num] = key;
   1.825 -      }
   1.826 -      
   1.827 -      Key operator[](int index) const { return keys[index]; }
   1.828 -    private:
   1.829 -      Key keys[2];
   1.830 -      int num;
   1.831 -    };
   1.832 -  }
   1.833 -
   1.834 -  /// \ingroup topology
   1.835 -  ///
   1.836 -  /// \brief Calculates the minimum cut in an undirected graph.
   1.837 -  ///
   1.838 -  /// Calculates the minimum cut in an undirected graph with the
   1.839 -  /// Nagamochi-Ibaraki algorithm. The algorithm separates the graph's
   1.840 -  /// nodes into two partitions with the minimum sum of edge capacities
   1.841 -  /// between the two partitions. The algorithm can be used to test
   1.842 -  /// the network reliability specifically to test how many links have
   1.843 -  /// to be destroyed in the network to split it at least two
   1.844 -  /// distinict subnetwork.
   1.845 -  ///
   1.846 -  /// The complexity of the algorithm is \f$ O(ne\log(n)) \f$ but with
   1.847 -  /// Fibonacci heap it can be decreased to \f$ O(ne+n^2\log(n))
   1.848 -  /// \f$. When capacity map is neutral then it uses BucketHeap which
   1.849 -  /// results \f$ O(ne) \f$ time complexity.
   1.850 -#ifdef DOXYGEN
   1.851 -  template <typename _Graph, typename _CapacityMap, typename _Traits>
   1.852 -#else
   1.853 -  template <typename _Graph = ListUGraph, 
   1.854 -	    typename _CapacityMap = typename _Graph::template UEdgeMap<int>, 
   1.855 -	    typename _Traits = MinCutDefaultTraits<_Graph, _CapacityMap> >
   1.856 -#endif
   1.857 -  class MinCut {
   1.858 -  public:
   1.859 -    /// \brief \ref Exception for uninitialized parameters.
   1.860 -    ///
   1.861 -    /// This error represents problems in the initialization
   1.862 -    /// of the parameters of the algorithms.
   1.863 -    class UninitializedParameter : public lemon::UninitializedParameter {
   1.864 -    public:
   1.865 -      virtual const char* what() const throw() {
   1.866 -	return "lemon::MinCut::UninitializedParameter";
   1.867 -      }
   1.868 -    };
   1.869 -
   1.870 -
   1.871 -  private:
   1.872 -
   1.873 -    typedef _Traits Traits;
   1.874 -    /// The type of the underlying graph.
   1.875 -    typedef typename Traits::Graph Graph;
   1.876 -    
   1.877 -    /// The type of the capacity of the edges.
   1.878 -    typedef typename Traits::CapacityMap::Value Value;
   1.879 -    /// The type of the map that stores the edge capacities.
   1.880 -    typedef typename Traits::CapacityMap CapacityMap;
   1.881 -    /// The type of the aux graph
   1.882 -    typedef typename Traits::AuxGraph AuxGraph;
   1.883 -    /// The type of the aux capacity map
   1.884 -    typedef typename Traits::AuxCapacityMap AuxCapacityMap;
   1.885 -    /// The cross reference type used for the current heap.
   1.886 -    typedef typename Traits::HeapCrossRef HeapCrossRef;
   1.887 -    /// The heap type used by the max cardinality algorithm.
   1.888 -    typedef typename Traits::Heap Heap;
   1.889 -    /// The node refrefernces between the original and aux graph type.
   1.890 -    typedef typename Traits::NodeRefMap NodeRefMap;
   1.891 -    /// The list node refrefernces in the original graph type.
   1.892 -    typedef typename Traits::ListRefMap ListRefMap;
   1.893 -
   1.894 -  public:
   1.895 -
   1.896 -    ///\name Named template parameters
   1.897 -
   1.898 -    ///@{
   1.899 -
   1.900 -    struct DefNeutralCapacityTraits : public Traits {
   1.901 -      typedef ConstMap<typename Graph::UEdge, Const<int, 1> > CapacityMap;
   1.902 -      static CapacityMap *createCapacityMap(const Graph&) {
   1.903 -	return new CapacityMap();
   1.904 -      }
   1.905 -    };
   1.906 -    /// \brief \ref named-templ-param "Named parameter" for setting  
   1.907 -    /// the capacity type to constMap<UEdge, int, 1>()
   1.908 -    ///
   1.909 -    /// \ref named-templ-param "Named parameter" for setting 
   1.910 -    /// the capacity type to constMap<UEdge, int, 1>()
   1.911 -    struct DefNeutralCapacity
   1.912 -      : public MinCut<Graph, CapacityMap, DefNeutralCapacityTraits> { 
   1.913 -      typedef MinCut<Graph, CapacityMap, DefNeutralCapacityTraits> Create;
   1.914 -    };
   1.915 -
   1.916 -
   1.917 -    template <class H, class CR>
   1.918 -    struct DefHeapTraits : public Traits {
   1.919 -      typedef CR HeapCrossRef;
   1.920 -      typedef H Heap;
   1.921 -      static HeapCrossRef *createHeapCrossRef(const AuxGraph &) {
   1.922 -	throw UninitializedParameter();
   1.923 -      }
   1.924 -      static Heap *createHeap(HeapCrossRef &) {
   1.925 -	throw UninitializedParameter();
   1.926 -      }
   1.927 -    };
   1.928 -    /// \brief \ref named-templ-param "Named parameter" for setting heap 
   1.929 -    /// and cross reference type
   1.930 -    ///
   1.931 -    /// \ref named-templ-param "Named parameter" for setting heap and cross 
   1.932 -    /// reference type
   1.933 -    template <class H, class CR = typename Graph::template NodeMap<int> >
   1.934 -    struct DefHeap
   1.935 -      : public MinCut<Graph, CapacityMap, DefHeapTraits<H, CR> > { 
   1.936 -      typedef MinCut< Graph, CapacityMap, DefHeapTraits<H, CR> > Create;
   1.937 -    };
   1.938 -
   1.939 -    template <class H, class CR>
   1.940 -    struct DefStandardHeapTraits : public Traits {
   1.941 -      typedef CR HeapCrossRef;
   1.942 -      typedef H Heap;
   1.943 -      static HeapCrossRef *createHeapCrossRef(const AuxGraph &graph) {
   1.944 -	return new HeapCrossRef(graph);
   1.945 -      }
   1.946 -      static Heap *createHeap(HeapCrossRef &crossref) {
   1.947 -	return new Heap(crossref);
   1.948 -      }
   1.949 -    };
   1.950 -
   1.951 -    /// \brief \ref named-templ-param "Named parameter" for setting heap and 
   1.952 -    /// cross reference type with automatic allocation
   1.953 -    ///
   1.954 -    /// \ref named-templ-param "Named parameter" for setting heap and cross 
   1.955 -    /// reference type. It can allocate the heap and the cross reference 
   1.956 -    /// object if the cross reference's constructor waits for the graph as 
   1.957 -    /// parameter and the heap's constructor waits for the cross reference.
   1.958 -    template <class H, class CR = typename Graph::template NodeMap<int> >
   1.959 -    struct DefStandardHeap
   1.960 -      : public MinCut<Graph, CapacityMap, DefStandardHeapTraits<H, CR> > { 
   1.961 -      typedef MinCut<Graph, CapacityMap, DefStandardHeapTraits<H, CR> > 
   1.962 -      Create;
   1.963 -    };
   1.964 -
   1.965 -    ///@}
   1.966 -
   1.967 -
   1.968 -  private:
   1.969 -    /// Pointer to the underlying graph.
   1.970 -    const Graph *_graph;
   1.971 -    /// Pointer to the capacity map
   1.972 -    const CapacityMap *_capacity;
   1.973 -    /// \brief Indicates if \ref _capacity is locally allocated 
   1.974 -    /// (\c true) or not.
   1.975 -    bool local_capacity;
   1.976 -
   1.977 -    /// Pointer to the aux graph.
   1.978 -    AuxGraph *_aux_graph;
   1.979 -    /// \brief Indicates if \ref _aux_graph is locally allocated 
   1.980 -    /// (\c true) or not.
   1.981 -    bool local_aux_graph;
   1.982 -    /// Pointer to the aux capacity map
   1.983 -    AuxCapacityMap *_aux_capacity;
   1.984 -    /// \brief Indicates if \ref _aux_capacity is locally allocated 
   1.985 -    /// (\c true) or not.
   1.986 -    bool local_aux_capacity;
   1.987 -    /// Pointer to the heap cross references.
   1.988 -    HeapCrossRef *_heap_cross_ref;
   1.989 -    /// \brief Indicates if \ref _heap_cross_ref is locally allocated 
   1.990 -    /// (\c true) or not.
   1.991 -    bool local_heap_cross_ref;
   1.992 -    /// Pointer to the heap.
   1.993 -    Heap *_heap;
   1.994 -    /// Indicates if \ref _heap is locally allocated (\c true) or not.
   1.995 -    bool local_heap;
   1.996 -
   1.997 -    /// The min cut value.
   1.998 -    Value _min_cut;
   1.999 -    /// The number of the nodes of the aux graph.
  1.1000 -    int _node_num;
  1.1001 -    /// The first and last node of the min cut in the next list;
  1.1002 -    typename Graph::Node _first_node, _last_node;
  1.1003 -
  1.1004 -    /// \brief The first and last element in the list associated
  1.1005 -    /// to the aux graph node.
  1.1006 -    NodeRefMap *_first, *_last;
  1.1007 -    /// \brief The next node in the node lists.
  1.1008 -    ListRefMap *_next;
  1.1009 -    
  1.1010 -    void create_structures() {
  1.1011 -      if (!_capacity) {
  1.1012 -        local_capacity = true;
  1.1013 -        _capacity = Traits::createCapacityMap(*_graph);
  1.1014 -      }
  1.1015 -      if(!_aux_graph) {
  1.1016 -	local_aux_graph = true;
  1.1017 -	_aux_graph = Traits::createAuxGraph();
  1.1018 -      }
  1.1019 -      if(!_aux_capacity) {
  1.1020 -	local_aux_capacity = true;
  1.1021 -	_aux_capacity = Traits::createAuxCapacityMap(*_aux_graph);
  1.1022 -      }
  1.1023 -
  1.1024 -      _first = Traits::createNodeRefMap(*_aux_graph);
  1.1025 -      _last = Traits::createNodeRefMap(*_aux_graph);
  1.1026 -
  1.1027 -      _next = Traits::createListRefMap(*_graph);
  1.1028 -
  1.1029 -      typename Graph::template NodeMap<typename AuxGraph::Node> ref(*_graph);
  1.1030 -
  1.1031 -      for (typename Graph::NodeIt it(*_graph); it != INVALID; ++it) {
  1.1032 -        _next->set(it, INVALID);
  1.1033 -        typename AuxGraph::Node node = _aux_graph->addNode();
  1.1034 -        _first->set(node, it);
  1.1035 -        _last->set(node, it);
  1.1036 -        ref.set(it, node);
  1.1037 -      }
  1.1038 -
  1.1039 -      for (typename Graph::UEdgeIt it(*_graph); it != INVALID; ++it) {
  1.1040 -        if (_graph->source(it) == _graph->target(it)) continue;
  1.1041 -        typename AuxGraph::UEdge uedge = 
  1.1042 -          _aux_graph->addEdge(ref[_graph->source(it)], 
  1.1043 -                               ref[_graph->target(it)]);
  1.1044 -        _aux_capacity->set(uedge, (*_capacity)[it]);
  1.1045 -        
  1.1046 -      }
  1.1047 -
  1.1048 -      if (!_heap_cross_ref) {
  1.1049 -	local_heap_cross_ref = true;
  1.1050 -	_heap_cross_ref = Traits::createHeapCrossRef(*_aux_graph);
  1.1051 -      }
  1.1052 -      if (!_heap) {
  1.1053 -	local_heap = true;
  1.1054 -	_heap = Traits::createHeap(*_heap_cross_ref);
  1.1055 -      }
  1.1056 -    }
  1.1057 -
  1.1058 -  public :
  1.1059 -
  1.1060 -    typedef MinCut Create;
  1.1061 -
  1.1062 -
  1.1063 -    /// \brief Constructor.
  1.1064 -    ///
  1.1065 -    ///\param graph the graph the algorithm will run on.
  1.1066 -    ///\param capacity the capacity map used by the algorithm.
  1.1067 -    MinCut(const Graph& graph, const CapacityMap& capacity) 
  1.1068 -      : _graph(&graph), 
  1.1069 -        _capacity(&capacity), local_capacity(false),
  1.1070 -        _aux_graph(0), local_aux_graph(false),
  1.1071 -        _aux_capacity(0), local_aux_capacity(false),
  1.1072 -        _heap_cross_ref(0), local_heap_cross_ref(false),
  1.1073 -        _heap(0), local_heap(false),
  1.1074 -        _first(0), _last(0), _next(0) {}
  1.1075 -
  1.1076 -    /// \brief Constructor.
  1.1077 -    ///
  1.1078 -    /// This constructor can be used only when the Traits class
  1.1079 -    /// defines how can we instantiate a local capacity map.
  1.1080 -    /// If the DefNeutralCapacity used the algorithm automatically
  1.1081 -    /// construct the capacity map.
  1.1082 -    ///
  1.1083 -    ///\param graph the graph the algorithm will run on.
  1.1084 -    MinCut(const Graph& graph) 
  1.1085 -      : _graph(&graph), 
  1.1086 -        _capacity(0), local_capacity(false),
  1.1087 -        _aux_graph(0), local_aux_graph(false),
  1.1088 -        _aux_capacity(0), local_aux_capacity(false),
  1.1089 -        _heap_cross_ref(0), local_heap_cross_ref(false),
  1.1090 -        _heap(0), local_heap(false),
  1.1091 -        _first(0), _last(0), _next(0) {}
  1.1092 -
  1.1093 -    /// \brief Destructor.
  1.1094 -    ///
  1.1095 -    /// Destructor.
  1.1096 -    ~MinCut() {
  1.1097 -      if (local_heap) delete _heap;
  1.1098 -      if (local_heap_cross_ref) delete _heap_cross_ref;
  1.1099 -      if (_first) delete _first;
  1.1100 -      if (_last) delete _last;
  1.1101 -      if (_next) delete _next;
  1.1102 -      if (local_aux_capacity) delete _aux_capacity;
  1.1103 -      if (local_aux_graph) delete _aux_graph;
  1.1104 -      if (local_capacity) delete _capacity;
  1.1105 -    }
  1.1106 -
  1.1107 -    /// \brief Sets the heap and the cross reference used by algorithm.
  1.1108 -    ///
  1.1109 -    /// Sets the heap and the cross reference used by algorithm.
  1.1110 -    /// If you don't use this function before calling \ref run(),
  1.1111 -    /// it will allocate one. The destuctor deallocates this
  1.1112 -    /// automatically allocated heap and cross reference, of course.
  1.1113 -    /// \return <tt> (*this) </tt>
  1.1114 -    MinCut &heap(Heap& heap, HeapCrossRef &crossRef)
  1.1115 -    {
  1.1116 -      if (local_heap_cross_ref) {
  1.1117 -	delete _heap_cross_ref;
  1.1118 -	local_heap_cross_ref=false;
  1.1119 -      }
  1.1120 -      _heap_cross_ref = &crossRef;
  1.1121 -      if (local_heap) {
  1.1122 -	delete _heap;
  1.1123 -	local_heap=false;
  1.1124 -      }
  1.1125 -      _heap = &heap;
  1.1126 -      return *this;
  1.1127 -    }
  1.1128 -
  1.1129 -    /// \brief Sets the aux graph.
  1.1130 -    ///
  1.1131 -    /// Sets the aux graph used by algorithm.
  1.1132 -    /// If you don't use this function before calling \ref run(),
  1.1133 -    /// it will allocate one. The destuctor deallocates this
  1.1134 -    /// automatically allocated graph, of course.
  1.1135 -    /// \return <tt> (*this) </tt>
  1.1136 -    MinCut &auxGraph(AuxGraph& aux_graph)
  1.1137 -    {
  1.1138 -      if(local_aux_graph) {
  1.1139 -	delete _aux_graph;
  1.1140 -	local_aux_graph=false;
  1.1141 -      }
  1.1142 -      _aux_graph = &aux_graph;
  1.1143 -      return *this;
  1.1144 -    }
  1.1145 -
  1.1146 -    /// \brief Sets the aux capacity map.
  1.1147 -    ///
  1.1148 -    /// Sets the aux capacity map used by algorithm.
  1.1149 -    /// If you don't use this function before calling \ref run(),
  1.1150 -    /// it will allocate one. The destuctor deallocates this
  1.1151 -    /// automatically allocated graph, of course.
  1.1152 -    /// \return <tt> (*this) </tt>
  1.1153 -    MinCut &auxCapacityMap(AuxCapacityMap& aux_capacity_map)
  1.1154 -    {
  1.1155 -      if(local_aux_capacity) {
  1.1156 -	delete _aux_capacity;
  1.1157 -	local_aux_capacity=false;
  1.1158 -      }
  1.1159 -      _aux_capacity = &aux_capacity_map;
  1.1160 -      return *this;
  1.1161 -    }
  1.1162 -
  1.1163 -    /// \name Execution control
  1.1164 -    /// The simplest way to execute the algorithm is to use
  1.1165 -    /// one of the member functions called \c run().
  1.1166 -    /// \n
  1.1167 -    /// If you need more control on the execution,
  1.1168 -    /// first you must call \ref init() and then call the start()
  1.1169 -    /// or proper times the processNextPhase() member functions.
  1.1170 -
  1.1171 -    ///@{
  1.1172 -
  1.1173 -    /// \brief Initializes the internal data structures.
  1.1174 -    ///
  1.1175 -    /// Initializes the internal data structures.
  1.1176 -    void init() {
  1.1177 -      create_structures();
  1.1178 -      _first_node = _last_node = INVALID;
  1.1179 -      _node_num = countNodes(*_graph);
  1.1180 -    }
  1.1181 -
  1.1182 -    /// \brief Processes the next phase
  1.1183 -    ///
  1.1184 -    /// Processes the next phase in the algorithm. The function
  1.1185 -    /// should be called countNodes(graph) - 1 times to get
  1.1186 -    /// surely the min cut in the graph. The  
  1.1187 -    ///
  1.1188 -    ///\return %True when the algorithm finished.
  1.1189 -    bool processNextPhase() {
  1.1190 -      if (_node_num <= 1) return true;
  1.1191 -      using namespace _min_cut_bits;
  1.1192 -
  1.1193 -      typedef typename AuxGraph::Node Node;
  1.1194 -      typedef typename AuxGraph::NodeIt NodeIt;
  1.1195 -      typedef typename AuxGraph::UEdge UEdge;
  1.1196 -      typedef typename AuxGraph::IncEdgeIt IncEdgeIt;
  1.1197 -      
  1.1198 -      typedef typename MaxCardinalitySearch<AuxGraph, AuxCapacityMap>::
  1.1199 -      template DefHeap<Heap, HeapCrossRef>::
  1.1200 -      template DefCardinalityMap<NullMap<Node, Value> >::
  1.1201 -      template DefProcessedMap<LastTwoMap<Node> >::
  1.1202 -      Create MaxCardinalitySearch;
  1.1203 -      
  1.1204 -      MaxCardinalitySearch mcs(*_aux_graph, *_aux_capacity);
  1.1205 -      for (NodeIt it(*_aux_graph); it != INVALID; ++it) {
  1.1206 -        _heap_cross_ref->set(it, Heap::PRE_HEAP);
  1.1207 -      }
  1.1208 -      mcs.heap(*_heap, *_heap_cross_ref);
  1.1209 -
  1.1210 -      LastTwoMap<Node> last_two_nodes(_node_num);
  1.1211 -      mcs.processedMap(last_two_nodes);
  1.1212 -
  1.1213 -      NullMap<Node, Value> cardinality;
  1.1214 -      mcs.cardinalityMap(cardinality);
  1.1215 -
  1.1216 -      mcs.run();
  1.1217 -
  1.1218 -      Node new_node = _aux_graph->addNode();
  1.1219 -
  1.1220 -      typename AuxGraph::template NodeMap<UEdge> edges(*_aux_graph, INVALID);
  1.1221 -      
  1.1222 -      Node first_node = last_two_nodes[0];
  1.1223 -      Node second_node = last_two_nodes[1];
  1.1224 -      
  1.1225 -      _next->set((*_last)[first_node], (*_first)[second_node]);
  1.1226 -      _first->set(new_node, (*_first)[first_node]);
  1.1227 -      _last->set(new_node, (*_last)[second_node]);
  1.1228 -
  1.1229 -      Value current_cut = 0;      
  1.1230 -      for (IncEdgeIt it(*_aux_graph, first_node); it != INVALID; ++it) {
  1.1231 -        Node node = _aux_graph->runningNode(it);
  1.1232 -        current_cut += (*_aux_capacity)[it];
  1.1233 -        if (node == second_node) continue;
  1.1234 -        if (edges[node] == INVALID) {
  1.1235 -          edges[node] = _aux_graph->addEdge(new_node, node);
  1.1236 -          (*_aux_capacity)[edges[node]] = (*_aux_capacity)[it];
  1.1237 -        } else {
  1.1238 -          (*_aux_capacity)[edges[node]] += (*_aux_capacity)[it];          
  1.1239 -        }
  1.1240 -      }
  1.1241 -
  1.1242 -      if (_first_node == INVALID || current_cut < _min_cut) {
  1.1243 -        _first_node = (*_first)[first_node];
  1.1244 -        _last_node = (*_last)[first_node];
  1.1245 -        _min_cut = current_cut;
  1.1246 -      }
  1.1247 -
  1.1248 -      _aux_graph->erase(first_node);
  1.1249 -
  1.1250 -      for (IncEdgeIt it(*_aux_graph, second_node); it != INVALID; ++it) {
  1.1251 -        Node node = _aux_graph->runningNode(it);
  1.1252 -        if (edges[node] == INVALID) {
  1.1253 -          edges[node] = _aux_graph->addEdge(new_node, node);
  1.1254 -          (*_aux_capacity)[edges[node]] = (*_aux_capacity)[it];
  1.1255 -        } else {
  1.1256 -          (*_aux_capacity)[edges[node]] += (*_aux_capacity)[it];          
  1.1257 -        }
  1.1258 -      }
  1.1259 -      _aux_graph->erase(second_node);
  1.1260 -
  1.1261 -      --_node_num;
  1.1262 -      return _node_num == 1;
  1.1263 -    }
  1.1264 -
  1.1265 -    /// \brief Executes the algorithm.
  1.1266 -    ///
  1.1267 -    /// Executes the algorithm.
  1.1268 -    ///
  1.1269 -    /// \pre init() must be called
  1.1270 -    void start() {
  1.1271 -      while (!processNextPhase());
  1.1272 -    }
  1.1273 -
  1.1274 -
  1.1275 -    /// \brief Runs %MinCut algorithm.
  1.1276 -    ///
  1.1277 -    /// This method runs the %Min cut algorithm
  1.1278 -    ///
  1.1279 -    /// \note mc.run(s) is just a shortcut of the following code.
  1.1280 -    ///\code
  1.1281 -    ///  mc.init();
  1.1282 -    ///  mc.start();
  1.1283 -    ///\endcode
  1.1284 -    void run() {
  1.1285 -      init();
  1.1286 -      start();
  1.1287 -    }
  1.1288 -
  1.1289 -    ///@}
  1.1290 -
  1.1291 -    /// \name Query Functions
  1.1292 -    /// The result of the %MinCut algorithm can be obtained using these
  1.1293 -    /// functions.\n
  1.1294 -    /// Before the use of these functions,
  1.1295 -    /// either run() or start() must be called.
  1.1296 -    
  1.1297 -    ///@{
  1.1298 -
  1.1299 -    /// \brief Returns the min cut value.
  1.1300 -    ///
  1.1301 -    /// Returns the min cut value if the algorithm finished.
  1.1302 -    /// After the first processNextPhase() it is a value of a
  1.1303 -    /// valid cut in the graph.
  1.1304 -    Value minCut() const {
  1.1305 -      return _min_cut;
  1.1306 -    }
  1.1307 -
  1.1308 -    /// \brief Returns a min cut in a NodeMap.
  1.1309 -    ///
  1.1310 -    /// It sets the nodes of one of the two partitions to true in
  1.1311 -    /// the given BoolNodeMap. The map contains a valid cut if the
  1.1312 -    /// map have been set false previously. 
  1.1313 -    template <typename NodeMap>
  1.1314 -    Value quickMinCut(NodeMap& nodeMap) const { 
  1.1315 -      for (typename Graph::Node it = _first_node; 
  1.1316 -           it != _last_node; it = (*_next)[it]) {
  1.1317 -             nodeMap.set(it, true);
  1.1318 -           }
  1.1319 -      nodeMap.set(_last_node, true);
  1.1320 -      return minCut();
  1.1321 -    }
  1.1322 -
  1.1323 -    /// \brief Returns a min cut in a NodeMap.
  1.1324 -    ///
  1.1325 -    /// It sets the nodes of one of the two partitions to true and
  1.1326 -    /// the other partition to false. The function first set all of the
  1.1327 -    /// nodes to false and after it call the quickMinCut() member.
  1.1328 -    template <typename NodeMap>
  1.1329 -    Value minCut(NodeMap& nodeMap) const { 
  1.1330 -      for (typename Graph::NodeIt it(*_graph); it != INVALID; ++it) {
  1.1331 -        nodeMap.set(it, false);      
  1.1332 -      }
  1.1333 -      quickMinCut(nodeMap);
  1.1334 -      return minCut();
  1.1335 -    }
  1.1336 -
  1.1337 -    /// \brief Returns a min cut in an EdgeMap.
  1.1338 -    ///
  1.1339 -    /// If an undirected edge is in a min cut then it will be
  1.1340 -    /// set to true and the others will be set to false in the given map.
  1.1341 -    template <typename EdgeMap>
  1.1342 -    Value cutEdges(EdgeMap& edgeMap) const {
  1.1343 -      typename Graph::template NodeMap<bool> cut(*_graph, false);
  1.1344 -      quickMinCut(cut);
  1.1345 -      for (typename Graph::EdgeIt it(*_graph); it != INVALID; ++it) {
  1.1346 -        edgeMap.set(it, cut[_graph->source(it)] ^ cut[_graph->target(it)]);
  1.1347 -      }
  1.1348 -      return minCut();
  1.1349 -    }
  1.1350 -
  1.1351 -    ///@}
  1.1352 -
  1.1353 -  };
  1.1354 -}
  1.1355 -
  1.1356 -#endif