RhodeCode

/* -*- C++ -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2003-2010

 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_MAX_CARDINALITY_SEARCH_H

#define LEMON_MAX_CARDINALITY_SEARCH_H

/// \ingroup search

/// \file 

/// \brief Maximum cardinality search in undirected digraphs.

#include <lemon/bin_heap.h>

#include <lemon/bucket_heap.h>

#include <lemon/error.h>

#include <lemon/maps.h>

#include <functional>

namespace lemon {

  /// \brief Default traits class of MaxCardinalitySearch class.

  ///

  /// Default traits class of MaxCardinalitySearch class.

  /// \param Digraph Digraph type.

  /// \param CapacityMap Type of capacity map.

  template <typename GR, typename CAP>

  struct MaxCardinalitySearchDefaultTraits {

    /// The digraph type the algorithm runs on. 

    typedef GR Digraph;

    template <typename CM>

    struct CapMapSelector {

      typedef CM CapacityMap;

      static CapacityMap *createCapacityMap(const Digraph& g) {

	return new CapacityMap(g);

      }

    };

    template <typename CM>

    struct CapMapSelector<ConstMap<CM, Const<int, 1> > > {

      typedef ConstMap<CM, Const<int, 1> > CapacityMap;

      static CapacityMap *createCapacityMap(const Digraph&) {

	return new CapacityMap;

      }

    };

    /// \brief The type of the map that stores the arc capacities.

    ///

    /// The type of the map that stores the arc capacities.

    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.

    typedef typename CapMapSelector<CAP>::CapacityMap CapacityMap;

    /// \brief The type of the capacity of the arcs.

    typedef typename CapacityMap::Value Value;

    /// \brief Instantiates a CapacityMap.

    ///

    /// This function instantiates a \ref CapacityMap.

    /// \param digraph is the digraph, to which we would like to define

    /// the CapacityMap.

    static CapacityMap *createCapacityMap(const Digraph& digraph) {

      return CapMapSelector<CapacityMap>::createCapacityMap(digraph);

    }

    /// \brief The cross reference type used by heap.

    ///

    /// The cross reference type used by heap.

    /// Usually it is \c Digraph::NodeMap<int>.

    typedef typename Digraph::template NodeMap<int> HeapCrossRef;

    /// \brief Instantiates a HeapCrossRef.

    ///

    /// This function instantiates a \ref HeapCrossRef. 

    /// \param digraph is the digraph, to which we would like to define the 

    /// HeapCrossRef.

    static HeapCrossRef *createHeapCrossRef(const Digraph &digraph) {

      return new HeapCrossRef(digraph);

    }

    template <typename CapacityMap>

    struct HeapSelector {

      template <typename Value, typename Ref>

      struct Selector { 

        typedef BinHeap<Value, Ref, std::greater<Value> > Heap;

      };

    };

    template <typename CapacityKey>

    struct HeapSelector<ConstMap<CapacityKey, Const<int, 1> > > {

      template <typename Value, typename Ref>

      struct Selector {

        typedef BucketHeap<Ref, false > Heap;

      };

    };

    /// \brief The heap type used by MaxCardinalitySearch algorithm.

    ///

    /// The heap type used by MaxCardinalitySearch algorithm. It should

    /// maximalize the priorities. The default heap type is

    /// the \ref BinHeap, but it is specialized when the

    /// CapacityMap is ConstMap<Digraph::Node, Const<int, 1> >

    /// to BucketHeap.

    ///

    /// \sa MaxCardinalitySearch

    typedef typename HeapSelector<CapacityMap>

    ::template Selector<Value, HeapCrossRef>

    ::Heap Heap;

    /// \brief Instantiates a Heap.

    ///

    /// This function instantiates a \ref Heap. 

    /// \param crossref The cross reference of the heap.

    static Heap *createHeap(HeapCrossRef& crossref) {

      return new Heap(crossref);

    }

    /// \brief The type of the map that stores whether a node is processed.

    ///

    /// The type of the map that stores whether a node is processed.

    /// It must meet the \ref concepts::WriteMap "WriteMap" concept.

    /// By default it is a NullMap.

    typedef NullMap<typename Digraph::Node, bool> ProcessedMap;

    /// \brief Instantiates a ProcessedMap.

    ///

    /// This function instantiates a \ref ProcessedMap. 

    /// \param digraph is the digraph, to which

    /// we would like to define the \ref ProcessedMap

#ifdef DOXYGEN

    static ProcessedMap *createProcessedMap(const Digraph &digraph)

#else

    static ProcessedMap *createProcessedMap(const Digraph &)

#endif

    {

      return new ProcessedMap();

    }

    /// \brief The type of the map that stores the cardinalities of the nodes.

    /// 

    /// The type of the map that stores the cardinalities of the nodes.

    /// It must meet the \ref concepts::WriteMap "WriteMap" concept.

    typedef typename Digraph::template NodeMap<Value> CardinalityMap;

    /// \brief Instantiates a CardinalityMap.

    ///

    /// This function instantiates a \ref CardinalityMap. 

    /// \param digraph is the digraph, to which we would like to define the \ref 

    /// CardinalityMap

    static CardinalityMap *createCardinalityMap(const Digraph &digraph) {

      return new CardinalityMap(digraph);

    }

  };

  /// \ingroup search

  ///

  /// \brief Maximum Cardinality Search algorithm class.

  ///

  /// This class provides an efficient implementation of Maximum Cardinality 

  /// Search algorithm. The maximum cardinality search first chooses any 

  /// node of the digraph. Then every time it chooses one unprocessed node

  /// with maximum cardinality, i.e the sum of capacities on out arcs to the nodes

  /// which were previusly processed.

  /// If there is a cut in the digraph the algorithm should choose

  /// again any unprocessed node of the digraph.

  /// The arc capacities are passed to the algorithm using a

  /// \ref concepts::ReadMap "ReadMap", so it is easy to change it to any 

  /// kind of capacity.

  ///

  /// The type of the capacity is determined by the \ref 

  /// concepts::ReadMap::Value "Value" of the capacity map.

  ///

  /// It is also possible to change the underlying priority heap.

  ///

  ///

  /// \param GR The digraph type the algorithm runs on. The value of

  /// Digraph is not used directly by the search algorithm, it 

  /// is only passed to \ref MaxCardinalitySearchDefaultTraits.

  /// \param CAP This read-only ArcMap determines the capacities of 

  /// the arcs. It is read once for each arc, so the map may involve in

  /// relatively time consuming process to compute the arc capacity if

  /// it is necessary. The default map type is \ref

  /// ConstMap "ConstMap<concepts::Digraph::Arc, Const<int,1> >". The value

  /// of CapacityMap is not used directly by search algorithm, it is only 

  /// passed to \ref MaxCardinalitySearchDefaultTraits.  

  /// \param TR Traits class to set various data types used by the 

  /// algorithm.  The default traits class is 

  /// \ref MaxCardinalitySearchDefaultTraits 

  /// "MaxCardinalitySearchDefaultTraits<GR, CAP>".  

  /// See \ref MaxCardinalitySearchDefaultTraits 

  /// for the documentation of a MaxCardinalitySearch traits class.

#ifdef DOXYGEN

  template <typename GR, typename CAP, typename TR>

#else

  template <typename GR, typename CAP = 

	    ConstMap<typename GR::Arc, Const<int,1> >,

	    typename TR = 

            MaxCardinalitySearchDefaultTraits<GR, CAP> >

#endif

  class MaxCardinalitySearch {

  public:

    typedef TR Traits;

    ///The type of the underlying digraph.

    typedef typename Traits::Digraph Digraph;

    ///The type of the capacity of the arcs.

    typedef typename Traits::CapacityMap::Value Value;

    ///The type of the map that stores the arc capacities.

    typedef typename Traits::CapacityMap CapacityMap;

    ///The type of the map indicating if a node is processed.

    typedef typename Traits::ProcessedMap ProcessedMap;

    ///The type of the map that stores the cardinalities of the nodes.

    typedef typename Traits::CardinalityMap CardinalityMap;

    ///The cross reference type used for the current heap.

    typedef typename Traits::HeapCrossRef HeapCrossRef;

    ///The heap type used by the algorithm. It maximizes the priorities.

    typedef typename Traits::Heap Heap;

  private:

    // Pointer to the underlying digraph.

    const Digraph *_graph;

    // Pointer to the capacity map

    const CapacityMap *_capacity;

    // Indicates if \ref _capacity is locally allocated (\c true) or not.

    bool local_capacity;

    // Pointer to the map of cardinality.

    CardinalityMap *_cardinality;

    // Indicates if \ref _cardinality is locally allocated (\c true) or not.

    bool local_cardinality;

    // Pointer to the map of processed status of the nodes.

    ProcessedMap *_processed;

    // Indicates if \ref _processed is locally allocated (\c true) or not.

    bool local_processed;

    // Pointer to the heap cross references.

    HeapCrossRef *_heap_cross_ref;

    // Indicates if \ref _heap_cross_ref is locally allocated (\c true) or not.

    bool local_heap_cross_ref;

    // Pointer to the heap.

    Heap *_heap;

    // Indicates if \ref _heap is locally allocated (\c true) or not.

    bool local_heap;

  public :

    typedef MaxCardinalitySearch Create;

    ///\name Named template parameters

    ///@{

    template <class T>

    struct DefCapacityMapTraits : public Traits {

      typedef T CapacityMap;

      static CapacityMap *createCapacityMap(const Digraph &) {

       	LEMON_ASSERT(false,"Uninitialized parameter.");

	return 0;

      }

    };

    /// \brief \ref named-templ-param "Named parameter" for setting 

    /// CapacityMap type

    ///

    /// \ref named-templ-param "Named parameter" for setting CapacityMap type

    /// for the algorithm.

    template <class T>

    struct SetCapacityMap 

      : public MaxCardinalitySearch<Digraph, CapacityMap, 

                                    DefCapacityMapTraits<T> > { 

      typedef MaxCardinalitySearch<Digraph, CapacityMap, 

                                   DefCapacityMapTraits<T> > Create;

    };

    template <class T>

    struct DefCardinalityMapTraits : public Traits {

      typedef T CardinalityMap;

      static CardinalityMap *createCardinalityMap(const Digraph &) 

      {

	LEMON_ASSERT(false,"Uninitialized parameter.");

	return 0;

      }

    };

    /// \brief \ref named-templ-param "Named parameter" for setting 

    /// CardinalityMap type

    ///

    /// \ref named-templ-param "Named parameter" for setting CardinalityMap 

    /// type for the algorithm.

    template <class T>

    struct SetCardinalityMap 

      : public MaxCardinalitySearch<Digraph, CapacityMap, 

                                    DefCardinalityMapTraits<T> > { 

      typedef MaxCardinalitySearch<Digraph, CapacityMap, 

                                   DefCardinalityMapTraits<T> > Create;

    };

    template <class T>

    struct DefProcessedMapTraits : public Traits {

      typedef T ProcessedMap;

      static ProcessedMap *createProcessedMap(const Digraph &) {

       	LEMON_ASSERT(false,"Uninitialized parameter.");

	return 0;

      }

    };

    /// \brief \ref named-templ-param "Named parameter" for setting 

    /// ProcessedMap type

    ///

    /// \ref named-templ-param "Named parameter" for setting ProcessedMap type

    /// for the algorithm.

    template <class T>

    struct SetProcessedMap 

      : public MaxCardinalitySearch<Digraph, CapacityMap, 

                                    DefProcessedMapTraits<T> > { 

      typedef MaxCardinalitySearch<Digraph, CapacityMap, 

                                   DefProcessedMapTraits<T> > Create;

    };

    template <class H, class CR>

    struct DefHeapTraits : public Traits {

      typedef CR HeapCrossRef;

      typedef H Heap;

      static HeapCrossRef *createHeapCrossRef(const Digraph &) {

     	LEMON_ASSERT(false,"Uninitialized parameter.");

	return 0;

      }

      static Heap *createHeap(HeapCrossRef &) {

       	LEMON_ASSERT(false,"Uninitialized parameter.");

	return 0;

      }

    };

    /// \brief \ref named-templ-param "Named parameter" for setting heap 

    /// and cross reference type

    ///

    /// \ref named-templ-param "Named parameter" for setting heap and cross 

    /// reference type for the algorithm.

    template <class H, class CR = typename Digraph::template NodeMap<int> >

    struct SetHeap

      : public MaxCardinalitySearch<Digraph, CapacityMap, 

                                    DefHeapTraits<H, CR> > { 

      typedef MaxCardinalitySearch< Digraph, CapacityMap, 

                                    DefHeapTraits<H, CR> > Create;

    };

    template <class H, class CR>

    struct DefStandardHeapTraits : public Traits {

      typedef CR HeapCrossRef;

      typedef H Heap;

      static HeapCrossRef *createHeapCrossRef(const Digraph &digraph) {

	return new HeapCrossRef(digraph);

      }

      static Heap *createHeap(HeapCrossRef &crossref) {

	return new Heap(crossref);

      }

    };

    /// \brief \ref named-templ-param "Named parameter" for setting heap and 

    /// cross reference type with automatic allocation

    ///

    /// \ref named-templ-param "Named parameter" for setting heap and cross 

    /// reference type. It can allocate the heap and the cross reference 

    /// object if the cross reference's constructor waits for the digraph as 

    /// parameter and the heap's constructor waits for the cross reference.

    template <class H, class CR = typename Digraph::template NodeMap<int> >

    struct SetStandardHeap

      : public MaxCardinalitySearch<Digraph, CapacityMap, 

                                    DefStandardHeapTraits<H, CR> > { 

      typedef MaxCardinalitySearch<Digraph, CapacityMap, 

                                   DefStandardHeapTraits<H, CR> > 

      Create;

    };

    ///@}

  protected:

    MaxCardinalitySearch() {}

  public:      

    /// \brief Constructor.

    ///

    ///\param digraph the digraph the algorithm will run on.

    ///\param capacity the capacity map used by the algorithm.

    MaxCardinalitySearch(const Digraph& digraph,

      _graph(&digraph),

      _capacity(&capacity), local_capacity(false),

      _cardinality(0), local_cardinality(false),

      _processed(0), local_processed(false),

      _heap_cross_ref(0), local_heap_cross_ref(false),

      _heap(0), local_heap(false)

    { }

    /// \brief Destructor.

    ~MaxCardinalitySearch() {

      if(local_capacity) delete _capacity;

      if(local_cardinality) delete _cardinality;

      if(local_processed) delete _processed;

      if(local_heap_cross_ref) delete _heap_cross_ref;

      if(local_heap) delete _heap;

    }

    /// \brief Sets the capacity map.

    ///

    /// Sets the capacity map.

    /// \return <tt> (*this) </tt>

    MaxCardinalitySearch &capacityMap(const CapacityMap &m) {

      if (local_capacity) {

	delete _capacity;

	local_capacity=false;

      }

      _capacity=&m;

      return *this;

    }

    /// \brief Returns a const reference to the capacity map.

    ///

    /// Returns a const reference to the capacity map used by

    /// the algorithm.

    const CapacityMap &capacityMap() const {

      return *_capacity;

    }

    /// \brief Sets the map storing the cardinalities calculated by the 

    /// algorithm.

    ///

    /// Sets the map storing the cardinalities calculated by the algorithm.

    /// If you don't use this function before calling \ref run(),

    /// it will allocate one. The destuctor deallocates this

    /// automatically allocated map, of course.

    /// \return <tt> (*this) </tt>

    MaxCardinalitySearch &cardinalityMap(CardinalityMap &m) {

      if(local_cardinality) {

	delete _cardinality;

	local_cardinality=false;

      }

      _cardinality = &m;

      return *this;

    }

    /// \brief Sets the map storing the processed nodes.

    ///

    /// Sets the map storing the processed nodes.

    /// If you don't use this function before calling \ref run(),

    /// it will allocate one. The destuctor deallocates this

    /// automatically allocated map, of course.

    /// \return <tt> (*this) </tt>

    MaxCardinalitySearch &processedMap(ProcessedMap &m) 

    {

      if(local_processed) {

	delete _processed;

	local_processed=false;

      }

      _processed = &m;

      return *this;

    }

    /// \brief Returns a const reference to the cardinality map.

    ///

    /// Returns a const reference to the cardinality map used by

    /// the algorithm.

    const ProcessedMap &processedMap() const {

      return *_processed;

    }

    /// \brief Sets the heap and the cross reference used by algorithm.

    ///

    /// Sets the heap and the cross reference used by algorithm.

    /// If you don't use this function before calling \ref run(),

    /// it will allocate one. The destuctor deallocates this

    /// automatically allocated map, of course.

    /// \return <tt> (*this) </tt>

    MaxCardinalitySearch &heap(Heap& hp, HeapCrossRef &cr) {

      if(local_heap_cross_ref) {

	delete _heap_cross_ref;

	local_heap_cross_ref = false;

      }

      _heap_cross_ref = &cr;

      if(local_heap) {

	delete _heap;

	local_heap = false;

      }

      _heap = &hp;

      return *this;

    }

    /// \brief Returns a const reference to the heap.

    ///

    /// Returns a const reference to the heap used by

    /// the algorithm.

    const Heap &heap() const {

      return *_heap;

    }

    /// \brief Returns a const reference to the cross reference.

    ///

    /// Returns a const reference to the cross reference

    /// of the heap.

    const HeapCrossRef &heapCrossRef() const {

      return *_heap_cross_ref;

    }

  private:

    typedef typename Digraph::Node Node;

    typedef typename Digraph::NodeIt NodeIt;

    typedef typename Digraph::Arc Arc;

    typedef typename Digraph::InArcIt InArcIt;

    void create_maps() {

      if(!_capacity) {

	local_capacity = true;

	_capacity = Traits::createCapacityMap(*_graph);

      }

      if(!_cardinality) {

	local_cardinality = true;

	_cardinality = Traits::createCardinalityMap(*_graph);

      }

      if(!_processed) {

	local_processed = true;

	_processed = Traits::createProcessedMap(*_graph);

      }

      if (!_heap_cross_ref) {

	local_heap_cross_ref = true;

	_heap_cross_ref = Traits::createHeapCrossRef(*_graph);

      }

      if (!_heap) {

	local_heap = true;

	_heap = Traits::createHeap(*_heap_cross_ref);

      }

    }

    void finalizeNodeData(Node node, Value capacity) {

      _processed->set(node, true);

      _cardinality->set(node, capacity);

    }

  public:

    /// \name Execution control

    /// The simplest way to execute the algorithm is to use

    /// one of the member functions called \ref run().

    /// \n

    /// If you need more control on the execution,

    /// first you must call \ref init(), then you can add several source nodes

    /// with \ref addSource().

    /// Finally \ref start() will perform the computation.

    ///@{

    /// \brief Initializes the internal data structures.

    ///

    /// Initializes the internal data structures, and clears the heap.

    void init() {

      create_maps();

      _heap->clear();

      for (NodeIt it(*_graph) ; it != INVALID ; ++it) {

	_processed->set(it, false);

	_heap_cross_ref->set(it, Heap::PRE_HEAP);

      }

    }

    /// \brief Adds a new source node.

    /// 

    /// Adds a new source node to the priority heap.

    ///

    /// It checks if the node has not yet been added to the heap.

    void addSource(Node source, Value capacity = 0) {

      if(_heap->state(source) == Heap::PRE_HEAP) {

	_heap->push(source, capacity);

      } 

    }

    /// \brief Processes the next node in the priority heap

    ///

    /// Processes the next node in the priority heap.

    ///

    /// \return The processed node.

    ///

    /// \warning The priority heap must not be empty!

    Node processNextNode() {

      Node node = _heap->top(); 

      finalizeNodeData(node, _heap->prio());

      _heap->pop();

      for (InArcIt it(*_graph, node); it != INVALID; ++it) {

	Node source = _graph->source(it);

	switch (_heap->state(source)) {

	case Heap::PRE_HEAP:

	  _heap->push(source, (*_capacity)[it]);

	  break;

	case Heap::IN_HEAP:

	  _heap->decrease(source, (*_heap)[source] + (*_capacity)[it]);

	  break;

	case Heap::POST_HEAP:

	  break;

	}

      }

      return node;

    }

    /// \brief Next node to be processed.

    ///

    /// Next node to be processed.

    ///

    /// \return The next node to be processed or INVALID if the 

    /// priority heap is empty.

    Node nextNode() { 

      return !_heap->empty() ? _heap->top() : INVALID;

    }

    /// \brief Returns \c false if there are nodes

    /// to be processed in the priority heap

    ///

    /// Returns \c false if there are nodes

    /// to be processed in the priority heap

    bool emptyQueue() { return _heap->empty(); }

    /// \brief Returns the number of the nodes to be processed 

    /// in the priority heap

    ///

    /// Returns the number of the nodes to be processed in the priority heap

    int emptySize() { return _heap->size(); }

    /// \brief Executes the algorithm.

    ///

    /// Executes the algorithm.

    ///

    ///\pre init() must be called and at least one node should be added

    /// with addSource() before using this function.

    ///

    /// This method runs the Maximum Cardinality Search algorithm from the 

    /// source node(s).

    void start() {

      while ( !_heap->empty() ) processNextNode();

    }

    /// \brief Executes the algorithm until \c dest is reached.

    ///

    /// Executes the algorithm until \c dest is reached.

    ///

    /// \pre init() must be called and at least one node should be added

    /// with addSource() before using this function.

    ///

    /// This method runs the %MaxCardinalitySearch algorithm from the source 

    /// nodes.

    void start(Node dest) {

      while ( !_heap->empty() && _heap->top()!=dest ) processNextNode();

      if ( !_heap->empty() ) finalizeNodeData(_heap->top(), _heap->prio());

    }

    /// \brief Executes the algorithm until a condition is met.

    ///

    /// Executes the algorithm until a condition is met.

    ///

    /// \pre init() must be called and at least one node should be added

    /// with addSource() before using this function.

    ///

    /// \param nm must be a bool (or convertible) node map. The algorithm

    /// will stop when it reaches a node \c v with <tt>nm[v]==true</tt>.

    template <typename NodeBoolMap>

    void start(const NodeBoolMap &nm) {

      while ( !_heap->empty() && !nm[_heap->top()] ) processNextNode();

      if ( !_heap->empty() ) finalizeNodeData(_heap->top(),_heap->prio());

    }

    /// \brief Runs the maximum cardinality search algorithm from node \c s.

    ///

    /// This method runs the %MaxCardinalitySearch algorithm from a root 

    /// node \c s.

    ///

    ///\note d.run(s) is just a shortcut of the following code.

    ///\code

    ///  d.init();

    ///  d.addSource(s);

    ///  d.start();

    ///\endcode

    void run(Node s) {

      init();

      addSource(s);

      start();

    }

    /// \brief Runs the maximum cardinality search algorithm for the 

    /// whole digraph.

    ///

    /// This method runs the %MaxCardinalitySearch algorithm from all 

    /// unprocessed node of the digraph.

    ///

    ///\note d.run(s) is just a shortcut of the following code.

    ///\code

    ///  d.init();

    ///  for (NodeIt it(digraph); it != INVALID; ++it) {

    ///    if (!d.reached(it)) {

    ///      d.addSource(s);

    ///      d.start();

    ///    }

    ///  }

    ///\endcode

    void run() {

      init();

      for (NodeIt it(*_graph); it != INVALID; ++it) {

        if (!reached(it)) {

          addSource(it);

          start();

        }

      }

    }

    ///@}

    /// \name Query Functions

    /// The results of the maximum cardinality search algorithm can be 

    /// obtained using these functions.

    /// \n

    /// Before the use of these functions, either run() or start() must be 

    /// called.

    ///@{

    /// \brief The cardinality of a node.

    ///

    /// Returns the cardinality of a node.

    /// \pre \ref run() must be called before using this function.

    /// \warning If node \c v in unreachable from the root the return value

    /// of this funcion is undefined.

    Value cardinality(Node node) const { return (*_cardinality)[node]; }

    /// \brief The current cardinality of a node.

    ///

    /// Returns the current cardinality of a node.

    /// \pre the given node should be reached but not processed

    Value currentCardinality(Node node) const { return (*_heap)[node]; }

    /// \brief Returns a reference to the NodeMap of cardinalities.

    ///

    /// Returns a reference to the NodeMap of cardinalities. \pre \ref run() 

    /// must be called before using this function.

    const CardinalityMap &cardinalityMap() const { return *_cardinality;}

    /// \brief Checks if a node is reachable from the root.

    ///

    /// Returns \c true if \c v is reachable from the root.

    /// \warning The source nodes are initated as unreached.

    /// \pre \ref run() must be called before using this function.

    bool reached(Node v) { return (*_heap_cross_ref)[v] != Heap::PRE_HEAP; }

    /// \brief Checks if a node is processed.

    ///

    /// Returns \c true if \c v is processed, i.e. the shortest

    /// path to \c v has already found.

    /// \pre \ref run() must be called before using this function.

    bool processed(Node v) { return (*_heap_cross_ref)[v] == Heap::POST_HEAP; }

    ///@}

  };

}

#endif