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				/* -- mode: C++; indent-tabs-mode: nil; --
				*
				* This file is a part of LEMON, a generic C++ optimization library.
				*
				* Copyright (C) 2003-2013
				* 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,
				const CapacityMap& capacity) :
				_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 Constructor.
				///
				///\param digraph the digraph the algorithm will run on.
				///
				///A constant 1 capacity map will be allocated.
				MaxCardinalitySearch(const Digraph& digraph) :
				_graph(&digraph),
				_capacity(0), 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