deba@1912: /* -*- C++ -*-
deba@1912: *
alpar@1956: * This file is a part of LEMON, a generic C++ optimization library
alpar@1956: *
alpar@1956: * Copyright (C) 2003-2006
alpar@1956: * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@1912: * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@1912: *
deba@1912: * Permission to use, modify and distribute this software is granted
deba@1912: * provided that this copyright notice appears in all copies. For
deba@1912: * precise terms see the accompanying LICENSE file.
deba@1912: *
deba@1912: * This software is provided "AS IS" with no warranty of any kind,
deba@1912: * express or implied, and with no claim as to its suitability for any
deba@1912: * purpose.
deba@1912: *
deba@1912: */
deba@1912:
deba@1912: #ifndef LEMON_DAG_SHORTEST_PATH_H
deba@1912: #define LEMON_DAG_SHORTEST_PATH_H
deba@1912:
deba@1912: ///\ingroup flowalgs
deba@1912: /// \file
deba@1912: /// \brief DagShortestPath algorithm.
deba@1912: ///
deba@1912:
deba@1912: #include <lemon/list_graph.h>
deba@1993: #include <lemon/bits/invalid.h>
deba@1912: #include <lemon/error.h>
deba@1912: #include <lemon/maps.h>
deba@1912: #include <lemon/topology.h>
deba@1912:
deba@1912: #include <limits>
deba@1912:
deba@1912: namespace lemon {
deba@1912:
deba@1912: /// \brief Default OperationTraits for the DagShortestPath algorithm class.
deba@1912: ///
deba@1912: /// It defines all computational operations and constants which are
deba@1912: /// used in the dag shortest path algorithm. The default implementation
deba@1912: /// is based on the numeric_limits class. If the numeric type does not
deba@1912: /// have infinity value then the maximum value is used as extremal
deba@1912: /// infinity value.
deba@1912: template <
deba@1912: typename Value,
deba@1912: bool has_infinity = std::numeric_limits<Value>::has_infinity>
deba@1912: struct DagShortestPathDefaultOperationTraits {
deba@1912: /// \brief Gives back the zero value of the type.
deba@1912: static Value zero() {
deba@1912: return static_cast<Value>(0);
deba@1912: }
deba@1912: /// \brief Gives back the positive infinity value of the type.
deba@1912: static Value infinity() {
deba@1912: return std::numeric_limits<Value>::infinity();
deba@1912: }
deba@1912: /// \brief Gives back the sum of the given two elements.
deba@1912: static Value plus(const Value& left, const Value& right) {
deba@1912: return left + right;
deba@1912: }
deba@1912: /// \brief Gives back true only if the first value less than the second.
deba@1912: static bool less(const Value& left, const Value& right) {
deba@1912: return left < right;
deba@1912: }
deba@1912: };
deba@1912:
deba@1912: template <typename Value>
deba@1912: struct DagShortestPathDefaultOperationTraits<Value, false> {
deba@1912: static Value zero() {
deba@1912: return static_cast<Value>(0);
deba@1912: }
deba@1912: static Value infinity() {
deba@1912: return std::numeric_limits<Value>::max();
deba@1912: }
deba@1912: static Value plus(const Value& left, const Value& right) {
deba@1912: if (left == infinity() || right == infinity()) return infinity();
deba@1912: return left + right;
deba@1912: }
deba@1912: static bool less(const Value& left, const Value& right) {
deba@1912: return left < right;
deba@1912: }
deba@1912: };
deba@1912:
deba@1912: /// \brief Default traits class of DagShortestPath class.
deba@1912: ///
deba@1912: /// Default traits class of DagShortestPath class.
deba@1912: /// \param _Graph Graph type.
deba@1912: /// \param _LegthMap Type of length map.
deba@1912: template<class _Graph, class _LengthMap>
deba@1912: struct DagShortestPathDefaultTraits {
deba@1912: /// The graph type the algorithm runs on.
deba@1912: typedef _Graph Graph;
deba@1912:
deba@1912: /// \brief The type of the map that stores the edge lengths.
deba@1912: ///
deba@1912: /// The type of the map that stores the edge lengths.
deba@1912: /// It must meet the \ref concept::ReadMap "ReadMap" concept.
deba@1912: typedef _LengthMap LengthMap;
deba@1912:
deba@1912: // The type of the length of the edges.
deba@1912: typedef typename _LengthMap::Value Value;
deba@1912:
deba@1912: /// \brief Operation traits for dag shortest path algorithm.
deba@1912: ///
deba@1912: /// It defines the infinity type on the given Value type
deba@1912: /// and the used operation.
deba@1912: /// \see DagShortestPathDefaultOperationTraits
deba@1912: typedef DagShortestPathDefaultOperationTraits<Value> OperationTraits;
deba@1912:
deba@1912: /// \brief The type of the map that stores the last edges of the
deba@1912: /// shortest paths.
deba@1912: ///
deba@1912: /// The type of the map that stores the last
deba@1912: /// edges of the shortest paths.
deba@1912: /// It must meet the \ref concept::WriteMap "WriteMap" concept.
deba@1912: ///
deba@1912: typedef typename Graph::template NodeMap<typename _Graph::Edge> PredMap;
deba@1912:
deba@1912: /// \brief Instantiates a PredMap.
deba@1912: ///
deba@1912: /// This function instantiates a \ref PredMap.
alpar@1946: /// \param graph is the graph, to which we would
alpar@1946: /// like to define the PredMap.
deba@1912: /// \todo The graph alone may be insufficient for the initialization
deba@1912: static PredMap *createPredMap(const _Graph& graph) {
deba@1912: return new PredMap(graph);
deba@1912: }
deba@1912:
deba@1912: /// \brief The type of the map that stores the dists of the nodes.
deba@1912: ///
deba@1912: /// The type of the map that stores the dists of the nodes.
deba@1912: /// It must meet the \ref concept::WriteMap "WriteMap" concept.
deba@1912: ///
deba@1912: typedef typename Graph::template NodeMap<typename _LengthMap::Value>
deba@1912: DistMap;
deba@1912:
deba@1912: /// \brief Instantiates a DistMap.
deba@1912: ///
deba@1912: /// This function instantiates a \ref DistMap.
alpar@1946: /// \param graph is the graph, to which we would like to define the
deba@1912: /// \ref DistMap
deba@1912: static DistMap *createDistMap(const _Graph& graph) {
deba@1912: return new DistMap(graph);
deba@1912: }
deba@1912:
deba@1912: };
deba@1912:
deba@1912: /// \brief Inverse OperationTraits for the DagShortestPath algorithm class.
deba@1912: ///
deba@1912: /// It defines all computational operations and constants which are
deba@1912: /// used in the dag shortest path algorithm. It is the inverse of
deba@1912: /// \ref DagShortestPathDefaultOperationTraits, so it can be used to
deba@1912: /// calculate the longest path. The default implementation
deba@1912: /// is based on the numeric_limits class. If the numeric type does not
deba@1912: /// have infinity value then the minimum value is used as extremal
deba@1912: /// infinity value.
deba@1912: template <
deba@1912: typename Value,
deba@1912: bool has_infinity = std::numeric_limits<Value>::has_infinity>
deba@1912: struct DagLongestPathOperationTraits {
deba@1912: /// \brief Gives back the zero value of the type.
deba@1912: static Value zero() {
deba@1912: return static_cast<Value>(0);
deba@1912: }
deba@1912: /// \brief Gives back the negative infinity value of the type.
deba@1912: static Value infinity() {
deba@1912: return -(std::numeric_limits<Value>::infinity());
deba@1912: }
deba@1912: /// \brief Gives back the sum of the given two elements.
deba@1912: static Value plus(const Value& left, const Value& right) {
deba@1912: return left + right;
deba@1912: }
deba@1912: /// \brief Gives back true only if the first value less than the second.
deba@1912: static bool less(const Value& left, const Value& right) {
deba@1912: return left > right;
deba@1912: }
deba@1912: };
deba@1912:
deba@1912: template <typename Value>
deba@1912: struct DagLongestPathOperationTraits<Value, false> {
deba@1912: static Value zero() {
deba@1912: return static_cast<Value>(0);
deba@1912: }
deba@1912: static Value infinity() {
deba@1912: return std::numeric_limits<Value>::min();
deba@1912: }
deba@1912: static Value plus(const Value& left, const Value& right) {
deba@1912: if (left == infinity() || right == infinity()) return infinity();
deba@1912: return left + right;
deba@1912: }
deba@1912: static bool less(const Value& left, const Value& right) {
deba@1912: return left > right;
deba@1912: }
deba@1912: };
deba@1912:
deba@1912: /// \brief Inverse traits class of DagShortestPath class.
deba@1912: ///
deba@1912: /// Inverse traits class of DagShortestPath class.
deba@1912: /// \param _Graph Graph type.
deba@1912: /// \param _LegthMap Type of length map.
deba@1912: template<class _Graph, class _LengthMap>
deba@1912: struct DagLongestPathTraits {
deba@1912: /// The graph type the algorithm runs on.
deba@1912: typedef _Graph Graph;
deba@1912:
deba@1912: /// \brief The type of the map that stores the edge lengths.
deba@1912: ///
deba@1912: /// The type of the map that stores the edge lengths.
deba@1912: /// It must meet the \ref concept::ReadMap "ReadMap" concept.
deba@1912: typedef _LengthMap LengthMap;
deba@1912:
deba@1912: // The type of the length of the edges.
deba@1912: typedef typename _LengthMap::Value Value;
deba@1912:
deba@1912: /// \brief Inverse operation traits for dag shortest path algorithm.
deba@1912: ///
deba@1912: /// It defines the infinity type on the given Value type
deba@1912: /// and the used operation.
deba@1912: /// \see DagLongestPathOperationTraits
deba@1912: typedef DagLongestPathOperationTraits<Value> OperationTraits;
deba@1912:
deba@1912: /// \brief The type of the map that stores the last edges of the
deba@1912: /// longest paths.
deba@1912: ///
deba@1912: /// The type of the map that stores the last
deba@1912: /// edges of the longest paths.
deba@1912: /// It must meet the \ref concept::WriteMap "WriteMap" concept.
deba@1912: ///
deba@1912: typedef typename Graph::template NodeMap<typename _Graph::Edge> PredMap;
deba@1912:
deba@1912: /// \brief Instantiates a PredMap.
deba@1912: ///
deba@1912: /// This function instantiates a \ref PredMap.
alpar@1946: /// \param graph is the graph,
alpar@1946: /// to which we would like to define the PredMap.
deba@1912: /// \todo The graph alone may be insufficient for the initialization
deba@1912: static PredMap *createPredMap(const _Graph& graph) {
deba@1912: return new PredMap(graph);
deba@1912: }
deba@1912:
deba@1912: /// \brief The type of the map that stores the dists of the nodes.
deba@1912: ///
deba@1912: /// The type of the map that stores the dists of the nodes.
deba@1912: /// It must meet the \ref concept::WriteMap "WriteMap" concept.
deba@1912: ///
deba@1912: typedef typename Graph::template NodeMap<typename _LengthMap::Value>
deba@1912: DistMap;
deba@1912:
deba@1912: /// \brief Instantiates a DistMap.
deba@1912: ///
deba@1912: /// This function instantiates a \ref DistMap.
alpar@1946: /// \param graph is the graph, to which we would like to define the
deba@1912: /// \ref DistMap
deba@1912: static DistMap *createDistMap(const _Graph& graph) {
deba@1912: return new DistMap(graph);
deba@1912: }
deba@1912:
deba@1912: };
deba@1912:
deba@1912:
deba@1912: /// \brief %DagShortestPath algorithm class.
deba@1912: ///
deba@1912: /// \ingroup flowalgs
deba@1912: /// This class provides an efficient implementation of a Dag sortest path
deba@1912: /// searching algorithm. The edge lengths are passed to the algorithm
deba@1912: /// using a \ref concept::ReadMap "ReadMap", so it is easy to change it
deba@1912: /// to any kind of length.
deba@1912: ///
deba@1912: /// The complexity of the algorithm is O(n + e).
deba@1912: ///
deba@1912: /// The type of the length is determined by the
deba@1912: /// \ref concept::ReadMap::Value "Value" of the length map.
deba@1912: ///
deba@1912: /// \param _Graph The graph type the algorithm runs on. The default value
deba@1912: /// is \ref ListGraph. The value of _Graph is not used directly by
deba@1912: /// DagShortestPath, it is only passed to \ref DagShortestPathDefaultTraits.
deba@1912: /// \param _LengthMap This read-only EdgeMap determines the lengths of the
deba@2111: /// edges. The default map type is \ref concept::Graph::EdgeMap
deba@1912: /// "Graph::EdgeMap<int>". The value of _LengthMap is not used directly
deba@1912: /// by DagShortestPath, it is only passed to \ref DagShortestPathDefaultTraits.
deba@1912: /// \param _Traits Traits class to set various data types used by the
deba@1912: /// algorithm. The default traits class is \ref DagShortestPathDefaultTraits
deba@1912: /// "DagShortestPathDefaultTraits<_Graph,_LengthMap>". See \ref
deba@1912: /// DagShortestPathDefaultTraits for the documentation of a DagShortestPath traits
deba@1912: /// class.
deba@1912: ///
deba@1912: /// \author Balazs Attila Mihaly (based on Balazs Dezso's work)
deba@1912:
deba@1912: #ifdef DOXYGEN
deba@1912: template <typename _Graph, typename _LengthMap, typename _Traits>
deba@1912: #else
deba@1912: template <typename _Graph=ListGraph,
deba@1912: typename _LengthMap=typename _Graph::template EdgeMap<int>,
deba@1912: typename _Traits=DagShortestPathDefaultTraits<_Graph,_LengthMap> >
deba@1912: #endif
deba@1912: class DagShortestPath {
deba@1912: public:
deba@1912:
deba@1912: /// \brief \ref Exception for uninitialized parameters.
deba@1912: ///
deba@1912: /// This error represents problems in the initialization
deba@1912: /// of the parameters of the algorithms.
deba@1912:
deba@1912: class UninitializedParameter : public lemon::UninitializedParameter {
deba@1912: public:
deba@1912: virtual const char* exceptionName() const {
deba@1912: return "lemon::DagShortestPath::UninitializedParameter";
deba@1912: }
deba@1912: };
deba@1912:
deba@1912: typedef _Traits Traits;
deba@1912: ///The type of the underlying graph.
deba@1912: typedef typename _Traits::Graph Graph;
deba@1912:
deba@1912: typedef typename Graph::Node Node;
deba@1912: typedef typename Graph::NodeIt NodeIt;
deba@1912: typedef typename Graph::Edge Edge;
deba@1912: typedef typename Graph::EdgeIt EdgeIt;
deba@1912: typedef typename Graph::OutEdgeIt OutEdgeIt;
deba@1912:
deba@1912: /// \brief The type of the length of the edges.
deba@1912: typedef typename _Traits::LengthMap::Value Value;
deba@1912: /// \brief The type of the map that stores the edge lengths.
deba@1912: typedef typename _Traits::LengthMap LengthMap;
deba@1912: /// \brief The type of the map that stores the last
deba@1912: /// edges of the shortest paths.
deba@1912: typedef typename _Traits::PredMap PredMap;
deba@1912: /// \brief The type of the map that stores the dists of the nodes.
deba@1912: typedef typename _Traits::DistMap DistMap;
deba@1912: /// \brief The operation traits.
deba@1912: typedef typename _Traits::OperationTraits OperationTraits;
deba@1912: /// \brief The Node weight map.
deba@1999: typedef typename Graph::template NodeMap<Value> WeightMap;
deba@1912: private:
deba@1912: /// Pointer to the underlying graph
deba@1912: const Graph *graph;
deba@1912: /// Pointer to the length map
deba@1912: const LengthMap *length;
deba@1912: ///Pointer to the map of predecessors edges
deba@1912: PredMap *_pred;
deba@1912: ///Indicates if \ref _pred is locally allocated (\c true) or not
deba@1912: bool local_pred;
deba@1912: ///Pointer to the map of distances
deba@1912: DistMap *_dist;
deba@1912: ///Indicates if \ref _dist is locally allocated (\c true) or not
deba@1912: bool local_dist;
deba@1912: ///Process step counter
deba@1912: unsigned int _process_step;
deba@1912:
deba@1912: std::vector<Node> _node_order;
deba@1912:
deba@1912: /// Creates the maps if necessary.
deba@1912: void create_maps() {
deba@1912: if(!_pred) {
deba@1912: local_pred = true;
deba@1912: _pred = Traits::createPredMap(*graph);
deba@1912: }
deba@1912: if(!_dist) {
deba@1912: local_dist = true;
deba@1912: _dist = Traits::createDistMap(*graph);
deba@1912: }
deba@1912: }
deba@1912:
deba@1912: public :
deba@1912:
deba@1912: typedef DagShortestPath Create;
deba@1912:
deba@1912: /// \name Named template parameters
deba@1912:
deba@1912: ///@{
deba@1912:
deba@1912: template <class T>
deba@1912: struct DefPredMapTraits : public Traits {
deba@1912: typedef T PredMap;
deba@1912: static PredMap *createPredMap(const Graph&) {
deba@1912: throw UninitializedParameter();
deba@1912: }
deba@1912: };
deba@1912:
deba@1912: /// \brief \ref named-templ-param "Named parameter" for setting PredMap
deba@1912: /// type
deba@1912: /// \ref named-templ-param "Named parameter" for setting PredMap type
deba@1912: ///
deba@1912: template <class T>
deba@1912: struct DefPredMap {
deba@1912: typedef DagShortestPath< Graph, LengthMap, DefPredMapTraits<T> > Create;
deba@1912: };
deba@1912:
deba@1912: template <class T>
deba@1912: struct DefDistMapTraits : public Traits {
deba@1912: typedef T DistMap;
deba@1912: static DistMap *createDistMap(const Graph& graph) {
deba@1912: throw UninitializedParameter();
deba@1912: }
deba@1912: };
deba@1912:
deba@1912: /// \brief \ref named-templ-param "Named parameter" for setting DistMap
deba@1912: /// type
deba@1912: ///
deba@1912: /// \ref named-templ-param "Named parameter" for setting DistMap type
deba@1912: ///
deba@1912: template <class T>
deba@1912: struct DefDistMap
deba@1912: : public DagShortestPath< Graph, LengthMap, DefDistMapTraits<T> > {
deba@1912: typedef DagShortestPath< Graph, LengthMap, DefDistMapTraits<T> > Create;
deba@1912: };
deba@1912:
deba@1912: template <class T>
deba@1912: struct DefOperationTraitsTraits : public Traits {
deba@1912: typedef T OperationTraits;
deba@1912: };
deba@1912:
deba@1912: /// \brief \ref named-templ-param "Named parameter" for setting
deba@1912: /// OperationTraits type
deba@1912: ///
deba@1912: /// \ref named-templ-param "Named parameter" for setting OperationTraits
deba@1912: /// type
deba@1912: template <class T>
deba@1912: struct DefOperationTraits
deba@1912: : public DagShortestPath< Graph, LengthMap, DefOperationTraitsTraits<T> > {
deba@1912: typedef DagShortestPath< Graph, LengthMap, DefOperationTraitsTraits<T> >
deba@1912: Create;
deba@1912: };
deba@1912:
deba@1912: ///@}
deba@1912:
deba@1912: protected:
deba@1912:
deba@1912: DagShortestPath() {}
deba@1912:
deba@1912: public:
deba@1912:
deba@1912: /// \brief Constructor.
deba@1912: ///
deba@1912: /// \param _graph the graph the algorithm will run on.
deba@1912: /// \param _length the length map used by the algorithm.
deba@1912: DagShortestPath(const Graph& _graph, const LengthMap& _length) :
deba@1912: graph(&_graph), length(&_length),
deba@1912: _pred(0), local_pred(false),
deba@1912: _dist(0), local_dist(false){}
deba@1912:
deba@1912: /// \brief Constructor with node weight map.
deba@1912: ///
deba@1912: /// \param _graph the graph the algorithm will run on.
deba@1912: /// \param _length the length map used by the algorithm.
deba@1912: /// The NodeMap _length will be used as the weight map.
deba@1912: /// Each edge will have the weight of its target node.
deba@1912: DagShortestPath(const Graph& _graph, const WeightMap& _length) :
deba@1912: graph(&_graph),
deba@1912: _pred(0), local_pred(false),
deba@1912: _dist(0), local_dist(false){
deba@1912: length=new LengthMap(_graph);
deba@1912: _dist=new DistMap(_graph);
deba@1912: for(EdgeIt eit(_graph);eit!=INVALID;++eit)
deba@1912: (const_cast<LengthMap*>(length))->set(eit,_length[_graph.target(eit)]);
deba@1912: }
deba@1912:
deba@1912: ///Destructor.
deba@1912: ~DagShortestPath() {
deba@1912: if(local_pred) delete _pred;
deba@1912: if(local_dist) delete _dist;
deba@1912: }
deba@1912:
deba@1912: /// \brief Sets the length map.
deba@1912: ///
deba@1912: /// Sets the length map.
deba@1912: /// \return \c (*this)
deba@1912: DagShortestPath &lengthMap(const LengthMap &m) {
deba@1912: length = &m;
deba@1912: return *this;
deba@1912: }
deba@1912:
deba@1912: /// \brief Sets the map storing the predecessor edges.
deba@1912: ///
deba@1912: /// Sets the map storing the predecessor edges.
deba@1912: /// If you don't use this function before calling \ref run(),
deba@1912: /// it will allocate one. The destuctor deallocates this
deba@1912: /// automatically allocated map, of course.
deba@1912: /// \return \c (*this)
deba@1912: DagShortestPath &predMap(PredMap &m) {
deba@1912: if(local_pred) {
deba@1912: delete _pred;
deba@1912: local_pred=false;
deba@1912: }
deba@1912: _pred = &m;
deba@1912: return *this;
deba@1912: }
deba@1912:
deba@1912: /// \brief Sets the map storing the distances calculated by the algorithm.
deba@1912: ///
deba@1912: /// Sets the map storing the distances calculated by the algorithm.
deba@1912: /// If you don't use this function before calling \ref run(),
deba@1912: /// it will allocate one. The destuctor deallocates this
deba@1912: /// automatically allocated map, of course.
deba@1912: /// \return \c (*this)
deba@1912: DagShortestPath &distMap(DistMap &m) {
deba@1912: if(local_dist) {
deba@1912: delete _dist;
deba@1912: local_dist=false;
deba@1912: }
deba@1912: _dist = &m;
deba@1912: return *this;
deba@1912: }
deba@1912:
deba@1912: /// \name Execution control
deba@1912: /// The simplest way to execute the algorithm is to use
deba@1912: /// one of the member functions called \c run(...)
deba@1912: /// \n
deba@1912: /// If you need more control on the execution,
deba@1912: /// first you must call \ref init(...), then you can add several source
deba@1912: /// nodes with \ref addSource().
deba@1912: /// Finally \ref start() will perform the actual path computation.
deba@1912: /// Some functions have an alternative form (\ref checkedInit(...),
deba@1912: /// \ref checkedRun(...)) which also verifies if the graph given in the
deba@1912: /// constructor is a dag.
deba@1912:
deba@1912: ///@{
deba@1912:
deba@1912: /// \brief Initializes the internal data structures.
deba@1912: ///
deba@1912: /// Initializes the internal data structures.
deba@1912: void init(const Value value = OperationTraits::infinity()) {
deba@1912: typedef typename Graph::template NodeMap<int> NodeOrderMap;
deba@1912: _process_step=0;
deba@1912: NodeOrderMap node_order(*graph);
deba@1912: topologicalSort(*graph,node_order);
deba@1912: _node_order.resize(countNodes(*graph),INVALID);
deba@1912: create_maps();
deba@1912: for (NodeIt it(*graph); it != INVALID; ++it) {
deba@1912: _node_order[node_order[it]]=it;
deba@1912: _pred->set(it, INVALID);
deba@1912: _dist->set(it, value);
deba@1912: }
deba@1912: }
deba@1912:
deba@1912: /// \brief Initializes the internal data structures
deba@1912: /// with a given topological sort (NodeMap).
deba@1912: ///
deba@1912: /// Initializes the internal data structures
deba@1912: /// with a given topological sort (NodeMap).
deba@1912: void init(const typename Graph::template NodeMap<int>& node_order,
deba@1912: const Value value = OperationTraits::infinity()) {
deba@1912: _process_step=0;
deba@1912: _node_order.resize(countNodes(*graph),INVALID);
deba@1912: create_maps();
deba@1912: for (NodeIt it(*graph); it != INVALID; ++it) {
deba@1912: _node_order[node_order[it]]=it;
deba@1912: _pred->set(it, INVALID);
deba@1912: _dist->set(it, value);
deba@1912: }
deba@1912: }
deba@1912:
deba@1912: /// \brief Initializes the internal data structures
deba@1912: /// with a given topological sort (std::vector).
deba@1912: ///
deba@1912: /// Initializes the internal data structures
deba@1912: /// with a given topological sort (std::vector).
deba@1912: void init(const std::vector<Node>& node_order,
deba@1912: const Value value = OperationTraits::infinity()) {
deba@1912: _process_step=0;
deba@1912: _node_order=node_order;
deba@1912: create_maps();
deba@1912: for (NodeIt it(*graph); it != INVALID; ++it) {
deba@1912: _pred->set(it, INVALID);
deba@1912: _dist->set(it, value);
deba@1912: }
deba@1912: }
deba@1912:
deba@1912: /// \brief Initializes the internal data structures. It also checks if the graph is dag.
deba@1912: ///
deba@1912: /// Initializes the internal data structures. It also checks if the graph is dag.
deba@1912: /// \return true if the graph (given in the constructor) is dag, false otherwise.
deba@1912: bool checkedInit(const Value value = OperationTraits::infinity()) {
deba@1912: typedef typename Graph::template NodeMap<int> NodeOrderMap;
deba@1912: NodeOrderMap node_order(*graph);
deba@1912: if(!checkedTopologicalSort(*graph,node_order))return false;
deba@1912: init(node_order,value);
deba@1912: return true;
deba@1912: }
deba@1912:
deba@1912: /// \brief Initializes the internal data structures with a given
deba@1912: /// topological sort (NodeMap). It also checks if the graph is dag.
deba@1912: ///
deba@1912: /// Initializes the internal data structures with a given
deba@1912: /// topological sort (NodeMap). It also checks if the graph is dag.
deba@1912: /// \return true if the graph (given in the constructor) is dag, false otherwise.
deba@1912: bool checkedInit(const typename Graph::template NodeMap<int>& node_order,
deba@1912: const Value value = OperationTraits::infinity()) {
deba@1912: for(NodeIt it(*graph);it!=INVALID;++it){
deba@1912: for(OutEdgeIt oeit(*graph,it);oeit!=INVALID;++oeit){
deba@1912: if(node_order[graph->target(oeit)]<node_order[it])return false;
deba@1912: }
deba@1912: }
deba@1912: init(node_order,value);
deba@1912: return true;
deba@1912: }
deba@1912:
deba@1912: /// \brief Initializes the internal data structures with a given
deba@1912: /// topological sort (std::vector). It also checks if the graph is dag.
deba@1912: ///
deba@1912: /// Initializes the internal data structures with a given
deba@1912: /// topological sort (std::vector). It also checks if the graph is dag.
deba@1912: /// \return true if the graph (given in the constructor) is dag, false otherwise.
deba@1912: bool checkedInit(const std::vector<Node>& node_order,
deba@1912: const Value value = OperationTraits::infinity()) {
deba@1912: typedef typename Graph::template NodeMap<bool> BoolNodeMap;
deba@1912: BoolNodeMap _processed(*graph,false);
deba@1912: for(unsigned int i=0;i<_node_order.size();++i){
deba@1912: _processed[node_order[i]]=true;
deba@1912: for(OutEdgeIt oeit(*graph,node_order[i]);oeit!=INVALID;++oeit){
deba@1912: if(_processed[graph->target(oeit)])return false;
deba@1912: }
deba@1912: }
deba@1912: init(node_order,value);
deba@1912: return true;
deba@1912: }
deba@1912:
deba@1912: /// \brief Adds a new source node.
deba@1912: ///
deba@1912: /// The optional second parameter is the initial distance of the node.
deba@1912: /// It just sets the distance of the node to the given value.
deba@1912: void addSource(Node source, Value dst = OperationTraits::zero()) {
deba@1912: if((*_dist)[source] != dst){
deba@1912: _dist->set(source, dst);
deba@1912: }
deba@1912: }
deba@1912:
deba@1912: /// \brief Executes one step from the dag shortest path algorithm.
deba@1912: ///
deba@1912: /// If the algoritm calculated the distances in the previous step
deba@1912: /// strictly for all at most k length paths then it will calculate the
deba@1912: /// distances strictly for all at most k + 1 length paths. With k
deba@1912: /// iteration this function calculates the at most k length paths.
deba@1912: ///\pre the queue is not empty
deba@1912: ///\return the currently processed node
deba@1912: Node processNextNode() {
deba@1912: if(reached(_node_order[_process_step])){
deba@1912: for (OutEdgeIt it(*graph, _node_order[_process_step]); it != INVALID; ++it) {
deba@1912: Node target = graph->target(it);
deba@1912: Value relaxed =
deba@1912: OperationTraits::plus((*_dist)[_node_order[_process_step]], (*length)[it]);
deba@1912: if (OperationTraits::less(relaxed, (*_dist)[target])) {
deba@1912: _pred->set(target, it);
deba@1912: _dist->set(target, relaxed);
deba@1912: }
deba@1912: }
deba@1912: }
deba@1912: ++_process_step;
deba@1912: return _node_order[_process_step-1];
deba@1912: }
deba@1912:
deba@1912: ///\brief Returns \c false if there are nodes
deba@1912: ///to be processed in the queue
deba@1912: ///
deba@1912: ///Returns \c false if there are nodes
deba@1912: ///to be processed in the queue
deba@1912: bool emptyQueue() { return _node_order.size()-1==_process_step; }
deba@1912:
deba@1912: ///\brief Returns the number of the nodes to be processed.
deba@1912: ///
deba@1912: ///Returns the number of the nodes to be processed in the queue.
deba@1912: int queueSize() { return _node_order.size()-1-_process_step; }
deba@1912:
deba@1912: /// \brief Executes the algorithm.
deba@1912: ///
deba@1912: /// \pre init() must be called and at least one node should be added
deba@1912: /// with addSource() before using this function.
deba@1912: ///
deba@1912: /// This method runs the %DagShortestPath algorithm from the root node(s)
deba@1912: /// in order to compute the shortest path to each node. The algorithm
deba@1912: /// computes
deba@1912: /// - The shortest path tree.
deba@1912: /// - The distance of each node from the root(s).
deba@1912: void start() {
deba@1912: while(!emptyQueue()) {
deba@1912: processNextNode();
deba@1912: }
deba@1912: }
deba@1912:
deba@1912: /// \brief Runs %DagShortestPath algorithm from node \c s.
deba@1912: ///
deba@1912: /// This method runs the %DagShortestPath algorithm from a root node \c s
deba@1912: /// in order to compute the shortest path to each node. The algorithm
deba@1912: /// computes
deba@1912: /// - The shortest path tree.
deba@1912: /// - The distance of each node from the root.
deba@1912: ///
deba@1912: /// \note d.run(s) is just a shortcut of the following code.
alpar@1946: ///\code
deba@1912: /// d.init();
deba@1912: /// d.addSource(s);
deba@1912: /// d.start();
alpar@1946: ///\endcode
deba@1912: void run(Node s) {
deba@1912: init();
deba@1912: addSource(s);
deba@1912: start();
deba@1912: }
deba@1912:
deba@1912: /// \brief Runs %DagShortestPath algorithm from node \c s.
deba@1912: /// It also checks if the graph is a dag.
deba@1912: ///
deba@1912: /// This method runs the %DagShortestPath algorithm from a root node \c s
deba@1912: /// in order to compute the shortest path to each node. The algorithm
deba@1912: /// computes
deba@1912: /// - The shortest path tree.
deba@1912: /// - The distance of each node from the root.
deba@1912: /// The algorithm checks if the graph given int the constructor is a dag.
deba@1912: bool checkedRun(Node s) {
deba@1912: if(!checkedInit())return false;
deba@1912: addSource(s);
deba@1912: start();
deba@1912: return true;
deba@1912: }
deba@1912:
deba@1912: ///@}
deba@1912:
deba@1912: /// \name Query Functions
deba@1912: /// The result of the %DagShortestPath algorithm can be obtained using these
deba@1912: /// functions.\n
deba@1912: /// Before the use of these functions,
deba@1912: /// either run() or start() must be called.
deba@1912:
deba@1912: ///@{
deba@1912:
deba@1912: /// \brief Copies the shortest path to \c t into \c p
deba@1912: ///
deba@1912: /// This function copies the shortest path to \c t into \c p.
deba@1912: /// If it \c t is a source itself or unreachable, then it does not
deba@1912: /// alter \c p.
deba@1912: ///
deba@1912: /// \return Returns \c true if a path to \c t was actually copied to \c p,
deba@1912: /// \c false otherwise.
deba@1912: /// \sa DirPath
deba@1912: template <typename Path>
deba@1912: bool getPath(Path &p, Node t) {
deba@1912: if(reached(t)) {
deba@1912: p.clear();
deba@1912: typename Path::Builder b(p);
deba@1912: for(b.setStartNode(t);predEdge(t)!=INVALID;t=predNode(t))
deba@1912: b.pushFront(predEdge(t));
deba@1912: b.commit();
deba@1912: return true;
deba@1912: }
deba@1912: return false;
deba@1912: }
deba@1912:
deba@1912: /// \brief The distance of a node from the root.
deba@1912: ///
deba@1912: /// Returns the distance of a node from the root.
deba@1912: /// \pre \ref run() must be called before using this function.
deba@1912: /// \warning If node \c v in unreachable from the root the return value
deba@1912: /// of this funcion is undefined.
deba@1912: Value dist(Node v) const { return (*_dist)[v]; }
deba@1912:
deba@1912: /// \brief Returns the 'previous edge' of the shortest path tree.
deba@1912: ///
deba@1912: /// For a node \c v it returns the 'previous edge' of the shortest path
deba@1912: /// tree, i.e. it returns the last edge of a shortest path from the root
deba@1912: /// to \c v. It is \ref INVALID if \c v is unreachable from the root or
deba@1912: /// if \c v=s. The shortest path tree used here is equal to the shortest
deba@1912: /// path tree used in \ref predNode().
deba@1912: /// \pre \ref run() must be called before using
deba@1912: /// this function.
deba@1912: Edge predEdge(Node v) const { return (*_pred)[v]; }
deba@1912:
deba@1912: /// \brief Returns the 'previous node' of the shortest path tree.
deba@1912: ///
deba@1912: /// For a node \c v it returns the 'previous node' of the shortest path
deba@1912: /// tree, i.e. it returns the last but one node from a shortest path from
deba@1912: /// the root to \c /v. It is INVALID if \c v is unreachable from the root
deba@1912: /// or if \c v=s. The shortest path tree used here is equal to the
deba@1912: /// shortest path tree used in \ref predEdge(). \pre \ref run() must be
deba@1912: /// called before using this function.
deba@1912: Node predNode(Node v) const {
deba@1912: return (*_pred)[v] == INVALID ? INVALID : graph->source((*_pred)[v]);
deba@1912: }
deba@1912:
deba@1912: /// \brief Returns a reference to the NodeMap of distances.
deba@1912: ///
deba@1912: /// Returns a reference to the NodeMap of distances. \pre \ref run() must
deba@1912: /// be called before using this function.
deba@1912: const DistMap &distMap() const { return *_dist;}
deba@1912:
deba@1912: /// \brief Returns a reference to the shortest path tree map.
deba@1912: ///
deba@1912: /// Returns a reference to the NodeMap of the edges of the
deba@1912: /// shortest path tree.
deba@1912: /// \pre \ref run() must be called before using this function.
deba@1912: const PredMap &predMap() const { return *_pred; }
deba@1912:
deba@1912: /// \brief Checks if a node is reachable from the root.
deba@1912: ///
deba@1912: /// Returns \c true if \c v is reachable from the root.
deba@1912: /// \pre \ref run() must be called before using this function.
deba@1912: ///
deba@1912: bool reached(Node v) { return (*_dist)[v] != OperationTraits::infinity(); }
deba@1912:
deba@1912: ///@}
deba@1912: };
deba@1912:
deba@1912: /// \brief Default traits class of DagShortestPath function.
deba@1912: ///
deba@1912: /// Default traits class of DagShortestPath function.
deba@1912: /// \param _Graph Graph type.
deba@1912: /// \param _LengthMap Type of length map.
deba@1912: template <typename _Graph, typename _LengthMap>
deba@1912: struct DagShortestPathWizardDefaultTraits {
deba@1912: /// \brief The graph type the algorithm runs on.
deba@1912: typedef _Graph Graph;
deba@1912:
deba@1912: /// \brief The type of the map that stores the edge lengths.
deba@1912: ///
deba@1912: /// The type of the map that stores the edge lengths.
deba@1912: /// It must meet the \ref concept::ReadMap "ReadMap" concept.
deba@1912: typedef _LengthMap LengthMap;
deba@1912:
deba@1912: /// \brief The value type of the length map.
deba@1912: typedef typename _LengthMap::Value Value;
deba@1912:
deba@1912: /// \brief Operation traits for dag shortest path algorithm.
deba@1912: ///
deba@1912: /// It defines the infinity type on the given Value type
deba@1912: /// and the used operation.
deba@1912: /// \see DagShortestPathDefaultOperationTraits
deba@1912: typedef DagShortestPathDefaultOperationTraits<Value> OperationTraits;
deba@1912:
deba@1912: /// \brief The type of the map that stores the last
deba@1912: /// edges of the shortest paths.
deba@1912: ///
deba@1912: /// The type of the map that stores the last
deba@1912: /// edges of the shortest paths.
deba@1912: /// It must meet the \ref concept::WriteMap "WriteMap" concept.
deba@1912: typedef NullMap <typename _Graph::Node,typename _Graph::Edge> PredMap;
deba@1912:
deba@1912: /// \brief Instantiates a PredMap.
deba@1912: ///
deba@1912: /// This function instantiates a \ref PredMap.
deba@1912: static PredMap *createPredMap(const _Graph &) {
deba@1912: return new PredMap();
deba@1912: }
deba@1912: /// \brief The type of the map that stores the dists of the nodes.
deba@1912: ///
deba@1912: /// The type of the map that stores the dists of the nodes.
deba@1912: /// It must meet the \ref concept::WriteMap "WriteMap" concept.
deba@1912: typedef NullMap<typename Graph::Node, Value> DistMap;
deba@1912: /// \brief Instantiates a DistMap.
deba@1912: ///
deba@1912: /// This function instantiates a \ref DistMap.
deba@1912: static DistMap *createDistMap(const _Graph &) {
deba@1912: return new DistMap();
deba@1912: }
deba@1912: };
deba@1912:
deba@1912: /// \brief Default traits used by \ref DagShortestPathWizard
deba@1912: ///
deba@1912: /// To make it easier to use DagShortestPath algorithm
deba@1912: /// we have created a wizard class.
deba@1912: /// This \ref DagShortestPathWizard class needs default traits,
deba@1912: /// as well as the \ref DagShortestPath class.
deba@1912: /// The \ref DagShortestPathWizardBase is a class to be the default traits of the
deba@1912: /// \ref DagShortestPathWizard class.
deba@1912: /// \todo More named parameters are required...
deba@1912: template<class _Graph,class _LengthMap>
deba@1912: class DagShortestPathWizardBase
deba@1912: : public DagShortestPathWizardDefaultTraits<_Graph,_LengthMap> {
deba@1912:
deba@1912: typedef DagShortestPathWizardDefaultTraits<_Graph,_LengthMap> Base;
deba@1912: protected:
deba@1912: /// Type of the nodes in the graph.
deba@1912: typedef typename Base::Graph::Node Node;
deba@1912:
deba@1912: /// Pointer to the underlying graph.
deba@1912: void *_graph;
deba@1912: /// Pointer to the length map
deba@1912: void *_length;
deba@1912: ///Pointer to the map of predecessors edges.
deba@1912: void *_pred;
deba@1912: ///Pointer to the map of distances.
deba@1912: void *_dist;
deba@1912: ///Pointer to the source node.
deba@1912: Node _source;
deba@1912:
deba@1912: public:
deba@1912: /// Constructor.
deba@1912:
deba@1912: /// This constructor does not require parameters, therefore it initiates
deba@1912: /// all of the attributes to default values (0, INVALID).
deba@1912: DagShortestPathWizardBase() : _graph(0), _length(0), _pred(0),
deba@1912: _dist(0), _source(INVALID) {}
deba@1912:
deba@1912: /// Constructor.
deba@1912:
deba@1912: /// This constructor requires some parameters,
deba@1912: /// listed in the parameters list.
deba@1912: /// Others are initiated to 0.
deba@1912: /// \param graph is the initial value of \ref _graph
deba@1912: /// \param length is the initial value of \ref _length
deba@1912: /// \param source is the initial value of \ref _source
deba@1912: DagShortestPathWizardBase(const _Graph& graph,
deba@1912: const _LengthMap& length,
deba@1912: Node source = INVALID) :
deba@1912: _graph((void *)&graph), _length((void *)&length), _pred(0),
deba@1912: _dist(0), _source(source) {}
deba@1912:
deba@1912: };
deba@1912:
deba@1912: /// A class to make the usage of DagShortestPath algorithm easier
deba@1912:
deba@1912: /// This class is created to make it easier to use DagShortestPath algorithm.
deba@1912: /// It uses the functions and features of the plain \ref DagShortestPath,
deba@1912: /// but it is much simpler to use it.
deba@1912: ///
deba@1912: /// Simplicity means that the way to change the types defined
deba@1912: /// in the traits class is based on functions that returns the new class
deba@1912: /// and not on templatable built-in classes.
deba@1912: /// When using the plain \ref DagShortestPath
deba@1912: /// the new class with the modified type comes from
deba@1912: /// the original class by using the ::
deba@1912: /// operator. In the case of \ref DagShortestPathWizard only
deba@1912: /// a function have to be called and it will
deba@1912: /// return the needed class.
deba@1912: ///
deba@1912: /// It does not have own \ref run method. When its \ref run method is called
deba@1912: /// it initiates a plain \ref DagShortestPath class, and calls the \ref
deba@1912: /// DagShortestPath::run() method of it.
deba@1912: template<class _Traits>
deba@1912: class DagShortestPathWizard : public _Traits {
deba@1912: typedef _Traits Base;
deba@1912:
deba@1912: ///The type of the underlying graph.
deba@1912: typedef typename _Traits::Graph Graph;
deba@1912:
deba@1912: typedef typename Graph::Node Node;
deba@1912: typedef typename Graph::NodeIt NodeIt;
deba@1912: typedef typename Graph::Edge Edge;
deba@1912: typedef typename Graph::OutEdgeIt EdgeIt;
deba@1912:
deba@1912: ///The type of the map that stores the edge lengths.
deba@1912: typedef typename _Traits::LengthMap LengthMap;
deba@1912:
deba@1912: ///The type of the length of the edges.
deba@1912: typedef typename LengthMap::Value Value;
deba@1912:
deba@1912: ///\brief The type of the map that stores the last
deba@1912: ///edges of the shortest paths.
deba@1912: typedef typename _Traits::PredMap PredMap;
deba@1912:
deba@1912: ///The type of the map that stores the dists of the nodes.
deba@1912: typedef typename _Traits::DistMap DistMap;
deba@1912:
deba@1912: public:
deba@1912: /// Constructor.
deba@1912: DagShortestPathWizard() : _Traits() {}
deba@1912:
deba@1912: /// \brief Constructor that requires parameters.
deba@1912: ///
deba@1912: /// Constructor that requires parameters.
deba@1912: /// These parameters will be the default values for the traits class.
deba@1912: DagShortestPathWizard(const Graph& graph, const LengthMap& length,
deba@1912: Node source = INVALID)
deba@1912: : _Traits(graph, length, source) {}
deba@1912:
deba@1912: /// \brief Copy constructor
deba@1912: DagShortestPathWizard(const _Traits &b) : _Traits(b) {}
deba@1912:
deba@1912: ~DagShortestPathWizard() {}
deba@1912:
deba@1912: /// \brief Runs DagShortestPath algorithm from a given node.
deba@1912: ///
deba@1912: /// Runs DagShortestPath algorithm from a given node.
deba@1912: /// The node can be given by the \ref source function.
deba@1912: void run() {
deba@1912: if(Base::_source == INVALID) throw UninitializedParameter();
deba@1912: DagShortestPath<Graph,LengthMap,_Traits>
deba@1912: bf(*(Graph*)Base::_graph, *(LengthMap*)Base::_length);
deba@1912: if (Base::_pred) bf.predMap(*(PredMap*)Base::_pred);
deba@1912: if (Base::_dist) bf.distMap(*(DistMap*)Base::_dist);
deba@1912: bf.run(Base::_source);
deba@1912: }
deba@1912:
deba@1912: /// \brief Runs DagShortestPath algorithm from the given node.
deba@1912: ///
deba@1912: /// Runs DagShortestPath algorithm from the given node.
alpar@1946: /// \param source is the given source.
deba@1912: void run(Node source) {
deba@1912: Base::_source = source;
deba@1912: run();
deba@1912: }
deba@1912:
deba@1912: template<class T>
deba@1912: struct DefPredMapBase : public Base {
deba@1912: typedef T PredMap;
deba@1912: static PredMap *createPredMap(const Graph &) { return 0; };
deba@1912: DefPredMapBase(const _Traits &b) : _Traits(b) {}
deba@1912: };
deba@1912:
deba@1912: ///\brief \ref named-templ-param "Named parameter"
deba@1912: ///function for setting PredMap type
deba@1912: ///
deba@1912: /// \ref named-templ-param "Named parameter"
deba@1912: ///function for setting PredMap type
deba@1912: ///
deba@1912: template<class T>
deba@1912: DagShortestPathWizard<DefPredMapBase<T> > predMap(const T &t)
deba@1912: {
deba@1912: Base::_pred=(void *)&t;
deba@1912: return DagShortestPathWizard<DefPredMapBase<T> >(*this);
deba@1912: }
deba@1912:
deba@1912: template<class T>
deba@1912: struct DefDistMapBase : public Base {
deba@1912: typedef T DistMap;
deba@1912: static DistMap *createDistMap(const Graph &) { return 0; };
deba@1912: DefDistMapBase(const _Traits &b) : _Traits(b) {}
deba@1912: };
deba@1912:
deba@1912: ///\brief \ref named-templ-param "Named parameter"
deba@1912: ///function for setting DistMap type
deba@1912: ///
deba@1912: /// \ref named-templ-param "Named parameter"
deba@1912: ///function for setting DistMap type
deba@1912: ///
deba@1912: template<class T>
deba@1912: DagShortestPathWizard<DefDistMapBase<T> > distMap(const T &t) {
deba@1912: Base::_dist=(void *)&t;
deba@1912: return DagShortestPathWizard<DefDistMapBase<T> >(*this);
deba@1912: }
deba@1912:
deba@1912: template<class T>
deba@1912: struct DefOperationTraitsBase : public Base {
deba@1912: typedef T OperationTraits;
deba@1912: DefOperationTraitsBase(const _Traits &b) : _Traits(b) {}
deba@1912: };
deba@1912:
deba@1912: ///\brief \ref named-templ-param "Named parameter"
deba@1912: ///function for setting OperationTraits type
deba@1912: ///
deba@1912: /// \ref named-templ-param "Named parameter"
deba@1912: ///function for setting OperationTraits type
deba@1912: ///
deba@1912: template<class T>
deba@1912: DagShortestPathWizard<DefOperationTraitsBase<T> > distMap() {
deba@1912: return DagShortestPathWizard<DefDistMapBase<T> >(*this);
deba@1912: }
deba@1912:
deba@1912: /// \brief Sets the source node, from which the DagShortestPath algorithm runs.
deba@1912: ///
deba@1912: /// Sets the source node, from which the DagShortestPath algorithm runs.
alpar@1946: /// \param source is the source node.
deba@1912: DagShortestPathWizard<_Traits>& source(Node source) {
deba@1912: Base::_source = source;
deba@1912: return *this;
deba@1912: }
deba@1912:
deba@1912: };
deba@1912:
deba@1912: /// \brief Function type interface for DagShortestPath algorithm.
deba@1912: ///
deba@1912: /// \ingroup flowalgs
deba@1912: /// Function type interface for DagShortestPath algorithm.
deba@1912: ///
deba@1912: /// This function also has several \ref named-templ-func-param
deba@1912: /// "named parameters", they are declared as the members of class
deba@1912: /// \ref DagShortestPathWizard.
deba@1912: /// The following
deba@1912: /// example shows how to use these parameters.
alpar@1946: ///\code
deba@1912: /// dagShortestPath(g,length,source).predMap(preds).run();
alpar@1946: ///\endcode
deba@1912: /// \warning Don't forget to put the \ref DagShortestPathWizard::run() "run()"
deba@1912: /// to the end of the parameter list.
deba@1912: /// \sa DagShortestPathWizard
deba@1912: /// \sa DagShortestPath
deba@1912: template<class _Graph, class _LengthMap>
deba@1912: DagShortestPathWizard<DagShortestPathWizardBase<_Graph,_LengthMap> >
deba@1912: dagShortestPath(const _Graph& graph,
deba@1912: const _LengthMap& length,
deba@1912: typename _Graph::Node source = INVALID) {
deba@1912: return DagShortestPathWizard<DagShortestPathWizardBase<_Graph,_LengthMap> >
deba@1912: (graph, length, source);
deba@1912: }
deba@1912:
deba@1912: } //END OF NAMESPACE LEMON
deba@1912:
deba@1912: #endif
deba@1912: