/* -*- C++ -*-

  *

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

  *

  * Copyright (C) 2003-2006

  * 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_DAG_SHORTEST_PATH_H

 #define LEMON_DAG_SHORTEST_PATH_H

 ///\ingroup flowalgs

 /// \file

 /// \brief DagShortestPath algorithm.

 ///

 #include <lemon/list_graph.h>

 #include <lemon/bits/invalid.h>

 #include <lemon/error.h>

 #include <lemon/maps.h>

 #include <lemon/topology.h>

 #include <limits>

 namespace lemon {

   /// \brief Default OperationTraits for the DagShortestPath algorithm class.

   ///  

   /// It defines all computational operations and constants which are

   /// used in the dag shortest path algorithm. The default implementation

   /// is based on the numeric_limits class. If the numeric type does not

   /// have infinity value then the maximum value is used as extremal

   /// infinity value.

   template <

     typename Value, 

     bool has_infinity = std::numeric_limits<Value>::has_infinity>

   struct DagShortestPathDefaultOperationTraits {

     /// \brief Gives back the zero value of the type.

     static Value zero() {

       return static_cast<Value>(0);

     }

     /// \brief Gives back the positive infinity value of the type.

     static Value infinity() {

       return std::numeric_limits<Value>::infinity();

     }

     /// \brief Gives back the sum of the given two elements.

     static Value plus(const Value& left, const Value& right) {

       return left + right;

     }

     /// \brief Gives back true only if the first value less than the second.

     static bool less(const Value& left, const Value& right) {

       return left < right;

     }

   };

   template <typename Value>

   struct DagShortestPathDefaultOperationTraits<Value, false> {

     static Value zero() {

       return static_cast<Value>(0);

     }

     static Value infinity() {

       return std::numeric_limits<Value>::max();

     }

     static Value plus(const Value& left, const Value& right) {

       if (left == infinity() || right == infinity()) return infinity();

       return left + right;

     }

     static bool less(const Value& left, const Value& right) {

       return left < right;

     }

   };

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

   ///

   /// Default traits class of DagShortestPath class.

   /// \param _Graph Graph type.

   /// \param _LegthMap Type of length map.

   template<class _Graph, class _LengthMap>

   struct DagShortestPathDefaultTraits {

     /// The graph type the algorithm runs on. 

     typedef _Graph Graph;

     /// \brief The type of the map that stores the edge lengths.

     ///

     /// The type of the map that stores the edge lengths.

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

     typedef _LengthMap LengthMap;

     // The type of the length of the edges.

     typedef typename _LengthMap::Value Value;

     /// \brief Operation traits for dag shortest path algorithm.

     ///

     /// It defines the infinity type on the given Value type

     /// and the used operation.

     /// \see DagShortestPathDefaultOperationTraits

     typedef DagShortestPathDefaultOperationTraits<Value> OperationTraits;

     /// \brief The type of the map that stores the last edges of the 

     /// shortest paths.

     /// 

     /// The type of the map that stores the last

     /// edges of the shortest paths.

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

     ///

     typedef typename Graph::template NodeMap<typename _Graph::Edge> PredMap;

     /// \brief Instantiates a PredMap.

     /// 

     /// This function instantiates a \ref PredMap. 

     /// \param graph is the graph, to which we would

     /// like to define the PredMap.

     /// \todo The graph alone may be insufficient for the initialization

     static PredMap *createPredMap(const _Graph& graph) {

       return new PredMap(graph);

     }

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

     ///

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

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

     ///

     typedef typename Graph::template NodeMap<typename _LengthMap::Value> 

     DistMap;

     /// \brief Instantiates a DistMap.

     ///

     /// This function instantiates a \ref DistMap. 

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

     /// \ref DistMap

     static DistMap *createDistMap(const _Graph& graph) {

       return new DistMap(graph);

     }

   };

   /// \brief Inverse OperationTraits for the DagShortestPath algorithm class.

   /// 

   /// It defines all computational operations and constants which are

   /// used in the dag shortest path algorithm. It is the inverse of

   /// \ref DagShortestPathDefaultOperationTraits, so it can be used to

   /// calculate the longest path. The default implementation

   /// is based on the numeric_limits class. If the numeric type does not

   /// have infinity value then the minimum value is used as extremal

   /// infinity value.

   template <

     typename Value, 

     bool has_infinity = std::numeric_limits<Value>::has_infinity>

   struct DagLongestPathOperationTraits {

     /// \brief Gives back the zero value of the type.

     static Value zero() {

       return static_cast<Value>(0);

     }

     /// \brief Gives back the negative infinity value of the type.

     static Value infinity() {

       return -(std::numeric_limits<Value>::infinity());

     }

     /// \brief Gives back the sum of the given two elements.

     static Value plus(const Value& left, const Value& right) {

       return left + right;

     }

     /// \brief Gives back true only if the first value less than the second.

     static bool less(const Value& left, const Value& right) {

       return left > right;

     }

   };

   template <typename Value>

   struct DagLongestPathOperationTraits<Value, false> {

     static Value zero() {

       return static_cast<Value>(0);

     }

     static Value infinity() {

       return std::numeric_limits<Value>::min();

     }

     static Value plus(const Value& left, const Value& right) {

       if (left == infinity() || right == infinity()) return infinity();

       return left + right;

     }

     static bool less(const Value& left, const Value& right) {

       return left > right;

     }

   };

   /// \brief Inverse traits class of DagShortestPath class.

   ///

   /// Inverse traits class of DagShortestPath class.

   /// \param _Graph Graph type.

   /// \param _LegthMap Type of length map.

   template<class _Graph, class _LengthMap>

   struct DagLongestPathTraits {

     /// The graph type the algorithm runs on. 

     typedef _Graph Graph;

     /// \brief The type of the map that stores the edge lengths.

     ///

     /// The type of the map that stores the edge lengths.

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

     typedef _LengthMap LengthMap;

     // The type of the length of the edges.

     typedef typename _LengthMap::Value Value;

     /// \brief Inverse operation traits for dag shortest path algorithm.

     ///

     /// It defines the infinity type on the given Value type

     /// and the used operation.

     /// \see DagLongestPathOperationTraits

     typedef DagLongestPathOperationTraits<Value> OperationTraits;

     /// \brief The type of the map that stores the last edges of the 

     /// longest paths.

     /// 

     /// The type of the map that stores the last

     /// edges of the longest paths.

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

     ///

     typedef typename Graph::template NodeMap<typename _Graph::Edge> PredMap;

     /// \brief Instantiates a PredMap.

     /// 

     /// This function instantiates a \ref PredMap. 

     /// \param graph is the graph,

     /// to which we would like to define the PredMap.

     /// \todo The graph alone may be insufficient for the initialization

     static PredMap *createPredMap(const _Graph& graph) {

       return new PredMap(graph);

     }

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

     ///

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

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

     ///

     typedef typename Graph::template NodeMap<typename _LengthMap::Value> 

     DistMap;

     /// \brief Instantiates a DistMap.

     ///

     /// This function instantiates a \ref DistMap. 

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

     /// \ref DistMap

     static DistMap *createDistMap(const _Graph& graph) {

       return new DistMap(graph);

     }

   };

   /// \brief %DagShortestPath algorithm class.

   ///

   /// \ingroup flowalgs

   /// This class provides an efficient implementation of a Dag sortest path

   /// searching algorithm. The edge lengths are passed to the algorithm

   /// using a \ref concept::ReadMap "ReadMap", so it is easy to change it

   /// to any kind of length.

   ///

   /// The complexity of the algorithm is O(n + e).

   ///

   /// The type of the length is determined by the

   /// \ref concept::ReadMap::Value "Value" of the length map.

   ///

   /// \param _Graph The graph type the algorithm runs on. The default value

   /// is \ref ListGraph. The value of _Graph is not used directly by

   /// DagShortestPath, it is only passed to \ref DagShortestPathDefaultTraits.

   /// \param _LengthMap This read-only EdgeMap determines the lengths of the

   /// edges. The default map type is \ref concept::Graph::EdgeMap 

   /// "Graph::EdgeMap<int>".  The value of _LengthMap is not used directly 

   /// by DagShortestPath, it is only passed to \ref DagShortestPathDefaultTraits.  

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

   /// algorithm.  The default traits class is \ref DagShortestPathDefaultTraits

   /// "DagShortestPathDefaultTraits<_Graph,_LengthMap>".  See \ref

   /// DagShortestPathDefaultTraits for the documentation of a DagShortestPath traits

   /// class.

   ///

   /// \author Balazs Attila Mihaly (based on Balazs Dezso's work)

 #ifdef DOXYGEN

   template <typename _Graph, typename _LengthMap, typename _Traits>

 #else

   template <typename _Graph=ListGraph,

 	    typename _LengthMap=typename _Graph::template EdgeMap<int>,

 	    typename _Traits=DagShortestPathDefaultTraits<_Graph,_LengthMap> >

 #endif

   class DagShortestPath {

   public:

     /// \brief \ref Exception for uninitialized parameters.

     ///

     /// This error represents problems in the initialization

     /// of the parameters of the algorithms.

     class UninitializedParameter : public lemon::UninitializedParameter {

     public:

       virtual const char* what() const throw() {

 	return "lemon::DagShortestPath::UninitializedParameter";

       }

     };

     typedef _Traits Traits;

     ///The type of the underlying graph.

     typedef typename _Traits::Graph Graph;

     typedef typename Graph::Node Node;

     typedef typename Graph::NodeIt NodeIt;

     typedef typename Graph::Edge Edge;

     typedef typename Graph::EdgeIt EdgeIt;

     typedef typename Graph::OutEdgeIt OutEdgeIt;

     /// \brief The type of the length of the edges.

     typedef typename _Traits::LengthMap::Value Value;

     /// \brief The type of the map that stores the edge lengths.

     typedef typename _Traits::LengthMap LengthMap;

     /// \brief The type of the map that stores the last

     /// edges of the shortest paths.

     typedef typename _Traits::PredMap PredMap;

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

     typedef typename _Traits::DistMap DistMap;

     /// \brief The operation traits.

     typedef typename _Traits::OperationTraits OperationTraits;

     /// \brief The Node weight map.

     typedef typename Graph::template NodeMap<Value> WeightMap;

   private:

     /// Pointer to the underlying graph

     const Graph *graph;

     /// Pointer to the length map

     const LengthMap *length;

     ///Pointer to the map of predecessors edges

     PredMap *_pred;

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

     bool local_pred;

     ///Pointer to the map of distances

     DistMap *_dist;

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

     bool local_dist;

     ///Process step counter

     unsigned int _process_step;

     std::vector<Node> _node_order;

     /// Creates the maps if necessary.

     void create_maps() {

       if(!_pred) {

 	local_pred = true;

 	_pred = Traits::createPredMap(*graph);

       }

       if(!_dist) {

 	local_dist = true;

 	_dist = Traits::createDistMap(*graph);

       }

     }

   public :

     typedef DagShortestPath Create;

     /// \name Named template parameters

     ///@{

     template <class T>

     struct DefPredMapTraits : public Traits {

       typedef T PredMap;

       static PredMap *createPredMap(const Graph&) {

 	throw UninitializedParameter();

       }

     };

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

     /// type

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

     ///

     template <class T>

     struct DefPredMap {

       typedef DagShortestPath< Graph, LengthMap, DefPredMapTraits<T> > Create;

     };

     template <class T>

     struct DefDistMapTraits : public Traits {

       typedef T DistMap;

       static DistMap *createDistMap(const Graph& graph) {

 	throw UninitializedParameter();

       }

     };

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

     /// type

     ///

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

     ///

     template <class T>

     struct DefDistMap 

       : public DagShortestPath< Graph, LengthMap, DefDistMapTraits<T> > {

       typedef DagShortestPath< Graph, LengthMap, DefDistMapTraits<T> > Create;

     };

     template <class T>

     struct DefOperationTraitsTraits : public Traits {

       typedef T OperationTraits;

     };

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

     /// OperationTraits type

     ///

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

     /// type

     template <class T>

     struct DefOperationTraits

       : public DagShortestPath< Graph, LengthMap, DefOperationTraitsTraits<T> > {

       typedef DagShortestPath< Graph, LengthMap, DefOperationTraitsTraits<T> >

       Create;

     };

     ///@}

   protected:

     DagShortestPath() {}

   public:      

     /// \brief Constructor.

     ///

     /// \param _graph the graph the algorithm will run on.

     /// \param _length the length map used by the algorithm.

     DagShortestPath(const Graph& _graph, const LengthMap& _length) :

       graph(&_graph), length(&_length),

       _pred(0), local_pred(false),

       _dist(0), local_dist(false){}

     /// \brief Constructor with node weight map.

     ///

     /// \param _graph the graph the algorithm will run on.

     /// \param _length the length map used by the algorithm.

     /// The NodeMap _length will be used as the weight map.

     /// Each edge will have the weight of its target node.

     DagShortestPath(const Graph& _graph, const WeightMap& _length) :

       graph(&_graph),

       _pred(0), local_pred(false),

       _dist(0), local_dist(false){

       length=new LengthMap(_graph);

       _dist=new DistMap(_graph);

       for(EdgeIt eit(_graph);eit!=INVALID;++eit)

 	(const_cast<LengthMap*>(length))->set(eit,_length[_graph.target(eit)]);

       }

     ///Destructor.

     ~DagShortestPath() {

       if(local_pred) delete _pred;

       if(local_dist) delete _dist;

     }

     /// \brief Sets the length map.

     ///

     /// Sets the length map.

     /// \return \c (*this)

     DagShortestPath &lengthMap(const LengthMap &m) {

       length = &m;

       return *this;

     }

     /// \brief Sets the map storing the predecessor edges.

     ///

     /// Sets the map storing the predecessor edges.

     /// 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 \c (*this)

     DagShortestPath &predMap(PredMap &m) {

       if(local_pred) {

 	delete _pred;

 	local_pred=false;

       }

       _pred = &m;

       return *this;

     }

     /// \brief Sets the map storing the distances calculated by the algorithm.

     ///

     /// Sets the map storing the distances 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 \c (*this)

     DagShortestPath &distMap(DistMap &m) {

       if(local_dist) {

 	delete _dist;

 	local_dist=false;

       }

       _dist = &m;

       return *this;

     }

     /// \name Execution control

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

     /// one of the member functions called \c 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 actual path computation.

     /// Some functions have an alternative form (\ref checkedInit(...),

     /// \ref checkedRun(...)) which also verifies if the graph given in the

     /// constructor is a dag.

     ///@{

     /// \brief Initializes the internal data structures.

     ///

     /// Initializes the internal data structures.

     void init(const Value value = OperationTraits::infinity()) {

       typedef typename Graph::template NodeMap<int> NodeOrderMap;

       _process_step=0;

       NodeOrderMap node_order(*graph);

       topologicalSort(*graph,node_order);

       _node_order.resize(countNodes(*graph),INVALID);

       create_maps();

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

         _node_order[node_order[it]]=it;

         _pred->set(it, INVALID);

         _dist->set(it, value);

       }

     }

     /// \brief Initializes the internal data structures

     /// with a given topological sort (NodeMap).

     ///

     /// Initializes the internal data structures

     /// with a given topological sort (NodeMap).

     void init(const typename Graph::template NodeMap<int>& node_order,

          const Value value = OperationTraits::infinity()) {

       _process_step=0;

       _node_order.resize(countNodes(*graph),INVALID);

       create_maps();

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

         _node_order[node_order[it]]=it;

         _pred->set(it, INVALID);

         _dist->set(it, value);

       }

     }

     /// \brief Initializes the internal data structures

     /// with a given topological sort (std::vector).

     ///

     /// Initializes the internal data structures

     /// with a given topological sort (std::vector).

     void init(const std::vector<Node>& node_order,

         const Value value = OperationTraits::infinity()) {

       _process_step=0;

       _node_order=node_order;

       create_maps();

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

         _pred->set(it, INVALID);

         _dist->set(it, value);

       }

     }

     /// \brief Initializes the internal data structures. It also checks if the graph is dag.

     ///

     /// Initializes the internal data structures. It also checks if the graph is dag.

     /// \return true if the graph (given in the constructor) is dag, false otherwise.

     bool checkedInit(const Value value = OperationTraits::infinity()) {

       typedef typename Graph::template NodeMap<int> NodeOrderMap;

       NodeOrderMap node_order(*graph);

       if(!checkedTopologicalSort(*graph,node_order))return false;

       init(node_order,value);

       return true;

     }

     /// \brief Initializes the internal data structures with a given

     /// topological sort (NodeMap). It also checks if the graph is dag.

     ///

     /// Initializes the internal data structures with a given

     /// topological sort (NodeMap). It also checks if the graph is dag.

     /// \return true if the graph (given in the constructor) is dag, false otherwise.

     bool checkedInit(const typename Graph::template NodeMap<int>& node_order, 

                      const Value value = OperationTraits::infinity()) {

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

         for(OutEdgeIt oeit(*graph,it);oeit!=INVALID;++oeit){

           if(node_order[graph->target(oeit)]<node_order[it])return false;

         }

       }

       init(node_order,value);

       return true;

     }

     /// \brief Initializes the internal data structures with a given

     /// topological sort (std::vector). It also checks if the graph is dag.

     ///

     /// Initializes the internal data structures with a given

     /// topological sort (std::vector). It also checks if the graph is dag.

     /// \return true if the graph (given in the constructor) is dag, false otherwise.

     bool checkedInit(const std::vector<Node>& node_order, 

                      const Value value = OperationTraits::infinity()) {

       typedef typename Graph::template NodeMap<bool> BoolNodeMap;

       BoolNodeMap _processed(*graph,false);

       for(unsigned int i=0;i<_node_order.size();++i){

         _processed[node_order[i]]=true;

         for(OutEdgeIt oeit(*graph,node_order[i]);oeit!=INVALID;++oeit){

           if(_processed[graph->target(oeit)])return false;

         }

       }

       init(node_order,value);

       return true;

     }

     /// \brief Adds a new source node.

     ///

     /// The optional second parameter is the initial distance of the node.

     /// It just sets the distance of the node to the given value.

     void addSource(Node source, Value dst = OperationTraits::zero()) {

       if((*_dist)[source] != dst){

         _dist->set(source, dst);

       }

     }

     /// \brief Executes one step from the dag shortest path algorithm.

     ///

     /// If the algoritm calculated the distances in the previous step 

     /// strictly for all at most k length paths then it will calculate the 

     /// distances strictly for all at most k + 1 length paths. With k

     /// iteration this function calculates the at most k length paths.

     ///\pre the queue is not empty

     ///\return the currently processed node

     Node processNextNode() {

       if(reached(_node_order[_process_step])){

         for (OutEdgeIt it(*graph, _node_order[_process_step]); it != INVALID; ++it) {

 	  Node target = graph->target(it);

 	  Value relaxed =

 	    OperationTraits::plus((*_dist)[_node_order[_process_step]], (*length)[it]);

 	  if (OperationTraits::less(relaxed, (*_dist)[target])) {

 	    _pred->set(target, it);

 	    _dist->set(target, relaxed);

 	  }

         }

       }

       ++_process_step;

       return _node_order[_process_step-1];

     }

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

     ///to be processed in the queue

     ///

     ///Returns \c false if there are nodes

     ///to be processed in the queue

     bool emptyQueue() { return _node_order.size()-1==_process_step; }

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

     ///

     ///Returns the number of the nodes to be processed in the queue.

     int queueSize() { return _node_order.size()-1-_process_step; }

     /// \brief 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 %DagShortestPath algorithm from the root node(s)

     /// in order to compute the shortest path to each node. The algorithm 

     /// computes 

     /// - The shortest path tree.

     /// - The distance of each node from the root(s).

     void start() {

       while(!emptyQueue()) {

 	processNextNode();

       }

     }

     /// \brief Runs %DagShortestPath algorithm from node \c s.

     ///    

     /// This method runs the %DagShortestPath algorithm from a root node \c s

     /// in order to compute the shortest path to each node. The algorithm 

     /// computes

     /// - The shortest path tree.

     /// - The distance of each node from the root.

     ///

     /// \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 %DagShortestPath algorithm from node \c s.

     /// It also checks if the graph is a dag.

     ///    

     /// This method runs the %DagShortestPath algorithm from a root node \c s

     /// in order to compute the shortest path to each node. The algorithm 

     /// computes

     /// - The shortest path tree.

     /// - The distance of each node from the root.

     /// The algorithm checks if the graph given int the constructor is a dag.

     bool checkedRun(Node s) {

       if(!checkedInit())return false;

       addSource(s);

       start();

       return true;

     }

     ///@}

     /// \name Query Functions

     /// The result of the %DagShortestPath algorithm can be obtained using these

     /// functions.\n

     /// Before the use of these functions,

     /// either run() or start() must be called.

     ///@{

     /// \brief Copies the shortest path to \c t into \c p

     ///    

     /// This function copies the shortest path to \c t into \c p.

     /// If it \c t is a source itself or unreachable, then it does not

     /// alter \c p.

     ///

     /// \return Returns \c true if a path to \c t was actually copied to \c p,

     /// \c false otherwise.

     /// \sa DirPath

     template <typename Path>

     bool getPath(Path &p, Node t) {

       if(reached(t)) {

 	p.clear();

 	typename Path::Builder b(p);

 	for(b.setStartNode(t);predEdge(t)!=INVALID;t=predNode(t))

 	  b.pushFront(predEdge(t));

 	b.commit();

 	return true;

       }

       return false;

     }

     /// \brief The distance of a node from the root.

     ///

     /// Returns the distance of a node from the root.

     /// \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 dist(Node v) const { return (*_dist)[v]; }

     /// \brief Returns the 'previous edge' of the shortest path tree.

     ///

     /// For a node \c v it returns the 'previous edge' of the shortest path 

     /// tree, i.e. it returns the last edge of a shortest path from the root 

     /// to \c v. It is \ref INVALID if \c v is unreachable from the root or 

     /// if \c v=s. The shortest path tree used here is equal to the shortest 

     /// path tree used in \ref predNode(). 

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

     /// this function.

     Edge predEdge(Node v) const { return (*_pred)[v]; }

     /// \brief Returns the 'previous node' of the shortest path tree.

     ///

     /// For a node \c v it returns the 'previous node' of the shortest path 

     /// tree, i.e. it returns the last but one node from a shortest path from 

     /// the root to \c /v. It is INVALID if \c v is unreachable from the root 

     /// or if \c v=s. The shortest path tree used here is equal to the 

     /// shortest path tree used in \ref predEdge().  \pre \ref run() must be 

     /// called before using this function.

     Node predNode(Node v) const { 

       return (*_pred)[v] == INVALID ? INVALID : graph->source((*_pred)[v]); 

     }

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

     ///

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

     /// be called before using this function.

     const DistMap &distMap() const { return *_dist;}

     /// \brief Returns a reference to the shortest path tree map.

     ///

     /// Returns a reference to the NodeMap of the edges of the

     /// shortest path tree.

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

     const PredMap &predMap() const { return *_pred; }

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

     ///

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

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

     ///

     bool reached(Node v) { return (*_dist)[v] != OperationTraits::infinity(); }

     ///@}

   };

   /// \brief Default traits class of DagShortestPath function.

   ///

   /// Default traits class of DagShortestPath function.

   /// \param _Graph Graph type.

   /// \param _LengthMap Type of length map.

   template <typename _Graph, typename _LengthMap>

   struct DagShortestPathWizardDefaultTraits {

     /// \brief The graph type the algorithm runs on. 

     typedef _Graph Graph;

     /// \brief The type of the map that stores the edge lengths.

     ///

     /// The type of the map that stores the edge lengths.

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

     typedef _LengthMap LengthMap;

     /// \brief The value type of the length map.

     typedef typename _LengthMap::Value Value;

     /// \brief Operation traits for dag shortest path algorithm.

     ///

     /// It defines the infinity type on the given Value type

     /// and the used operation.

     /// \see DagShortestPathDefaultOperationTraits

     typedef DagShortestPathDefaultOperationTraits<Value> OperationTraits;

     /// \brief The type of the map that stores the last

     /// edges of the shortest paths.

     /// 

     /// The type of the map that stores the last

     /// edges of the shortest paths.

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

     typedef NullMap <typename _Graph::Node,typename _Graph::Edge> PredMap;

     /// \brief Instantiates a PredMap.

     /// 

     /// This function instantiates a \ref PredMap. 

     static PredMap *createPredMap(const _Graph &) {

       return new PredMap();

     }

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

     ///

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

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

     typedef NullMap<typename Graph::Node, Value> DistMap;

     /// \brief Instantiates a DistMap.

     ///

     /// This function instantiates a \ref DistMap. 

     static DistMap *createDistMap(const _Graph &) {

       return new DistMap();

     }

   };

   /// \brief Default traits used by \ref DagShortestPathWizard

   ///

   /// To make it easier to use DagShortestPath algorithm

   /// we have created a wizard class.

   /// This \ref DagShortestPathWizard class needs default traits,

   /// as well as the \ref DagShortestPath class.

   /// The \ref DagShortestPathWizardBase is a class to be the default traits of the

   /// \ref DagShortestPathWizard class.

   /// \todo More named parameters are required...

   template<class _Graph,class _LengthMap>

   class DagShortestPathWizardBase 

     : public DagShortestPathWizardDefaultTraits<_Graph,_LengthMap> {

     typedef DagShortestPathWizardDefaultTraits<_Graph,_LengthMap> Base;

   protected:

     /// Type of the nodes in the graph.

     typedef typename Base::Graph::Node Node;

     /// Pointer to the underlying graph.

     void *_graph;

     /// Pointer to the length map

     void *_length;

     ///Pointer to the map of predecessors edges.

     void *_pred;

     ///Pointer to the map of distances.

     void *_dist;

     ///Pointer to the source node.

     Node _source;

     public:

     /// Constructor.

     /// This constructor does not require parameters, therefore it initiates

     /// all of the attributes to default values (0, INVALID).

     DagShortestPathWizardBase() : _graph(0), _length(0), _pred(0),

 			   _dist(0), _source(INVALID) {}

     /// Constructor.

     /// This constructor requires some parameters,

     /// listed in the parameters list.

     /// Others are initiated to 0.

     /// \param graph is the initial value of  \ref _graph

     /// \param length is the initial value of  \ref _length

     /// \param source is the initial value of  \ref _source

     DagShortestPathWizardBase(const _Graph& graph, 

 			  const _LengthMap& length, 

 			  Node source = INVALID) :

       _graph((void *)&graph), _length((void *)&length), _pred(0),

       _dist(0), _source(source) {}

   };

   /// A class to make the usage of DagShortestPath algorithm easier

   /// This class is created to make it easier to use DagShortestPath algorithm.

   /// It uses the functions and features of the plain \ref DagShortestPath,

   /// but it is much simpler to use it.

   ///

   /// Simplicity means that the way to change the types defined

   /// in the traits class is based on functions that returns the new class

   /// and not on templatable built-in classes.

   /// When using the plain \ref DagShortestPath

   /// the new class with the modified type comes from

   /// the original class by using the ::

   /// operator. In the case of \ref DagShortestPathWizard only

   /// a function have to be called and it will

   /// return the needed class.

   ///

   /// It does not have own \ref run method. When its \ref run method is called

   /// it initiates a plain \ref DagShortestPath class, and calls the \ref 

   /// DagShortestPath::run() method of it.

   template<class _Traits>

   class DagShortestPathWizard : public _Traits {

     typedef _Traits Base;

     ///The type of the underlying graph.

     typedef typename _Traits::Graph Graph;

     typedef typename Graph::Node Node;

     typedef typename Graph::NodeIt NodeIt;

     typedef typename Graph::Edge Edge;

     typedef typename Graph::OutEdgeIt EdgeIt;

     ///The type of the map that stores the edge lengths.

     typedef typename _Traits::LengthMap LengthMap;

     ///The type of the length of the edges.

     typedef typename LengthMap::Value Value;

     ///\brief The type of the map that stores the last

     ///edges of the shortest paths.

     typedef typename _Traits::PredMap PredMap;

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

     typedef typename _Traits::DistMap DistMap;

   public:

     /// Constructor.

     DagShortestPathWizard() : _Traits() {}

     /// \brief Constructor that requires parameters.

     ///

     /// Constructor that requires parameters.

     /// These parameters will be the default values for the traits class.

     DagShortestPathWizard(const Graph& graph, const LengthMap& length, 

 		      Node source = INVALID) 

       : _Traits(graph, length, source) {}

     /// \brief Copy constructor

     DagShortestPathWizard(const _Traits &b) : _Traits(b) {}

     ~DagShortestPathWizard() {}

     /// \brief Runs DagShortestPath algorithm from a given node.

     ///    

     /// Runs DagShortestPath algorithm from a given node.

     /// The node can be given by the \ref source function.

     void run() {

       if(Base::_source == INVALID) throw UninitializedParameter();

       DagShortestPath<Graph,LengthMap,_Traits> 

 	bf(*(Graph*)Base::_graph, *(LengthMap*)Base::_length);

       if (Base::_pred) bf.predMap(*(PredMap*)Base::_pred);

       if (Base::_dist) bf.distMap(*(DistMap*)Base::_dist);

       bf.run(Base::_source);

     }

     /// \brief Runs DagShortestPath algorithm from the given node.

     ///

     /// Runs DagShortestPath algorithm from the given node.

     /// \param source is the given source.

     void run(Node source) {

       Base::_source = source;

       run();

     }

     template<class T>

     struct DefPredMapBase : public Base {

       typedef T PredMap;

       static PredMap *createPredMap(const Graph &) { return 0; };

       DefPredMapBase(const _Traits &b) : _Traits(b) {}

     };

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

     ///function for setting PredMap type

     ///

     /// \ref named-templ-param "Named parameter"

     ///function for setting PredMap type

     ///

     template<class T>

     DagShortestPathWizard<DefPredMapBase<T> > predMap(const T &t) 

     {

       Base::_pred=(void *)&t;

       return DagShortestPathWizard<DefPredMapBase<T> >(*this);

     }

     template<class T>

     struct DefDistMapBase : public Base {

       typedef T DistMap;

       static DistMap *createDistMap(const Graph &) { return 0; };

       DefDistMapBase(const _Traits &b) : _Traits(b) {}

     };

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

     ///function for setting DistMap type

     ///

     /// \ref named-templ-param "Named parameter"

     ///function for setting DistMap type

     ///

     template<class T>

     DagShortestPathWizard<DefDistMapBase<T> > distMap(const T &t) {

       Base::_dist=(void *)&t;

       return DagShortestPathWizard<DefDistMapBase<T> >(*this);

     }

     template<class T>

     struct DefOperationTraitsBase : public Base {

       typedef T OperationTraits;

       DefOperationTraitsBase(const _Traits &b) : _Traits(b) {}

     };

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

     ///function for setting OperationTraits type

     ///

     /// \ref named-templ-param "Named parameter"

     ///function for setting OperationTraits type

     ///

     template<class T>

     DagShortestPathWizard<DefOperationTraitsBase<T> > distMap() {

       return DagShortestPathWizard<DefDistMapBase<T> >(*this);

     }

     /// \brief Sets the source node, from which the DagShortestPath algorithm runs.

     ///

     /// Sets the source node, from which the DagShortestPath algorithm runs.

     /// \param source is the source node.

     DagShortestPathWizard<_Traits>& source(Node source) {

       Base::_source = source;

       return *this;

     }

   };

   /// \brief Function type interface for DagShortestPath algorithm.

   ///

   /// \ingroup flowalgs

   /// Function type interface for DagShortestPath algorithm.

   ///

   /// This function also has several \ref named-templ-func-param 

   /// "named parameters", they are declared as the members of class 

   /// \ref DagShortestPathWizard.

   /// The following

   /// example shows how to use these parameters.

   ///\code

   /// dagShortestPath(g,length,source).predMap(preds).run();

   ///\endcode

   /// \warning Don't forget to put the \ref DagShortestPathWizard::run() "run()"

   /// to the end of the parameter list.

   /// \sa DagShortestPathWizard

   /// \sa DagShortestPath

   template<class _Graph, class _LengthMap>

   DagShortestPathWizard<DagShortestPathWizardBase<_Graph,_LengthMap> >

   dagShortestPath(const _Graph& graph,

 	      const _LengthMap& length, 

 	      typename _Graph::Node source = INVALID) {

     return DagShortestPathWizard<DagShortestPathWizardBase<_Graph,_LengthMap> >

       (graph, length, source);

   }

 } //END OF NAMESPACE LEMON

 #endif