/* -*- C++ -*-

  * lemon/floyd_warshall.h - Part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2005 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_FLOYD_WARSHALL_H

 #define LEMON_FLOYD_WARSHALL_H

 ///\ingroup flowalgs

 /// \file

 /// \brief FloydWarshall algorithm.

 ///

 /// \todo getPath() should be implemented! (also for BFS and DFS)

 #include <lemon/list_graph.h>

 #include <lemon/graph_utils.h>

 #include <lemon/invalid.h>

 #include <lemon/error.h>

 #include <lemon/matrix_maps.h>

 #include <lemon/maps.h>

 #include <limits>

 namespace lemon {

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

   ///  

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

   /// used in the Floyd-Warshall 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 FloydWarshallDefaultOperationTraits {

     /// \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 FloydWarshallDefaultOperationTraits<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 FloydWarshall class.

   ///

   /// Default traits class of FloydWarshall class.

   /// \param _Graph Graph type.

   /// \param _LegthMap Type of length map.

   template<class _Graph, class _LengthMap>

   struct FloydWarshallDefaultTraits {

     /// 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 belmann-ford algorithm.

     ///

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

     /// and the used operation.

     /// \see FloydWarshallDefaultOperationTraits

     typedef FloydWarshallDefaultOperationTraits<Value> OperationTraits;

     /// \brief The type of the matrix 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 be a matrix map with \c Graph::Edge value type.

     ///

     typedef DynamicMatrixMap<Graph, typename Graph::Node, 

 			     typename Graph::Edge> PredMap;

     /// \brief Instantiates a PredMap.

     /// 

     /// This function instantiates a \ref PredMap. 

     /// \param G 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::WriteMatrixMap "WriteMatrixMap" concept.

     ///

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

     /// \brief Instantiates a DistMap.

     ///

     /// This function instantiates a \ref DistMap. 

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

     /// \ref DistMap

     static DistMap *createDistMap(const _Graph& graph) {

       return new DistMap(graph);

     }

   };

   /// \brief FloydWarshall algorithm class.

   ///

   /// \ingroup flowalgs

   /// This class provides an efficient implementation of \c FloydWarshall 

   /// 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 algorithm solves the shortest path problem for each pairs

   /// of node when the edges can have negative length but the graph should

   /// not contain circle with negative sum of length. If we can assume

   /// that all edge is non-negative in the graph then the dijkstra algorithm

   /// should be used from each node rather and if the graph is sparse and

   /// there are negative circles then the johson algorithm.

   ///

   /// The complexity of this algorithm is O(n^3 + 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

   /// FloydWarshall, it is only passed to \ref FloydWarshallDefaultTraits.

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

   /// edges. It is read once for each edge, so the map may involve in

   /// relatively time consuming process to compute the edge length if

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

   /// concept::StaticGraph::EdgeMap "Graph::EdgeMap<int>".  The value

   /// of _LengthMap is not used directly by FloydWarshall, it is only passed 

   /// to \ref FloydWarshallDefaultTraits.  \param _Traits Traits class to set

   /// various data types used by the algorithm.  The default traits

   /// class is \ref FloydWarshallDefaultTraits

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

   /// FloydWarshallDefaultTraits for the documentation of a FloydWarshall 

   /// traits class.

   ///

   /// \author Balazs Dezso

 #ifdef DOXYGEN

   template <typename _Graph, typename _LengthMap typename _Traits >

 #else

   template <typename _Graph=ListGraph,

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

 	    typename _Traits=FloydWarshallDefaultTraits<_Graph,_LengthMap> >

 #endif

   class FloydWarshall {

   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* exceptionName() const {

 	return "lemon::FloydWarshall::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;

     /// \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. The type of the PredMap

     /// is a matrix map for Edges

     typedef typename _Traits::PredMap PredMap;

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

     /// The type of the DistMap is a matrix map for Values

     typedef typename _Traits::DistMap DistMap;

     /// \brief The operation traits.

     typedef typename _Traits::OperationTraits OperationTraits;

   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;

     /// 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 :

     /// \name Named template parameters

     ///@{

     template <class T>

     struct DefPredMapTraits : public Traits {

       typedef T PredMap;

       static PredMap *createPredMap(const Graph& 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 

       : public FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > {

       typedef FloydWarshall< 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 FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > {

       typedef FloydWarshall< 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 PredMap type

     template <class T>

     struct DefOperationTraits

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

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

       Create;

     };

     ///@}

   protected:

     FloydWarshall() {}

   public:      

     typedef FloydWarshall Create;

     /// \brief Constructor.

     ///

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

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

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

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

       _pred(0), local_pred(false),

       _dist(0), local_dist(false) {}

     ///Destructor.

     ~FloydWarshall() {

       if(local_pred) delete _pred;

       if(local_dist) delete _dist;

     }

     /// \brief Sets the length map.

     ///

     /// Sets the length map.

     /// \return \c (*this)

     FloydWarshall &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)

     FloydWarshall &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)

     FloydWarshall &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,

     /// Finally \ref start() will perform the actual path

     /// computation.

     ///@{

     /// \brief Initializes the internal data structures.

     /// 

     /// Initializes the internal data structures.

     void init() {

       create_maps();

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

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

 	  _pred->set(it, jt, INVALID);

 	  _dist->set(it, jt, OperationTraits::infinity());

 	}

 	_dist->set(it, it, OperationTraits::zero());

       }

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

 	Node source = graph->source(it);

 	Node target = graph->target(it);	

 	if (OperationTraits::less((*length)[it], (*_dist)(source, target))) {

 	  _dist->set(source, target, (*length)[it]);

 	  _pred->set(source, target, it);

 	}

       }

     }

     /// \brief Executes the algorithm.

     ///

     /// This method runs the %FloydWarshall algorithm in order to compute 

     /// the shortest path to each node pairs. The algorithm 

     /// computes 

     /// - The shortest path tree for each node.

     /// - The distance between each node pairs.

     void start() {

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

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

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

 	    Value relaxed = OperationTraits::plus((*_dist)(it, kt),

 						  (*_dist)(kt, jt));

 	    if (OperationTraits::less(relaxed, (*_dist)(it, jt))) {

 	      _dist->set(it, jt, relaxed);

 	      _pred->set(it, jt, (*_pred)(kt, jt));

 	    }

 	  }

 	}

       }

     }

     /// \brief Executes the algorithm and checks the negative circles.

     ///

     /// This method runs the %FloydWarshall algorithm in order to compute 

     /// the shortest path to each node pairs. If there is a negative circle 

     /// in the graph it gives back false. 

     /// The algorithm computes 

     /// - The shortest path tree for each node.

     /// - The distance between each node pairs.

     bool checkedStart() {

       start();

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

 	if (OperationTraits::less((*dist)(it, it), OperationTraits::zero())) {

 	  return false;

 	}

       }

       return true;

     }

     /// \brief Runs %FloydWarshall algorithm.

     ///    

     /// This method runs the %FloydWarshall algorithm from a each node

     /// in order to compute the shortest path to each node pairs. 

     /// The algorithm computes

     /// - The shortest path tree for each node.

     /// - The distance between each node pairs.

     ///

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

     /// \code

     ///  d.init();

     ///  d.start();

     /// \endcode

     void run() {

       init();

       start();

     }

     ///@}

     /// \name Query Functions

     /// The result of the %FloydWarshall 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.

     /// \todo Is it the right way to handle unreachable nodes?

     /// \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 source, Node target) {

       if (connected(source, target)) {

 	p.clear();

 	typename Path::Builder b(target);

 	for(b.setStartNode(target); pred(source, target) != INVALID;

 	    target = predNode(target)) {

 	  b.pushFront(pred(source, target));

 	}

 	b.commit();

 	return true;

       }

       return false;

     }

     /// \brief The distance between two nodes.

     ///

     /// Returns the distance between two nodes.

     /// \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 source, Node target) const { 

       return (*_dist)(source, target); 

     }

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

     ///

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

     /// path tree to direction of the node \c root 

     /// i.e. it returns the last edge of a shortest path from the node \c root 

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

     /// or if \c node=root. 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.

     /// \todo predEdge could be a better name.

     Edge pred(Node root, Node node) const { 

       return (*_pred)(root, node); 

     }

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

     ///

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

     /// tree to direction of the node \c root, i.e. it returns the last but 

     /// one node from a shortest path from the \c root to \c node. It is 

     /// INVALID if \c node is unreachable from the root or if \c node=root. 

     /// The shortest path tree used here is equal to the 

     /// shortest path tree used in \ref pred().  

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

     Node predNode(Node root, Node node) const { 

       return (*_pred)(root, node) == INVALID ? 

       INVALID : graph->source((*_pred)(root, node)); 

     }

     /// \brief Returns a reference to the matrix node map of distances.

     ///

     /// Returns a reference to the matrix node map 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 matrix node map 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 connected(Node source, Node target) { 

       return (*_dist)(source, target) != OperationTraits::infinity(); 

     }

     ///@}

   };

 } //END OF NAMESPACE LEMON

 #endif