/* -*- 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. /// #include #include #include #include #include #include #include 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::has_infinity> struct FloydWarshallDefaultOperationTraits { /// \brief Gives back the zero value of the type. static Value zero() { return static_cast(0); } /// \brief Gives back the positive infinity value of the type. static Value infinity() { return std::numeric_limits::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 struct FloydWarshallDefaultOperationTraits { static Value zero() { return static_cast(0); } static Value infinity() { return std::numeric_limits::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 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 floyd-warshall algorithm. /// /// It defines the infinity type on the given Value type /// and the used operation. /// \see FloydWarshallDefaultOperationTraits typedef FloydWarshallDefaultOperationTraits 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 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 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 Floyd-Warshall /// 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 pair /// of node when the edges can have negative length but the graph should /// not contain cycles 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 johnson 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". 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 #else template , 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 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 struct DefPredMap : public FloydWarshall< Graph, LengthMap, DefPredMapTraits > { typedef FloydWarshall< Graph, LengthMap, DefPredMapTraits > Create; }; template 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 struct DefDistMap : public FloydWarshall< Graph, LengthMap, DefDistMapTraits > { typedef FloydWarshall< Graph, LengthMap, DefDistMapTraits > Create; }; template 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 struct DefOperationTraits : public FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits > { typedef FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits > 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 cycles. /// /// This method runs the %FloydWarshall algorithm in order to compute /// the shortest path to each node pairs. If there is a negative cycle /// 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. /// \return Returns \c true if a path to \c t was actually copied to \c p, /// \c false otherwise. /// \sa DirPath template bool getPath(Path &p, Node source, Node target) { if (connected(source, target)) { p.clear(); typename Path::Builder b(target); for(b.setStartNode(target); predEdge(source, target) != INVALID; target = predNode(target)) { b.pushFront(predEdge(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. Edge predEdge(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 predEdge(). /// \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