diff -r 755cdc461ddd -r 29428f7b8b66 lemon/floyd_warshall.h --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/lemon/floyd_warshall.h Mon Oct 03 10:20:56 2005 +0000 @@ -0,0 +1,525 @@ +/* -*- 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 +#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 belmann-ford 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 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 NodeMatrixMap 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::WriteMap "WriteMap" concept. + /// + typedef NodeMatrixMap 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 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 + + + template , + typename _Traits=FloydWarshallDefaultTraits<_Graph,_LengthMap> > + 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 + class DefPredMap + : public FloydWarshall< Graph, LengthMap, DefPredMapTraits > {}; + + 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 + class DefDistMap + : public FloydWarshall< Graph, LengthMap, DefDistMapTraits > {}; + + 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 + class DefOperationTraits + : public FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits > { + }; + + ///@} + + public: + + /// \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, it == jt ? + OperationTraits::zero() : OperationTraits::infinity()); + } + } + 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 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 + 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 +