deba@1699: /* -*- C++ -*-
deba@1699: *
alpar@1956: * This file is a part of LEMON, a generic C++ optimization library
alpar@1956: *
alpar@1956: * Copyright (C) 2003-2006
alpar@1956: * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@1699: * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@1699: *
deba@1699: * Permission to use, modify and distribute this software is granted
deba@1699: * provided that this copyright notice appears in all copies. For
deba@1699: * precise terms see the accompanying LICENSE file.
deba@1699: *
deba@1699: * This software is provided "AS IS" with no warranty of any kind,
deba@1699: * express or implied, and with no claim as to its suitability for any
deba@1699: * purpose.
deba@1699: *
deba@1699: */
deba@1699:
deba@1699: #ifndef LEMON_BELMANN_FORD_H
deba@1699: #define LEMON_BELMANN_FORD_H
deba@1699:
deba@1858: /// \ingroup flowalgs
deba@1699: /// \file
deba@1864: /// \brief BellmanFord algorithm.
deba@1699: ///
deba@1699:
deba@1699: #include <lemon/list_graph.h>
deba@1993: #include <lemon/bits/invalid.h>
deba@1699: #include <lemon/error.h>
deba@1699: #include <lemon/maps.h>
deba@1699:
deba@1699: #include <limits>
deba@1699:
deba@1699: namespace lemon {
deba@1699:
deba@1864: /// \brief Default OperationTraits for the BellmanFord algorithm class.
deba@1699: ///
deba@1699: /// It defines all computational operations and constants which are
deba@1864: /// used in the bellman ford algorithm. The default implementation
deba@1699: /// is based on the numeric_limits class. If the numeric type does not
deba@1699: /// have infinity value then the maximum value is used as extremal
deba@1699: /// infinity value.
deba@1699: template <
deba@1699: typename Value,
deba@1699: bool has_infinity = std::numeric_limits<Value>::has_infinity>
deba@1864: struct BellmanFordDefaultOperationTraits {
deba@1699: /// \brief Gives back the zero value of the type.
deba@1699: static Value zero() {
deba@1699: return static_cast<Value>(0);
deba@1699: }
deba@1699: /// \brief Gives back the positive infinity value of the type.
deba@1699: static Value infinity() {
deba@1699: return std::numeric_limits<Value>::infinity();
deba@1699: }
deba@1699: /// \brief Gives back the sum of the given two elements.
deba@1699: static Value plus(const Value& left, const Value& right) {
deba@1699: return left + right;
deba@1699: }
deba@1699: /// \brief Gives back true only if the first value less than the second.
deba@1699: static bool less(const Value& left, const Value& right) {
deba@1699: return left < right;
deba@1699: }
deba@1699: };
deba@1699:
deba@1699: template <typename Value>
deba@1864: struct BellmanFordDefaultOperationTraits<Value, false> {
deba@1699: static Value zero() {
deba@1699: return static_cast<Value>(0);
deba@1699: }
deba@1699: static Value infinity() {
deba@1699: return std::numeric_limits<Value>::max();
deba@1699: }
deba@1699: static Value plus(const Value& left, const Value& right) {
deba@1699: if (left == infinity() || right == infinity()) return infinity();
deba@1699: return left + right;
deba@1699: }
deba@1699: static bool less(const Value& left, const Value& right) {
deba@1699: return left < right;
deba@1699: }
deba@1699: };
deba@1699:
deba@1864: /// \brief Default traits class of BellmanFord class.
deba@1699: ///
deba@1864: /// Default traits class of BellmanFord class.
deba@1699: /// \param _Graph Graph type.
deba@1699: /// \param _LegthMap Type of length map.
deba@1699: template<class _Graph, class _LengthMap>
deba@1864: struct BellmanFordDefaultTraits {
deba@1699: /// The graph type the algorithm runs on.
deba@1699: typedef _Graph Graph;
deba@1699:
deba@1699: /// \brief The type of the map that stores the edge lengths.
deba@1699: ///
deba@1699: /// The type of the map that stores the edge lengths.
deba@1699: /// It must meet the \ref concept::ReadMap "ReadMap" concept.
deba@1699: typedef _LengthMap LengthMap;
deba@1699:
deba@1699: // The type of the length of the edges.
deba@1699: typedef typename _LengthMap::Value Value;
deba@1699:
deba@1864: /// \brief Operation traits for bellman-ford algorithm.
deba@1699: ///
deba@1699: /// It defines the infinity type on the given Value type
deba@1699: /// and the used operation.
deba@1864: /// \see BellmanFordDefaultOperationTraits
deba@1864: typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
deba@1699:
deba@1699: /// \brief The type of the map that stores the last edges of the
deba@1699: /// shortest paths.
deba@1699: ///
deba@1699: /// The type of the map that stores the last
deba@1699: /// edges of the shortest paths.
deba@1699: /// It must meet the \ref concept::WriteMap "WriteMap" concept.
deba@1699: ///
deba@1699: typedef typename Graph::template NodeMap<typename _Graph::Edge> PredMap;
deba@1699:
deba@1699: /// \brief Instantiates a PredMap.
deba@1699: ///
deba@1699: /// This function instantiates a \ref PredMap.
deba@1858: /// \param graph is the graph, to which we would like to define the PredMap.
deba@1699: static PredMap *createPredMap(const _Graph& graph) {
deba@1699: return new PredMap(graph);
deba@1699: }
deba@1699:
deba@1699: /// \brief The type of the map that stores the dists of the nodes.
deba@1699: ///
deba@1699: /// The type of the map that stores the dists of the nodes.
deba@1699: /// It must meet the \ref concept::WriteMap "WriteMap" concept.
deba@1699: ///
deba@1699: typedef typename Graph::template NodeMap<typename _LengthMap::Value>
deba@1699: DistMap;
deba@1699:
deba@1699: /// \brief Instantiates a DistMap.
deba@1699: ///
deba@1699: /// This function instantiates a \ref DistMap.
deba@1858: /// \param graph is the graph, to which we would like to define the
deba@1699: /// \ref DistMap
deba@1699: static DistMap *createDistMap(const _Graph& graph) {
deba@1699: return new DistMap(graph);
deba@1699: }
deba@1699:
deba@1699: };
deba@1699:
deba@1864: /// \brief %BellmanFord algorithm class.
deba@1699: ///
deba@1699: /// \ingroup flowalgs
deba@1864: /// This class provides an efficient implementation of \c Bellman-Ford
deba@1699: /// algorithm. The edge lengths are passed to the algorithm using a
deba@1699: /// \ref concept::ReadMap "ReadMap", so it is easy to change it to any
deba@1699: /// kind of length.
deba@1699: ///
deba@1864: /// The Bellman-Ford algorithm solves the shortest path from one node
deba@1723: /// problem when the edges can have negative length but the graph should
deba@1754: /// not contain cycles with negative sum of length. If we can assume
deba@1723: /// that all edge is non-negative in the graph then the dijkstra algorithm
deba@1723: /// should be used rather.
deba@1723: ///
deba@2042: /// The maximal time complexity of the algorithm is \f$ O(ne) \f$.
deba@1723: ///
deba@1699: /// The type of the length is determined by the
deba@1699: /// \ref concept::ReadMap::Value "Value" of the length map.
deba@1699: ///
deba@1699: /// \param _Graph The graph type the algorithm runs on. The default value
deba@1699: /// is \ref ListGraph. The value of _Graph is not used directly by
deba@1864: /// BellmanFord, it is only passed to \ref BellmanFordDefaultTraits.
deba@1699: /// \param _LengthMap This read-only EdgeMap determines the lengths of the
deba@1699: /// edges. The default map type is \ref concept::StaticGraph::EdgeMap
deba@1699: /// "Graph::EdgeMap<int>". The value of _LengthMap is not used directly
deba@1864: /// by BellmanFord, it is only passed to \ref BellmanFordDefaultTraits.
deba@1699: /// \param _Traits Traits class to set various data types used by the
deba@1864: /// algorithm. The default traits class is \ref BellmanFordDefaultTraits
deba@1864: /// "BellmanFordDefaultTraits<_Graph,_LengthMap>". See \ref
deba@1864: /// BellmanFordDefaultTraits for the documentation of a BellmanFord traits
deba@1699: /// class.
deba@1699: ///
deba@1699: /// \author Balazs Dezso
deba@1699:
deba@1710: #ifdef DOXYGEN
deba@1710: template <typename _Graph, typename _LengthMap, typename _Traits>
deba@1710: #else
deba@1699: template <typename _Graph=ListGraph,
deba@1699: typename _LengthMap=typename _Graph::template EdgeMap<int>,
deba@1864: typename _Traits=BellmanFordDefaultTraits<_Graph,_LengthMap> >
deba@1710: #endif
deba@1864: class BellmanFord {
deba@1699: public:
deba@1699:
deba@1699: /// \brief \ref Exception for uninitialized parameters.
deba@1699: ///
deba@1699: /// This error represents problems in the initialization
deba@1699: /// of the parameters of the algorithms.
deba@1699:
deba@1699: class UninitializedParameter : public lemon::UninitializedParameter {
deba@1699: public:
deba@1699: virtual const char* exceptionName() const {
deba@1864: return "lemon::BellmanFord::UninitializedParameter";
deba@1699: }
deba@1699: };
deba@1699:
deba@1699: typedef _Traits Traits;
deba@1699: ///The type of the underlying graph.
deba@1699: typedef typename _Traits::Graph Graph;
deba@1699:
deba@1699: typedef typename Graph::Node Node;
deba@1699: typedef typename Graph::NodeIt NodeIt;
deba@1699: typedef typename Graph::Edge Edge;
deba@1781: typedef typename Graph::OutEdgeIt OutEdgeIt;
deba@1699:
deba@1699: /// \brief The type of the length of the edges.
deba@1699: typedef typename _Traits::LengthMap::Value Value;
deba@1699: /// \brief The type of the map that stores the edge lengths.
deba@1699: typedef typename _Traits::LengthMap LengthMap;
deba@1699: /// \brief The type of the map that stores the last
deba@1699: /// edges of the shortest paths.
deba@1699: typedef typename _Traits::PredMap PredMap;
deba@1699: /// \brief The type of the map that stores the dists of the nodes.
deba@1699: typedef typename _Traits::DistMap DistMap;
deba@1699: /// \brief The operation traits.
deba@1699: typedef typename _Traits::OperationTraits OperationTraits;
deba@1699: private:
deba@1699: /// Pointer to the underlying graph.
deba@1699: const Graph *graph;
deba@1699: /// Pointer to the length map
deba@1699: const LengthMap *length;
deba@1699: ///Pointer to the map of predecessors edges.
deba@1699: PredMap *_pred;
deba@1699: ///Indicates if \ref _pred is locally allocated (\c true) or not.
deba@1699: bool local_pred;
deba@1699: ///Pointer to the map of distances.
deba@1699: DistMap *_dist;
deba@1699: ///Indicates if \ref _dist is locally allocated (\c true) or not.
deba@1699: bool local_dist;
deba@1699:
deba@1781: typedef typename Graph::template NodeMap<bool> MaskMap;
deba@1781: MaskMap *_mask;
deba@1781:
deba@1781: std::vector<Node> _process;
deba@1781:
deba@1699: /// Creates the maps if necessary.
deba@1699: void create_maps() {
deba@1699: if(!_pred) {
deba@1699: local_pred = true;
deba@1699: _pred = Traits::createPredMap(*graph);
deba@1699: }
deba@1699: if(!_dist) {
deba@1699: local_dist = true;
deba@1699: _dist = Traits::createDistMap(*graph);
deba@1699: }
deba@1781: _mask = new MaskMap(*graph, false);
deba@1699: }
deba@1699:
deba@1699: public :
deba@1699:
deba@1864: typedef BellmanFord Create;
deba@1710:
deba@1699: /// \name Named template parameters
deba@1699:
deba@1699: ///@{
deba@1699:
deba@1699: template <class T>
deba@1699: struct DefPredMapTraits : public Traits {
deba@1699: typedef T PredMap;
deba@1710: static PredMap *createPredMap(const Graph&) {
deba@1699: throw UninitializedParameter();
deba@1699: }
deba@1699: };
deba@1699:
deba@1699: /// \brief \ref named-templ-param "Named parameter" for setting PredMap
deba@1699: /// type
deba@1699: /// \ref named-templ-param "Named parameter" for setting PredMap type
deba@1699: ///
deba@1699: template <class T>
deba@1858: struct DefPredMap
deba@1864: : public BellmanFord< Graph, LengthMap, DefPredMapTraits<T> > {
deba@1864: typedef BellmanFord< Graph, LengthMap, DefPredMapTraits<T> > Create;
deba@1710: };
deba@1699:
deba@1699: template <class T>
deba@1699: struct DefDistMapTraits : public Traits {
deba@1699: typedef T DistMap;
klao@2010: static DistMap *createDistMap(const Graph&) {
deba@1699: throw UninitializedParameter();
deba@1699: }
deba@1699: };
deba@1699:
deba@1699: /// \brief \ref named-templ-param "Named parameter" for setting DistMap
deba@1699: /// type
deba@1699: ///
deba@1699: /// \ref named-templ-param "Named parameter" for setting DistMap type
deba@1699: ///
deba@1699: template <class T>
deba@1710: struct DefDistMap
deba@1864: : public BellmanFord< Graph, LengthMap, DefDistMapTraits<T> > {
deba@1864: typedef BellmanFord< Graph, LengthMap, DefDistMapTraits<T> > Create;
deba@1710: };
deba@1699:
deba@1699: template <class T>
deba@1699: struct DefOperationTraitsTraits : public Traits {
deba@1699: typedef T OperationTraits;
deba@1699: };
deba@1699:
deba@1699: /// \brief \ref named-templ-param "Named parameter" for setting
deba@1699: /// OperationTraits type
deba@1699: ///
deba@1710: /// \ref named-templ-param "Named parameter" for setting OperationTraits
deba@1710: /// type
deba@1699: template <class T>
deba@1710: struct DefOperationTraits
deba@1864: : public BellmanFord< Graph, LengthMap, DefOperationTraitsTraits<T> > {
deba@1864: typedef BellmanFord< Graph, LengthMap, DefOperationTraitsTraits<T> >
deba@1710: Create;
deba@1699: };
deba@1699:
deba@1699: ///@}
deba@1699:
deba@1710: protected:
deba@1710:
deba@1864: BellmanFord() {}
deba@1710:
deba@1699: public:
deba@1699:
deba@1699: /// \brief Constructor.
deba@1699: ///
deba@1699: /// \param _graph the graph the algorithm will run on.
deba@1699: /// \param _length the length map used by the algorithm.
deba@1864: BellmanFord(const Graph& _graph, const LengthMap& _length) :
deba@1699: graph(&_graph), length(&_length),
deba@1699: _pred(0), local_pred(false),
deba@2074: _dist(0), local_dist(false), _mask(0) {}
deba@1699:
deba@1699: ///Destructor.
deba@1864: ~BellmanFord() {
deba@1699: if(local_pred) delete _pred;
deba@1699: if(local_dist) delete _dist;
deba@2074: if(_mask) delete _mask;
deba@1699: }
deba@1699:
deba@1699: /// \brief Sets the length map.
deba@1699: ///
deba@1699: /// Sets the length map.
deba@1699: /// \return \c (*this)
deba@1864: BellmanFord &lengthMap(const LengthMap &m) {
deba@1699: length = &m;
deba@1699: return *this;
deba@1699: }
deba@1699:
deba@1699: /// \brief Sets the map storing the predecessor edges.
deba@1699: ///
deba@1699: /// Sets the map storing the predecessor edges.
deba@1699: /// If you don't use this function before calling \ref run(),
deba@1699: /// it will allocate one. The destuctor deallocates this
deba@1699: /// automatically allocated map, of course.
deba@1699: /// \return \c (*this)
deba@1864: BellmanFord &predMap(PredMap &m) {
deba@1699: if(local_pred) {
deba@1699: delete _pred;
deba@1699: local_pred=false;
deba@1699: }
deba@1699: _pred = &m;
deba@1699: return *this;
deba@1699: }
deba@1699:
deba@1699: /// \brief Sets the map storing the distances calculated by the algorithm.
deba@1699: ///
deba@1699: /// Sets the map storing the distances calculated by the algorithm.
deba@1699: /// If you don't use this function before calling \ref run(),
deba@1699: /// it will allocate one. The destuctor deallocates this
deba@1699: /// automatically allocated map, of course.
deba@1699: /// \return \c (*this)
deba@1864: BellmanFord &distMap(DistMap &m) {
deba@1699: if(local_dist) {
deba@1699: delete _dist;
deba@1699: local_dist=false;
deba@1699: }
deba@1699: _dist = &m;
deba@1699: return *this;
deba@1699: }
deba@1699:
deba@1699: /// \name Execution control
deba@1699: /// The simplest way to execute the algorithm is to use
deba@1699: /// one of the member functions called \c run(...).
deba@1699: /// \n
deba@1699: /// If you need more control on the execution,
deba@1699: /// first you must call \ref init(), then you can add several source nodes
deba@1699: /// with \ref addSource().
deba@1699: /// Finally \ref start() will perform the actual path
deba@1699: /// computation.
deba@1699:
deba@1699: ///@{
deba@1699:
deba@1699: /// \brief Initializes the internal data structures.
deba@1699: ///
deba@1699: /// Initializes the internal data structures.
deba@1710: void init(const Value value = OperationTraits::infinity()) {
deba@1699: create_maps();
deba@1699: for (NodeIt it(*graph); it != INVALID; ++it) {
deba@1699: _pred->set(it, INVALID);
deba@1710: _dist->set(it, value);
deba@1699: }
deba@1781: _process.clear();
deba@1781: if (OperationTraits::less(value, OperationTraits::infinity())) {
deba@1781: for (NodeIt it(*graph); it != INVALID; ++it) {
deba@1781: _process.push_back(it);
deba@1783: _mask->set(it, true);
deba@1781: }
deba@1781: }
deba@1699: }
deba@1699:
deba@1699: /// \brief Adds a new source node.
deba@1699: ///
deba@1699: /// The optional second parameter is the initial distance of the node.
deba@1699: /// It just sets the distance of the node to the given value.
deba@1699: void addSource(Node source, Value dst = OperationTraits::zero()) {
deba@1699: _dist->set(source, dst);
deba@1781: if (!(*_mask)[source]) {
deba@1781: _process.push_back(source);
deba@1781: _mask->set(source, true);
deba@1781: }
deba@1781: }
deba@1781:
deba@1864: /// \brief Executes one round from the bellman ford algorithm.
deba@1781: ///
deba@2059: /// If the algoritm calculated the distances in the previous round
deba@2059: /// exactly for all at most \f$ k \f$ length path lengths then it will
deba@2059: /// calculate the distances exactly for all at most \f$ k + 1 \f$
deba@2059: /// length path lengths. With \f$ k \f$ iteration this function
deba@2059: /// calculates the at most \f$ k \f$ length path lengths.
deba@2059: ///
deba@2059: /// \warning The paths with limited edge number cannot be retrieved
deba@2059: /// easily with \ref getPath() or \ref predEdge() functions. If you
deba@2059: /// need the shortest path and not just the distance you should store
deba@2059: /// after each iteration the \ref predEdgeMap() map and manually build
deba@2059: /// the path.
deba@2059: ///
deba@2059: /// \return %True when the algorithm have not found more shorter
deba@2059: /// paths.
deba@1781: bool processNextRound() {
deba@1781: for (int i = 0; i < (int)_process.size(); ++i) {
deba@1781: _mask->set(_process[i], false);
deba@1781: }
deba@1781: std::vector<Node> nextProcess;
deba@1781: std::vector<Value> values(_process.size());
deba@1781: for (int i = 0; i < (int)_process.size(); ++i) {
klao@1857: values[i] = (*_dist)[_process[i]];
deba@1781: }
deba@1781: for (int i = 0; i < (int)_process.size(); ++i) {
deba@1781: for (OutEdgeIt it(*graph, _process[i]); it != INVALID; ++it) {
deba@1781: Node target = graph->target(it);
deba@1781: Value relaxed = OperationTraits::plus(values[i], (*length)[it]);
deba@1781: if (OperationTraits::less(relaxed, (*_dist)[target])) {
deba@1781: _pred->set(target, it);
deba@1781: _dist->set(target, relaxed);
deba@1781: if (!(*_mask)[target]) {
deba@1781: _mask->set(target, true);
deba@1781: nextProcess.push_back(target);
deba@1781: }
deba@1781: }
deba@1781: }
deba@1781: }
deba@1781: _process.swap(nextProcess);
deba@1781: return _process.empty();
deba@1781: }
deba@1781:
deba@1864: /// \brief Executes one weak round from the bellman ford algorithm.
deba@1781: ///
deba@1781: /// If the algorithm calculated the distances in the
alpar@1816: /// previous round at least for all at most k length paths then it will
alpar@1816: /// calculate the distances at least for all at most k + 1 length paths.
alpar@1816: /// This function does not make it possible to calculate strictly the
alpar@1816: /// at most k length minimal paths, this is why it is
alpar@1816: /// called just weak round.
deba@1858: /// \return %True when the algorithm have not found more shorter paths.
deba@1781: bool processNextWeakRound() {
deba@1781: for (int i = 0; i < (int)_process.size(); ++i) {
deba@1781: _mask->set(_process[i], false);
deba@1781: }
deba@1781: std::vector<Node> nextProcess;
deba@1781: for (int i = 0; i < (int)_process.size(); ++i) {
deba@1781: for (OutEdgeIt it(*graph, _process[i]); it != INVALID; ++it) {
deba@1781: Node target = graph->target(it);
deba@1781: Value relaxed =
deba@1781: OperationTraits::plus((*_dist)[_process[i]], (*length)[it]);
deba@1781: if (OperationTraits::less(relaxed, (*_dist)[target])) {
deba@1781: _pred->set(target, it);
deba@1781: _dist->set(target, relaxed);
deba@1781: if (!(*_mask)[target]) {
deba@1781: _mask->set(target, true);
deba@1781: nextProcess.push_back(target);
deba@1781: }
deba@1781: }
deba@1781: }
deba@1781: }
deba@1781: _process.swap(nextProcess);
deba@1781: return _process.empty();
deba@1699: }
deba@1699:
deba@1699: /// \brief Executes the algorithm.
deba@1699: ///
deba@1699: /// \pre init() must be called and at least one node should be added
deba@1699: /// with addSource() before using this function.
deba@1699: ///
deba@1864: /// This method runs the %BellmanFord algorithm from the root node(s)
deba@1699: /// in order to compute the shortest path to each node. The algorithm
deba@1699: /// computes
deba@1699: /// - The shortest path tree.
deba@1699: /// - The distance of each node from the root(s).
deba@1699: void start() {
deba@1723: int num = countNodes(*graph) - 1;
deba@1723: for (int i = 0; i < num; ++i) {
deba@1781: if (processNextWeakRound()) break;
deba@1699: }
deba@1699: }
deba@1723:
deba@1754: /// \brief Executes the algorithm and checks the negative cycles.
deba@1723: ///
deba@1723: /// \pre init() must be called and at least one node should be added
deba@1723: /// with addSource() before using this function. If there is
deba@1754: /// a negative cycles in the graph it gives back false.
deba@1723: ///
deba@1864: /// This method runs the %BellmanFord algorithm from the root node(s)
deba@1723: /// in order to compute the shortest path to each node. The algorithm
deba@1723: /// computes
deba@1723: /// - The shortest path tree.
deba@1723: /// - The distance of each node from the root(s).
deba@1723: bool checkedStart() {
deba@1723: int num = countNodes(*graph);
deba@1723: for (int i = 0; i < num; ++i) {
deba@1781: if (processNextWeakRound()) return true;
deba@1723: }
deba@1723: return false;
deba@1723: }
deba@1781:
deba@1781: /// \brief Executes the algorithm with path length limit.
deba@1781: ///
deba@1781: /// \pre init() must be called and at least one node should be added
deba@1781: /// with addSource() before using this function.
deba@1781: ///
deba@2059: /// This method runs the %BellmanFord algorithm from the root
deba@2059: /// node(s) in order to compute the shortest path lengths with at
deba@2059: /// most \c num edge.
deba@2059: ///
deba@2059: /// \warning The paths with limited edge number cannot be retrieved
deba@2059: /// easily with \ref getPath() or \ref predEdge() functions. If you
deba@2059: /// need the shortest path and not just the distance you should store
deba@2059: /// after each iteration the \ref predEdgeMap() map and manually build
deba@2059: /// the path.
deba@2059: ///
deba@2059: /// The algorithm computes
deba@2059: /// - The predecessor edge from each node.
deba@1781: /// - The limited distance of each node from the root(s).
deba@2059: void limitedStart(int num) {
deba@2059: for (int i = 0; i < num; ++i) {
deba@1781: if (processNextRound()) break;
deba@1781: }
deba@1781: }
deba@1699:
deba@1864: /// \brief Runs %BellmanFord algorithm from node \c s.
deba@1699: ///
deba@1864: /// This method runs the %BellmanFord algorithm from a root node \c s
deba@1699: /// in order to compute the shortest path to each node. The algorithm
deba@1699: /// computes
deba@1699: /// - The shortest path tree.
deba@1699: /// - The distance of each node from the root.
deba@1699: ///
deba@1699: /// \note d.run(s) is just a shortcut of the following code.
alpar@1946: ///\code
deba@1699: /// d.init();
deba@1699: /// d.addSource(s);
deba@1699: /// d.start();
alpar@1946: ///\endcode
deba@1699: void run(Node s) {
deba@1699: init();
deba@1699: addSource(s);
deba@1699: start();
deba@1699: }
deba@1699:
deba@1864: /// \brief Runs %BellmanFord algorithm with limited path length
klao@1857: /// from node \c s.
klao@1857: ///
deba@1864: /// This method runs the %BellmanFord algorithm from a root node \c s
klao@1857: /// in order to compute the shortest path with at most \c len edges
klao@1857: /// to each node. The algorithm computes
klao@1857: /// - The shortest path tree.
klao@1857: /// - The distance of each node from the root.
klao@1857: ///
klao@1857: /// \note d.run(s, len) is just a shortcut of the following code.
alpar@1946: ///\code
klao@1857: /// d.init();
klao@1857: /// d.addSource(s);
klao@1857: /// d.limitedStart(len);
alpar@1946: ///\endcode
klao@1857: void run(Node s, int len) {
klao@1857: init();
klao@1857: addSource(s);
klao@1857: limitedStart(len);
klao@1857: }
klao@1857:
deba@1699: ///@}
deba@1699:
deba@1699: /// \name Query Functions
deba@1864: /// The result of the %BellmanFord algorithm can be obtained using these
deba@1699: /// functions.\n
deba@1699: /// Before the use of these functions,
deba@1699: /// either run() or start() must be called.
deba@1699:
deba@1699: ///@{
deba@1699:
deba@2070: /// \brief Lemon iterator for get a active nodes.
deba@2070: ///
deba@2070: /// Lemon iterator for get a active nodes. This class provides a
deba@2070: /// common style lemon iterator which gives back a subset of the
deba@2070: /// nodes. The iterated nodes are active in the algorithm after
deba@2070: /// the last phase so these should be checked in the next phase to
deba@2070: /// find augmenting edges from these.
deba@2070: class ActiveIt {
deba@2070: public:
deba@2070:
deba@2070: /// \brief Constructor.
deba@2070: ///
deba@2070: /// Constructor for get the nodeset of the variable.
deba@2070: ActiveIt(const BellmanFord& algorithm) : _algorithm(&algorithm)
deba@2070: {
deba@2070: _index = _algorithm->_process.size() - 1;
deba@2070: }
deba@2070:
deba@2070: /// \brief Invalid constructor.
deba@2070: ///
deba@2070: /// Invalid constructor.
deba@2070: ActiveIt(Invalid) : _algorithm(0), _index(-1) {}
deba@2070:
deba@2070: /// \brief Conversion to node.
deba@2070: ///
deba@2070: /// Conversion to node.
deba@2070: operator Node() const {
deba@2070: return _index >= 0 ? _algorithm->_process[_index] : INVALID;
deba@2070: }
deba@2070:
deba@2070: /// \brief Increment operator.
deba@2070: ///
deba@2070: /// Increment operator.
deba@2070: ActiveIt& operator++() {
deba@2070: --_index;
deba@2070: return *this;
deba@2070: }
deba@2070:
deba@2070: bool operator==(const ActiveIt& it) const {
deba@2070: return (Node)(*this) == (Node)it;
deba@2070: }
deba@2070: bool operator!=(const ActiveIt& it) const {
deba@2070: return (Node)(*this) != (Node)it;
deba@2070: }
deba@2070: bool operator<(const ActiveIt& it) const {
deba@2070: return (Node)(*this) < (Node)it;
deba@2070: }
deba@2070:
deba@2070: private:
deba@2070: const BellmanFord* _algorithm;
deba@2070: int _index;
deba@2070: };
deba@2070:
deba@1699: /// \brief Copies the shortest path to \c t into \c p
deba@1699: ///
deba@1699: /// This function copies the shortest path to \c t into \c p.
deba@1699: /// If it \c t is a source itself or unreachable, then it does not
deba@1699: /// alter \c p.
deba@1765: ///
deba@1699: /// \return Returns \c true if a path to \c t was actually copied to \c p,
deba@1699: /// \c false otherwise.
deba@1699: /// \sa DirPath
deba@1699: template <typename Path>
deba@1699: bool getPath(Path &p, Node t) {
deba@1699: if(reached(t)) {
deba@1699: p.clear();
deba@1699: typename Path::Builder b(p);
deba@1763: for(b.setStartNode(t);predEdge(t)!=INVALID;t=predNode(t))
deba@1763: b.pushFront(predEdge(t));
deba@1699: b.commit();
deba@1699: return true;
deba@1699: }
deba@1699: return false;
deba@1699: }
deba@2070:
deba@2070: /// \brief Copies a negative cycle into path \c p.
deba@2070: ///
deba@2070: /// This function copies a negative cycle into path \c p.
deba@2070: /// If the algorithm have not found yet negative cycle it will not change
deba@2070: /// the given path and gives back false.
deba@2070: ///
deba@2070: /// \return Returns \c true if a cycle was actually copied to \c p,
deba@2070: /// \c false otherwise.
deba@2070: /// \sa DirPath
deba@2070: template <typename Path>
deba@2070: bool getNegativeCycle(Path& p) {
deba@2070: typename Graph::template NodeMap<int> state(*graph, 0);
deba@2070: for (ActiveIt it(*this); it != INVALID; ++it) {
deba@2070: if (state[it] == 0) {
deba@2070: for (Node t = it; predEdge(t) != INVALID; t = predNode(t)) {
deba@2070: if (state[t] == 0) {
deba@2070: state[t] = 1;
deba@2070: } else if (state[t] == 2) {
deba@2070: break;
deba@2070: } else {
deba@2070: p.clear();
deba@2070: typename Path::Builder b(p);
deba@2070: b.setStartNode(t);
deba@2070: b.pushFront(predEdge(t));
deba@2070: for(Node s = predNode(t); s != t; s = predNode(s)) {
deba@2070: b.pushFront(predEdge(s));
deba@2070: }
deba@2070: b.commit();
deba@2070: return true;
deba@2070: }
deba@2070: }
deba@2070: for (Node t = it; predEdge(t) != INVALID; t = predNode(t)) {
deba@2070: if (state[t] == 1) {
deba@2070: state[t] = 2;
deba@2070: } else {
deba@2070: break;
deba@2070: }
deba@2070: }
deba@2070: }
deba@2070: }
deba@2070: return false;
deba@2070: }
deba@1699:
deba@1699: /// \brief The distance of a node from the root.
deba@1699: ///
deba@1699: /// Returns the distance of a node from the root.
deba@1699: /// \pre \ref run() must be called before using this function.
deba@1699: /// \warning If node \c v in unreachable from the root the return value
deba@1699: /// of this funcion is undefined.
deba@1699: Value dist(Node v) const { return (*_dist)[v]; }
deba@1699:
deba@1699: /// \brief Returns the 'previous edge' of the shortest path tree.
deba@1699: ///
deba@1699: /// For a node \c v it returns the 'previous edge' of the shortest path
deba@1699: /// tree, i.e. it returns the last edge of a shortest path from the root
deba@1699: /// to \c v. It is \ref INVALID if \c v is unreachable from the root or
deba@1699: /// if \c v=s. The shortest path tree used here is equal to the shortest
deba@1699: /// path tree used in \ref predNode().
deba@1699: /// \pre \ref run() must be called before using
deba@1699: /// this function.
deba@1763: Edge predEdge(Node v) const { return (*_pred)[v]; }
deba@1699:
deba@1699: /// \brief Returns the 'previous node' of the shortest path tree.
deba@1699: ///
deba@1699: /// For a node \c v it returns the 'previous node' of the shortest path
deba@1699: /// tree, i.e. it returns the last but one node from a shortest path from
deba@1699: /// the root to \c /v. It is INVALID if \c v is unreachable from the root
deba@1699: /// or if \c v=s. The shortest path tree used here is equal to the
deba@1763: /// shortest path tree used in \ref predEdge(). \pre \ref run() must be
deba@1699: /// called before using this function.
deba@1699: Node predNode(Node v) const {
deba@1699: return (*_pred)[v] == INVALID ? INVALID : graph->source((*_pred)[v]);
deba@1699: }
deba@1699:
deba@1699: /// \brief Returns a reference to the NodeMap of distances.
deba@1699: ///
deba@1699: /// Returns a reference to the NodeMap of distances. \pre \ref run() must
deba@1699: /// be called before using this function.
deba@1699: const DistMap &distMap() const { return *_dist;}
deba@1699:
deba@1699: /// \brief Returns a reference to the shortest path tree map.
deba@1699: ///
deba@1699: /// Returns a reference to the NodeMap of the edges of the
deba@1699: /// shortest path tree.
deba@1699: /// \pre \ref run() must be called before using this function.
deba@1699: const PredMap &predMap() const { return *_pred; }
deba@1699:
deba@1699: /// \brief Checks if a node is reachable from the root.
deba@1699: ///
deba@1699: /// Returns \c true if \c v is reachable from the root.
deba@1699: /// \pre \ref run() must be called before using this function.
deba@1699: ///
deba@1699: bool reached(Node v) { return (*_dist)[v] != OperationTraits::infinity(); }
deba@1699:
deba@1699: ///@}
deba@1699: };
deba@1699:
deba@1864: /// \brief Default traits class of BellmanFord function.
deba@1699: ///
deba@1864: /// Default traits class of BellmanFord function.
deba@1699: /// \param _Graph Graph type.
deba@1699: /// \param _LengthMap Type of length map.
deba@1699: template <typename _Graph, typename _LengthMap>
deba@1864: struct BellmanFordWizardDefaultTraits {
deba@1699: /// \brief The graph type the algorithm runs on.
deba@1699: typedef _Graph Graph;
deba@1699:
deba@1699: /// \brief The type of the map that stores the edge lengths.
deba@1699: ///
deba@1699: /// The type of the map that stores the edge lengths.
deba@1699: /// It must meet the \ref concept::ReadMap "ReadMap" concept.
deba@1699: typedef _LengthMap LengthMap;
deba@1699:
deba@1699: /// \brief The value type of the length map.
deba@1699: typedef typename _LengthMap::Value Value;
deba@1699:
deba@1864: /// \brief Operation traits for bellman-ford algorithm.
deba@1699: ///
deba@1699: /// It defines the infinity type on the given Value type
deba@1699: /// and the used operation.
deba@1864: /// \see BellmanFordDefaultOperationTraits
deba@1864: typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
deba@1699:
deba@1699: /// \brief The type of the map that stores the last
deba@1699: /// edges of the shortest paths.
deba@1699: ///
deba@1699: /// The type of the map that stores the last
deba@1699: /// edges of the shortest paths.
deba@1699: /// It must meet the \ref concept::WriteMap "WriteMap" concept.
deba@1699: typedef NullMap <typename _Graph::Node,typename _Graph::Edge> PredMap;
deba@1699:
deba@1699: /// \brief Instantiates a PredMap.
deba@1699: ///
deba@1699: /// This function instantiates a \ref PredMap.
deba@1699: static PredMap *createPredMap(const _Graph &) {
deba@1699: return new PredMap();
deba@1699: }
deba@1699: /// \brief The type of the map that stores the dists of the nodes.
deba@1699: ///
deba@1699: /// The type of the map that stores the dists of the nodes.
deba@1699: /// It must meet the \ref concept::WriteMap "WriteMap" concept.
deba@1699: typedef NullMap<typename Graph::Node, Value> DistMap;
deba@1699: /// \brief Instantiates a DistMap.
deba@1699: ///
deba@1699: /// This function instantiates a \ref DistMap.
deba@1699: static DistMap *createDistMap(const _Graph &) {
deba@1699: return new DistMap();
deba@1699: }
deba@1699: };
deba@1699:
deba@1864: /// \brief Default traits used by \ref BellmanFordWizard
deba@1699: ///
deba@1864: /// To make it easier to use BellmanFord algorithm
deba@1699: /// we have created a wizard class.
deba@1864: /// This \ref BellmanFordWizard class needs default traits,
deba@1864: /// as well as the \ref BellmanFord class.
deba@1864: /// The \ref BellmanFordWizardBase is a class to be the default traits of the
deba@1864: /// \ref BellmanFordWizard class.
deba@1699: /// \todo More named parameters are required...
deba@1699: template<class _Graph,class _LengthMap>
deba@1864: class BellmanFordWizardBase
deba@1864: : public BellmanFordWizardDefaultTraits<_Graph,_LengthMap> {
deba@1699:
deba@1864: typedef BellmanFordWizardDefaultTraits<_Graph,_LengthMap> Base;
deba@1699: protected:
deba@1699: /// Type of the nodes in the graph.
deba@1699: typedef typename Base::Graph::Node Node;
deba@1699:
deba@1699: /// Pointer to the underlying graph.
deba@1699: void *_graph;
deba@1699: /// Pointer to the length map
deba@1699: void *_length;
deba@1699: ///Pointer to the map of predecessors edges.
deba@1699: void *_pred;
deba@1699: ///Pointer to the map of distances.
deba@1699: void *_dist;
deba@1699: ///Pointer to the source node.
deba@1699: Node _source;
deba@1699:
deba@1699: public:
deba@1699: /// Constructor.
deba@1699:
deba@1699: /// This constructor does not require parameters, therefore it initiates
deba@1699: /// all of the attributes to default values (0, INVALID).
deba@1864: BellmanFordWizardBase() : _graph(0), _length(0), _pred(0),
deba@1699: _dist(0), _source(INVALID) {}
deba@1699:
deba@1699: /// Constructor.
deba@1699:
deba@1699: /// This constructor requires some parameters,
deba@1699: /// listed in the parameters list.
deba@1699: /// Others are initiated to 0.
deba@1699: /// \param graph is the initial value of \ref _graph
deba@1699: /// \param length is the initial value of \ref _length
deba@1699: /// \param source is the initial value of \ref _source
deba@1864: BellmanFordWizardBase(const _Graph& graph,
deba@1699: const _LengthMap& length,
deba@1699: Node source = INVALID) :
deba@1699: _graph((void *)&graph), _length((void *)&length), _pred(0),
deba@1699: _dist(0), _source(source) {}
deba@1699:
deba@1699: };
deba@1699:
deba@1864: /// A class to make the usage of BellmanFord algorithm easier
deba@1699:
deba@1864: /// This class is created to make it easier to use BellmanFord algorithm.
deba@1864: /// It uses the functions and features of the plain \ref BellmanFord,
deba@1699: /// but it is much simpler to use it.
deba@1699: ///
deba@1699: /// Simplicity means that the way to change the types defined
deba@1699: /// in the traits class is based on functions that returns the new class
deba@1699: /// and not on templatable built-in classes.
deba@1864: /// When using the plain \ref BellmanFord
deba@1699: /// the new class with the modified type comes from
deba@1699: /// the original class by using the ::
deba@1864: /// operator. In the case of \ref BellmanFordWizard only
deba@1699: /// a function have to be called and it will
deba@1699: /// return the needed class.
deba@1699: ///
deba@1699: /// It does not have own \ref run method. When its \ref run method is called
deba@1864: /// it initiates a plain \ref BellmanFord class, and calls the \ref
deba@1864: /// BellmanFord::run method of it.
deba@1699: template<class _Traits>
deba@1864: class BellmanFordWizard : public _Traits {
deba@1699: typedef _Traits Base;
deba@1699:
deba@1699: ///The type of the underlying graph.
deba@1699: typedef typename _Traits::Graph Graph;
deba@1699:
deba@1699: typedef typename Graph::Node Node;
deba@1699: typedef typename Graph::NodeIt NodeIt;
deba@1699: typedef typename Graph::Edge Edge;
deba@1699: typedef typename Graph::OutEdgeIt EdgeIt;
deba@1699:
deba@1699: ///The type of the map that stores the edge lengths.
deba@1699: typedef typename _Traits::LengthMap LengthMap;
deba@1699:
deba@1699: ///The type of the length of the edges.
deba@1699: typedef typename LengthMap::Value Value;
deba@1699:
deba@1699: ///\brief The type of the map that stores the last
deba@1699: ///edges of the shortest paths.
deba@1699: typedef typename _Traits::PredMap PredMap;
deba@1699:
deba@1699: ///The type of the map that stores the dists of the nodes.
deba@1699: typedef typename _Traits::DistMap DistMap;
deba@1699:
deba@1699: public:
deba@1699: /// Constructor.
deba@1864: BellmanFordWizard() : _Traits() {}
deba@1699:
deba@1699: /// \brief Constructor that requires parameters.
deba@1699: ///
deba@1699: /// Constructor that requires parameters.
deba@1699: /// These parameters will be the default values for the traits class.
deba@1864: BellmanFordWizard(const Graph& graph, const LengthMap& length,
deba@1699: Node source = INVALID)
deba@1699: : _Traits(graph, length, source) {}
deba@1699:
deba@1699: /// \brief Copy constructor
deba@1864: BellmanFordWizard(const _Traits &b) : _Traits(b) {}
deba@1699:
deba@1864: ~BellmanFordWizard() {}
deba@1699:
deba@1864: /// \brief Runs BellmanFord algorithm from a given node.
deba@1699: ///
deba@1864: /// Runs BellmanFord algorithm from a given node.
deba@1699: /// The node can be given by the \ref source function.
deba@1699: void run() {
deba@1699: if(Base::_source == INVALID) throw UninitializedParameter();
deba@1864: BellmanFord<Graph,LengthMap,_Traits>
deba@1699: bf(*(Graph*)Base::_graph, *(LengthMap*)Base::_length);
deba@1699: if (Base::_pred) bf.predMap(*(PredMap*)Base::_pred);
deba@1699: if (Base::_dist) bf.distMap(*(DistMap*)Base::_dist);
deba@1699: bf.run(Base::_source);
deba@1699: }
deba@1699:
deba@1864: /// \brief Runs BellmanFord algorithm from the given node.
deba@1699: ///
deba@1864: /// Runs BellmanFord algorithm from the given node.
deba@1858: /// \param source is the given source.
deba@1699: void run(Node source) {
deba@1699: Base::_source = source;
deba@1699: run();
deba@1699: }
deba@1699:
deba@1699: template<class T>
deba@1699: struct DefPredMapBase : public Base {
deba@1699: typedef T PredMap;
deba@1699: static PredMap *createPredMap(const Graph &) { return 0; };
deba@1699: DefPredMapBase(const _Traits &b) : _Traits(b) {}
deba@1699: };
deba@1699:
deba@1699: ///\brief \ref named-templ-param "Named parameter"
deba@1699: ///function for setting PredMap type
deba@1699: ///
deba@1699: /// \ref named-templ-param "Named parameter"
deba@1699: ///function for setting PredMap type
deba@1699: ///
deba@1699: template<class T>
deba@1864: BellmanFordWizard<DefPredMapBase<T> > predMap(const T &t)
deba@1699: {
deba@1699: Base::_pred=(void *)&t;
deba@1864: return BellmanFordWizard<DefPredMapBase<T> >(*this);
deba@1699: }
deba@1699:
deba@1699: template<class T>
deba@1699: struct DefDistMapBase : public Base {
deba@1699: typedef T DistMap;
deba@1699: static DistMap *createDistMap(const Graph &) { return 0; };
deba@1699: DefDistMapBase(const _Traits &b) : _Traits(b) {}
deba@1699: };
deba@1699:
deba@1699: ///\brief \ref named-templ-param "Named parameter"
deba@1699: ///function for setting DistMap type
deba@1699: ///
deba@1699: /// \ref named-templ-param "Named parameter"
deba@1699: ///function for setting DistMap type
deba@1699: ///
deba@1699: template<class T>
deba@1864: BellmanFordWizard<DefDistMapBase<T> > distMap(const T &t) {
deba@1699: Base::_dist=(void *)&t;
deba@1864: return BellmanFordWizard<DefDistMapBase<T> >(*this);
deba@1699: }
deba@1710:
deba@1710: template<class T>
deba@1710: struct DefOperationTraitsBase : public Base {
deba@1710: typedef T OperationTraits;
deba@1710: DefOperationTraitsBase(const _Traits &b) : _Traits(b) {}
deba@1710: };
deba@1710:
deba@1710: ///\brief \ref named-templ-param "Named parameter"
deba@1710: ///function for setting OperationTraits type
deba@1710: ///
deba@1710: /// \ref named-templ-param "Named parameter"
deba@1710: ///function for setting OperationTraits type
deba@1710: ///
deba@1710: template<class T>
deba@1864: BellmanFordWizard<DefOperationTraitsBase<T> > distMap() {
deba@1864: return BellmanFordWizard<DefDistMapBase<T> >(*this);
deba@1710: }
deba@1699:
deba@1864: /// \brief Sets the source node, from which the BellmanFord algorithm runs.
deba@1699: ///
deba@1864: /// Sets the source node, from which the BellmanFord algorithm runs.
deba@1858: /// \param source is the source node.
deba@1864: BellmanFordWizard<_Traits>& source(Node source) {
deba@1699: Base::_source = source;
deba@1699: return *this;
deba@1699: }
deba@1699:
deba@1699: };
deba@1699:
deba@1864: /// \brief Function type interface for BellmanFord algorithm.
deba@1699: ///
deba@1699: /// \ingroup flowalgs
deba@1864: /// Function type interface for BellmanFord algorithm.
deba@1699: ///
deba@1699: /// This function also has several \ref named-templ-func-param
deba@1699: /// "named parameters", they are declared as the members of class
deba@1864: /// \ref BellmanFordWizard.
deba@1699: /// The following
deba@1699: /// example shows how to use these parameters.
alpar@1946: ///\code
deba@1864: /// bellmanford(g,length,source).predMap(preds).run();
alpar@1946: ///\endcode
deba@1864: /// \warning Don't forget to put the \ref BellmanFordWizard::run() "run()"
deba@1699: /// to the end of the parameter list.
deba@1864: /// \sa BellmanFordWizard
deba@1864: /// \sa BellmanFord
deba@1699: template<class _Graph, class _LengthMap>
deba@1864: BellmanFordWizard<BellmanFordWizardBase<_Graph,_LengthMap> >
deba@1864: bellmanFord(const _Graph& graph,
deba@1699: const _LengthMap& length,
deba@1699: typename _Graph::Node source = INVALID) {
deba@1864: return BellmanFordWizard<BellmanFordWizardBase<_Graph,_LengthMap> >
deba@1699: (graph, length, source);
deba@1699: }
deba@1699:
deba@1699: } //END OF NAMESPACE LEMON
deba@1699:
deba@1699: #endif
deba@1699: