# HG changeset patch
# User Peter Kovacs <kpeter@inf.elte.hu>
# Date 1248470383 -7200
# Node ID c9b9da1a90a022b261c4cc379373efba6256bc85
# Parent 9f529abcaebf13f19e61ba24fdd2c3631860af91
Port Bellman-Ford algorithm from SVN -r3524 (#51)
diff -r 9f529abcaebf -r c9b9da1a90a0 lemon/Makefile.am
--- a/lemon/Makefile.am Thu Jun 11 23:13:24 2009 +0200
+++ b/lemon/Makefile.am Fri Jul 24 23:19:43 2009 +0200
@@ -57,6 +57,7 @@
lemon/adaptors.h \
lemon/arg_parser.h \
lemon/assert.h \
+ lemon/bellman_ford.h \
lemon/bfs.h \
lemon/bin_heap.h \
lemon/bucket_heap.h \
diff -r 9f529abcaebf -r c9b9da1a90a0 lemon/bellman_ford.h
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/bellman_ford.h Fri Jul 24 23:19:43 2009 +0200
@@ -0,0 +1,1042 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2008
+ * 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_BELMANN_FORD_H
+#define LEMON_BELMANN_FORD_H
+
+/// \ingroup shortest_path
+/// \file
+/// \brief Bellman-Ford algorithm.
+///
+
+#include <lemon/bits/path_dump.h>
+#include <lemon/core.h>
+#include <lemon/error.h>
+#include <lemon/maps.h>
+
+#include <limits>
+
+namespace lemon {
+
+ /// \brief Default OperationTraits for the BellmanFord algorithm class.
+ ///
+ /// It defines all computational operations and constants which are
+ /// used in the Bellman-Ford 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 BellmanFordDefaultOperationTraits {
+ /// \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 BellmanFordDefaultOperationTraits<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 BellmanFord class.
+ ///
+ /// Default traits class of BellmanFord class.
+ /// \param _Digraph Digraph type.
+ /// \param _LegthMap Type of length map.
+ template<class _Digraph, class _LengthMap>
+ struct BellmanFordDefaultTraits {
+ /// The digraph type the algorithm runs on.
+ typedef _Digraph Digraph;
+
+ /// \brief The type of the map that stores the arc lengths.
+ ///
+ /// The type of the map that stores the arc lengths.
+ /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
+ typedef _LengthMap LengthMap;
+
+ // The type of the length of the arcs.
+ typedef typename _LengthMap::Value Value;
+
+ /// \brief Operation traits for Bellman-Ford algorithm.
+ ///
+ /// It defines the infinity type on the given Value type
+ /// and the used operation.
+ /// \see BellmanFordDefaultOperationTraits
+ typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
+
+ /// \brief The type of the map that stores the last arcs of the
+ /// shortest paths.
+ ///
+ /// The type of the map that stores the last
+ /// arcs of the shortest paths.
+ /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
+ ///
+ typedef typename Digraph::template NodeMap<typename _Digraph::Arc> PredMap;
+
+ /// \brief Instantiates a PredMap.
+ ///
+ /// This function instantiates a \ref PredMap.
+ /// \param digraph is the digraph, to which we would like to define the PredMap.
+ static PredMap *createPredMap(const _Digraph& digraph) {
+ return new PredMap(digraph);
+ }
+
+ /// \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 concepts::WriteMap "WriteMap" concept.
+ ///
+ typedef typename Digraph::template NodeMap<typename _LengthMap::Value>
+ DistMap;
+
+ /// \brief Instantiates a DistMap.
+ ///
+ /// This function instantiates a \ref DistMap.
+ /// \param digraph is the digraph, to which we would like to define the
+ /// \ref DistMap
+ static DistMap *createDistMap(const _Digraph& digraph) {
+ return new DistMap(digraph);
+ }
+
+ };
+
+ /// \brief %BellmanFord algorithm class.
+ ///
+ /// \ingroup shortest_path
+ /// This class provides an efficient implementation of \c Bellman-Ford
+ /// algorithm. The arc lengths are passed to the algorithm using a
+ /// \ref concepts::ReadMap "ReadMap", so it is easy to change it to any
+ /// kind of length.
+ ///
+ /// The Bellman-Ford algorithm solves the shortest path from one node
+ /// problem when the arcs can have negative length but the digraph should
+ /// not contain cycles with negative sum of length. If we can assume
+ /// that all arc is non-negative in the digraph then the dijkstra algorithm
+ /// should be used rather.
+ ///
+ /// The maximal time complexity of the algorithm is \f$ O(ne) \f$.
+ ///
+ /// The type of the length is determined by the
+ /// \ref concepts::ReadMap::Value "Value" of the length map.
+ ///
+ /// \param _Digraph The digraph type the algorithm runs on. The default value
+ /// is \ref ListDigraph. The value of _Digraph is not used directly by
+ /// BellmanFord, it is only passed to \ref BellmanFordDefaultTraits.
+ /// \param _LengthMap This read-only ArcMap determines the lengths of the
+ /// arcs. The default map type is \ref concepts::Digraph::ArcMap
+ /// "Digraph::ArcMap<int>". The value of _LengthMap is not used directly
+ /// by BellmanFord, it is only passed to \ref BellmanFordDefaultTraits.
+ /// \param _Traits Traits class to set various data types used by the
+ /// algorithm. The default traits class is \ref BellmanFordDefaultTraits
+ /// "BellmanFordDefaultTraits<_Digraph,_LengthMap>". See \ref
+ /// BellmanFordDefaultTraits for the documentation of a BellmanFord traits
+ /// class.
+#ifdef DOXYGEN
+ template <typename _Digraph, typename _LengthMap, typename _Traits>
+#else
+ template <typename _Digraph,
+ typename _LengthMap=typename _Digraph::template ArcMap<int>,
+ typename _Traits=BellmanFordDefaultTraits<_Digraph,_LengthMap> >
+#endif
+ class BellmanFord {
+ public:
+
+ typedef _Traits Traits;
+ ///The type of the underlying digraph.
+ typedef typename _Traits::Digraph Digraph;
+
+ typedef typename Digraph::Node Node;
+ typedef typename Digraph::NodeIt NodeIt;
+ typedef typename Digraph::Arc Arc;
+ typedef typename Digraph::OutArcIt OutArcIt;
+
+ /// \brief The type of the length of the arcs.
+ typedef typename _Traits::LengthMap::Value Value;
+ /// \brief The type of the map that stores the arc lengths.
+ typedef typename _Traits::LengthMap LengthMap;
+ /// \brief The type of the map that stores the last
+ /// arcs of the shortest paths.
+ typedef typename _Traits::PredMap PredMap;
+ /// \brief The type of the map that stores the dists of the nodes.
+ typedef typename _Traits::DistMap DistMap;
+ /// \brief The operation traits.
+ typedef typename _Traits::OperationTraits OperationTraits;
+ private:
+ /// Pointer to the underlying digraph.
+ const Digraph *digraph;
+ /// Pointer to the length map
+ const LengthMap *length;
+ ///Pointer to the map of predecessors arcs.
+ 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;
+
+ typedef typename Digraph::template NodeMap<bool> MaskMap;
+ MaskMap *_mask;
+
+ std::vector<Node> _process;
+
+ /// Creates the maps if necessary.
+ void create_maps() {
+ if(!_pred) {
+ local_pred = true;
+ _pred = Traits::createPredMap(*digraph);
+ }
+ if(!_dist) {
+ local_dist = true;
+ _dist = Traits::createDistMap(*digraph);
+ }
+ _mask = new MaskMap(*digraph, false);
+ }
+
+ public :
+
+ typedef BellmanFord Create;
+
+ /// \name Named template parameters
+
+ ///@{
+
+ template <class T>
+ struct DefPredMapTraits : public Traits {
+ typedef T PredMap;
+ static PredMap *createPredMap(const Digraph&) {
+ LEMON_ASSERT(false, "PredMap is not initialized");
+ return 0; // ignore warnings
+ }
+ };
+
+ /// \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 SetPredMap
+ : public BellmanFord< Digraph, LengthMap, DefPredMapTraits<T> > {
+ typedef BellmanFord< Digraph, LengthMap, DefPredMapTraits<T> > Create;
+ };
+
+ template <class T>
+ struct DefDistMapTraits : public Traits {
+ typedef T DistMap;
+ static DistMap *createDistMap(const Digraph&) {
+ LEMON_ASSERT(false, "DistMap is not initialized");
+ return 0; // ignore warnings
+ }
+ };
+
+ /// \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 SetDistMap
+ : public BellmanFord< Digraph, LengthMap, DefDistMapTraits<T> > {
+ typedef BellmanFord< Digraph, LengthMap, DefDistMapTraits<T> > Create;
+ };
+
+ template <class T>
+ struct DefOperationTraitsTraits : public Traits {
+ typedef T OperationTraits;
+ };
+
+ /// \brief \ref named-templ-param "Named parameter" for setting
+ /// OperationTraits type
+ ///
+ /// \ref named-templ-param "Named parameter" for setting OperationTraits
+ /// type
+ template <class T>
+ struct SetOperationTraits
+ : public BellmanFord< Digraph, LengthMap, DefOperationTraitsTraits<T> > {
+ typedef BellmanFord< Digraph, LengthMap, DefOperationTraitsTraits<T> >
+ Create;
+ };
+
+ ///@}
+
+ protected:
+
+ BellmanFord() {}
+
+ public:
+
+ /// \brief Constructor.
+ ///
+ /// \param _graph the digraph the algorithm will run on.
+ /// \param _length the length map used by the algorithm.
+ BellmanFord(const Digraph& _graph, const LengthMap& _length) :
+ digraph(&_graph), length(&_length),
+ _pred(0), local_pred(false),
+ _dist(0), local_dist(false), _mask(0) {}
+
+ ///Destructor.
+ ~BellmanFord() {
+ if(local_pred) delete _pred;
+ if(local_dist) delete _dist;
+ if(_mask) delete _mask;
+ }
+
+ /// \brief Sets the length map.
+ ///
+ /// Sets the length map.
+ /// \return \c (*this)
+ BellmanFord &lengthMap(const LengthMap &m) {
+ length = &m;
+ return *this;
+ }
+
+ /// \brief Sets the map storing the predecessor arcs.
+ ///
+ /// Sets the map storing the predecessor arcs.
+ /// 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)
+ BellmanFord &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)
+ BellmanFord &distMap(DistMap &m) {
+ if(local_dist) {
+ delete _dist;
+ local_dist=false;
+ }
+ _dist = &m;
+ return *this;
+ }
+
+ /// \name Execution control
+ /// The simplest way to execute the algorithm is to use
+ /// one of the member functions called \c run(...).
+ /// \n
+ /// If you need more control on the execution,
+ /// first you must call \ref init(), then you can add several source nodes
+ /// with \ref addSource().
+ /// Finally \ref start() will perform the actual path
+ /// computation.
+
+ ///@{
+
+ /// \brief Initializes the internal data structures.
+ ///
+ /// Initializes the internal data structures.
+ void init(const Value value = OperationTraits::infinity()) {
+ create_maps();
+ for (NodeIt it(*digraph); it != INVALID; ++it) {
+ _pred->set(it, INVALID);
+ _dist->set(it, value);
+ }
+ _process.clear();
+ if (OperationTraits::less(value, OperationTraits::infinity())) {
+ for (NodeIt it(*digraph); it != INVALID; ++it) {
+ _process.push_back(it);
+ _mask->set(it, true);
+ }
+ }
+ }
+
+ /// \brief Adds a new source node.
+ ///
+ /// Adds a new source node. The optional second parameter is the
+ /// initial distance of the node. It just sets the distance of the
+ /// node to the given value.
+ void addSource(Node source, Value dst = OperationTraits::zero()) {
+ _dist->set(source, dst);
+ if (!(*_mask)[source]) {
+ _process.push_back(source);
+ _mask->set(source, true);
+ }
+ }
+
+ /// \brief Executes one round from the Bellman-Ford algorithm.
+ ///
+ /// If the algoritm calculated the distances in the previous round
+ /// exactly for all at most \f$ k \f$ length path lengths then it will
+ /// calculate the distances exactly for all at most \f$ k + 1 \f$
+ /// length path lengths. With \f$ k \f$ iteration this function
+ /// calculates the at most \f$ k \f$ length path lengths.
+ ///
+ /// \warning The paths with limited arc number cannot be retrieved
+ /// easily with \ref path() or \ref predArc() functions. If you
+ /// need the shortest path and not just the distance you should store
+ /// after each iteration the \ref predMap() map and manually build
+ /// the path.
+ ///
+ /// \return \c true when the algorithm have not found more shorter
+ /// paths.
+ bool processNextRound() {
+ for (int i = 0; i < int(_process.size()); ++i) {
+ _mask->set(_process[i], false);
+ }
+ std::vector<Node> nextProcess;
+ std::vector<Value> values(_process.size());
+ for (int i = 0; i < int(_process.size()); ++i) {
+ values[i] = (*_dist)[_process[i]];
+ }
+ for (int i = 0; i < int(_process.size()); ++i) {
+ for (OutArcIt it(*digraph, _process[i]); it != INVALID; ++it) {
+ Node target = digraph->target(it);
+ Value relaxed = OperationTraits::plus(values[i], (*length)[it]);
+ if (OperationTraits::less(relaxed, (*_dist)[target])) {
+ _pred->set(target, it);
+ _dist->set(target, relaxed);
+ if (!(*_mask)[target]) {
+ _mask->set(target, true);
+ nextProcess.push_back(target);
+ }
+ }
+ }
+ }
+ _process.swap(nextProcess);
+ return _process.empty();
+ }
+
+ /// \brief Executes one weak round from the Bellman-Ford algorithm.
+ ///
+ /// If the algorithm calculated the distances in the
+ /// previous round at least for all at most k length paths then it will
+ /// calculate the distances at least for all at most k + 1 length paths.
+ /// This function does not make it possible to calculate strictly the
+ /// at most k length minimal paths, this is why it is
+ /// called just weak round.
+ /// \return \c true when the algorithm have not found more shorter paths.
+ bool processNextWeakRound() {
+ for (int i = 0; i < int(_process.size()); ++i) {
+ _mask->set(_process[i], false);
+ }
+ std::vector<Node> nextProcess;
+ for (int i = 0; i < int(_process.size()); ++i) {
+ for (OutArcIt it(*digraph, _process[i]); it != INVALID; ++it) {
+ Node target = digraph->target(it);
+ Value relaxed =
+ OperationTraits::plus((*_dist)[_process[i]], (*length)[it]);
+ if (OperationTraits::less(relaxed, (*_dist)[target])) {
+ _pred->set(target, it);
+ _dist->set(target, relaxed);
+ if (!(*_mask)[target]) {
+ _mask->set(target, true);
+ nextProcess.push_back(target);
+ }
+ }
+ }
+ }
+ _process.swap(nextProcess);
+ return _process.empty();
+ }
+
+ /// \brief Executes the algorithm.
+ ///
+ /// \pre init() must be called and at least one node should be added
+ /// with addSource() before using this function.
+ ///
+ /// This method runs the %BellmanFord algorithm from the root node(s)
+ /// in order to compute the shortest path to each node. The algorithm
+ /// computes
+ /// - The shortest path tree.
+ /// - The distance of each node from the root(s).
+ void start() {
+ int num = countNodes(*digraph) - 1;
+ for (int i = 0; i < num; ++i) {
+ if (processNextWeakRound()) break;
+ }
+ }
+
+ /// \brief Executes the algorithm and checks the negative cycles.
+ ///
+ /// \pre init() must be called and at least one node should be added
+ /// with addSource() before using this function.
+ ///
+ /// This method runs the %BellmanFord algorithm from the root node(s)
+ /// in order to compute the shortest path to each node. The algorithm
+ /// computes
+ /// - The shortest path tree.
+ /// - The distance of each node from the root(s).
+ ///
+ /// \return \c false if there is a negative cycle in the digraph.
+ bool checkedStart() {
+ int num = countNodes(*digraph);
+ for (int i = 0; i < num; ++i) {
+ if (processNextWeakRound()) return true;
+ }
+ return _process.empty();
+ }
+
+ /// \brief Executes the algorithm with path length limit.
+ ///
+ /// \pre init() must be called and at least one node should be added
+ /// with addSource() before using this function.
+ ///
+ /// This method runs the %BellmanFord algorithm from the root
+ /// node(s) in order to compute the shortest path lengths with at
+ /// most \c num arc.
+ ///
+ /// \warning The paths with limited arc number cannot be retrieved
+ /// easily with \ref path() or \ref predArc() functions. If you
+ /// need the shortest path and not just the distance you should store
+ /// after each iteration the \ref predMap() map and manually build
+ /// the path.
+ ///
+ /// The algorithm computes
+ /// - The predecessor arc from each node.
+ /// - The limited distance of each node from the root(s).
+ void limitedStart(int num) {
+ for (int i = 0; i < num; ++i) {
+ if (processNextRound()) break;
+ }
+ }
+
+ /// \brief Runs %BellmanFord algorithm from node \c s.
+ ///
+ /// This method runs the %BellmanFord algorithm from a root node \c s
+ /// in order to compute the shortest path to each node. The algorithm
+ /// computes
+ /// - The shortest path tree.
+ /// - The distance of each node from the root.
+ ///
+ /// \note d.run(s) is just a shortcut of the following code.
+ ///\code
+ /// d.init();
+ /// d.addSource(s);
+ /// d.start();
+ ///\endcode
+ void run(Node s) {
+ init();
+ addSource(s);
+ start();
+ }
+
+ /// \brief Runs %BellmanFord algorithm with limited path length
+ /// from node \c s.
+ ///
+ /// This method runs the %BellmanFord algorithm from a root node \c s
+ /// in order to compute the shortest path with at most \c len arcs
+ /// to each node. The algorithm computes
+ /// - The shortest path tree.
+ /// - The distance of each node from the root.
+ ///
+ /// \note d.run(s, num) is just a shortcut of the following code.
+ ///\code
+ /// d.init();
+ /// d.addSource(s);
+ /// d.limitedStart(num);
+ ///\endcode
+ void run(Node s, int num) {
+ init();
+ addSource(s);
+ limitedStart(num);
+ }
+
+ ///@}
+
+ /// \name Query Functions
+ /// The result of the %BellmanFord algorithm can be obtained using these
+ /// functions.\n
+ /// Before the use of these functions,
+ /// either run() or start() must be called.
+
+ ///@{
+
+ /// \brief Lemon iterator for get the active nodes.
+ ///
+ /// Lemon iterator for get the active nodes. This class provides a
+ /// common style lemon iterator which gives back a subset of the
+ /// nodes. The iterated nodes are active in the algorithm after
+ /// the last phase so these should be checked in the next phase to
+ /// find augmenting arcs from these.
+ class ActiveIt {
+ public:
+
+ /// \brief Constructor.
+ ///
+ /// Constructor for get the nodeset of the variable.
+ ActiveIt(const BellmanFord& algorithm) : _algorithm(&algorithm)
+ {
+ _index = _algorithm->_process.size() - 1;
+ }
+
+ /// \brief Invalid constructor.
+ ///
+ /// Invalid constructor.
+ ActiveIt(Invalid) : _algorithm(0), _index(-1) {}
+
+ /// \brief Conversion to node.
+ ///
+ /// Conversion to node.
+ operator Node() const {
+ return _index >= 0 ? _algorithm->_process[_index] : INVALID;
+ }
+
+ /// \brief Increment operator.
+ ///
+ /// Increment operator.
+ ActiveIt& operator++() {
+ --_index;
+ return *this;
+ }
+
+ bool operator==(const ActiveIt& it) const {
+ return static_cast<Node>(*this) == static_cast<Node>(it);
+ }
+ bool operator!=(const ActiveIt& it) const {
+ return static_cast<Node>(*this) != static_cast<Node>(it);
+ }
+ bool operator<(const ActiveIt& it) const {
+ return static_cast<Node>(*this) < static_cast<Node>(it);
+ }
+
+ private:
+ const BellmanFord* _algorithm;
+ int _index;
+ };
+
+ typedef PredMapPath<Digraph, PredMap> Path;
+
+ /// \brief Gives back the shortest path.
+ ///
+ /// Gives back the shortest path.
+ /// \pre The \c t should be reachable from the source.
+ Path path(Node t)
+ {
+ return Path(*digraph, *_pred, t);
+ }
+
+
+ // TODO : implement negative cycle
+// /// \brief Gives back a negative cycle.
+// ///
+// /// This function gives back a negative cycle.
+// /// If the algorithm have not found yet negative cycle it will give back
+// /// an empty path.
+// Path negativeCycle() {
+// typename Digraph::template NodeMap<int> state(*digraph, 0);
+// for (ActiveIt it(*this); it != INVALID; ++it) {
+// if (state[it] == 0) {
+// for (Node t = it; predArc(t) != INVALID; t = predNode(t)) {
+// if (state[t] == 0) {
+// state[t] = 1;
+// } else if (state[t] == 2) {
+// break;
+// } else {
+// p.clear();
+// typename Path::Builder b(p);
+// b.setStartNode(t);
+// b.pushFront(predArc(t));
+// for(Node s = predNode(t); s != t; s = predNode(s)) {
+// b.pushFront(predArc(s));
+// }
+// b.commit();
+// return true;
+// }
+// }
+// for (Node t = it; predArc(t) != INVALID; t = predNode(t)) {
+// if (state[t] == 1) {
+// state[t] = 2;
+// } else {
+// break;
+// }
+// }
+// }
+// }
+// return false;
+// }
+
+ /// \brief The distance of a node from the root.
+ ///
+ /// Returns the distance of a node from the root.
+ /// \pre \ref run() must be called before using this function.
+ /// \warning If node \c v in unreachable from the root the return value
+ /// of this funcion is undefined.
+ Value dist(Node v) const { return (*_dist)[v]; }
+
+ /// \brief Returns the 'previous arc' of the shortest path tree.
+ ///
+ /// For a node \c v it returns the 'previous arc' of the shortest path
+ /// tree, i.e. it returns the last arc of a shortest path from the root
+ /// to \c v. It is \ref INVALID if \c v is unreachable from the root or
+ /// if \c v=s. The shortest path tree used here is equal to the shortest
+ /// path tree used in \ref predNode().
+ /// \pre \ref run() must be called before using
+ /// this function.
+ Arc predArc(Node v) const { return (*_pred)[v]; }
+
+ /// \brief Returns the 'previous node' of the shortest path tree.
+ ///
+ /// For a node \c v it returns the 'previous node' of the shortest path
+ /// tree, i.e. it returns the last but one node from a shortest path from
+ /// the root to \c /v. It is INVALID if \c v is unreachable from the root
+ /// or if \c v=s. The shortest path tree used here is equal to the
+ /// shortest path tree used in \ref predArc(). \pre \ref run() must be
+ /// called before using this function.
+ Node predNode(Node v) const {
+ return (*_pred)[v] == INVALID ? INVALID : digraph->source((*_pred)[v]);
+ }
+
+ /// \brief Returns a reference to the NodeMap of distances.
+ ///
+ /// Returns a reference to the NodeMap of distances. \pre \ref run() must
+ /// be called before using this function.
+ const DistMap &distMap() const { return *_dist;}
+
+ /// \brief Returns a reference to the shortest path tree map.
+ ///
+ /// Returns a reference to the NodeMap of the arcs of the
+ /// shortest path tree.
+ /// \pre \ref run() must be called before using this function.
+ const PredMap &predMap() const { return *_pred; }
+
+ /// \brief Checks if a node is reachable from the root.
+ ///
+ /// Returns \c true if \c v is reachable from the root.
+ /// \pre \ref run() must be called before using this function.
+ ///
+ bool reached(Node v) { return (*_dist)[v] != OperationTraits::infinity(); }
+
+ ///@}
+ };
+
+ /// \brief Default traits class of BellmanFord function.
+ ///
+ /// Default traits class of BellmanFord function.
+ /// \param _Digraph Digraph type.
+ /// \param _LengthMap Type of length map.
+ template <typename _Digraph, typename _LengthMap>
+ struct BellmanFordWizardDefaultTraits {
+ /// \brief The digraph type the algorithm runs on.
+ typedef _Digraph Digraph;
+
+ /// \brief The type of the map that stores the arc lengths.
+ ///
+ /// The type of the map that stores the arc lengths.
+ /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
+ typedef _LengthMap LengthMap;
+
+ /// \brief The value type of the length map.
+ typedef typename _LengthMap::Value Value;
+
+ /// \brief Operation traits for Bellman-Ford algorithm.
+ ///
+ /// It defines the infinity type on the given Value type
+ /// and the used operation.
+ /// \see BellmanFordDefaultOperationTraits
+ typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
+
+ /// \brief The type of the map that stores the last
+ /// arcs of the shortest paths.
+ ///
+ /// The type of the map that stores the last
+ /// arcs of the shortest paths.
+ /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
+ typedef NullMap <typename _Digraph::Node,typename _Digraph::Arc> PredMap;
+
+ /// \brief Instantiates a PredMap.
+ ///
+ /// This function instantiates a \ref PredMap.
+ static PredMap *createPredMap(const _Digraph &) {
+ return new PredMap();
+ }
+ /// \brief The type of the map that stores the dists of the nodes.
+ ///
+ /// The type of the map that stores the dists of the nodes.
+ /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
+ typedef NullMap<typename Digraph::Node, Value> DistMap;
+ /// \brief Instantiates a DistMap.
+ ///
+ /// This function instantiates a \ref DistMap.
+ static DistMap *createDistMap(const _Digraph &) {
+ return new DistMap();
+ }
+ };
+
+ /// \brief Default traits used by \ref BellmanFordWizard
+ ///
+ /// To make it easier to use BellmanFord algorithm
+ /// we have created a wizard class.
+ /// This \ref BellmanFordWizard class needs default traits,
+ /// as well as the \ref BellmanFord class.
+ /// The \ref BellmanFordWizardBase is a class to be the default traits of the
+ /// \ref BellmanFordWizard class.
+ /// \todo More named parameters are required...
+ template<class _Digraph,class _LengthMap>
+ class BellmanFordWizardBase
+ : public BellmanFordWizardDefaultTraits<_Digraph,_LengthMap> {
+
+ typedef BellmanFordWizardDefaultTraits<_Digraph,_LengthMap> Base;
+ protected:
+ /// Type of the nodes in the digraph.
+ typedef typename Base::Digraph::Node Node;
+
+ /// Pointer to the underlying digraph.
+ void *_graph;
+ /// Pointer to the length map
+ void *_length;
+ ///Pointer to the map of predecessors arcs.
+ void *_pred;
+ ///Pointer to the map of distances.
+ void *_dist;
+ ///Pointer to the source node.
+ Node _source;
+
+ public:
+ /// Constructor.
+
+ /// This constructor does not require parameters, therefore it initiates
+ /// all of the attributes to default values (0, INVALID).
+ BellmanFordWizardBase() : _graph(0), _length(0), _pred(0),
+ _dist(0), _source(INVALID) {}
+
+ /// Constructor.
+
+ /// This constructor requires some parameters,
+ /// listed in the parameters list.
+ /// Others are initiated to 0.
+ /// \param digraph is the initial value of \ref _graph
+ /// \param length is the initial value of \ref _length
+ /// \param source is the initial value of \ref _source
+ BellmanFordWizardBase(const _Digraph& digraph,
+ const _LengthMap& length,
+ Node source = INVALID) :
+ _graph(reinterpret_cast<void*>(const_cast<_Digraph*>(&digraph))),
+ _length(reinterpret_cast<void*>(const_cast<_LengthMap*>(&length))),
+ _pred(0), _dist(0), _source(source) {}
+
+ };
+
+ /// A class to make the usage of BellmanFord algorithm easier
+
+ /// This class is created to make it easier to use BellmanFord algorithm.
+ /// It uses the functions and features of the plain \ref BellmanFord,
+ /// but it is much simpler to use it.
+ ///
+ /// Simplicity means that the way to change the types defined
+ /// in the traits class is based on functions that returns the new class
+ /// and not on templatable built-in classes.
+ /// When using the plain \ref BellmanFord
+ /// the new class with the modified type comes from
+ /// the original class by using the ::
+ /// operator. In the case of \ref BellmanFordWizard only
+ /// a function have to be called and it will
+ /// return the needed class.
+ ///
+ /// It does not have own \ref run method. When its \ref run method is called
+ /// it initiates a plain \ref BellmanFord class, and calls the \ref
+ /// BellmanFord::run method of it.
+ template<class _Traits>
+ class BellmanFordWizard : public _Traits {
+ typedef _Traits Base;
+
+ ///The type of the underlying digraph.
+ typedef typename _Traits::Digraph Digraph;
+
+ typedef typename Digraph::Node Node;
+ typedef typename Digraph::NodeIt NodeIt;
+ typedef typename Digraph::Arc Arc;
+ typedef typename Digraph::OutArcIt ArcIt;
+
+ ///The type of the map that stores the arc lengths.
+ typedef typename _Traits::LengthMap LengthMap;
+
+ ///The type of the length of the arcs.
+ typedef typename LengthMap::Value Value;
+
+ ///\brief The type of the map that stores the last
+ ///arcs of the shortest paths.
+ typedef typename _Traits::PredMap PredMap;
+
+ ///The type of the map that stores the dists of the nodes.
+ typedef typename _Traits::DistMap DistMap;
+
+ public:
+ /// Constructor.
+ BellmanFordWizard() : _Traits() {}
+
+ /// \brief Constructor that requires parameters.
+ ///
+ /// Constructor that requires parameters.
+ /// These parameters will be the default values for the traits class.
+ BellmanFordWizard(const Digraph& digraph, const LengthMap& length,
+ Node src = INVALID)
+ : _Traits(digraph, length, src) {}
+
+ /// \brief Copy constructor
+ BellmanFordWizard(const _Traits &b) : _Traits(b) {}
+
+ ~BellmanFordWizard() {}
+
+ /// \brief Runs BellmanFord algorithm from a given node.
+ ///
+ /// Runs BellmanFord algorithm from a given node.
+ /// The node can be given by the \ref source function.
+ void run() {
+ LEMON_ASSERT(Base::_source != INVALID, "Source node is not given");
+ BellmanFord<Digraph,LengthMap,_Traits>
+ bf(*reinterpret_cast<const Digraph*>(Base::_graph),
+ *reinterpret_cast<const LengthMap*>(Base::_length));
+ if (Base::_pred) bf.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
+ if (Base::_dist) bf.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
+ bf.run(Base::_source);
+ }
+
+ /// \brief Runs BellmanFord algorithm from the given node.
+ ///
+ /// Runs BellmanFord algorithm from the given node.
+ /// \param src is the given source.
+ void run(Node src) {
+ Base::_source = src;
+ run();
+ }
+
+ template<class T>
+ struct DefPredMapBase : public Base {
+ typedef T PredMap;
+ static PredMap *createPredMap(const Digraph &) { return 0; };
+ DefPredMapBase(const _Traits &b) : _Traits(b) {}
+ };
+
+ ///\brief \ref named-templ-param "Named parameter"
+ ///function for setting PredMap type
+ ///
+ /// \ref named-templ-param "Named parameter"
+ ///function for setting PredMap type
+ ///
+ template<class T>
+ BellmanFordWizard<DefPredMapBase<T> > predMap(const T &t)
+ {
+ Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
+ return BellmanFordWizard<DefPredMapBase<T> >(*this);
+ }
+
+ template<class T>
+ struct DefDistMapBase : public Base {
+ typedef T DistMap;
+ static DistMap *createDistMap(const Digraph &) { return 0; };
+ DefDistMapBase(const _Traits &b) : _Traits(b) {}
+ };
+
+ ///\brief \ref named-templ-param "Named parameter"
+ ///function for setting DistMap type
+ ///
+ /// \ref named-templ-param "Named parameter"
+ ///function for setting DistMap type
+ ///
+ template<class T>
+ BellmanFordWizard<DefDistMapBase<T> > distMap(const T &t) {
+ Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
+ return BellmanFordWizard<DefDistMapBase<T> >(*this);
+ }
+
+ template<class T>
+ struct DefOperationTraitsBase : public Base {
+ typedef T OperationTraits;
+ DefOperationTraitsBase(const _Traits &b) : _Traits(b) {}
+ };
+
+ ///\brief \ref named-templ-param "Named parameter"
+ ///function for setting OperationTraits type
+ ///
+ /// \ref named-templ-param "Named parameter"
+ ///function for setting OperationTraits type
+ ///
+ template<class T>
+ BellmanFordWizard<DefOperationTraitsBase<T> > distMap() {
+ return BellmanFordWizard<DefDistMapBase<T> >(*this);
+ }
+
+ /// \brief Sets the source node, from which the BellmanFord algorithm runs.
+ ///
+ /// Sets the source node, from which the BellmanFord algorithm runs.
+ /// \param src is the source node.
+ BellmanFordWizard<_Traits>& source(Node src) {
+ Base::_source = src;
+ return *this;
+ }
+
+ };
+
+ /// \brief Function type interface for BellmanFord algorithm.
+ ///
+ /// \ingroup shortest_path
+ /// Function type interface for BellmanFord algorithm.
+ ///
+ /// This function also has several \ref named-templ-func-param
+ /// "named parameters", they are declared as the members of class
+ /// \ref BellmanFordWizard.
+ /// The following
+ /// example shows how to use these parameters.
+ ///\code
+ /// bellmanford(g,length,source).predMap(preds).run();
+ ///\endcode
+ /// \warning Don't forget to put the \ref BellmanFordWizard::run() "run()"
+ /// to the end of the parameter list.
+ /// \sa BellmanFordWizard
+ /// \sa BellmanFord
+ template<class _Digraph, class _LengthMap>
+ BellmanFordWizard<BellmanFordWizardBase<_Digraph,_LengthMap> >
+ bellmanFord(const _Digraph& digraph,
+ const _LengthMap& length,
+ typename _Digraph::Node source = INVALID) {
+ return BellmanFordWizard<BellmanFordWizardBase<_Digraph,_LengthMap> >
+ (digraph, length, source);
+ }
+
+} //END OF NAMESPACE LEMON
+
+#endif
+