Better doc.
2 * lemon/floyd_warshall.h - Part of LEMON, a generic C++ optimization library
4 * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5 * (Egervary Research Group on Combinatorial Optimization, EGRES).
7 * Permission to use, modify and distribute this software is granted
8 * provided that this copyright notice appears in all copies. For
9 * precise terms see the accompanying LICENSE file.
11 * This software is provided "AS IS" with no warranty of any kind,
12 * express or implied, and with no claim as to its suitability for any
17 #ifndef LEMON_FLOYD_WARSHALL_H
18 #define LEMON_FLOYD_WARSHALL_H
22 /// \brief FloydWarshall algorithm.
25 #include <lemon/list_graph.h>
26 #include <lemon/graph_utils.h>
27 #include <lemon/invalid.h>
28 #include <lemon/error.h>
29 #include <lemon/matrix_maps.h>
30 #include <lemon/maps.h>
36 /// \brief Default OperationTraits for the FloydWarshall algorithm class.
38 /// It defines all computational operations and constants which are
39 /// used in the Floyd-Warshall algorithm. The default implementation
40 /// is based on the numeric_limits class. If the numeric type does not
41 /// have infinity value then the maximum value is used as extremal
45 bool has_infinity = std::numeric_limits<Value>::has_infinity>
46 struct FloydWarshallDefaultOperationTraits {
47 /// \brief Gives back the zero value of the type.
49 return static_cast<Value>(0);
51 /// \brief Gives back the positive infinity value of the type.
52 static Value infinity() {
53 return std::numeric_limits<Value>::infinity();
55 /// \brief Gives back the sum of the given two elements.
56 static Value plus(const Value& left, const Value& right) {
59 /// \brief Gives back true only if the first value less than the second.
60 static bool less(const Value& left, const Value& right) {
65 template <typename Value>
66 struct FloydWarshallDefaultOperationTraits<Value, false> {
68 return static_cast<Value>(0);
70 static Value infinity() {
71 return std::numeric_limits<Value>::max();
73 static Value plus(const Value& left, const Value& right) {
74 if (left == infinity() || right == infinity()) return infinity();
77 static bool less(const Value& left, const Value& right) {
82 /// \brief Default traits class of FloydWarshall class.
84 /// Default traits class of FloydWarshall class.
85 /// \param _Graph Graph type.
86 /// \param _LegthMap Type of length map.
87 template<class _Graph, class _LengthMap>
88 struct FloydWarshallDefaultTraits {
89 /// The graph type the algorithm runs on.
92 /// \brief The type of the map that stores the edge lengths.
94 /// The type of the map that stores the edge lengths.
95 /// It must meet the \ref concept::ReadMap "ReadMap" concept.
96 typedef _LengthMap LengthMap;
98 // The type of the length of the edges.
99 typedef typename _LengthMap::Value Value;
101 /// \brief Operation traits for belmann-ford algorithm.
103 /// It defines the infinity type on the given Value type
104 /// and the used operation.
105 /// \see FloydWarshallDefaultOperationTraits
106 typedef FloydWarshallDefaultOperationTraits<Value> OperationTraits;
108 /// \brief The type of the matrix map that stores the last edges of the
111 /// The type of the map that stores the last edges of the shortest paths.
112 /// It must be a matrix map with \c Graph::Edge value type.
114 typedef DynamicMatrixMap<Graph, typename Graph::Node,
115 typename Graph::Edge> PredMap;
117 /// \brief Instantiates a PredMap.
119 /// This function instantiates a \ref PredMap.
120 /// \param G is the graph, to which we would like to define the PredMap.
121 /// \todo The graph alone may be insufficient for the initialization
122 static PredMap *createPredMap(const _Graph& graph) {
123 return new PredMap(graph);
126 /// \brief The type of the map that stores the dists of the nodes.
128 /// The type of the map that stores the dists of the nodes.
129 /// It must meet the \ref concept::WriteMatrixMap "WriteMatrixMap" concept.
131 typedef DynamicMatrixMap<Graph, typename Graph::Node, Value> DistMap;
133 /// \brief Instantiates a DistMap.
135 /// This function instantiates a \ref DistMap.
136 /// \param G is the graph, to which we would like to define the
138 static DistMap *createDistMap(const _Graph& graph) {
139 return new DistMap(graph);
144 /// \brief %FloydWarshall algorithm class.
146 /// \ingroup flowalgs
147 /// This class provides an efficient implementation of \c Floyd-Warshall
148 /// algorithm. The edge lengths are passed to the algorithm using a
149 /// \ref concept::ReadMap "ReadMap", so it is easy to change it to any
152 /// The algorithm solves the shortest path problem for each pair
153 /// of node when the edges can have negative length but the graph should
154 /// not contain cycles with negative sum of length. If we can assume
155 /// that all edge is non-negative in the graph then the dijkstra algorithm
156 /// should be used from each node rather and if the graph is sparse and
157 /// there are negative circles then the johnson algorithm.
159 /// The complexity of this algorithm is O(n^3 + e).
161 /// The type of the length is determined by the
162 /// \ref concept::ReadMap::Value "Value" of the length map.
164 /// \param _Graph The graph type the algorithm runs on. The default value
165 /// is \ref ListGraph. The value of _Graph is not used directly by
166 /// FloydWarshall, it is only passed to \ref FloydWarshallDefaultTraits.
167 /// \param _LengthMap This read-only EdgeMap determines the lengths of the
168 /// edges. It is read once for each edge, so the map may involve in
169 /// relatively time consuming process to compute the edge length if
170 /// it is necessary. The default map type is \ref
171 /// concept::StaticGraph::EdgeMap "Graph::EdgeMap<int>". The value
172 /// of _LengthMap is not used directly by FloydWarshall, it is only passed
173 /// to \ref FloydWarshallDefaultTraits. \param _Traits Traits class to set
174 /// various data types used by the algorithm. The default traits
175 /// class is \ref FloydWarshallDefaultTraits
176 /// "FloydWarshallDefaultTraits<_Graph,_LengthMap>". See \ref
177 /// FloydWarshallDefaultTraits for the documentation of a FloydWarshall
180 /// \author Balazs Dezso
183 template <typename _Graph, typename _LengthMap typename _Traits >
185 template <typename _Graph=ListGraph,
186 typename _LengthMap=typename _Graph::template EdgeMap<int>,
187 typename _Traits=FloydWarshallDefaultTraits<_Graph,_LengthMap> >
189 class FloydWarshall {
192 /// \brief \ref Exception for uninitialized parameters.
194 /// This error represents problems in the initialization
195 /// of the parameters of the algorithms.
197 class UninitializedParameter : public lemon::UninitializedParameter {
199 virtual const char* exceptionName() const {
200 return "lemon::FloydWarshall::UninitializedParameter";
204 typedef _Traits Traits;
205 ///The type of the underlying graph.
206 typedef typename _Traits::Graph Graph;
208 typedef typename Graph::Node Node;
209 typedef typename Graph::NodeIt NodeIt;
210 typedef typename Graph::Edge Edge;
211 typedef typename Graph::EdgeIt EdgeIt;
213 /// \brief The type of the length of the edges.
214 typedef typename _Traits::LengthMap::Value Value;
215 /// \brief The type of the map that stores the edge lengths.
216 typedef typename _Traits::LengthMap LengthMap;
217 /// \brief The type of the map that stores the last
218 /// edges of the shortest paths. The type of the PredMap
219 /// is a matrix map for Edges
220 typedef typename _Traits::PredMap PredMap;
221 /// \brief The type of the map that stores the dists of the nodes.
222 /// The type of the DistMap is a matrix map for Values
223 typedef typename _Traits::DistMap DistMap;
224 /// \brief The operation traits.
225 typedef typename _Traits::OperationTraits OperationTraits;
227 /// Pointer to the underlying graph.
229 /// Pointer to the length map
230 const LengthMap *length;
231 ///Pointer to the map of predecessors edges.
233 ///Indicates if \ref _pred is locally allocated (\c true) or not.
235 ///Pointer to the map of distances.
237 ///Indicates if \ref _dist is locally allocated (\c true) or not.
240 /// Creates the maps if necessary.
244 _pred = Traits::createPredMap(*graph);
248 _dist = Traits::createDistMap(*graph);
254 /// \name Named template parameters
259 struct DefPredMapTraits : public Traits {
261 static PredMap *createPredMap(const Graph& graph) {
262 throw UninitializedParameter();
266 /// \brief \ref named-templ-param "Named parameter" for setting PredMap
268 /// \ref named-templ-param "Named parameter" for setting PredMap type
272 : public FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > {
273 typedef FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > Create;
277 struct DefDistMapTraits : public Traits {
279 static DistMap *createDistMap(const Graph& graph) {
280 throw UninitializedParameter();
283 /// \brief \ref named-templ-param "Named parameter" for setting DistMap
286 /// \ref named-templ-param "Named parameter" for setting DistMap type
290 : public FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > {
291 typedef FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > Create;
295 struct DefOperationTraitsTraits : public Traits {
296 typedef T OperationTraits;
299 /// \brief \ref named-templ-param "Named parameter" for setting
300 /// OperationTraits type
302 /// \ref named-templ-param "Named parameter" for setting PredMap type
304 struct DefOperationTraits
305 : public FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> > {
306 typedef FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> >
318 typedef FloydWarshall Create;
320 /// \brief Constructor.
322 /// \param _graph the graph the algorithm will run on.
323 /// \param _length the length map used by the algorithm.
324 FloydWarshall(const Graph& _graph, const LengthMap& _length) :
325 graph(&_graph), length(&_length),
326 _pred(0), local_pred(false),
327 _dist(0), local_dist(false) {}
331 if(local_pred) delete _pred;
332 if(local_dist) delete _dist;
335 /// \brief Sets the length map.
337 /// Sets the length map.
338 /// \return \c (*this)
339 FloydWarshall &lengthMap(const LengthMap &m) {
344 /// \brief Sets the map storing the predecessor edges.
346 /// Sets the map storing the predecessor edges.
347 /// If you don't use this function before calling \ref run(),
348 /// it will allocate one. The destuctor deallocates this
349 /// automatically allocated map, of course.
350 /// \return \c (*this)
351 FloydWarshall &predMap(PredMap &m) {
360 /// \brief Sets the map storing the distances calculated by the algorithm.
362 /// Sets the map storing the distances calculated by the algorithm.
363 /// If you don't use this function before calling \ref run(),
364 /// it will allocate one. The destuctor deallocates this
365 /// automatically allocated map, of course.
366 /// \return \c (*this)
367 FloydWarshall &distMap(DistMap &m) {
376 ///\name Execution control
377 /// The simplest way to execute the algorithm is to use
378 /// one of the member functions called \c run(...).
380 /// If you need more control on the execution,
381 /// Finally \ref start() will perform the actual path
386 /// \brief Initializes the internal data structures.
388 /// Initializes the internal data structures.
391 for (NodeIt it(*graph); it != INVALID; ++it) {
392 for (NodeIt jt(*graph); jt != INVALID; ++jt) {
393 _pred->set(it, jt, INVALID);
394 _dist->set(it, jt, OperationTraits::infinity());
396 _dist->set(it, it, OperationTraits::zero());
398 for (EdgeIt it(*graph); it != INVALID; ++it) {
399 Node source = graph->source(it);
400 Node target = graph->target(it);
401 if (OperationTraits::less((*length)[it], (*_dist)(source, target))) {
402 _dist->set(source, target, (*length)[it]);
403 _pred->set(source, target, it);
408 /// \brief Executes the algorithm.
410 /// This method runs the %FloydWarshall algorithm in order to compute
411 /// the shortest path to each node pairs. The algorithm
413 /// - The shortest path tree for each node.
414 /// - The distance between each node pairs.
416 for (NodeIt kt(*graph); kt != INVALID; ++kt) {
417 for (NodeIt it(*graph); it != INVALID; ++it) {
418 for (NodeIt jt(*graph); jt != INVALID; ++jt) {
419 Value relaxed = OperationTraits::plus((*_dist)(it, kt),
421 if (OperationTraits::less(relaxed, (*_dist)(it, jt))) {
422 _dist->set(it, jt, relaxed);
423 _pred->set(it, jt, (*_pred)(kt, jt));
430 /// \brief Executes the algorithm and checks the negative cycles.
432 /// This method runs the %FloydWarshall algorithm in order to compute
433 /// the shortest path to each node pairs. If there is a negative cycle
434 /// in the graph it gives back false.
435 /// The algorithm computes
436 /// - The shortest path tree for each node.
437 /// - The distance between each node pairs.
438 bool checkedStart() {
440 for (NodeIt it(*graph); it != INVALID; ++it) {
441 if (OperationTraits::less((*dist)(it, it), OperationTraits::zero())) {
448 /// \brief Runs %FloydWarshall algorithm.
450 /// This method runs the %FloydWarshall algorithm from a each node
451 /// in order to compute the shortest path to each node pairs.
452 /// The algorithm computes
453 /// - The shortest path tree for each node.
454 /// - The distance between each node pairs.
456 /// \note d.run(s) is just a shortcut of the following code.
468 /// \name Query Functions
469 /// The result of the %FloydWarshall algorithm can be obtained using these
471 /// Before the use of these functions,
472 /// either run() or start() must be called.
476 /// \brief Copies the shortest path to \c t into \c p
478 /// This function copies the shortest path to \c t into \c p.
479 /// If it \c t is a source itself or unreachable, then it does not
481 /// \return Returns \c true if a path to \c t was actually copied to \c p,
482 /// \c false otherwise.
484 template <typename Path>
485 bool getPath(Path &p, Node source, Node target) {
486 if (connected(source, target)) {
488 typename Path::Builder b(target);
489 for(b.setStartNode(target); predEdge(source, target) != INVALID;
490 target = predNode(target)) {
491 b.pushFront(predEdge(source, target));
499 /// \brief The distance between two nodes.
501 /// Returns the distance between two nodes.
502 /// \pre \ref run() must be called before using this function.
503 /// \warning If node \c v in unreachable from the root the return value
504 /// of this funcion is undefined.
505 Value dist(Node source, Node target) const {
506 return (*_dist)(source, target);
509 /// \brief Returns the 'previous edge' of the shortest path tree.
511 /// For the node \c node it returns the 'previous edge' of the shortest
512 /// path tree to direction of the node \c root
513 /// i.e. it returns the last edge of a shortest path from the node \c root
514 /// to \c node. It is \ref INVALID if \c node is unreachable from the root
515 /// or if \c node=root. The shortest path tree used here is equal to the
516 /// shortest path tree used in \ref predNode().
517 /// \pre \ref run() must be called before using this function.
518 Edge predEdge(Node root, Node node) const {
519 return (*_pred)(root, node);
522 /// \brief Returns the 'previous node' of the shortest path tree.
524 /// For a node \c node it returns the 'previous node' of the shortest path
525 /// tree to direction of the node \c root, i.e. it returns the last but
526 /// one node from a shortest path from the \c root to \c node. It is
527 /// INVALID if \c node is unreachable from the root or if \c node=root.
528 /// The shortest path tree used here is equal to the
529 /// shortest path tree used in \ref predEdge().
530 /// \pre \ref run() must be called before using this function.
531 Node predNode(Node root, Node node) const {
532 return (*_pred)(root, node) == INVALID ?
533 INVALID : graph->source((*_pred)(root, node));
536 /// \brief Returns a reference to the matrix node map of distances.
538 /// Returns a reference to the matrix node map of distances.
540 /// \pre \ref run() must be called before using this function.
541 const DistMap &distMap() const { return *_dist;}
543 /// \brief Returns a reference to the shortest path tree map.
545 /// Returns a reference to the matrix node map of the edges of the
546 /// shortest path tree.
547 /// \pre \ref run() must be called before using this function.
548 const PredMap &predMap() const { return *_pred;}
550 /// \brief Checks if a node is reachable from the root.
552 /// Returns \c true if \c v is reachable from the root.
553 /// \pre \ref run() must be called before using this function.
555 bool connected(Node source, Node target) {
556 return (*_dist)(source, target) != OperationTraits::infinity();
562 } //END OF NAMESPACE LEMON