Revert to long long int since currently I don't know a better solution.
3 * This file is a part of LEMON, a generic C++ optimization library
5 * Copyright (C) 2003-2008
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
19 #ifndef LEMON_FLOYD_WARSHALL_H
20 #define LEMON_FLOYD_WARSHALL_H
22 ///\ingroup shortest_path
24 /// \brief FloydWarshall algorithm.
27 #include <lemon/list_graph.h>
28 #include <lemon/graph_utils.h>
29 #include <lemon/bits/path_dump.h>
30 #include <lemon/bits/invalid.h>
31 #include <lemon/error.h>
32 #include <lemon/matrix_maps.h>
33 #include <lemon/maps.h>
39 /// \brief Default OperationTraits for the FloydWarshall algorithm class.
41 /// It defines all computational operations and constants which are
42 /// used in the Floyd-Warshall algorithm. The default implementation
43 /// is based on the numeric_limits class. If the numeric type does not
44 /// have infinity value then the maximum value is used as extremal
48 bool has_infinity = std::numeric_limits<Value>::has_infinity>
49 struct FloydWarshallDefaultOperationTraits {
50 /// \brief Gives back the zero value of the type.
52 return static_cast<Value>(0);
54 /// \brief Gives back the positive infinity value of the type.
55 static Value infinity() {
56 return std::numeric_limits<Value>::infinity();
58 /// \brief Gives back the sum of the given two elements.
59 static Value plus(const Value& left, const Value& right) {
62 /// \brief Gives back true only if the first value less than the second.
63 static bool less(const Value& left, const Value& right) {
68 template <typename Value>
69 struct FloydWarshallDefaultOperationTraits<Value, false> {
71 return static_cast<Value>(0);
73 static Value infinity() {
74 return std::numeric_limits<Value>::max();
76 static Value plus(const Value& left, const Value& right) {
77 if (left == infinity() || right == infinity()) return infinity();
80 static bool less(const Value& left, const Value& right) {
85 /// \brief Default traits class of FloydWarshall class.
87 /// Default traits class of FloydWarshall class.
88 /// \param _Graph Graph type.
89 /// \param _LegthMap Type of length map.
90 template<class _Graph, class _LengthMap>
91 struct FloydWarshallDefaultTraits {
92 /// The graph type the algorithm runs on.
95 /// \brief The type of the map that stores the edge lengths.
97 /// The type of the map that stores the edge lengths.
98 /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
99 typedef _LengthMap LengthMap;
101 // The type of the length of the edges.
102 typedef typename _LengthMap::Value Value;
104 /// \brief Operation traits for floyd-warshall algorithm.
106 /// It defines the infinity type on the given Value type
107 /// and the used operation.
108 /// \see FloydWarshallDefaultOperationTraits
109 typedef FloydWarshallDefaultOperationTraits<Value> OperationTraits;
111 /// \brief The type of the matrix map that stores the last edges of the
114 /// The type of the map that stores the last edges of the shortest paths.
115 /// It must be a matrix map with \c Graph::Edge value type.
117 typedef DynamicMatrixMap<Graph, typename Graph::Node,
118 typename Graph::Edge> PredMap;
120 /// \brief Instantiates a PredMap.
122 /// This function instantiates a \ref PredMap.
123 /// \param graph is the graph,
124 /// to which we would like to define the PredMap.
125 /// \todo The graph alone may be insufficient for the initialization
126 static PredMap *createPredMap(const _Graph& graph) {
127 return new PredMap(graph);
130 /// \brief The type of the map that stores the dists of the nodes.
132 /// The type of the map that stores the dists of the nodes.
133 /// It must meet the \ref concepts::WriteMatrixMap "WriteMatrixMap" concept.
135 typedef DynamicMatrixMap<Graph, typename Graph::Node, Value> DistMap;
137 /// \brief Instantiates a DistMap.
139 /// This function instantiates a \ref DistMap.
140 /// \param graph is the graph, to which we would like to define the
142 static DistMap *createDistMap(const _Graph& graph) {
143 return new DistMap(graph);
148 /// \brief %FloydWarshall algorithm class.
150 /// \ingroup shortest_path
151 /// This class provides an efficient implementation of \c Floyd-Warshall
152 /// algorithm. The edge lengths are passed to the algorithm using a
153 /// \ref concepts::ReadMap "ReadMap", so it is easy to change it to any
156 /// The algorithm solves the shortest path problem for each pair
157 /// of node when the edges can have negative length but the graph should
158 /// not contain cycles with negative sum of length. If we can assume
159 /// that all edge is non-negative in the graph then the dijkstra algorithm
160 /// should be used from each node rather and if the graph is sparse and
161 /// there are negative circles then the johnson algorithm.
163 /// The complexity of this algorithm is \f$ O(n^3+e) \f$.
165 /// The type of the length is determined by the
166 /// \ref concepts::ReadMap::Value "Value" of the length map.
168 /// \param _Graph The graph type the algorithm runs on. The default value
169 /// is \ref ListGraph. The value of _Graph is not used directly by
170 /// FloydWarshall, it is only passed to \ref FloydWarshallDefaultTraits.
171 /// \param _LengthMap This read-only EdgeMap determines the lengths of the
172 /// edges. It is read once for each edge, so the map may involve in
173 /// relatively time consuming process to compute the edge length if
174 /// it is necessary. The default map type is \ref
175 /// concepts::Graph::EdgeMap "Graph::EdgeMap<int>". The value
176 /// of _LengthMap is not used directly by FloydWarshall, it is only passed
177 /// to \ref FloydWarshallDefaultTraits. \param _Traits Traits class to set
178 /// various data types used by the algorithm. The default traits
179 /// class is \ref FloydWarshallDefaultTraits
180 /// "FloydWarshallDefaultTraits<_Graph,_LengthMap>". See \ref
181 /// FloydWarshallDefaultTraits for the documentation of a FloydWarshall
184 /// \author Balazs Dezso
185 /// \todo A function type interface would be nice.
186 /// \todo Implement \c nextNode() and \c nextEdge()
188 template <typename _Graph, typename _LengthMap, typename _Traits >
190 template <typename _Graph=ListGraph,
191 typename _LengthMap=typename _Graph::template EdgeMap<int>,
192 typename _Traits=FloydWarshallDefaultTraits<_Graph,_LengthMap> >
194 class FloydWarshall {
197 /// \brief \ref Exception for uninitialized parameters.
199 /// This error represents problems in the initialization
200 /// of the parameters of the algorithms.
202 class UninitializedParameter : public lemon::UninitializedParameter {
204 virtual const char* what() const throw() {
205 return "lemon::FloydWarshall::UninitializedParameter";
209 typedef _Traits Traits;
210 ///The type of the underlying graph.
211 typedef typename _Traits::Graph Graph;
213 typedef typename Graph::Node Node;
214 typedef typename Graph::NodeIt NodeIt;
215 typedef typename Graph::Edge Edge;
216 typedef typename Graph::EdgeIt EdgeIt;
218 /// \brief The type of the length of the edges.
219 typedef typename _Traits::LengthMap::Value Value;
220 /// \brief The type of the map that stores the edge lengths.
221 typedef typename _Traits::LengthMap LengthMap;
222 /// \brief The type of the map that stores the last
223 /// edges of the shortest paths. The type of the PredMap
224 /// is a matrix map for Edges
225 typedef typename _Traits::PredMap PredMap;
226 /// \brief The type of the map that stores the dists of the nodes.
227 /// The type of the DistMap is a matrix map for Values
229 /// \todo It should rather be
230 /// called \c DistMatrix
231 typedef typename _Traits::DistMap DistMap;
232 /// \brief The operation traits.
233 typedef typename _Traits::OperationTraits OperationTraits;
235 /// Pointer to the underlying graph.
237 /// Pointer to the length map
238 const LengthMap *length;
239 ///Pointer to the map of predecessors edges.
241 ///Indicates if \ref _pred is locally allocated (\c true) or not.
243 ///Pointer to the map of distances.
245 ///Indicates if \ref _dist is locally allocated (\c true) or not.
248 /// Creates the maps if necessary.
252 _pred = Traits::createPredMap(*graph);
256 _dist = Traits::createDistMap(*graph);
262 /// \name Named template parameters
267 struct DefPredMapTraits : public Traits {
269 static PredMap *createPredMap(const Graph& graph) {
270 throw UninitializedParameter();
274 /// \brief \ref named-templ-param "Named parameter" for setting PredMap
276 /// \ref named-templ-param "Named parameter" for setting PredMap type
280 : public FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > {
281 typedef FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > Create;
285 struct DefDistMapTraits : public Traits {
287 static DistMap *createDistMap(const Graph& graph) {
288 throw UninitializedParameter();
291 /// \brief \ref named-templ-param "Named parameter" for setting DistMap
294 /// \ref named-templ-param "Named parameter" for setting DistMap type
298 : public FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > {
299 typedef FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > Create;
303 struct DefOperationTraitsTraits : public Traits {
304 typedef T OperationTraits;
307 /// \brief \ref named-templ-param "Named parameter" for setting
308 /// OperationTraits type
310 /// \ref named-templ-param "Named parameter" for setting PredMap type
312 struct DefOperationTraits
313 : public FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> > {
314 typedef FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> >
326 typedef FloydWarshall Create;
328 /// \brief Constructor.
330 /// \param _graph the graph the algorithm will run on.
331 /// \param _length the length map used by the algorithm.
332 FloydWarshall(const Graph& _graph, const LengthMap& _length) :
333 graph(&_graph), length(&_length),
334 _pred(0), local_pred(false),
335 _dist(0), local_dist(false) {}
339 if(local_pred) delete _pred;
340 if(local_dist) delete _dist;
343 /// \brief Sets the length map.
345 /// Sets the length map.
346 /// \return \c (*this)
347 FloydWarshall &lengthMap(const LengthMap &m) {
352 /// \brief Sets the map storing the predecessor edges.
354 /// Sets the map storing the predecessor edges.
355 /// If you don't use this function before calling \ref run(),
356 /// it will allocate one. The destuctor deallocates this
357 /// automatically allocated map, of course.
358 /// \return \c (*this)
359 FloydWarshall &predMap(PredMap &m) {
368 /// \brief Sets the map storing the distances calculated by the algorithm.
370 /// Sets the map storing the distances calculated by the algorithm.
371 /// If you don't use this function before calling \ref run(),
372 /// it will allocate one. The destuctor deallocates this
373 /// automatically allocated map, of course.
374 /// \return \c (*this)
375 FloydWarshall &distMap(DistMap &m) {
384 ///\name Execution control
385 /// The simplest way to execute the algorithm is to use
386 /// one of the member functions called \c run(...).
388 /// If you need more control on the execution,
389 /// Finally \ref start() will perform the actual path
394 /// \brief Initializes the internal data structures.
396 /// Initializes the internal data structures.
399 for (NodeIt it(*graph); it != INVALID; ++it) {
400 for (NodeIt jt(*graph); jt != INVALID; ++jt) {
401 _pred->set(it, jt, INVALID);
402 _dist->set(it, jt, OperationTraits::infinity());
404 _dist->set(it, it, OperationTraits::zero());
406 for (EdgeIt it(*graph); it != INVALID; ++it) {
407 Node source = graph->source(it);
408 Node target = graph->target(it);
409 if (OperationTraits::less((*length)[it], (*_dist)(source, target))) {
410 _dist->set(source, target, (*length)[it]);
411 _pred->set(source, target, it);
416 /// \brief Executes the algorithm.
418 /// This method runs the %FloydWarshall algorithm in order to compute
419 /// the shortest path to each node pairs. The algorithm
421 /// - The shortest path tree for each node.
422 /// - The distance between each node pairs.
424 for (NodeIt kt(*graph); kt != INVALID; ++kt) {
425 for (NodeIt it(*graph); it != INVALID; ++it) {
426 for (NodeIt jt(*graph); jt != INVALID; ++jt) {
427 Value relaxed = OperationTraits::plus((*_dist)(it, kt),
429 if (OperationTraits::less(relaxed, (*_dist)(it, jt))) {
430 _dist->set(it, jt, relaxed);
431 _pred->set(it, jt, (*_pred)(kt, jt));
438 /// \brief Executes the algorithm and checks the negative cycles.
440 /// This method runs the %FloydWarshall algorithm in order to compute
441 /// the shortest path to each node pairs. If there is a negative cycle
442 /// in the graph it gives back false.
443 /// The algorithm computes
444 /// - The shortest path tree for each node.
445 /// - The distance between each node pairs.
446 bool checkedStart() {
448 for (NodeIt it(*graph); it != INVALID; ++it) {
449 if (OperationTraits::less((*dist)(it, it), OperationTraits::zero())) {
456 /// \brief Runs %FloydWarshall algorithm.
458 /// This method runs the %FloydWarshall algorithm from a each node
459 /// in order to compute the shortest path to each node pairs.
460 /// The algorithm computes
461 /// - The shortest path tree for each node.
462 /// - The distance between each node pairs.
464 /// \note d.run(s) is just a shortcut of the following code.
476 /// \name Query Functions
477 /// The result of the %FloydWarshall algorithm can be obtained using these
479 /// Before the use of these functions,
480 /// either run() or start() must be called.
484 typedef PredMatrixMapPath<Graph, PredMap> Path;
486 ///Gives back the shortest path.
488 ///Gives back the shortest path.
489 ///\pre The \c t should be reachable from the \c t.
490 Path path(Node s, Node t)
492 return Path(*graph, *_pred, s, t);
495 /// \brief The distance between two nodes.
497 /// Returns the distance between two nodes.
498 /// \pre \ref run() must be called before using this function.
499 /// \warning If node \c v in unreachable from the root the return value
500 /// of this funcion is undefined.
501 Value dist(Node source, Node target) const {
502 return (*_dist)(source, target);
505 /// \brief Returns the 'previous edge' of the shortest path tree.
507 /// For the node \c node it returns the 'previous edge' of the shortest
508 /// path tree to direction of the node \c root
509 /// i.e. it returns the last edge of a shortest path from the node \c root
510 /// to \c node. It is \ref INVALID if \c node is unreachable from the root
511 /// or if \c node=root. The shortest path tree used here is equal to the
512 /// shortest path tree used in \ref predNode().
513 /// \pre \ref run() must be called before using this function.
514 Edge predEdge(Node root, Node node) const {
515 return (*_pred)(root, node);
518 /// \brief Returns the 'previous node' of the shortest path tree.
520 /// For a node \c node it returns the 'previous node' of the shortest path
521 /// tree to direction of the node \c root, i.e. it returns the last but
522 /// one node from a shortest path from the \c root to \c node. It is
523 /// INVALID if \c node is unreachable from the root or if \c node=root.
524 /// The shortest path tree used here is equal to the
525 /// shortest path tree used in \ref predEdge().
526 /// \pre \ref run() must be called before using this function.
527 Node predNode(Node root, Node node) const {
528 return (*_pred)(root, node) == INVALID ?
529 INVALID : graph->source((*_pred)(root, node));
532 /// \brief Returns a reference to the matrix node map of distances.
534 /// Returns a reference to the matrix node map of distances.
536 /// \pre \ref run() must be called before using this function.
537 const DistMap &distMap() const { return *_dist;}
539 /// \brief Returns a reference to the shortest path tree map.
541 /// Returns a reference to the matrix node map of the edges of the
542 /// shortest path tree.
543 /// \pre \ref run() must be called before using this function.
544 const PredMap &predMap() const { return *_pred;}
546 /// \brief Checks if a node is reachable from the root.
548 /// Returns \c true if \c v is reachable from the root.
549 /// \pre \ref run() must be called before using this function.
551 bool connected(Node source, Node target) {
552 return (*_dist)(source, target) != OperationTraits::infinity();
558 } //END OF NAMESPACE LEMON