1 | /* -*- C++ -*- |
---|
2 | * lemon/floyd_warshall.h - Part of LEMON, a generic C++ optimization library |
---|
3 | * |
---|
4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
6 | * |
---|
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. |
---|
10 | * |
---|
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 |
---|
13 | * purpose. |
---|
14 | * |
---|
15 | */ |
---|
16 | |
---|
17 | #ifndef LEMON_FLOYD_WARSHALL_H |
---|
18 | #define LEMON_FLOYD_WARSHALL_H |
---|
19 | |
---|
20 | ///\ingroup flowalgs |
---|
21 | /// \file |
---|
22 | /// \brief FloydWarshall algorithm. |
---|
23 | /// |
---|
24 | |
---|
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> |
---|
31 | |
---|
32 | #include <limits> |
---|
33 | |
---|
34 | namespace lemon { |
---|
35 | |
---|
36 | /// \brief Default OperationTraits for the FloydWarshall algorithm class. |
---|
37 | /// |
---|
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 |
---|
42 | /// infinity value. |
---|
43 | template < |
---|
44 | typename Value, |
---|
45 | bool has_infinity = std::numeric_limits<Value>::has_infinity> |
---|
46 | struct FloydWarshallDefaultOperationTraits { |
---|
47 | /// \brief Gives back the zero value of the type. |
---|
48 | static Value zero() { |
---|
49 | return static_cast<Value>(0); |
---|
50 | } |
---|
51 | /// \brief Gives back the positive infinity value of the type. |
---|
52 | static Value infinity() { |
---|
53 | return std::numeric_limits<Value>::infinity(); |
---|
54 | } |
---|
55 | /// \brief Gives back the sum of the given two elements. |
---|
56 | static Value plus(const Value& left, const Value& right) { |
---|
57 | return left + right; |
---|
58 | } |
---|
59 | /// \brief Gives back true only if the first value less than the second. |
---|
60 | static bool less(const Value& left, const Value& right) { |
---|
61 | return left < right; |
---|
62 | } |
---|
63 | }; |
---|
64 | |
---|
65 | template <typename Value> |
---|
66 | struct FloydWarshallDefaultOperationTraits<Value, false> { |
---|
67 | static Value zero() { |
---|
68 | return static_cast<Value>(0); |
---|
69 | } |
---|
70 | static Value infinity() { |
---|
71 | return std::numeric_limits<Value>::max(); |
---|
72 | } |
---|
73 | static Value plus(const Value& left, const Value& right) { |
---|
74 | if (left == infinity() || right == infinity()) return infinity(); |
---|
75 | return left + right; |
---|
76 | } |
---|
77 | static bool less(const Value& left, const Value& right) { |
---|
78 | return left < right; |
---|
79 | } |
---|
80 | }; |
---|
81 | |
---|
82 | /// \brief Default traits class of FloydWarshall class. |
---|
83 | /// |
---|
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. |
---|
90 | typedef _Graph Graph; |
---|
91 | |
---|
92 | /// \brief The type of the map that stores the edge lengths. |
---|
93 | /// |
---|
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; |
---|
97 | |
---|
98 | // The type of the length of the edges. |
---|
99 | typedef typename _LengthMap::Value Value; |
---|
100 | |
---|
101 | /// \brief Operation traits for floyd-warshall algorithm. |
---|
102 | /// |
---|
103 | /// It defines the infinity type on the given Value type |
---|
104 | /// and the used operation. |
---|
105 | /// \see FloydWarshallDefaultOperationTraits |
---|
106 | typedef FloydWarshallDefaultOperationTraits<Value> OperationTraits; |
---|
107 | |
---|
108 | /// \brief The type of the matrix map that stores the last edges of the |
---|
109 | /// shortest paths. |
---|
110 | /// |
---|
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. |
---|
113 | /// |
---|
114 | typedef DynamicMatrixMap<Graph, typename Graph::Node, |
---|
115 | typename Graph::Edge> PredMap; |
---|
116 | |
---|
117 | /// \brief Instantiates a PredMap. |
---|
118 | /// |
---|
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); |
---|
124 | } |
---|
125 | |
---|
126 | /// \brief The type of the map that stores the dists of the nodes. |
---|
127 | /// |
---|
128 | /// The type of the map that stores the dists of the nodes. |
---|
129 | /// It must meet the \ref concept::WriteMatrixMap "WriteMatrixMap" concept. |
---|
130 | /// |
---|
131 | typedef DynamicMatrixMap<Graph, typename Graph::Node, Value> DistMap; |
---|
132 | |
---|
133 | /// \brief Instantiates a DistMap. |
---|
134 | /// |
---|
135 | /// This function instantiates a \ref DistMap. |
---|
136 | /// \param G is the graph, to which we would like to define the |
---|
137 | /// \ref DistMap |
---|
138 | static DistMap *createDistMap(const _Graph& graph) { |
---|
139 | return new DistMap(graph); |
---|
140 | } |
---|
141 | |
---|
142 | }; |
---|
143 | |
---|
144 | /// \brief %FloydWarshall algorithm class. |
---|
145 | /// |
---|
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 |
---|
150 | /// kind of length. |
---|
151 | /// |
---|
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. |
---|
158 | /// |
---|
159 | /// The complexity of this algorithm is O(n^3 + e). |
---|
160 | /// |
---|
161 | /// The type of the length is determined by the |
---|
162 | /// \ref concept::ReadMap::Value "Value" of the length map. |
---|
163 | /// |
---|
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 |
---|
178 | /// traits class. |
---|
179 | /// |
---|
180 | /// \author Balazs Dezso |
---|
181 | |
---|
182 | #ifdef DOXYGEN |
---|
183 | template <typename _Graph, typename _LengthMap typename _Traits > |
---|
184 | #else |
---|
185 | template <typename _Graph=ListGraph, |
---|
186 | typename _LengthMap=typename _Graph::template EdgeMap<int>, |
---|
187 | typename _Traits=FloydWarshallDefaultTraits<_Graph,_LengthMap> > |
---|
188 | #endif |
---|
189 | class FloydWarshall { |
---|
190 | public: |
---|
191 | |
---|
192 | /// \brief \ref Exception for uninitialized parameters. |
---|
193 | /// |
---|
194 | /// This error represents problems in the initialization |
---|
195 | /// of the parameters of the algorithms. |
---|
196 | |
---|
197 | class UninitializedParameter : public lemon::UninitializedParameter { |
---|
198 | public: |
---|
199 | virtual const char* exceptionName() const { |
---|
200 | return "lemon::FloydWarshall::UninitializedParameter"; |
---|
201 | } |
---|
202 | }; |
---|
203 | |
---|
204 | typedef _Traits Traits; |
---|
205 | ///The type of the underlying graph. |
---|
206 | typedef typename _Traits::Graph Graph; |
---|
207 | |
---|
208 | typedef typename Graph::Node Node; |
---|
209 | typedef typename Graph::NodeIt NodeIt; |
---|
210 | typedef typename Graph::Edge Edge; |
---|
211 | typedef typename Graph::EdgeIt EdgeIt; |
---|
212 | |
---|
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; |
---|
226 | private: |
---|
227 | /// Pointer to the underlying graph. |
---|
228 | const Graph *graph; |
---|
229 | /// Pointer to the length map |
---|
230 | const LengthMap *length; |
---|
231 | ///Pointer to the map of predecessors edges. |
---|
232 | PredMap *_pred; |
---|
233 | ///Indicates if \ref _pred is locally allocated (\c true) or not. |
---|
234 | bool local_pred; |
---|
235 | ///Pointer to the map of distances. |
---|
236 | DistMap *_dist; |
---|
237 | ///Indicates if \ref _dist is locally allocated (\c true) or not. |
---|
238 | bool local_dist; |
---|
239 | |
---|
240 | /// Creates the maps if necessary. |
---|
241 | void create_maps() { |
---|
242 | if(!_pred) { |
---|
243 | local_pred = true; |
---|
244 | _pred = Traits::createPredMap(*graph); |
---|
245 | } |
---|
246 | if(!_dist) { |
---|
247 | local_dist = true; |
---|
248 | _dist = Traits::createDistMap(*graph); |
---|
249 | } |
---|
250 | } |
---|
251 | |
---|
252 | public : |
---|
253 | |
---|
254 | /// \name Named template parameters |
---|
255 | |
---|
256 | ///@{ |
---|
257 | |
---|
258 | template <class T> |
---|
259 | struct DefPredMapTraits : public Traits { |
---|
260 | typedef T PredMap; |
---|
261 | static PredMap *createPredMap(const Graph& graph) { |
---|
262 | throw UninitializedParameter(); |
---|
263 | } |
---|
264 | }; |
---|
265 | |
---|
266 | /// \brief \ref named-templ-param "Named parameter" for setting PredMap |
---|
267 | /// type |
---|
268 | /// \ref named-templ-param "Named parameter" for setting PredMap type |
---|
269 | /// |
---|
270 | template <class T> |
---|
271 | struct DefPredMap |
---|
272 | : public FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > { |
---|
273 | typedef FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > Create; |
---|
274 | }; |
---|
275 | |
---|
276 | template <class T> |
---|
277 | struct DefDistMapTraits : public Traits { |
---|
278 | typedef T DistMap; |
---|
279 | static DistMap *createDistMap(const Graph& graph) { |
---|
280 | throw UninitializedParameter(); |
---|
281 | } |
---|
282 | }; |
---|
283 | /// \brief \ref named-templ-param "Named parameter" for setting DistMap |
---|
284 | /// type |
---|
285 | /// |
---|
286 | /// \ref named-templ-param "Named parameter" for setting DistMap type |
---|
287 | /// |
---|
288 | template <class T> |
---|
289 | struct DefDistMap |
---|
290 | : public FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > { |
---|
291 | typedef FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > Create; |
---|
292 | }; |
---|
293 | |
---|
294 | template <class T> |
---|
295 | struct DefOperationTraitsTraits : public Traits { |
---|
296 | typedef T OperationTraits; |
---|
297 | }; |
---|
298 | |
---|
299 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
300 | /// OperationTraits type |
---|
301 | /// |
---|
302 | /// \ref named-templ-param "Named parameter" for setting PredMap type |
---|
303 | template <class T> |
---|
304 | struct DefOperationTraits |
---|
305 | : public FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> > { |
---|
306 | typedef FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> > |
---|
307 | Create; |
---|
308 | }; |
---|
309 | |
---|
310 | ///@} |
---|
311 | |
---|
312 | protected: |
---|
313 | |
---|
314 | FloydWarshall() {} |
---|
315 | |
---|
316 | public: |
---|
317 | |
---|
318 | typedef FloydWarshall Create; |
---|
319 | |
---|
320 | /// \brief Constructor. |
---|
321 | /// |
---|
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) {} |
---|
328 | |
---|
329 | ///Destructor. |
---|
330 | ~FloydWarshall() { |
---|
331 | if(local_pred) delete _pred; |
---|
332 | if(local_dist) delete _dist; |
---|
333 | } |
---|
334 | |
---|
335 | /// \brief Sets the length map. |
---|
336 | /// |
---|
337 | /// Sets the length map. |
---|
338 | /// \return \c (*this) |
---|
339 | FloydWarshall &lengthMap(const LengthMap &m) { |
---|
340 | length = &m; |
---|
341 | return *this; |
---|
342 | } |
---|
343 | |
---|
344 | /// \brief Sets the map storing the predecessor edges. |
---|
345 | /// |
---|
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) { |
---|
352 | if(local_pred) { |
---|
353 | delete _pred; |
---|
354 | local_pred=false; |
---|
355 | } |
---|
356 | _pred = &m; |
---|
357 | return *this; |
---|
358 | } |
---|
359 | |
---|
360 | /// \brief Sets the map storing the distances calculated by the algorithm. |
---|
361 | /// |
---|
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) { |
---|
368 | if(local_dist) { |
---|
369 | delete _dist; |
---|
370 | local_dist=false; |
---|
371 | } |
---|
372 | _dist = &m; |
---|
373 | return *this; |
---|
374 | } |
---|
375 | |
---|
376 | ///\name Execution control |
---|
377 | /// The simplest way to execute the algorithm is to use |
---|
378 | /// one of the member functions called \c run(...). |
---|
379 | /// \n |
---|
380 | /// If you need more control on the execution, |
---|
381 | /// Finally \ref start() will perform the actual path |
---|
382 | /// computation. |
---|
383 | |
---|
384 | ///@{ |
---|
385 | |
---|
386 | /// \brief Initializes the internal data structures. |
---|
387 | /// |
---|
388 | /// Initializes the internal data structures. |
---|
389 | void init() { |
---|
390 | create_maps(); |
---|
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()); |
---|
395 | } |
---|
396 | _dist->set(it, it, OperationTraits::zero()); |
---|
397 | } |
---|
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); |
---|
404 | } |
---|
405 | } |
---|
406 | } |
---|
407 | |
---|
408 | /// \brief Executes the algorithm. |
---|
409 | /// |
---|
410 | /// This method runs the %FloydWarshall algorithm in order to compute |
---|
411 | /// the shortest path to each node pairs. The algorithm |
---|
412 | /// computes |
---|
413 | /// - The shortest path tree for each node. |
---|
414 | /// - The distance between each node pairs. |
---|
415 | void start() { |
---|
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), |
---|
420 | (*_dist)(kt, jt)); |
---|
421 | if (OperationTraits::less(relaxed, (*_dist)(it, jt))) { |
---|
422 | _dist->set(it, jt, relaxed); |
---|
423 | _pred->set(it, jt, (*_pred)(kt, jt)); |
---|
424 | } |
---|
425 | } |
---|
426 | } |
---|
427 | } |
---|
428 | } |
---|
429 | |
---|
430 | /// \brief Executes the algorithm and checks the negative cycles. |
---|
431 | /// |
---|
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() { |
---|
439 | start(); |
---|
440 | for (NodeIt it(*graph); it != INVALID; ++it) { |
---|
441 | if (OperationTraits::less((*dist)(it, it), OperationTraits::zero())) { |
---|
442 | return false; |
---|
443 | } |
---|
444 | } |
---|
445 | return true; |
---|
446 | } |
---|
447 | |
---|
448 | /// \brief Runs %FloydWarshall algorithm. |
---|
449 | /// |
---|
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. |
---|
455 | /// |
---|
456 | /// \note d.run(s) is just a shortcut of the following code. |
---|
457 | /// \code |
---|
458 | /// d.init(); |
---|
459 | /// d.start(); |
---|
460 | /// \endcode |
---|
461 | void run() { |
---|
462 | init(); |
---|
463 | start(); |
---|
464 | } |
---|
465 | |
---|
466 | ///@} |
---|
467 | |
---|
468 | /// \name Query Functions |
---|
469 | /// The result of the %FloydWarshall algorithm can be obtained using these |
---|
470 | /// functions.\n |
---|
471 | /// Before the use of these functions, |
---|
472 | /// either run() or start() must be called. |
---|
473 | |
---|
474 | ///@{ |
---|
475 | |
---|
476 | /// \brief Copies the shortest path to \c t into \c p |
---|
477 | /// |
---|
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 |
---|
480 | /// alter \c p. |
---|
481 | /// \return Returns \c true if a path to \c t was actually copied to \c p, |
---|
482 | /// \c false otherwise. |
---|
483 | /// \sa DirPath |
---|
484 | template <typename Path> |
---|
485 | bool getPath(Path &p, Node source, Node target) { |
---|
486 | if (connected(source, target)) { |
---|
487 | p.clear(); |
---|
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)); |
---|
492 | } |
---|
493 | b.commit(); |
---|
494 | return true; |
---|
495 | } |
---|
496 | return false; |
---|
497 | } |
---|
498 | |
---|
499 | /// \brief The distance between two nodes. |
---|
500 | /// |
---|
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); |
---|
507 | } |
---|
508 | |
---|
509 | /// \brief Returns the 'previous edge' of the shortest path tree. |
---|
510 | /// |
---|
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); |
---|
520 | } |
---|
521 | |
---|
522 | /// \brief Returns the 'previous node' of the shortest path tree. |
---|
523 | /// |
---|
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)); |
---|
534 | } |
---|
535 | |
---|
536 | /// \brief Returns a reference to the matrix node map of distances. |
---|
537 | /// |
---|
538 | /// Returns a reference to the matrix node map of distances. |
---|
539 | /// |
---|
540 | /// \pre \ref run() must be called before using this function. |
---|
541 | const DistMap &distMap() const { return *_dist;} |
---|
542 | |
---|
543 | /// \brief Returns a reference to the shortest path tree map. |
---|
544 | /// |
---|
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;} |
---|
549 | |
---|
550 | /// \brief Checks if a node is reachable from the root. |
---|
551 | /// |
---|
552 | /// Returns \c true if \c v is reachable from the root. |
---|
553 | /// \pre \ref run() must be called before using this function. |
---|
554 | /// |
---|
555 | bool connected(Node source, Node target) { |
---|
556 | return (*_dist)(source, target) != OperationTraits::infinity(); |
---|
557 | } |
---|
558 | |
---|
559 | ///@} |
---|
560 | }; |
---|
561 | |
---|
562 | } //END OF NAMESPACE LEMON |
---|
563 | |
---|
564 | #endif |
---|
565 | |
---|