1 | /* -*- C++ -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2008 |
---|
6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
8 | * |
---|
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. |
---|
12 | * |
---|
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 |
---|
15 | * purpose. |
---|
16 | * |
---|
17 | */ |
---|
18 | |
---|
19 | #ifndef LEMON_HOWARD_H |
---|
20 | #define LEMON_HOWARD_H |
---|
21 | |
---|
22 | /// \ingroup min_mean_cycle |
---|
23 | /// |
---|
24 | /// \file |
---|
25 | /// \brief Howard's algorithm for finding a minimum mean cycle. |
---|
26 | |
---|
27 | #include <vector> |
---|
28 | #include <limits> |
---|
29 | #include <lemon/core.h> |
---|
30 | #include <lemon/path.h> |
---|
31 | #include <lemon/tolerance.h> |
---|
32 | #include <lemon/connectivity.h> |
---|
33 | |
---|
34 | namespace lemon { |
---|
35 | |
---|
36 | /// \brief Default traits class of Howard class. |
---|
37 | /// |
---|
38 | /// Default traits class of Howard class. |
---|
39 | /// \tparam GR The type of the digraph. |
---|
40 | /// \tparam LEN The type of the length map. |
---|
41 | /// It must conform to the \ref concepts::ReadMap "ReadMap" concept. |
---|
42 | #ifdef DOXYGEN |
---|
43 | template <typename GR, typename LEN> |
---|
44 | #else |
---|
45 | template <typename GR, typename LEN, |
---|
46 | bool integer = std::numeric_limits<typename LEN::Value>::is_integer> |
---|
47 | #endif |
---|
48 | struct HowardDefaultTraits |
---|
49 | { |
---|
50 | /// The type of the digraph |
---|
51 | typedef GR Digraph; |
---|
52 | /// The type of the length map |
---|
53 | typedef LEN LengthMap; |
---|
54 | /// The type of the arc lengths |
---|
55 | typedef typename LengthMap::Value Value; |
---|
56 | |
---|
57 | /// \brief The large value type used for internal computations |
---|
58 | /// |
---|
59 | /// The large value type used for internal computations. |
---|
60 | /// It is \c long \c long if the \c Value type is integer, |
---|
61 | /// otherwise it is \c double. |
---|
62 | /// \c Value must be convertible to \c LargeValue. |
---|
63 | typedef double LargeValue; |
---|
64 | |
---|
65 | /// The tolerance type used for internal computations |
---|
66 | typedef lemon::Tolerance<LargeValue> Tolerance; |
---|
67 | |
---|
68 | /// \brief The path type of the found cycles |
---|
69 | /// |
---|
70 | /// The path type of the found cycles. |
---|
71 | /// It must conform to the \ref lemon::concepts::Path "Path" concept |
---|
72 | /// and it must have an \c addBack() function. |
---|
73 | typedef lemon::Path<Digraph> Path; |
---|
74 | }; |
---|
75 | |
---|
76 | // Default traits class for integer value types |
---|
77 | template <typename GR, typename LEN> |
---|
78 | struct HowardDefaultTraits<GR, LEN, true> |
---|
79 | { |
---|
80 | typedef GR Digraph; |
---|
81 | typedef LEN LengthMap; |
---|
82 | typedef typename LengthMap::Value Value; |
---|
83 | #ifdef LEMON_HAVE_LONG_LONG |
---|
84 | typedef long long LargeValue; |
---|
85 | #else |
---|
86 | typedef long LargeValue; |
---|
87 | #endif |
---|
88 | typedef lemon::Tolerance<LargeValue> Tolerance; |
---|
89 | typedef lemon::Path<Digraph> Path; |
---|
90 | }; |
---|
91 | |
---|
92 | |
---|
93 | /// \addtogroup min_mean_cycle |
---|
94 | /// @{ |
---|
95 | |
---|
96 | /// \brief Implementation of Howard's algorithm for finding a minimum |
---|
97 | /// mean cycle. |
---|
98 | /// |
---|
99 | /// This class implements Howard's policy iteration algorithm for finding |
---|
100 | /// a directed cycle of minimum mean length (cost) in a digraph |
---|
101 | /// \ref amo93networkflows, \ref dasdan98minmeancycle. |
---|
102 | /// This class provides the most efficient algorithm for the |
---|
103 | /// minimum mean cycle problem, though the best known theoretical |
---|
104 | /// bound on its running time is exponential. |
---|
105 | /// |
---|
106 | /// \tparam GR The type of the digraph the algorithm runs on. |
---|
107 | /// \tparam LEN The type of the length map. The default |
---|
108 | /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
---|
109 | /// \tparam TR The traits class that defines various types used by the |
---|
110 | /// algorithm. By default, it is \ref HowardDefaultTraits |
---|
111 | /// "HowardDefaultTraits<GR, LEN>". |
---|
112 | /// In most cases, this parameter should not be set directly, |
---|
113 | /// consider to use the named template parameters instead. |
---|
114 | #ifdef DOXYGEN |
---|
115 | template <typename GR, typename LEN, typename TR> |
---|
116 | #else |
---|
117 | template < typename GR, |
---|
118 | typename LEN = typename GR::template ArcMap<int>, |
---|
119 | typename TR = HowardDefaultTraits<GR, LEN> > |
---|
120 | #endif |
---|
121 | class Howard |
---|
122 | { |
---|
123 | public: |
---|
124 | |
---|
125 | /// The type of the digraph |
---|
126 | typedef typename TR::Digraph Digraph; |
---|
127 | /// The type of the length map |
---|
128 | typedef typename TR::LengthMap LengthMap; |
---|
129 | /// The type of the arc lengths |
---|
130 | typedef typename TR::Value Value; |
---|
131 | |
---|
132 | /// \brief The large value type |
---|
133 | /// |
---|
134 | /// The large value type used for internal computations. |
---|
135 | /// By default, it is \c long \c long if the \c Value type is integer, |
---|
136 | /// otherwise it is \c double. |
---|
137 | typedef typename TR::LargeValue LargeValue; |
---|
138 | |
---|
139 | /// The tolerance type |
---|
140 | typedef typename TR::Tolerance Tolerance; |
---|
141 | |
---|
142 | /// \brief The path type of the found cycles |
---|
143 | /// |
---|
144 | /// The path type of the found cycles. |
---|
145 | /// Using the \ref HowardDefaultTraits "default traits class", |
---|
146 | /// it is \ref lemon::Path "Path<Digraph>". |
---|
147 | typedef typename TR::Path Path; |
---|
148 | |
---|
149 | /// The \ref HowardDefaultTraits "traits class" of the algorithm |
---|
150 | typedef TR Traits; |
---|
151 | |
---|
152 | private: |
---|
153 | |
---|
154 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
---|
155 | |
---|
156 | // The digraph the algorithm runs on |
---|
157 | const Digraph &_gr; |
---|
158 | // The length of the arcs |
---|
159 | const LengthMap &_length; |
---|
160 | |
---|
161 | // Data for the found cycles |
---|
162 | bool _curr_found, _best_found; |
---|
163 | LargeValue _curr_length, _best_length; |
---|
164 | int _curr_size, _best_size; |
---|
165 | Node _curr_node, _best_node; |
---|
166 | |
---|
167 | Path *_cycle_path; |
---|
168 | bool _local_path; |
---|
169 | |
---|
170 | // Internal data used by the algorithm |
---|
171 | typename Digraph::template NodeMap<Arc> _policy; |
---|
172 | typename Digraph::template NodeMap<bool> _reached; |
---|
173 | typename Digraph::template NodeMap<int> _level; |
---|
174 | typename Digraph::template NodeMap<LargeValue> _dist; |
---|
175 | |
---|
176 | // Data for storing the strongly connected components |
---|
177 | int _comp_num; |
---|
178 | typename Digraph::template NodeMap<int> _comp; |
---|
179 | std::vector<std::vector<Node> > _comp_nodes; |
---|
180 | std::vector<Node>* _nodes; |
---|
181 | typename Digraph::template NodeMap<std::vector<Arc> > _in_arcs; |
---|
182 | |
---|
183 | // Queue used for BFS search |
---|
184 | std::vector<Node> _queue; |
---|
185 | int _qfront, _qback; |
---|
186 | |
---|
187 | Tolerance _tolerance; |
---|
188 | |
---|
189 | // Infinite constant |
---|
190 | const LargeValue INF; |
---|
191 | |
---|
192 | public: |
---|
193 | |
---|
194 | /// \name Named Template Parameters |
---|
195 | /// @{ |
---|
196 | |
---|
197 | template <typename T> |
---|
198 | struct SetLargeValueTraits : public Traits { |
---|
199 | typedef T LargeValue; |
---|
200 | typedef lemon::Tolerance<T> Tolerance; |
---|
201 | }; |
---|
202 | |
---|
203 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
204 | /// \c LargeValue type. |
---|
205 | /// |
---|
206 | /// \ref named-templ-param "Named parameter" for setting \c LargeValue |
---|
207 | /// type. It is used for internal computations in the algorithm. |
---|
208 | template <typename T> |
---|
209 | struct SetLargeValue |
---|
210 | : public Howard<GR, LEN, SetLargeValueTraits<T> > { |
---|
211 | typedef Howard<GR, LEN, SetLargeValueTraits<T> > Create; |
---|
212 | }; |
---|
213 | |
---|
214 | template <typename T> |
---|
215 | struct SetPathTraits : public Traits { |
---|
216 | typedef T Path; |
---|
217 | }; |
---|
218 | |
---|
219 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
220 | /// \c %Path type. |
---|
221 | /// |
---|
222 | /// \ref named-templ-param "Named parameter" for setting the \c %Path |
---|
223 | /// type of the found cycles. |
---|
224 | /// It must conform to the \ref lemon::concepts::Path "Path" concept |
---|
225 | /// and it must have an \c addBack() function. |
---|
226 | template <typename T> |
---|
227 | struct SetPath |
---|
228 | : public Howard<GR, LEN, SetPathTraits<T> > { |
---|
229 | typedef Howard<GR, LEN, SetPathTraits<T> > Create; |
---|
230 | }; |
---|
231 | |
---|
232 | /// @} |
---|
233 | |
---|
234 | protected: |
---|
235 | |
---|
236 | Howard() {} |
---|
237 | |
---|
238 | public: |
---|
239 | |
---|
240 | /// \brief Constructor. |
---|
241 | /// |
---|
242 | /// The constructor of the class. |
---|
243 | /// |
---|
244 | /// \param digraph The digraph the algorithm runs on. |
---|
245 | /// \param length The lengths (costs) of the arcs. |
---|
246 | Howard( const Digraph &digraph, |
---|
247 | const LengthMap &length ) : |
---|
248 | _gr(digraph), _length(length), _best_found(false), |
---|
249 | _best_length(0), _best_size(1), _cycle_path(NULL), _local_path(false), |
---|
250 | _policy(digraph), _reached(digraph), _level(digraph), _dist(digraph), |
---|
251 | _comp(digraph), _in_arcs(digraph), |
---|
252 | INF(std::numeric_limits<LargeValue>::has_infinity ? |
---|
253 | std::numeric_limits<LargeValue>::infinity() : |
---|
254 | std::numeric_limits<LargeValue>::max()) |
---|
255 | {} |
---|
256 | |
---|
257 | /// Destructor. |
---|
258 | ~Howard() { |
---|
259 | if (_local_path) delete _cycle_path; |
---|
260 | } |
---|
261 | |
---|
262 | /// \brief Set the path structure for storing the found cycle. |
---|
263 | /// |
---|
264 | /// This function sets an external path structure for storing the |
---|
265 | /// found cycle. |
---|
266 | /// |
---|
267 | /// If you don't call this function before calling \ref run() or |
---|
268 | /// \ref findMinMean(), it will allocate a local \ref Path "path" |
---|
269 | /// structure. The destuctor deallocates this automatically |
---|
270 | /// allocated object, of course. |
---|
271 | /// |
---|
272 | /// \note The algorithm calls only the \ref lemon::Path::addBack() |
---|
273 | /// "addBack()" function of the given path structure. |
---|
274 | /// |
---|
275 | /// \return <tt>(*this)</tt> |
---|
276 | Howard& cycle(Path &path) { |
---|
277 | if (_local_path) { |
---|
278 | delete _cycle_path; |
---|
279 | _local_path = false; |
---|
280 | } |
---|
281 | _cycle_path = &path; |
---|
282 | return *this; |
---|
283 | } |
---|
284 | |
---|
285 | /// \brief Set the tolerance used by the algorithm. |
---|
286 | /// |
---|
287 | /// This function sets the tolerance object used by the algorithm. |
---|
288 | /// |
---|
289 | /// \return <tt>(*this)</tt> |
---|
290 | Howard& tolerance(const Tolerance& tolerance) { |
---|
291 | _tolerance = tolerance; |
---|
292 | return *this; |
---|
293 | } |
---|
294 | |
---|
295 | /// \brief Return a const reference to the tolerance. |
---|
296 | /// |
---|
297 | /// This function returns a const reference to the tolerance object |
---|
298 | /// used by the algorithm. |
---|
299 | const Tolerance& tolerance() const { |
---|
300 | return _tolerance; |
---|
301 | } |
---|
302 | |
---|
303 | /// \name Execution control |
---|
304 | /// The simplest way to execute the algorithm is to call the \ref run() |
---|
305 | /// function.\n |
---|
306 | /// If you only need the minimum mean length, you may call |
---|
307 | /// \ref findMinMean(). |
---|
308 | |
---|
309 | /// @{ |
---|
310 | |
---|
311 | /// \brief Run the algorithm. |
---|
312 | /// |
---|
313 | /// This function runs the algorithm. |
---|
314 | /// It can be called more than once (e.g. if the underlying digraph |
---|
315 | /// and/or the arc lengths have been modified). |
---|
316 | /// |
---|
317 | /// \return \c true if a directed cycle exists in the digraph. |
---|
318 | /// |
---|
319 | /// \note <tt>mmc.run()</tt> is just a shortcut of the following code. |
---|
320 | /// \code |
---|
321 | /// return mmc.findMinMean() && mmc.findCycle(); |
---|
322 | /// \endcode |
---|
323 | bool run() { |
---|
324 | return findMinMean() && findCycle(); |
---|
325 | } |
---|
326 | |
---|
327 | /// \brief Find the minimum cycle mean. |
---|
328 | /// |
---|
329 | /// This function finds the minimum mean length of the directed |
---|
330 | /// cycles in the digraph. |
---|
331 | /// |
---|
332 | /// \return \c true if a directed cycle exists in the digraph. |
---|
333 | bool findMinMean() { |
---|
334 | // Initialize and find strongly connected components |
---|
335 | init(); |
---|
336 | findComponents(); |
---|
337 | |
---|
338 | // Find the minimum cycle mean in the components |
---|
339 | for (int comp = 0; comp < _comp_num; ++comp) { |
---|
340 | // Find the minimum mean cycle in the current component |
---|
341 | if (!buildPolicyGraph(comp)) continue; |
---|
342 | while (true) { |
---|
343 | findPolicyCycle(); |
---|
344 | if (!computeNodeDistances()) break; |
---|
345 | } |
---|
346 | // Update the best cycle (global minimum mean cycle) |
---|
347 | if ( _curr_found && (!_best_found || |
---|
348 | _curr_length * _best_size < _best_length * _curr_size) ) { |
---|
349 | _best_found = true; |
---|
350 | _best_length = _curr_length; |
---|
351 | _best_size = _curr_size; |
---|
352 | _best_node = _curr_node; |
---|
353 | } |
---|
354 | } |
---|
355 | return _best_found; |
---|
356 | } |
---|
357 | |
---|
358 | /// \brief Find a minimum mean directed cycle. |
---|
359 | /// |
---|
360 | /// This function finds a directed cycle of minimum mean length |
---|
361 | /// in the digraph using the data computed by findMinMean(). |
---|
362 | /// |
---|
363 | /// \return \c true if a directed cycle exists in the digraph. |
---|
364 | /// |
---|
365 | /// \pre \ref findMinMean() must be called before using this function. |
---|
366 | bool findCycle() { |
---|
367 | if (!_best_found) return false; |
---|
368 | _cycle_path->addBack(_policy[_best_node]); |
---|
369 | for ( Node v = _best_node; |
---|
370 | (v = _gr.target(_policy[v])) != _best_node; ) { |
---|
371 | _cycle_path->addBack(_policy[v]); |
---|
372 | } |
---|
373 | return true; |
---|
374 | } |
---|
375 | |
---|
376 | /// @} |
---|
377 | |
---|
378 | /// \name Query Functions |
---|
379 | /// The results of the algorithm can be obtained using these |
---|
380 | /// functions.\n |
---|
381 | /// The algorithm should be executed before using them. |
---|
382 | |
---|
383 | /// @{ |
---|
384 | |
---|
385 | /// \brief Return the total length of the found cycle. |
---|
386 | /// |
---|
387 | /// This function returns the total length of the found cycle. |
---|
388 | /// |
---|
389 | /// \pre \ref run() or \ref findMinMean() must be called before |
---|
390 | /// using this function. |
---|
391 | Value cycleLength() const { |
---|
392 | return static_cast<Value>(_best_length); |
---|
393 | } |
---|
394 | |
---|
395 | /// \brief Return the number of arcs on the found cycle. |
---|
396 | /// |
---|
397 | /// This function returns the number of arcs on the found cycle. |
---|
398 | /// |
---|
399 | /// \pre \ref run() or \ref findMinMean() must be called before |
---|
400 | /// using this function. |
---|
401 | int cycleArcNum() const { |
---|
402 | return _best_size; |
---|
403 | } |
---|
404 | |
---|
405 | /// \brief Return the mean length of the found cycle. |
---|
406 | /// |
---|
407 | /// This function returns the mean length of the found cycle. |
---|
408 | /// |
---|
409 | /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the |
---|
410 | /// following code. |
---|
411 | /// \code |
---|
412 | /// return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum(); |
---|
413 | /// \endcode |
---|
414 | /// |
---|
415 | /// \pre \ref run() or \ref findMinMean() must be called before |
---|
416 | /// using this function. |
---|
417 | double cycleMean() const { |
---|
418 | return static_cast<double>(_best_length) / _best_size; |
---|
419 | } |
---|
420 | |
---|
421 | /// \brief Return the found cycle. |
---|
422 | /// |
---|
423 | /// This function returns a const reference to the path structure |
---|
424 | /// storing the found cycle. |
---|
425 | /// |
---|
426 | /// \pre \ref run() or \ref findCycle() must be called before using |
---|
427 | /// this function. |
---|
428 | const Path& cycle() const { |
---|
429 | return *_cycle_path; |
---|
430 | } |
---|
431 | |
---|
432 | ///@} |
---|
433 | |
---|
434 | private: |
---|
435 | |
---|
436 | // Initialize |
---|
437 | void init() { |
---|
438 | if (!_cycle_path) { |
---|
439 | _local_path = true; |
---|
440 | _cycle_path = new Path; |
---|
441 | } |
---|
442 | _queue.resize(countNodes(_gr)); |
---|
443 | _best_found = false; |
---|
444 | _best_length = 0; |
---|
445 | _best_size = 1; |
---|
446 | _cycle_path->clear(); |
---|
447 | } |
---|
448 | |
---|
449 | // Find strongly connected components and initialize _comp_nodes |
---|
450 | // and _in_arcs |
---|
451 | void findComponents() { |
---|
452 | _comp_num = stronglyConnectedComponents(_gr, _comp); |
---|
453 | _comp_nodes.resize(_comp_num); |
---|
454 | if (_comp_num == 1) { |
---|
455 | _comp_nodes[0].clear(); |
---|
456 | for (NodeIt n(_gr); n != INVALID; ++n) { |
---|
457 | _comp_nodes[0].push_back(n); |
---|
458 | _in_arcs[n].clear(); |
---|
459 | for (InArcIt a(_gr, n); a != INVALID; ++a) { |
---|
460 | _in_arcs[n].push_back(a); |
---|
461 | } |
---|
462 | } |
---|
463 | } else { |
---|
464 | for (int i = 0; i < _comp_num; ++i) |
---|
465 | _comp_nodes[i].clear(); |
---|
466 | for (NodeIt n(_gr); n != INVALID; ++n) { |
---|
467 | int k = _comp[n]; |
---|
468 | _comp_nodes[k].push_back(n); |
---|
469 | _in_arcs[n].clear(); |
---|
470 | for (InArcIt a(_gr, n); a != INVALID; ++a) { |
---|
471 | if (_comp[_gr.source(a)] == k) _in_arcs[n].push_back(a); |
---|
472 | } |
---|
473 | } |
---|
474 | } |
---|
475 | } |
---|
476 | |
---|
477 | // Build the policy graph in the given strongly connected component |
---|
478 | // (the out-degree of every node is 1) |
---|
479 | bool buildPolicyGraph(int comp) { |
---|
480 | _nodes = &(_comp_nodes[comp]); |
---|
481 | if (_nodes->size() < 1 || |
---|
482 | (_nodes->size() == 1 && _in_arcs[(*_nodes)[0]].size() == 0)) { |
---|
483 | return false; |
---|
484 | } |
---|
485 | for (int i = 0; i < int(_nodes->size()); ++i) { |
---|
486 | _dist[(*_nodes)[i]] = INF; |
---|
487 | } |
---|
488 | Node u, v; |
---|
489 | Arc e; |
---|
490 | for (int i = 0; i < int(_nodes->size()); ++i) { |
---|
491 | v = (*_nodes)[i]; |
---|
492 | for (int j = 0; j < int(_in_arcs[v].size()); ++j) { |
---|
493 | e = _in_arcs[v][j]; |
---|
494 | u = _gr.source(e); |
---|
495 | if (_length[e] < _dist[u]) { |
---|
496 | _dist[u] = _length[e]; |
---|
497 | _policy[u] = e; |
---|
498 | } |
---|
499 | } |
---|
500 | } |
---|
501 | return true; |
---|
502 | } |
---|
503 | |
---|
504 | // Find the minimum mean cycle in the policy graph |
---|
505 | void findPolicyCycle() { |
---|
506 | for (int i = 0; i < int(_nodes->size()); ++i) { |
---|
507 | _level[(*_nodes)[i]] = -1; |
---|
508 | } |
---|
509 | LargeValue clength; |
---|
510 | int csize; |
---|
511 | Node u, v; |
---|
512 | _curr_found = false; |
---|
513 | for (int i = 0; i < int(_nodes->size()); ++i) { |
---|
514 | u = (*_nodes)[i]; |
---|
515 | if (_level[u] >= 0) continue; |
---|
516 | for (; _level[u] < 0; u = _gr.target(_policy[u])) { |
---|
517 | _level[u] = i; |
---|
518 | } |
---|
519 | if (_level[u] == i) { |
---|
520 | // A cycle is found |
---|
521 | clength = _length[_policy[u]]; |
---|
522 | csize = 1; |
---|
523 | for (v = u; (v = _gr.target(_policy[v])) != u; ) { |
---|
524 | clength += _length[_policy[v]]; |
---|
525 | ++csize; |
---|
526 | } |
---|
527 | if ( !_curr_found || |
---|
528 | (clength * _curr_size < _curr_length * csize) ) { |
---|
529 | _curr_found = true; |
---|
530 | _curr_length = clength; |
---|
531 | _curr_size = csize; |
---|
532 | _curr_node = u; |
---|
533 | } |
---|
534 | } |
---|
535 | } |
---|
536 | } |
---|
537 | |
---|
538 | // Contract the policy graph and compute node distances |
---|
539 | bool computeNodeDistances() { |
---|
540 | // Find the component of the main cycle and compute node distances |
---|
541 | // using reverse BFS |
---|
542 | for (int i = 0; i < int(_nodes->size()); ++i) { |
---|
543 | _reached[(*_nodes)[i]] = false; |
---|
544 | } |
---|
545 | _qfront = _qback = 0; |
---|
546 | _queue[0] = _curr_node; |
---|
547 | _reached[_curr_node] = true; |
---|
548 | _dist[_curr_node] = 0; |
---|
549 | Node u, v; |
---|
550 | Arc e; |
---|
551 | while (_qfront <= _qback) { |
---|
552 | v = _queue[_qfront++]; |
---|
553 | for (int j = 0; j < int(_in_arcs[v].size()); ++j) { |
---|
554 | e = _in_arcs[v][j]; |
---|
555 | u = _gr.source(e); |
---|
556 | if (_policy[u] == e && !_reached[u]) { |
---|
557 | _reached[u] = true; |
---|
558 | _dist[u] = _dist[v] + _length[e] * _curr_size - _curr_length; |
---|
559 | _queue[++_qback] = u; |
---|
560 | } |
---|
561 | } |
---|
562 | } |
---|
563 | |
---|
564 | // Connect all other nodes to this component and compute node |
---|
565 | // distances using reverse BFS |
---|
566 | _qfront = 0; |
---|
567 | while (_qback < int(_nodes->size())-1) { |
---|
568 | v = _queue[_qfront++]; |
---|
569 | for (int j = 0; j < int(_in_arcs[v].size()); ++j) { |
---|
570 | e = _in_arcs[v][j]; |
---|
571 | u = _gr.source(e); |
---|
572 | if (!_reached[u]) { |
---|
573 | _reached[u] = true; |
---|
574 | _policy[u] = e; |
---|
575 | _dist[u] = _dist[v] + _length[e] * _curr_size - _curr_length; |
---|
576 | _queue[++_qback] = u; |
---|
577 | } |
---|
578 | } |
---|
579 | } |
---|
580 | |
---|
581 | // Improve node distances |
---|
582 | bool improved = false; |
---|
583 | for (int i = 0; i < int(_nodes->size()); ++i) { |
---|
584 | v = (*_nodes)[i]; |
---|
585 | for (int j = 0; j < int(_in_arcs[v].size()); ++j) { |
---|
586 | e = _in_arcs[v][j]; |
---|
587 | u = _gr.source(e); |
---|
588 | LargeValue delta = _dist[v] + _length[e] * _curr_size - _curr_length; |
---|
589 | if (_tolerance.less(delta, _dist[u])) { |
---|
590 | _dist[u] = delta; |
---|
591 | _policy[u] = e; |
---|
592 | improved = true; |
---|
593 | } |
---|
594 | } |
---|
595 | } |
---|
596 | return improved; |
---|
597 | } |
---|
598 | |
---|
599 | }; //class Howard |
---|
600 | |
---|
601 | ///@} |
---|
602 | |
---|
603 | } //namespace lemon |
---|
604 | |
---|
605 | #endif //LEMON_HOWARD_H |
---|