1 /* -*- mode: C++; indent-tabs-mode: nil; -*- |
|
2 * |
|
3 * This file is a part of LEMON, a generic C++ optimization library. |
|
4 * |
|
5 * Copyright (C) 2003-2009 |
|
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_FIB_HEAP_H |
|
20 #define LEMON_FIB_HEAP_H |
|
21 |
|
22 ///\file |
|
23 ///\ingroup auxdat |
|
24 ///\brief Fibonacci Heap implementation. |
|
25 |
|
26 #include <vector> |
|
27 #include <functional> |
|
28 #include <lemon/math.h> |
|
29 |
|
30 namespace lemon { |
|
31 |
|
32 /// \ingroup auxdat |
|
33 /// |
|
34 ///\brief Fibonacci Heap. |
|
35 /// |
|
36 ///This class implements the \e Fibonacci \e heap data structure. A \e heap |
|
37 ///is a data structure for storing items with specified values called \e |
|
38 ///priorities in such a way that finding the item with minimum priority is |
|
39 ///efficient. \c CMP specifies the ordering of the priorities. In a heap |
|
40 ///one can change the priority of an item, add or erase an item, etc. |
|
41 /// |
|
42 ///The methods \ref increase and \ref erase are not efficient in a Fibonacci |
|
43 ///heap. In case of many calls to these operations, it is better to use a |
|
44 ///\ref BinHeap "binary heap". |
|
45 /// |
|
46 ///\param PRIO Type of the priority of the items. |
|
47 ///\param IM A read and writable Item int map, used internally |
|
48 ///to handle the cross references. |
|
49 ///\param CMP A class for the ordering of the priorities. The |
|
50 ///default is \c std::less<PRIO>. |
|
51 /// |
|
52 ///\sa BinHeap |
|
53 ///\sa Dijkstra |
|
54 #ifdef DOXYGEN |
|
55 template <typename PRIO, typename IM, typename CMP> |
|
56 #else |
|
57 template <typename PRIO, typename IM, typename CMP = std::less<PRIO> > |
|
58 #endif |
|
59 class FibHeap { |
|
60 public: |
|
61 ///\e |
|
62 typedef IM ItemIntMap; |
|
63 ///\e |
|
64 typedef PRIO Prio; |
|
65 ///\e |
|
66 typedef typename ItemIntMap::Key Item; |
|
67 ///\e |
|
68 typedef std::pair<Item,Prio> Pair; |
|
69 ///\e |
|
70 typedef CMP Compare; |
|
71 |
|
72 private: |
|
73 class Store; |
|
74 |
|
75 std::vector<Store> _data; |
|
76 int _minimum; |
|
77 ItemIntMap &_iim; |
|
78 Compare _comp; |
|
79 int _num; |
|
80 |
|
81 public: |
|
82 |
|
83 /// \brief Type to represent the items states. |
|
84 /// |
|
85 /// Each Item element have a state associated to it. It may be "in heap", |
|
86 /// "pre heap" or "post heap". The latter two are indifferent from the |
|
87 /// heap's point of view, but may be useful to the user. |
|
88 /// |
|
89 /// The item-int map must be initialized in such way that it assigns |
|
90 /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap. |
|
91 enum State { |
|
92 IN_HEAP = 0, ///< = 0. |
|
93 PRE_HEAP = -1, ///< = -1. |
|
94 POST_HEAP = -2 ///< = -2. |
|
95 }; |
|
96 |
|
97 /// \brief The constructor |
|
98 /// |
|
99 /// \c map should be given to the constructor, since it is |
|
100 /// used internally to handle the cross references. |
|
101 explicit FibHeap(ItemIntMap &map) |
|
102 : _minimum(0), _iim(map), _num() {} |
|
103 |
|
104 /// \brief The constructor |
|
105 /// |
|
106 /// \c map should be given to the constructor, since it is used |
|
107 /// internally to handle the cross references. \c comp is an |
|
108 /// object for ordering of the priorities. |
|
109 FibHeap(ItemIntMap &map, const Compare &comp) |
|
110 : _minimum(0), _iim(map), _comp(comp), _num() {} |
|
111 |
|
112 /// \brief The number of items stored in the heap. |
|
113 /// |
|
114 /// Returns the number of items stored in the heap. |
|
115 int size() const { return _num; } |
|
116 |
|
117 /// \brief Checks if the heap stores no items. |
|
118 /// |
|
119 /// Returns \c true if and only if the heap stores no items. |
|
120 bool empty() const { return _num==0; } |
|
121 |
|
122 /// \brief Make empty this heap. |
|
123 /// |
|
124 /// Make empty this heap. It does not change the cross reference |
|
125 /// map. If you want to reuse a heap what is not surely empty you |
|
126 /// should first clear the heap and after that you should set the |
|
127 /// cross reference map for each item to \c PRE_HEAP. |
|
128 void clear() { |
|
129 _data.clear(); _minimum = 0; _num = 0; |
|
130 } |
|
131 |
|
132 /// \brief \c item gets to the heap with priority \c value independently |
|
133 /// if \c item was already there. |
|
134 /// |
|
135 /// This method calls \ref push(\c item, \c value) if \c item is not |
|
136 /// stored in the heap and it calls \ref decrease(\c item, \c value) or |
|
137 /// \ref increase(\c item, \c value) otherwise. |
|
138 void set (const Item& item, const Prio& value) { |
|
139 int i=_iim[item]; |
|
140 if ( i >= 0 && _data[i].in ) { |
|
141 if ( _comp(value, _data[i].prio) ) decrease(item, value); |
|
142 if ( _comp(_data[i].prio, value) ) increase(item, value); |
|
143 } else push(item, value); |
|
144 } |
|
145 |
|
146 /// \brief Adds \c item to the heap with priority \c value. |
|
147 /// |
|
148 /// Adds \c item to the heap with priority \c value. |
|
149 /// \pre \c item must not be stored in the heap. |
|
150 void push (const Item& item, const Prio& value) { |
|
151 int i=_iim[item]; |
|
152 if ( i < 0 ) { |
|
153 int s=_data.size(); |
|
154 _iim.set( item, s ); |
|
155 Store st; |
|
156 st.name=item; |
|
157 _data.push_back(st); |
|
158 i=s; |
|
159 } else { |
|
160 _data[i].parent=_data[i].child=-1; |
|
161 _data[i].degree=0; |
|
162 _data[i].in=true; |
|
163 _data[i].marked=false; |
|
164 } |
|
165 |
|
166 if ( _num ) { |
|
167 _data[_data[_minimum].right_neighbor].left_neighbor=i; |
|
168 _data[i].right_neighbor=_data[_minimum].right_neighbor; |
|
169 _data[_minimum].right_neighbor=i; |
|
170 _data[i].left_neighbor=_minimum; |
|
171 if ( _comp( value, _data[_minimum].prio) ) _minimum=i; |
|
172 } else { |
|
173 _data[i].right_neighbor=_data[i].left_neighbor=i; |
|
174 _minimum=i; |
|
175 } |
|
176 _data[i].prio=value; |
|
177 ++_num; |
|
178 } |
|
179 |
|
180 /// \brief Returns the item with minimum priority relative to \c Compare. |
|
181 /// |
|
182 /// This method returns the item with minimum priority relative to \c |
|
183 /// Compare. |
|
184 /// \pre The heap must be nonempty. |
|
185 Item top() const { return _data[_minimum].name; } |
|
186 |
|
187 /// \brief Returns the minimum priority relative to \c Compare. |
|
188 /// |
|
189 /// It returns the minimum priority relative to \c Compare. |
|
190 /// \pre The heap must be nonempty. |
|
191 const Prio& prio() const { return _data[_minimum].prio; } |
|
192 |
|
193 /// \brief Returns the priority of \c item. |
|
194 /// |
|
195 /// It returns the priority of \c item. |
|
196 /// \pre \c item must be in the heap. |
|
197 const Prio& operator[](const Item& item) const { |
|
198 return _data[_iim[item]].prio; |
|
199 } |
|
200 |
|
201 /// \brief Deletes the item with minimum priority relative to \c Compare. |
|
202 /// |
|
203 /// This method deletes the item with minimum priority relative to \c |
|
204 /// Compare from the heap. |
|
205 /// \pre The heap must be non-empty. |
|
206 void pop() { |
|
207 /*The first case is that there are only one root.*/ |
|
208 if ( _data[_minimum].left_neighbor==_minimum ) { |
|
209 _data[_minimum].in=false; |
|
210 if ( _data[_minimum].degree!=0 ) { |
|
211 makeroot(_data[_minimum].child); |
|
212 _minimum=_data[_minimum].child; |
|
213 balance(); |
|
214 } |
|
215 } else { |
|
216 int right=_data[_minimum].right_neighbor; |
|
217 unlace(_minimum); |
|
218 _data[_minimum].in=false; |
|
219 if ( _data[_minimum].degree > 0 ) { |
|
220 int left=_data[_minimum].left_neighbor; |
|
221 int child=_data[_minimum].child; |
|
222 int last_child=_data[child].left_neighbor; |
|
223 |
|
224 makeroot(child); |
|
225 |
|
226 _data[left].right_neighbor=child; |
|
227 _data[child].left_neighbor=left; |
|
228 _data[right].left_neighbor=last_child; |
|
229 _data[last_child].right_neighbor=right; |
|
230 } |
|
231 _minimum=right; |
|
232 balance(); |
|
233 } // the case where there are more roots |
|
234 --_num; |
|
235 } |
|
236 |
|
237 /// \brief Deletes \c item from the heap. |
|
238 /// |
|
239 /// This method deletes \c item from the heap, if \c item was already |
|
240 /// stored in the heap. It is quite inefficient in Fibonacci heaps. |
|
241 void erase (const Item& item) { |
|
242 int i=_iim[item]; |
|
243 |
|
244 if ( i >= 0 && _data[i].in ) { |
|
245 if ( _data[i].parent!=-1 ) { |
|
246 int p=_data[i].parent; |
|
247 cut(i,p); |
|
248 cascade(p); |
|
249 } |
|
250 _minimum=i; //As if its prio would be -infinity |
|
251 pop(); |
|
252 } |
|
253 } |
|
254 |
|
255 /// \brief Decreases the priority of \c item to \c value. |
|
256 /// |
|
257 /// This method decreases the priority of \c item to \c value. |
|
258 /// \pre \c item must be stored in the heap with priority at least \c |
|
259 /// value relative to \c Compare. |
|
260 void decrease (Item item, const Prio& value) { |
|
261 int i=_iim[item]; |
|
262 _data[i].prio=value; |
|
263 int p=_data[i].parent; |
|
264 |
|
265 if ( p!=-1 && _comp(value, _data[p].prio) ) { |
|
266 cut(i,p); |
|
267 cascade(p); |
|
268 } |
|
269 if ( _comp(value, _data[_minimum].prio) ) _minimum=i; |
|
270 } |
|
271 |
|
272 /// \brief Increases the priority of \c item to \c value. |
|
273 /// |
|
274 /// This method sets the priority of \c item to \c value. Though |
|
275 /// there is no precondition on the priority of \c item, this |
|
276 /// method should be used only if it is indeed necessary to increase |
|
277 /// (relative to \c Compare) the priority of \c item, because this |
|
278 /// method is inefficient. |
|
279 void increase (Item item, const Prio& value) { |
|
280 erase(item); |
|
281 push(item, value); |
|
282 } |
|
283 |
|
284 |
|
285 /// \brief Returns if \c item is in, has already been in, or has never |
|
286 /// been in the heap. |
|
287 /// |
|
288 /// This method returns PRE_HEAP if \c item has never been in the |
|
289 /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
|
290 /// otherwise. In the latter case it is possible that \c item will |
|
291 /// get back to the heap again. |
|
292 State state(const Item &item) const { |
|
293 int i=_iim[item]; |
|
294 if( i>=0 ) { |
|
295 if ( _data[i].in ) i=0; |
|
296 else i=-2; |
|
297 } |
|
298 return State(i); |
|
299 } |
|
300 |
|
301 /// \brief Sets the state of the \c item in the heap. |
|
302 /// |
|
303 /// Sets the state of the \c item in the heap. It can be used to |
|
304 /// manually clear the heap when it is important to achive the |
|
305 /// better time _complexity. |
|
306 /// \param i The item. |
|
307 /// \param st The state. It should not be \c IN_HEAP. |
|
308 void state(const Item& i, State st) { |
|
309 switch (st) { |
|
310 case POST_HEAP: |
|
311 case PRE_HEAP: |
|
312 if (state(i) == IN_HEAP) { |
|
313 erase(i); |
|
314 } |
|
315 _iim[i] = st; |
|
316 break; |
|
317 case IN_HEAP: |
|
318 break; |
|
319 } |
|
320 } |
|
321 |
|
322 private: |
|
323 |
|
324 void balance() { |
|
325 |
|
326 int maxdeg=int( std::floor( 2.08*log(double(_data.size()))))+1; |
|
327 |
|
328 std::vector<int> A(maxdeg,-1); |
|
329 |
|
330 /* |
|
331 *Recall that now minimum does not point to the minimum prio element. |
|
332 *We set minimum to this during balance(). |
|
333 */ |
|
334 int anchor=_data[_minimum].left_neighbor; |
|
335 int next=_minimum; |
|
336 bool end=false; |
|
337 |
|
338 do { |
|
339 int active=next; |
|
340 if ( anchor==active ) end=true; |
|
341 int d=_data[active].degree; |
|
342 next=_data[active].right_neighbor; |
|
343 |
|
344 while (A[d]!=-1) { |
|
345 if( _comp(_data[active].prio, _data[A[d]].prio) ) { |
|
346 fuse(active,A[d]); |
|
347 } else { |
|
348 fuse(A[d],active); |
|
349 active=A[d]; |
|
350 } |
|
351 A[d]=-1; |
|
352 ++d; |
|
353 } |
|
354 A[d]=active; |
|
355 } while ( !end ); |
|
356 |
|
357 |
|
358 while ( _data[_minimum].parent >=0 ) |
|
359 _minimum=_data[_minimum].parent; |
|
360 int s=_minimum; |
|
361 int m=_minimum; |
|
362 do { |
|
363 if ( _comp(_data[s].prio, _data[_minimum].prio) ) _minimum=s; |
|
364 s=_data[s].right_neighbor; |
|
365 } while ( s != m ); |
|
366 } |
|
367 |
|
368 void makeroot(int c) { |
|
369 int s=c; |
|
370 do { |
|
371 _data[s].parent=-1; |
|
372 s=_data[s].right_neighbor; |
|
373 } while ( s != c ); |
|
374 } |
|
375 |
|
376 void cut(int a, int b) { |
|
377 /* |
|
378 *Replacing a from the children of b. |
|
379 */ |
|
380 --_data[b].degree; |
|
381 |
|
382 if ( _data[b].degree !=0 ) { |
|
383 int child=_data[b].child; |
|
384 if ( child==a ) |
|
385 _data[b].child=_data[child].right_neighbor; |
|
386 unlace(a); |
|
387 } |
|
388 |
|
389 |
|
390 /*Lacing a to the roots.*/ |
|
391 int right=_data[_minimum].right_neighbor; |
|
392 _data[_minimum].right_neighbor=a; |
|
393 _data[a].left_neighbor=_minimum; |
|
394 _data[a].right_neighbor=right; |
|
395 _data[right].left_neighbor=a; |
|
396 |
|
397 _data[a].parent=-1; |
|
398 _data[a].marked=false; |
|
399 } |
|
400 |
|
401 void cascade(int a) { |
|
402 if ( _data[a].parent!=-1 ) { |
|
403 int p=_data[a].parent; |
|
404 |
|
405 if ( _data[a].marked==false ) _data[a].marked=true; |
|
406 else { |
|
407 cut(a,p); |
|
408 cascade(p); |
|
409 } |
|
410 } |
|
411 } |
|
412 |
|
413 void fuse(int a, int b) { |
|
414 unlace(b); |
|
415 |
|
416 /*Lacing b under a.*/ |
|
417 _data[b].parent=a; |
|
418 |
|
419 if (_data[a].degree==0) { |
|
420 _data[b].left_neighbor=b; |
|
421 _data[b].right_neighbor=b; |
|
422 _data[a].child=b; |
|
423 } else { |
|
424 int child=_data[a].child; |
|
425 int last_child=_data[child].left_neighbor; |
|
426 _data[child].left_neighbor=b; |
|
427 _data[b].right_neighbor=child; |
|
428 _data[last_child].right_neighbor=b; |
|
429 _data[b].left_neighbor=last_child; |
|
430 } |
|
431 |
|
432 ++_data[a].degree; |
|
433 |
|
434 _data[b].marked=false; |
|
435 } |
|
436 |
|
437 /* |
|
438 *It is invoked only if a has siblings. |
|
439 */ |
|
440 void unlace(int a) { |
|
441 int leftn=_data[a].left_neighbor; |
|
442 int rightn=_data[a].right_neighbor; |
|
443 _data[leftn].right_neighbor=rightn; |
|
444 _data[rightn].left_neighbor=leftn; |
|
445 } |
|
446 |
|
447 |
|
448 class Store { |
|
449 friend class FibHeap; |
|
450 |
|
451 Item name; |
|
452 int parent; |
|
453 int left_neighbor; |
|
454 int right_neighbor; |
|
455 int child; |
|
456 int degree; |
|
457 bool marked; |
|
458 bool in; |
|
459 Prio prio; |
|
460 |
|
461 Store() : parent(-1), child(-1), degree(), marked(false), in(true) {} |
|
462 }; |
|
463 }; |
|
464 |
|
465 } //namespace lemon |
|
466 |
|
467 #endif //LEMON_FIB_HEAP_H |
|
468 |
|