1 | /* -*- C++ -*- |
---|
2 | * lemon/fib_heap.h - Part of LEMON, a generic C++ optimization library |
---|
3 | * |
---|
4 | * Copyright (C) 2006 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_FIB_HEAP_H |
---|
18 | #define LEMON_FIB_HEAP_H |
---|
19 | |
---|
20 | ///\file |
---|
21 | ///\ingroup auxdat |
---|
22 | ///\brief Fibonacci Heap implementation. |
---|
23 | |
---|
24 | #include <vector> |
---|
25 | #include <functional> |
---|
26 | #include <cmath> |
---|
27 | |
---|
28 | namespace lemon { |
---|
29 | |
---|
30 | /// \ingroup auxdat |
---|
31 | |
---|
32 | /// Fibonacci Heap. |
---|
33 | |
---|
34 | ///This class implements the \e Fibonacci \e heap data structure. A \e heap |
---|
35 | ///is a data structure for storing items with specified values called \e |
---|
36 | ///priorities in such a way that finding the item with minimum priority is |
---|
37 | ///efficient. \c Compare specifies the ordering of the priorities. In a heap |
---|
38 | ///one can change the priority of an item, add or erase an item, etc. |
---|
39 | /// |
---|
40 | ///The methods \ref increase and \ref erase are not efficient in a Fibonacci |
---|
41 | ///heap. In case of many calls to these operations, it is better to use a |
---|
42 | ///\e binary \e heap. |
---|
43 | /// |
---|
44 | ///\param Item Type of the items to be stored. |
---|
45 | ///\param Prio Type of the priority of the items. |
---|
46 | ///\param ItemIntMap A read and writable Item int map, used internally |
---|
47 | ///to handle the cross references. |
---|
48 | ///\param Compare A class for the ordering of the priorities. The |
---|
49 | ///default is \c std::less<Prio>. |
---|
50 | /// |
---|
51 | ///\sa BinHeap |
---|
52 | ///\sa Dijkstra |
---|
53 | ///\author Jacint Szabo |
---|
54 | |
---|
55 | #ifdef DOXYGEN |
---|
56 | template <typename Item, |
---|
57 | typename Prio, |
---|
58 | typename ItemIntMap, |
---|
59 | typename Compare> |
---|
60 | #else |
---|
61 | template <typename Item, |
---|
62 | typename Prio, |
---|
63 | typename ItemIntMap, |
---|
64 | typename Compare = std::less<Prio> > |
---|
65 | #endif |
---|
66 | class FibHeap { |
---|
67 | public: |
---|
68 | typedef Prio PrioType; |
---|
69 | |
---|
70 | private: |
---|
71 | class store; |
---|
72 | |
---|
73 | std::vector<store> container; |
---|
74 | int minimum; |
---|
75 | ItemIntMap &iimap; |
---|
76 | Compare comp; |
---|
77 | int num_items; |
---|
78 | |
---|
79 | public: |
---|
80 | ///Status of the nodes |
---|
81 | enum state_enum { |
---|
82 | ///The node is in the heap |
---|
83 | IN_HEAP = 0, |
---|
84 | ///The node has never been in the heap |
---|
85 | PRE_HEAP = -1, |
---|
86 | ///The node was in the heap but it got out of it |
---|
87 | POST_HEAP = -2 |
---|
88 | }; |
---|
89 | |
---|
90 | /// \brief The constructor |
---|
91 | /// |
---|
92 | /// \c _iimap should be given to the constructor, since it is |
---|
93 | /// used internally to handle the cross references. |
---|
94 | explicit FibHeap(ItemIntMap &_iimap) |
---|
95 | : minimum(0), iimap(_iimap), num_items() {} |
---|
96 | |
---|
97 | /// \brief The constructor |
---|
98 | /// |
---|
99 | /// \c _iimap should be given to the constructor, since it is used |
---|
100 | /// internally to handle the cross references. \c _comp is an |
---|
101 | /// object for ordering of the priorities. |
---|
102 | FibHeap(ItemIntMap &_iimap, const Compare &_comp) : minimum(0), |
---|
103 | iimap(_iimap), comp(_comp), num_items() {} |
---|
104 | |
---|
105 | /// \brief The number of items stored in the heap. |
---|
106 | /// |
---|
107 | /// Returns the number of items stored in the heap. |
---|
108 | int size() const { return num_items; } |
---|
109 | |
---|
110 | /// \brief Checks if the heap stores no items. |
---|
111 | /// |
---|
112 | /// Returns \c true if and only if the heap stores no items. |
---|
113 | bool empty() const { return num_items==0; } |
---|
114 | |
---|
115 | /// \brief Make empty this heap. |
---|
116 | /// |
---|
117 | /// Make empty this heap. |
---|
118 | void clear() { |
---|
119 | if (num_items != 0) { |
---|
120 | for (int i = 0; i < (int)container.size(); ++i) { |
---|
121 | iimap[container[i].name] = -2; |
---|
122 | } |
---|
123 | } |
---|
124 | container.clear(); minimum = 0; num_items = 0; |
---|
125 | } |
---|
126 | |
---|
127 | /// \brief \c item gets to the heap with priority \c value independently |
---|
128 | /// if \c item was already there. |
---|
129 | /// |
---|
130 | /// This method calls \ref push(\c item, \c value) if \c item is not |
---|
131 | /// stored in the heap and it calls \ref decrease(\c item, \c value) or |
---|
132 | /// \ref increase(\c item, \c value) otherwise. |
---|
133 | void set (Item const item, PrioType const value); |
---|
134 | |
---|
135 | /// \brief Adds \c item to the heap with priority \c value. |
---|
136 | /// |
---|
137 | /// Adds \c item to the heap with priority \c value. |
---|
138 | /// \pre \c item must not be stored in the heap. |
---|
139 | void push (Item const item, PrioType const value); |
---|
140 | |
---|
141 | /// \brief Returns the item with minimum priority relative to \c Compare. |
---|
142 | /// |
---|
143 | /// This method returns the item with minimum priority relative to \c |
---|
144 | /// Compare. |
---|
145 | /// \pre The heap must be nonempty. |
---|
146 | Item top() const { return container[minimum].name; } |
---|
147 | |
---|
148 | /// \brief Returns the minimum priority relative to \c Compare. |
---|
149 | /// |
---|
150 | /// It returns the minimum priority relative to \c Compare. |
---|
151 | /// \pre The heap must be nonempty. |
---|
152 | PrioType prio() const { return container[minimum].prio; } |
---|
153 | |
---|
154 | /// \brief Returns the priority of \c item. |
---|
155 | /// |
---|
156 | /// This function returns the priority of \c item. |
---|
157 | /// \pre \c item must be in the heap. |
---|
158 | PrioType& operator[](const Item& item) { |
---|
159 | return container[iimap[item]].prio; |
---|
160 | } |
---|
161 | |
---|
162 | /// \brief Returns the priority of \c item. |
---|
163 | /// |
---|
164 | /// It returns the priority of \c item. |
---|
165 | /// \pre \c item must be in the heap. |
---|
166 | const PrioType& operator[](const Item& item) const { |
---|
167 | return container[iimap[item]].prio; |
---|
168 | } |
---|
169 | |
---|
170 | |
---|
171 | /// \brief Deletes the item with minimum priority relative to \c Compare. |
---|
172 | /// |
---|
173 | /// This method deletes the item with minimum priority relative to \c |
---|
174 | /// Compare from the heap. |
---|
175 | /// \pre The heap must be non-empty. |
---|
176 | void pop(); |
---|
177 | |
---|
178 | /// \brief Deletes \c item from the heap. |
---|
179 | /// |
---|
180 | /// This method deletes \c item from the heap, if \c item was already |
---|
181 | /// stored in the heap. It is quite inefficient in Fibonacci heaps. |
---|
182 | void erase (const Item& item); |
---|
183 | |
---|
184 | /// \brief Decreases the priority of \c item to \c value. |
---|
185 | /// |
---|
186 | /// This method decreases the priority of \c item to \c value. |
---|
187 | /// \pre \c item must be stored in the heap with priority at least \c |
---|
188 | /// value relative to \c Compare. |
---|
189 | void decrease (Item item, PrioType const value); |
---|
190 | |
---|
191 | /// \brief Increases the priority of \c item to \c value. |
---|
192 | /// |
---|
193 | /// This method sets the priority of \c item to \c value. Though |
---|
194 | /// there is no precondition on the priority of \c item, this |
---|
195 | /// method should be used only if it is indeed necessary to increase |
---|
196 | /// (relative to \c Compare) the priority of \c item, because this |
---|
197 | /// method is inefficient. |
---|
198 | void increase (Item item, PrioType const value) { |
---|
199 | erase(item); |
---|
200 | push(item, value); |
---|
201 | } |
---|
202 | |
---|
203 | |
---|
204 | /// \brief Returns if \c item is in, has already been in, or has never |
---|
205 | /// been in the heap. |
---|
206 | /// |
---|
207 | /// This method returns PRE_HEAP if \c item has never been in the |
---|
208 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
---|
209 | /// otherwise. In the latter case it is possible that \c item will |
---|
210 | /// get back to the heap again. |
---|
211 | state_enum state(const Item &item) const { |
---|
212 | int i=iimap[item]; |
---|
213 | if( i>=0 ) { |
---|
214 | if ( container[i].in ) i=0; |
---|
215 | else i=-2; |
---|
216 | } |
---|
217 | return state_enum(i); |
---|
218 | } |
---|
219 | |
---|
220 | /// \brief Sets the state of the \c item in the heap. |
---|
221 | /// |
---|
222 | /// Sets the state of the \c item in the heap. It can be used to |
---|
223 | /// manually clear the heap when it is important to achive the |
---|
224 | /// better time complexity. |
---|
225 | /// \param i The item. |
---|
226 | /// \param st The state. It should not be \c IN_HEAP. |
---|
227 | void state(const Item& i, state_enum st) { |
---|
228 | switch (st) { |
---|
229 | case POST_HEAP: |
---|
230 | case PRE_HEAP: |
---|
231 | if (state(i) == IN_HEAP) { |
---|
232 | erase(i); |
---|
233 | } |
---|
234 | index[i] = st; |
---|
235 | break; |
---|
236 | } |
---|
237 | } |
---|
238 | |
---|
239 | private: |
---|
240 | |
---|
241 | void balance(); |
---|
242 | void makeroot(int c); |
---|
243 | void cut(int a, int b); |
---|
244 | void cascade(int a); |
---|
245 | void fuse(int a, int b); |
---|
246 | void unlace(int a); |
---|
247 | |
---|
248 | |
---|
249 | class store { |
---|
250 | friend class FibHeap; |
---|
251 | |
---|
252 | Item name; |
---|
253 | int parent; |
---|
254 | int left_neighbor; |
---|
255 | int right_neighbor; |
---|
256 | int child; |
---|
257 | int degree; |
---|
258 | bool marked; |
---|
259 | bool in; |
---|
260 | PrioType prio; |
---|
261 | |
---|
262 | store() : parent(-1), child(-1), degree(), marked(false), in(true) {} |
---|
263 | }; |
---|
264 | }; |
---|
265 | |
---|
266 | |
---|
267 | |
---|
268 | // ********************************************************************** |
---|
269 | // IMPLEMENTATIONS |
---|
270 | // ********************************************************************** |
---|
271 | |
---|
272 | template <typename Item, typename Prio, typename ItemIntMap, |
---|
273 | typename Compare> |
---|
274 | void FibHeap<Item, Prio, ItemIntMap, Compare>::set |
---|
275 | (Item const item, PrioType const value) |
---|
276 | { |
---|
277 | int i=iimap[item]; |
---|
278 | if ( i >= 0 && container[i].in ) { |
---|
279 | if ( comp(value, container[i].prio) ) decrease(item, value); |
---|
280 | if ( comp(container[i].prio, value) ) increase(item, value); |
---|
281 | } else push(item, value); |
---|
282 | } |
---|
283 | |
---|
284 | template <typename Item, typename Prio, typename ItemIntMap, |
---|
285 | typename Compare> |
---|
286 | void FibHeap<Item, Prio, ItemIntMap, Compare>::push |
---|
287 | (Item const item, PrioType const value) { |
---|
288 | int i=iimap[item]; |
---|
289 | if ( i < 0 ) { |
---|
290 | int s=container.size(); |
---|
291 | iimap.set( item, s ); |
---|
292 | store st; |
---|
293 | st.name=item; |
---|
294 | container.push_back(st); |
---|
295 | i=s; |
---|
296 | } else { |
---|
297 | container[i].parent=container[i].child=-1; |
---|
298 | container[i].degree=0; |
---|
299 | container[i].in=true; |
---|
300 | container[i].marked=false; |
---|
301 | } |
---|
302 | |
---|
303 | if ( num_items ) { |
---|
304 | container[container[minimum].right_neighbor].left_neighbor=i; |
---|
305 | container[i].right_neighbor=container[minimum].right_neighbor; |
---|
306 | container[minimum].right_neighbor=i; |
---|
307 | container[i].left_neighbor=minimum; |
---|
308 | if ( comp( value, container[minimum].prio) ) minimum=i; |
---|
309 | } else { |
---|
310 | container[i].right_neighbor=container[i].left_neighbor=i; |
---|
311 | minimum=i; |
---|
312 | } |
---|
313 | container[i].prio=value; |
---|
314 | ++num_items; |
---|
315 | } |
---|
316 | |
---|
317 | template <typename Item, typename Prio, typename ItemIntMap, |
---|
318 | typename Compare> |
---|
319 | void FibHeap<Item, Prio, ItemIntMap, Compare>::pop() { |
---|
320 | /*The first case is that there are only one root.*/ |
---|
321 | if ( container[minimum].left_neighbor==minimum ) { |
---|
322 | container[minimum].in=false; |
---|
323 | if ( container[minimum].degree!=0 ) { |
---|
324 | makeroot(container[minimum].child); |
---|
325 | minimum=container[minimum].child; |
---|
326 | balance(); |
---|
327 | } |
---|
328 | } else { |
---|
329 | int right=container[minimum].right_neighbor; |
---|
330 | unlace(minimum); |
---|
331 | container[minimum].in=false; |
---|
332 | if ( container[minimum].degree > 0 ) { |
---|
333 | int left=container[minimum].left_neighbor; |
---|
334 | int child=container[minimum].child; |
---|
335 | int last_child=container[child].left_neighbor; |
---|
336 | |
---|
337 | makeroot(child); |
---|
338 | |
---|
339 | container[left].right_neighbor=child; |
---|
340 | container[child].left_neighbor=left; |
---|
341 | container[right].left_neighbor=last_child; |
---|
342 | container[last_child].right_neighbor=right; |
---|
343 | } |
---|
344 | minimum=right; |
---|
345 | balance(); |
---|
346 | } // the case where there are more roots |
---|
347 | --num_items; |
---|
348 | } |
---|
349 | |
---|
350 | |
---|
351 | template <typename Item, typename Prio, typename ItemIntMap, |
---|
352 | typename Compare> |
---|
353 | void FibHeap<Item, Prio, ItemIntMap, Compare>::erase |
---|
354 | (const Item& item) { |
---|
355 | int i=iimap[item]; |
---|
356 | |
---|
357 | if ( i >= 0 && container[i].in ) { |
---|
358 | if ( container[i].parent!=-1 ) { |
---|
359 | int p=container[i].parent; |
---|
360 | cut(i,p); |
---|
361 | cascade(p); |
---|
362 | } |
---|
363 | minimum=i; //As if its prio would be -infinity |
---|
364 | pop(); |
---|
365 | } |
---|
366 | } |
---|
367 | |
---|
368 | template <typename Item, typename Prio, typename ItemIntMap, |
---|
369 | typename Compare> |
---|
370 | void FibHeap<Item, Prio, ItemIntMap, Compare>::decrease |
---|
371 | (Item item, PrioType const value) { |
---|
372 | int i=iimap[item]; |
---|
373 | container[i].prio=value; |
---|
374 | int p=container[i].parent; |
---|
375 | |
---|
376 | if ( p!=-1 && comp(value, container[p].prio) ) { |
---|
377 | cut(i,p); |
---|
378 | cascade(p); |
---|
379 | } |
---|
380 | if ( comp(value, container[minimum].prio) ) minimum=i; |
---|
381 | } |
---|
382 | |
---|
383 | |
---|
384 | template <typename Item, typename Prio, typename ItemIntMap, |
---|
385 | typename Compare> |
---|
386 | void FibHeap<Item, Prio, ItemIntMap, Compare>::balance() { |
---|
387 | |
---|
388 | int maxdeg=int( std::floor( 2.08*log(double(container.size()))))+1; |
---|
389 | |
---|
390 | std::vector<int> A(maxdeg,-1); |
---|
391 | |
---|
392 | /* |
---|
393 | *Recall that now minimum does not point to the minimum prio element. |
---|
394 | *We set minimum to this during balance(). |
---|
395 | */ |
---|
396 | int anchor=container[minimum].left_neighbor; |
---|
397 | int next=minimum; |
---|
398 | bool end=false; |
---|
399 | |
---|
400 | do { |
---|
401 | int active=next; |
---|
402 | if ( anchor==active ) end=true; |
---|
403 | int d=container[active].degree; |
---|
404 | next=container[active].right_neighbor; |
---|
405 | |
---|
406 | while (A[d]!=-1) { |
---|
407 | if( comp(container[active].prio, container[A[d]].prio) ) { |
---|
408 | fuse(active,A[d]); |
---|
409 | } else { |
---|
410 | fuse(A[d],active); |
---|
411 | active=A[d]; |
---|
412 | } |
---|
413 | A[d]=-1; |
---|
414 | ++d; |
---|
415 | } |
---|
416 | A[d]=active; |
---|
417 | } while ( !end ); |
---|
418 | |
---|
419 | |
---|
420 | while ( container[minimum].parent >=0 ) minimum=container[minimum].parent; |
---|
421 | int s=minimum; |
---|
422 | int m=minimum; |
---|
423 | do { |
---|
424 | if ( comp(container[s].prio, container[minimum].prio) ) minimum=s; |
---|
425 | s=container[s].right_neighbor; |
---|
426 | } while ( s != m ); |
---|
427 | } |
---|
428 | |
---|
429 | template <typename Item, typename Prio, typename ItemIntMap, |
---|
430 | typename Compare> |
---|
431 | void FibHeap<Item, Prio, ItemIntMap, Compare>::makeroot |
---|
432 | (int c) { |
---|
433 | int s=c; |
---|
434 | do { |
---|
435 | container[s].parent=-1; |
---|
436 | s=container[s].right_neighbor; |
---|
437 | } while ( s != c ); |
---|
438 | } |
---|
439 | |
---|
440 | |
---|
441 | template <typename Item, typename Prio, typename ItemIntMap, |
---|
442 | typename Compare> |
---|
443 | void FibHeap<Item, Prio, ItemIntMap, Compare>::cut |
---|
444 | (int a, int b) { |
---|
445 | /* |
---|
446 | *Replacing a from the children of b. |
---|
447 | */ |
---|
448 | --container[b].degree; |
---|
449 | |
---|
450 | if ( container[b].degree !=0 ) { |
---|
451 | int child=container[b].child; |
---|
452 | if ( child==a ) |
---|
453 | container[b].child=container[child].right_neighbor; |
---|
454 | unlace(a); |
---|
455 | } |
---|
456 | |
---|
457 | |
---|
458 | /*Lacing a to the roots.*/ |
---|
459 | int right=container[minimum].right_neighbor; |
---|
460 | container[minimum].right_neighbor=a; |
---|
461 | container[a].left_neighbor=minimum; |
---|
462 | container[a].right_neighbor=right; |
---|
463 | container[right].left_neighbor=a; |
---|
464 | |
---|
465 | container[a].parent=-1; |
---|
466 | container[a].marked=false; |
---|
467 | } |
---|
468 | |
---|
469 | |
---|
470 | template <typename Item, typename Prio, typename ItemIntMap, |
---|
471 | typename Compare> |
---|
472 | void FibHeap<Item, Prio, ItemIntMap, Compare>::cascade |
---|
473 | (int a) |
---|
474 | { |
---|
475 | if ( container[a].parent!=-1 ) { |
---|
476 | int p=container[a].parent; |
---|
477 | |
---|
478 | if ( container[a].marked==false ) container[a].marked=true; |
---|
479 | else { |
---|
480 | cut(a,p); |
---|
481 | cascade(p); |
---|
482 | } |
---|
483 | } |
---|
484 | } |
---|
485 | |
---|
486 | |
---|
487 | template <typename Item, typename Prio, typename ItemIntMap, |
---|
488 | typename Compare> |
---|
489 | void FibHeap<Item, Prio, ItemIntMap, Compare>::fuse |
---|
490 | (int a, int b) { |
---|
491 | unlace(b); |
---|
492 | |
---|
493 | /*Lacing b under a.*/ |
---|
494 | container[b].parent=a; |
---|
495 | |
---|
496 | if (container[a].degree==0) { |
---|
497 | container[b].left_neighbor=b; |
---|
498 | container[b].right_neighbor=b; |
---|
499 | container[a].child=b; |
---|
500 | } else { |
---|
501 | int child=container[a].child; |
---|
502 | int last_child=container[child].left_neighbor; |
---|
503 | container[child].left_neighbor=b; |
---|
504 | container[b].right_neighbor=child; |
---|
505 | container[last_child].right_neighbor=b; |
---|
506 | container[b].left_neighbor=last_child; |
---|
507 | } |
---|
508 | |
---|
509 | ++container[a].degree; |
---|
510 | |
---|
511 | container[b].marked=false; |
---|
512 | } |
---|
513 | |
---|
514 | |
---|
515 | /* |
---|
516 | *It is invoked only if a has siblings. |
---|
517 | */ |
---|
518 | template <typename Item, typename Prio, typename ItemIntMap, |
---|
519 | typename Compare> |
---|
520 | void FibHeap<Item, Prio, ItemIntMap, Compare>::unlace |
---|
521 | (int a) { |
---|
522 | int leftn=container[a].left_neighbor; |
---|
523 | int rightn=container[a].right_neighbor; |
---|
524 | container[leftn].right_neighbor=rightn; |
---|
525 | container[rightn].left_neighbor=leftn; |
---|
526 | } |
---|
527 | |
---|
528 | |
---|
529 | } //namespace lemon |
---|
530 | |
---|
531 | #endif //LEMON_FIB_HEAP_H |
---|
532 | |
---|