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 | |
---|