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_BINOM_HEAP_H |
---|
20 | #define LEMON_BINOM_HEAP_H |
---|
21 | |
---|
22 | ///\file |
---|
23 | ///\ingroup heaps |
---|
24 | ///\brief Binomial Heap implementation. |
---|
25 | |
---|
26 | #include <vector> |
---|
27 | #include <utility> |
---|
28 | #include <functional> |
---|
29 | #include <lemon/math.h> |
---|
30 | #include <lemon/counter.h> |
---|
31 | |
---|
32 | namespace lemon { |
---|
33 | |
---|
34 | /// \ingroup heaps |
---|
35 | /// |
---|
36 | ///\brief Binomial heap data structure. |
---|
37 | /// |
---|
38 | /// This class implements the \e binomial \e heap data structure. |
---|
39 | /// It fully conforms to the \ref concepts::Heap "heap concept". |
---|
40 | /// |
---|
41 | /// The methods \ref increase() and \ref erase() are not efficient |
---|
42 | /// in a binomial heap. In case of many calls of these operations, |
---|
43 | /// it is better to use other heap structure, e.g. \ref BinHeap |
---|
44 | /// "binary heap". |
---|
45 | /// |
---|
46 | /// \tparam PR Type of the priorities of the items. |
---|
47 | /// \tparam IM A read-writable item map with \c int values, used |
---|
48 | /// internally to handle the cross references. |
---|
49 | /// \tparam CMP A functor class for comparing the priorities. |
---|
50 | /// The default is \c std::less<PR>. |
---|
51 | #ifdef DOXYGEN |
---|
52 | template <typename PR, typename IM, typename CMP> |
---|
53 | #else |
---|
54 | template <typename PR, typename IM, typename CMP = std::less<PR> > |
---|
55 | #endif |
---|
56 | class BinomHeap { |
---|
57 | public: |
---|
58 | /// Type of the item-int map. |
---|
59 | typedef IM ItemIntMap; |
---|
60 | /// Type of the priorities. |
---|
61 | typedef PR Prio; |
---|
62 | /// Type of the items stored in the heap. |
---|
63 | typedef typename ItemIntMap::Key Item; |
---|
64 | /// Functor type for comparing the priorities. |
---|
65 | typedef CMP Compare; |
---|
66 | |
---|
67 | /// \brief Type to represent the states of the items. |
---|
68 | /// |
---|
69 | /// Each item has a state associated to it. It can be "in heap", |
---|
70 | /// "pre-heap" or "post-heap". The latter two are indifferent from the |
---|
71 | /// heap's point of view, but may be useful to the user. |
---|
72 | /// |
---|
73 | /// The item-int map must be initialized in such way that it assigns |
---|
74 | /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap. |
---|
75 | enum State { |
---|
76 | IN_HEAP = 0, ///< = 0. |
---|
77 | PRE_HEAP = -1, ///< = -1. |
---|
78 | POST_HEAP = -2 ///< = -2. |
---|
79 | }; |
---|
80 | |
---|
81 | private: |
---|
82 | class store; |
---|
83 | |
---|
84 | std::vector<store> _data; |
---|
85 | int _min, _head; |
---|
86 | ItemIntMap &_iim; |
---|
87 | Compare _comp; |
---|
88 | int _num_items; |
---|
89 | |
---|
90 | public: |
---|
91 | /// \brief Constructor. |
---|
92 | /// |
---|
93 | /// Constructor. |
---|
94 | /// \param map A map that assigns \c int values to the items. |
---|
95 | /// It is used internally to handle the cross references. |
---|
96 | /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. |
---|
97 | explicit BinomHeap(ItemIntMap &map) |
---|
98 | : _min(0), _head(-1), _iim(map), _num_items(0) {} |
---|
99 | |
---|
100 | /// \brief Constructor. |
---|
101 | /// |
---|
102 | /// Constructor. |
---|
103 | /// \param map A map that assigns \c int values to the items. |
---|
104 | /// It is used internally to handle the cross references. |
---|
105 | /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. |
---|
106 | /// \param comp The function object used for comparing the priorities. |
---|
107 | BinomHeap(ItemIntMap &map, const Compare &comp) |
---|
108 | : _min(0), _head(-1), _iim(map), _comp(comp), _num_items(0) {} |
---|
109 | |
---|
110 | /// \brief The number of items stored in the heap. |
---|
111 | /// |
---|
112 | /// This function returns the number of items stored in the heap. |
---|
113 | int size() const { return _num_items; } |
---|
114 | |
---|
115 | /// \brief Check if the heap is empty. |
---|
116 | /// |
---|
117 | /// This function returns \c true if the heap is empty. |
---|
118 | bool empty() const { return _num_items==0; } |
---|
119 | |
---|
120 | /// \brief Make the heap empty. |
---|
121 | /// |
---|
122 | /// This functon makes the heap empty. |
---|
123 | /// It does not change the cross reference map. If you want to reuse |
---|
124 | /// a heap that is not surely empty, you should first clear it and |
---|
125 | /// then you should set the cross reference map to \c PRE_HEAP |
---|
126 | /// for each item. |
---|
127 | void clear() { |
---|
128 | _data.clear(); _min=0; _num_items=0; _head=-1; |
---|
129 | } |
---|
130 | |
---|
131 | /// \brief Set the priority of an item or insert it, if it is |
---|
132 | /// not stored in the heap. |
---|
133 | /// |
---|
134 | /// This method sets the priority of the given item if it is |
---|
135 | /// already stored in the heap. Otherwise it inserts the given |
---|
136 | /// item into the heap with the given priority. |
---|
137 | /// \param item The item. |
---|
138 | /// \param value The priority. |
---|
139 | void set (const Item& item, const Prio& value) { |
---|
140 | int i=_iim[item]; |
---|
141 | if ( i >= 0 && _data[i].in ) { |
---|
142 | if ( _comp(value, _data[i].prio) ) decrease(item, value); |
---|
143 | if ( _comp(_data[i].prio, value) ) increase(item, value); |
---|
144 | } else push(item, value); |
---|
145 | } |
---|
146 | |
---|
147 | /// \brief Insert an item into the heap with the given priority. |
---|
148 | /// |
---|
149 | /// This function inserts the given item into the heap with the |
---|
150 | /// given priority. |
---|
151 | /// \param item The item to insert. |
---|
152 | /// \param value The priority of the item. |
---|
153 | /// \pre \e item must not be stored in the heap. |
---|
154 | void push (const Item& item, const Prio& value) { |
---|
155 | int i=_iim[item]; |
---|
156 | if ( i<0 ) { |
---|
157 | int s=_data.size(); |
---|
158 | _iim.set( item,s ); |
---|
159 | store st; |
---|
160 | st.name=item; |
---|
161 | _data.push_back(st); |
---|
162 | i=s; |
---|
163 | } |
---|
164 | else { |
---|
165 | _data[i].parent=_data[i].right_neighbor=_data[i].child=-1; |
---|
166 | _data[i].degree=0; |
---|
167 | _data[i].in=true; |
---|
168 | } |
---|
169 | _data[i].prio=value; |
---|
170 | |
---|
171 | if( 0==_num_items ) { _head=i; _min=i; } |
---|
172 | else { merge(i); } |
---|
173 | |
---|
174 | _min = findMin(); |
---|
175 | |
---|
176 | ++_num_items; |
---|
177 | } |
---|
178 | |
---|
179 | /// \brief Return the item having minimum priority. |
---|
180 | /// |
---|
181 | /// This function returns the item having minimum priority. |
---|
182 | /// \pre The heap must be non-empty. |
---|
183 | Item top() const { return _data[_min].name; } |
---|
184 | |
---|
185 | /// \brief The minimum priority. |
---|
186 | /// |
---|
187 | /// This function returns the minimum priority. |
---|
188 | /// \pre The heap must be non-empty. |
---|
189 | Prio prio() const { return _data[_min].prio; } |
---|
190 | |
---|
191 | /// \brief The priority of the given item. |
---|
192 | /// |
---|
193 | /// This function returns the priority of the given item. |
---|
194 | /// \param item The item. |
---|
195 | /// \pre \e item must be in the heap. |
---|
196 | const Prio& operator[](const Item& item) const { |
---|
197 | return _data[_iim[item]].prio; |
---|
198 | } |
---|
199 | |
---|
200 | /// \brief Remove the item having minimum priority. |
---|
201 | /// |
---|
202 | /// This function removes the item having minimum priority. |
---|
203 | /// \pre The heap must be non-empty. |
---|
204 | void pop() { |
---|
205 | _data[_min].in=false; |
---|
206 | |
---|
207 | int head_child=-1; |
---|
208 | if ( _data[_min].child!=-1 ) { |
---|
209 | int child=_data[_min].child; |
---|
210 | int neighb; |
---|
211 | int prev=-1; |
---|
212 | while( child!=-1 ) { |
---|
213 | neighb=_data[child].right_neighbor; |
---|
214 | _data[child].parent=-1; |
---|
215 | _data[child].right_neighbor=prev; |
---|
216 | head_child=child; |
---|
217 | prev=child; |
---|
218 | child=neighb; |
---|
219 | } |
---|
220 | } |
---|
221 | |
---|
222 | // The first case is that there are only one root. |
---|
223 | if ( -1==_data[_head].right_neighbor ) { |
---|
224 | _head=head_child; |
---|
225 | } |
---|
226 | // The case where there are more roots. |
---|
227 | else { |
---|
228 | if( _head!=_min ) { unlace(_min); } |
---|
229 | else { _head=_data[_head].right_neighbor; } |
---|
230 | |
---|
231 | merge(head_child); |
---|
232 | } |
---|
233 | _min=findMin(); |
---|
234 | --_num_items; |
---|
235 | } |
---|
236 | |
---|
237 | /// \brief Remove the given item from the heap. |
---|
238 | /// |
---|
239 | /// This function removes the given item from the heap if it is |
---|
240 | /// already stored. |
---|
241 | /// \param item The item to delete. |
---|
242 | /// \pre \e item must be in the heap. |
---|
243 | void erase (const Item& item) { |
---|
244 | int i=_iim[item]; |
---|
245 | if ( i >= 0 && _data[i].in ) { |
---|
246 | decrease( item, _data[_min].prio-1 ); |
---|
247 | pop(); |
---|
248 | } |
---|
249 | } |
---|
250 | |
---|
251 | /// \brief Decrease the priority of an item to the given value. |
---|
252 | /// |
---|
253 | /// This function decreases the priority of an item to the given value. |
---|
254 | /// \param item The item. |
---|
255 | /// \param value The priority. |
---|
256 | /// \pre \e item must be stored in the heap with priority at least \e value. |
---|
257 | void decrease (Item item, const Prio& value) { |
---|
258 | int i=_iim[item]; |
---|
259 | |
---|
260 | if( _comp( value,_data[i].prio ) ) { |
---|
261 | _data[i].prio=value; |
---|
262 | |
---|
263 | int p_loc=_data[i].parent, loc=i; |
---|
264 | int parent, child, neighb; |
---|
265 | |
---|
266 | while( -1!=p_loc && _comp(_data[loc].prio,_data[p_loc].prio) ) { |
---|
267 | |
---|
268 | // parent set for other loc_child |
---|
269 | child=_data[loc].child; |
---|
270 | while( -1!=child ) { |
---|
271 | _data[child].parent=p_loc; |
---|
272 | child=_data[child].right_neighbor; |
---|
273 | } |
---|
274 | |
---|
275 | // parent set for other p_loc_child |
---|
276 | child=_data[p_loc].child; |
---|
277 | while( -1!=child ) { |
---|
278 | _data[child].parent=loc; |
---|
279 | child=_data[child].right_neighbor; |
---|
280 | } |
---|
281 | |
---|
282 | child=_data[p_loc].child; |
---|
283 | _data[p_loc].child=_data[loc].child; |
---|
284 | if( child==loc ) |
---|
285 | child=p_loc; |
---|
286 | _data[loc].child=child; |
---|
287 | |
---|
288 | // left_neighb set for p_loc |
---|
289 | if( _data[loc].child!=p_loc ) { |
---|
290 | while( _data[child].right_neighbor!=loc ) |
---|
291 | child=_data[child].right_neighbor; |
---|
292 | _data[child].right_neighbor=p_loc; |
---|
293 | } |
---|
294 | |
---|
295 | // left_neighb set for loc |
---|
296 | parent=_data[p_loc].parent; |
---|
297 | if( -1!=parent ) child=_data[parent].child; |
---|
298 | else child=_head; |
---|
299 | |
---|
300 | if( child!=p_loc ) { |
---|
301 | while( _data[child].right_neighbor!=p_loc ) |
---|
302 | child=_data[child].right_neighbor; |
---|
303 | _data[child].right_neighbor=loc; |
---|
304 | } |
---|
305 | |
---|
306 | neighb=_data[p_loc].right_neighbor; |
---|
307 | _data[p_loc].right_neighbor=_data[loc].right_neighbor; |
---|
308 | _data[loc].right_neighbor=neighb; |
---|
309 | |
---|
310 | _data[p_loc].parent=loc; |
---|
311 | _data[loc].parent=parent; |
---|
312 | |
---|
313 | if( -1!=parent && _data[parent].child==p_loc ) |
---|
314 | _data[parent].child=loc; |
---|
315 | |
---|
316 | /*if new parent will be the first root*/ |
---|
317 | if( _head==p_loc ) |
---|
318 | _head=loc; |
---|
319 | |
---|
320 | p_loc=_data[loc].parent; |
---|
321 | } |
---|
322 | } |
---|
323 | if( _comp(value,_data[_min].prio) ) { |
---|
324 | _min=i; |
---|
325 | } |
---|
326 | } |
---|
327 | |
---|
328 | /// \brief Increase the priority of an item to the given value. |
---|
329 | /// |
---|
330 | /// This function increases the priority of an item to the given value. |
---|
331 | /// \param item The item. |
---|
332 | /// \param value The priority. |
---|
333 | /// \pre \e item must be stored in the heap with priority at most \e value. |
---|
334 | void increase (Item item, const Prio& value) { |
---|
335 | erase(item); |
---|
336 | push(item, value); |
---|
337 | } |
---|
338 | |
---|
339 | /// \brief Return the state of an item. |
---|
340 | /// |
---|
341 | /// This method returns \c PRE_HEAP if the given item has never |
---|
342 | /// been in the heap, \c IN_HEAP if it is in the heap at the moment, |
---|
343 | /// and \c POST_HEAP otherwise. |
---|
344 | /// In the latter case it is possible that the item will get back |
---|
345 | /// to the heap again. |
---|
346 | /// \param item The item. |
---|
347 | State state(const Item &item) const { |
---|
348 | int i=_iim[item]; |
---|
349 | if( i>=0 ) { |
---|
350 | if ( _data[i].in ) i=0; |
---|
351 | else i=-2; |
---|
352 | } |
---|
353 | return State(i); |
---|
354 | } |
---|
355 | |
---|
356 | /// \brief Set the state of an item in the heap. |
---|
357 | /// |
---|
358 | /// This function sets the state of the given item in the heap. |
---|
359 | /// It can be used to manually clear the heap when it is important |
---|
360 | /// to achive better time complexity. |
---|
361 | /// \param i The item. |
---|
362 | /// \param st The state. It should not be \c IN_HEAP. |
---|
363 | void state(const Item& i, State st) { |
---|
364 | switch (st) { |
---|
365 | case POST_HEAP: |
---|
366 | case PRE_HEAP: |
---|
367 | if (state(i) == IN_HEAP) { |
---|
368 | erase(i); |
---|
369 | } |
---|
370 | _iim[i] = st; |
---|
371 | break; |
---|
372 | case IN_HEAP: |
---|
373 | break; |
---|
374 | } |
---|
375 | } |
---|
376 | |
---|
377 | private: |
---|
378 | int findMin() { |
---|
379 | int min_loc=-1, min_val; |
---|
380 | int x=_head; |
---|
381 | if( x!=-1 ) { |
---|
382 | min_val=_data[x].prio; |
---|
383 | min_loc=x; |
---|
384 | x=_data[x].right_neighbor; |
---|
385 | |
---|
386 | while( x!=-1 ) { |
---|
387 | if( _comp( _data[x].prio,min_val ) ) { |
---|
388 | min_val=_data[x].prio; |
---|
389 | min_loc=x; |
---|
390 | } |
---|
391 | x=_data[x].right_neighbor; |
---|
392 | } |
---|
393 | } |
---|
394 | return min_loc; |
---|
395 | } |
---|
396 | |
---|
397 | void merge(int a) { |
---|
398 | interleave(a); |
---|
399 | |
---|
400 | int x=_head; |
---|
401 | if( -1!=x ) { |
---|
402 | int x_prev=-1, x_next=_data[x].right_neighbor; |
---|
403 | while( -1!=x_next ) { |
---|
404 | if( _data[x].degree!=_data[x_next].degree || ( -1!=_data[x_next].right_neighbor && _data[_data[x_next].right_neighbor].degree==_data[x].degree ) ) { |
---|
405 | x_prev=x; |
---|
406 | x=x_next; |
---|
407 | } |
---|
408 | else { |
---|
409 | if( _comp(_data[x].prio,_data[x_next].prio) ) { |
---|
410 | _data[x].right_neighbor=_data[x_next].right_neighbor; |
---|
411 | fuse(x_next,x); |
---|
412 | } |
---|
413 | else { |
---|
414 | if( -1==x_prev ) { _head=x_next; } |
---|
415 | else { |
---|
416 | _data[x_prev].right_neighbor=x_next; |
---|
417 | } |
---|
418 | fuse(x,x_next); |
---|
419 | x=x_next; |
---|
420 | } |
---|
421 | } |
---|
422 | x_next=_data[x].right_neighbor; |
---|
423 | } |
---|
424 | } |
---|
425 | } |
---|
426 | |
---|
427 | void interleave(int a) { |
---|
428 | int other=-1, head_other=-1; |
---|
429 | |
---|
430 | while( -1!=a || -1!=_head ) { |
---|
431 | if( -1==a ) { |
---|
432 | if( -1==head_other ) { |
---|
433 | head_other=_head; |
---|
434 | } |
---|
435 | else { |
---|
436 | _data[other].right_neighbor=_head; |
---|
437 | } |
---|
438 | _head=-1; |
---|
439 | } |
---|
440 | else if( -1==_head ) { |
---|
441 | if( -1==head_other ) { |
---|
442 | head_other=a; |
---|
443 | } |
---|
444 | else { |
---|
445 | _data[other].right_neighbor=a; |
---|
446 | } |
---|
447 | a=-1; |
---|
448 | } |
---|
449 | else { |
---|
450 | if( _data[a].degree<_data[_head].degree ) { |
---|
451 | if( -1==head_other ) { |
---|
452 | head_other=a; |
---|
453 | } |
---|
454 | else { |
---|
455 | _data[other].right_neighbor=a; |
---|
456 | } |
---|
457 | other=a; |
---|
458 | a=_data[a].right_neighbor; |
---|
459 | } |
---|
460 | else { |
---|
461 | if( -1==head_other ) { |
---|
462 | head_other=_head; |
---|
463 | } |
---|
464 | else { |
---|
465 | _data[other].right_neighbor=_head; |
---|
466 | } |
---|
467 | other=_head; |
---|
468 | _head=_data[_head].right_neighbor; |
---|
469 | } |
---|
470 | } |
---|
471 | } |
---|
472 | _head=head_other; |
---|
473 | } |
---|
474 | |
---|
475 | // Lacing a under b |
---|
476 | void fuse(int a, int b) { |
---|
477 | _data[a].parent=b; |
---|
478 | _data[a].right_neighbor=_data[b].child; |
---|
479 | _data[b].child=a; |
---|
480 | |
---|
481 | ++_data[b].degree; |
---|
482 | } |
---|
483 | |
---|
484 | // It is invoked only if a has siblings. |
---|
485 | void unlace(int a) { |
---|
486 | int neighb=_data[a].right_neighbor; |
---|
487 | int other=_head; |
---|
488 | |
---|
489 | while( _data[other].right_neighbor!=a ) |
---|
490 | other=_data[other].right_neighbor; |
---|
491 | _data[other].right_neighbor=neighb; |
---|
492 | } |
---|
493 | |
---|
494 | private: |
---|
495 | |
---|
496 | class store { |
---|
497 | friend class BinomHeap; |
---|
498 | |
---|
499 | Item name; |
---|
500 | int parent; |
---|
501 | int right_neighbor; |
---|
502 | int child; |
---|
503 | int degree; |
---|
504 | bool in; |
---|
505 | Prio prio; |
---|
506 | |
---|
507 | store() : parent(-1), right_neighbor(-1), child(-1), degree(0), in(true) {} |
---|
508 | }; |
---|
509 | }; |
---|
510 | |
---|
511 | } //namespace lemon |
---|
512 | |
---|
513 | #endif //LEMON_BINOM_HEAP_H |
---|
514 | |
---|