1 | /* -*- C++ -*- |
---|
2 | * lemon/linear_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_LINEAR_HEAP_H |
---|
18 | #define LEMON_LINEAR_HEAP_H |
---|
19 | |
---|
20 | ///\ingroup auxdat |
---|
21 | ///\file |
---|
22 | ///\brief Binary Heap implementation. |
---|
23 | |
---|
24 | #include <vector> |
---|
25 | #include <utility> |
---|
26 | #include <functional> |
---|
27 | |
---|
28 | namespace lemon { |
---|
29 | |
---|
30 | /// \ingroup auxdat |
---|
31 | |
---|
32 | /// \brief A Linear Heap implementation. |
---|
33 | /// |
---|
34 | /// This class implements the \e linear \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. The linear heap is very simple implementation, it can store |
---|
38 | /// only integer priorities and it stores for each priority in the [0..C] |
---|
39 | /// range a list of items. So it should be used only when the priorities |
---|
40 | /// are small. It is not intended to use as dijkstra heap. |
---|
41 | /// |
---|
42 | /// \param _Item Type of the items to be stored. |
---|
43 | /// \param _ItemIntMap A read and writable Item int map, used internally |
---|
44 | /// to handle the cross references. |
---|
45 | /// \param minimize If the given parameter is true then the heap gives back |
---|
46 | /// the lowest priority. |
---|
47 | template <typename _Item, typename _ItemIntMap, bool minimize = true > |
---|
48 | class LinearHeap { |
---|
49 | |
---|
50 | public: |
---|
51 | typedef _Item Item; |
---|
52 | typedef int Prio; |
---|
53 | typedef std::pair<Item, Prio> Pair; |
---|
54 | typedef _ItemIntMap ItemIntMap; |
---|
55 | |
---|
56 | /// \brief Type to represent the items states. |
---|
57 | /// |
---|
58 | /// Each Item element have a state associated to it. It may be "in heap", |
---|
59 | /// "pre heap" or "post heap". The latter two are indifferent from the |
---|
60 | /// heap's point of view, but may be useful to the user. |
---|
61 | /// |
---|
62 | /// The ItemIntMap \e should be initialized in such way that it maps |
---|
63 | /// PRE_HEAP (-1) to any element to be put in the heap... |
---|
64 | enum state_enum { |
---|
65 | IN_HEAP = 0, |
---|
66 | PRE_HEAP = -1, |
---|
67 | POST_HEAP = -2 |
---|
68 | }; |
---|
69 | |
---|
70 | public: |
---|
71 | /// \brief The constructor. |
---|
72 | /// |
---|
73 | /// The constructor. |
---|
74 | /// \param _index should be given to the constructor, since it is used |
---|
75 | /// internally to handle the cross references. The value of the map |
---|
76 | /// should be PRE_HEAP (-1) for each element. |
---|
77 | explicit LinearHeap(ItemIntMap &_index) : index(_index), minimal(0) {} |
---|
78 | |
---|
79 | /// The number of items stored in the heap. |
---|
80 | /// |
---|
81 | /// \brief Returns the number of items stored in the heap. |
---|
82 | int size() const { return data.size(); } |
---|
83 | |
---|
84 | /// \brief Checks if the heap stores no items. |
---|
85 | /// |
---|
86 | /// Returns \c true if and only if the heap stores no items. |
---|
87 | bool empty() const { return data.empty(); } |
---|
88 | |
---|
89 | /// \brief Make empty this heap. |
---|
90 | /// |
---|
91 | /// Make empty this heap. |
---|
92 | void clear() { |
---|
93 | for (int i = 0; i < (int)data.size(); ++i) { |
---|
94 | index[data[i].item] = -2; |
---|
95 | } |
---|
96 | data.clear(); first.clear(); minimal = 0; |
---|
97 | } |
---|
98 | |
---|
99 | private: |
---|
100 | |
---|
101 | void relocate_last(int idx) { |
---|
102 | if (idx + 1 < (int)data.size()) { |
---|
103 | data[idx] = data.back(); |
---|
104 | if (data[idx].prev != -1) { |
---|
105 | data[data[idx].prev].next = idx; |
---|
106 | } else { |
---|
107 | first[data[idx].value] = idx; |
---|
108 | } |
---|
109 | if (data[idx].next != -1) { |
---|
110 | data[data[idx].next].prev = idx; |
---|
111 | } |
---|
112 | index[data[idx].item] = idx; |
---|
113 | } |
---|
114 | data.pop_back(); |
---|
115 | } |
---|
116 | |
---|
117 | void unlace(int idx) { |
---|
118 | if (data[idx].prev != -1) { |
---|
119 | data[data[idx].prev].next = data[idx].next; |
---|
120 | } else { |
---|
121 | first[data[idx].value] = data[idx].next; |
---|
122 | } |
---|
123 | if (data[idx].next != -1) { |
---|
124 | data[data[idx].next].prev = data[idx].prev; |
---|
125 | } |
---|
126 | } |
---|
127 | |
---|
128 | void lace(int idx) { |
---|
129 | if ((int)first.size() <= data[idx].value) { |
---|
130 | first.resize(data[idx].value + 1, -1); |
---|
131 | } |
---|
132 | data[idx].next = first[data[idx].value]; |
---|
133 | if (data[idx].next != -1) { |
---|
134 | data[data[idx].next].prev = idx; |
---|
135 | } |
---|
136 | first[data[idx].value] = idx; |
---|
137 | data[idx].prev = -1; |
---|
138 | } |
---|
139 | |
---|
140 | public: |
---|
141 | /// \brief Insert a pair of item and priority into the heap. |
---|
142 | /// |
---|
143 | /// Adds \c p.first to the heap with priority \c p.second. |
---|
144 | /// \param p The pair to insert. |
---|
145 | void push(const Pair& p) { |
---|
146 | push(p.first, p.second); |
---|
147 | } |
---|
148 | |
---|
149 | /// \brief Insert an item into the heap with the given priority. |
---|
150 | /// |
---|
151 | /// Adds \c i to the heap with priority \c p. |
---|
152 | /// \param i The item to insert. |
---|
153 | /// \param p The priority of the item. |
---|
154 | void push(const Item &i, const Prio &p) { |
---|
155 | int idx = data.size(); |
---|
156 | index[i] = idx; |
---|
157 | data.push_back(LinearItem(i, p)); |
---|
158 | lace(idx); |
---|
159 | if (p < minimal) { |
---|
160 | minimal = p; |
---|
161 | } |
---|
162 | } |
---|
163 | |
---|
164 | /// \brief Returns the item with minimum priority. |
---|
165 | /// |
---|
166 | /// This method returns the item with minimum priority. |
---|
167 | /// \pre The heap must be nonempty. |
---|
168 | Item top() const { |
---|
169 | while (first[minimal] == -1) { |
---|
170 | ++minimal; |
---|
171 | } |
---|
172 | return data[first[minimal]].item; |
---|
173 | } |
---|
174 | |
---|
175 | /// \brief Returns the minimum priority. |
---|
176 | /// |
---|
177 | /// It returns the minimum priority. |
---|
178 | /// \pre The heap must be nonempty. |
---|
179 | Prio prio() const { |
---|
180 | while (first[minimal] == -1) { |
---|
181 | ++minimal; |
---|
182 | } |
---|
183 | return minimal; |
---|
184 | } |
---|
185 | |
---|
186 | /// \brief Deletes the item with minimum priority. |
---|
187 | /// |
---|
188 | /// This method deletes the item with minimum priority from the heap. |
---|
189 | /// \pre The heap must be non-empty. |
---|
190 | void pop() { |
---|
191 | while (first[minimal] == -1) { |
---|
192 | ++minimal; |
---|
193 | } |
---|
194 | int idx = first[minimal]; |
---|
195 | index[data[idx].item] = -2; |
---|
196 | unlace(idx); |
---|
197 | relocate_last(idx); |
---|
198 | } |
---|
199 | |
---|
200 | /// \brief Deletes \c i from the heap. |
---|
201 | /// |
---|
202 | /// This method deletes item \c i from the heap, if \c i was |
---|
203 | /// already stored in the heap. |
---|
204 | /// \param i The item to erase. |
---|
205 | void erase(const Item &i) { |
---|
206 | int idx = index[i]; |
---|
207 | index[data[idx].item] = -2; |
---|
208 | unlace(idx); |
---|
209 | relocate_last(idx); |
---|
210 | } |
---|
211 | |
---|
212 | |
---|
213 | /// \brief Returns the priority of \c i. |
---|
214 | /// |
---|
215 | /// This function returns the priority of item \c i. |
---|
216 | /// \pre \c i must be in the heap. |
---|
217 | /// \param i The item. |
---|
218 | Prio operator[](const Item &i) const { |
---|
219 | int idx = index[i]; |
---|
220 | return data[idx].value; |
---|
221 | } |
---|
222 | |
---|
223 | /// \brief \c i gets to the heap with priority \c p independently |
---|
224 | /// if \c i was already there. |
---|
225 | /// |
---|
226 | /// This method calls \ref push(\c i, \c p) if \c i is not stored |
---|
227 | /// in the heap and sets the priority of \c i to \c p otherwise. |
---|
228 | /// \param i The item. |
---|
229 | /// \param p The priority. |
---|
230 | void set(const Item &i, const Prio &p) { |
---|
231 | int idx = index[i]; |
---|
232 | if (idx < 0) { |
---|
233 | push(i,p); |
---|
234 | } else if (p > data[idx].value) { |
---|
235 | increase(i, p); |
---|
236 | } else { |
---|
237 | decrease(i, p); |
---|
238 | } |
---|
239 | } |
---|
240 | |
---|
241 | /// \brief Decreases the priority of \c i to \c p. |
---|
242 | |
---|
243 | /// This method decreases the priority of item \c i to \c p. |
---|
244 | /// \pre \c i must be stored in the heap with priority at least \c |
---|
245 | /// p relative to \c Compare. |
---|
246 | /// \param i The item. |
---|
247 | /// \param p The priority. |
---|
248 | void decrease(const Item &i, const Prio &p) { |
---|
249 | int idx = index[i]; |
---|
250 | unlace(idx); |
---|
251 | data[idx].value = p; |
---|
252 | if (p < minimal) { |
---|
253 | minimal = p; |
---|
254 | } |
---|
255 | lace(idx); |
---|
256 | } |
---|
257 | |
---|
258 | /// \brief Increases the priority of \c i to \c p. |
---|
259 | /// |
---|
260 | /// This method sets the priority of item \c i to \c p. |
---|
261 | /// \pre \c i must be stored in the heap with priority at most \c |
---|
262 | /// p relative to \c Compare. |
---|
263 | /// \param i The item. |
---|
264 | /// \param p The priority. |
---|
265 | void increase(const Item &i, const Prio &p) { |
---|
266 | int idx = index[i]; |
---|
267 | unlace(idx); |
---|
268 | data[idx].value = p; |
---|
269 | lace(idx); |
---|
270 | } |
---|
271 | |
---|
272 | /// \brief Returns if \c item is in, has already been in, or has |
---|
273 | /// never been in the heap. |
---|
274 | /// |
---|
275 | /// This method returns PRE_HEAP if \c item has never been in the |
---|
276 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
---|
277 | /// otherwise. In the latter case it is possible that \c item will |
---|
278 | /// get back to the heap again. |
---|
279 | /// \param i The item. |
---|
280 | state_enum state(const Item &i) const { |
---|
281 | int idx = index[i]; |
---|
282 | if (idx >= 0) idx = 0; |
---|
283 | return state_enum(idx); |
---|
284 | } |
---|
285 | |
---|
286 | private: |
---|
287 | |
---|
288 | struct LinearItem { |
---|
289 | LinearItem(const Item& _item, int _value) |
---|
290 | : item(_item), value(_value) {} |
---|
291 | |
---|
292 | Item item; |
---|
293 | int value; |
---|
294 | |
---|
295 | int prev, next; |
---|
296 | }; |
---|
297 | |
---|
298 | ItemIntMap& index; |
---|
299 | std::vector<int> first; |
---|
300 | std::vector<LinearItem> data; |
---|
301 | mutable int minimal; |
---|
302 | |
---|
303 | }; // class LinearHeap |
---|
304 | |
---|
305 | |
---|
306 | template <typename _Item, typename _ItemIntMap> |
---|
307 | class LinearHeap<_Item, _ItemIntMap, false> { |
---|
308 | |
---|
309 | public: |
---|
310 | typedef _Item Item; |
---|
311 | typedef int Prio; |
---|
312 | typedef std::pair<Item, Prio> Pair; |
---|
313 | typedef _ItemIntMap ItemIntMap; |
---|
314 | |
---|
315 | enum state_enum { |
---|
316 | IN_HEAP = 0, |
---|
317 | PRE_HEAP = -1, |
---|
318 | POST_HEAP = -2 |
---|
319 | }; |
---|
320 | |
---|
321 | public: |
---|
322 | |
---|
323 | explicit LinearHeap(ItemIntMap &_index) : index(_index), maximal(-1) {} |
---|
324 | |
---|
325 | int size() const { return data.size(); } |
---|
326 | bool empty() const { return data.empty(); } |
---|
327 | |
---|
328 | void clear() { |
---|
329 | for (int i = 0; i < (int)data.size(); ++i) { |
---|
330 | index[data[i].item] = -2; |
---|
331 | } |
---|
332 | data.clear(); first.clear(); maximal = -1; |
---|
333 | } |
---|
334 | |
---|
335 | private: |
---|
336 | |
---|
337 | void relocate_last(int idx) { |
---|
338 | if (idx + 1 != (int)data.size()) { |
---|
339 | data[idx] = data.back(); |
---|
340 | if (data[idx].prev != -1) { |
---|
341 | data[data[idx].prev].next = idx; |
---|
342 | } else { |
---|
343 | first[data[idx].value] = idx; |
---|
344 | } |
---|
345 | if (data[idx].next != -1) { |
---|
346 | data[data[idx].next].prev = idx; |
---|
347 | } |
---|
348 | index[data[idx].item] = idx; |
---|
349 | } |
---|
350 | data.pop_back(); |
---|
351 | } |
---|
352 | |
---|
353 | void unlace(int idx) { |
---|
354 | if (data[idx].prev != -1) { |
---|
355 | data[data[idx].prev].next = data[idx].next; |
---|
356 | } else { |
---|
357 | first[data[idx].value] = data[idx].next; |
---|
358 | } |
---|
359 | if (data[idx].next != -1) { |
---|
360 | data[data[idx].next].prev = data[idx].prev; |
---|
361 | } |
---|
362 | } |
---|
363 | |
---|
364 | void lace(int idx) { |
---|
365 | if ((int)first.size() <= data[idx].value) { |
---|
366 | first.resize(data[idx].value + 1, -1); |
---|
367 | } |
---|
368 | data[idx].next = first[data[idx].value]; |
---|
369 | if (data[idx].next != -1) { |
---|
370 | data[data[idx].next].prev = idx; |
---|
371 | } |
---|
372 | first[data[idx].value] = idx; |
---|
373 | data[idx].prev = -1; |
---|
374 | } |
---|
375 | |
---|
376 | public: |
---|
377 | |
---|
378 | void push(const Pair& p) { |
---|
379 | push(p.first, p.second); |
---|
380 | } |
---|
381 | |
---|
382 | void push(const Item &i, const Prio &p) { |
---|
383 | int idx = data.size(); |
---|
384 | index[i] = idx; |
---|
385 | data.push_back(LinearItem(i, p)); |
---|
386 | lace(idx); |
---|
387 | if (data[idx].value > maximal) { |
---|
388 | maximal = data[idx].value; |
---|
389 | } |
---|
390 | } |
---|
391 | |
---|
392 | Item top() const { |
---|
393 | while (first[maximal] == -1) { |
---|
394 | --maximal; |
---|
395 | } |
---|
396 | return data[first[maximal]].item; |
---|
397 | } |
---|
398 | |
---|
399 | Prio prio() const { |
---|
400 | while (first[maximal] == -1) { |
---|
401 | --maximal; |
---|
402 | } |
---|
403 | return maximal; |
---|
404 | } |
---|
405 | |
---|
406 | void pop() { |
---|
407 | while (first[maximal] == -1) { |
---|
408 | --maximal; |
---|
409 | } |
---|
410 | int idx = first[maximal]; |
---|
411 | index[data[idx].item] = -2; |
---|
412 | unlace(idx); |
---|
413 | relocate_last(idx); |
---|
414 | } |
---|
415 | |
---|
416 | void erase(const Item &i) { |
---|
417 | int idx = index[i]; |
---|
418 | index[data[idx].item] = -2; |
---|
419 | unlace(idx); |
---|
420 | relocate_last(idx); |
---|
421 | } |
---|
422 | |
---|
423 | Prio operator[](const Item &i) const { |
---|
424 | int idx = index[i]; |
---|
425 | return data[idx].value; |
---|
426 | } |
---|
427 | |
---|
428 | void set(const Item &i, const Prio &p) { |
---|
429 | int idx = index[i]; |
---|
430 | if (idx < 0) { |
---|
431 | push(i,p); |
---|
432 | } else if (p > data[idx].value) { |
---|
433 | decrease(i, p); |
---|
434 | } else { |
---|
435 | increase(i, p); |
---|
436 | } |
---|
437 | } |
---|
438 | |
---|
439 | void decrease(const Item &i, const Prio &p) { |
---|
440 | int idx = index[i]; |
---|
441 | unlace(idx); |
---|
442 | data[idx].value = p; |
---|
443 | if (p > maximal) { |
---|
444 | maximal = p; |
---|
445 | } |
---|
446 | lace(idx); |
---|
447 | } |
---|
448 | |
---|
449 | void increase(const Item &i, const Prio &p) { |
---|
450 | int idx = index[i]; |
---|
451 | unlace(idx); |
---|
452 | data[idx].value = p; |
---|
453 | lace(idx); |
---|
454 | } |
---|
455 | |
---|
456 | state_enum state(const Item &i) const { |
---|
457 | int idx = index[i]; |
---|
458 | if (idx >= 0) idx = 0; |
---|
459 | return state_enum(idx); |
---|
460 | } |
---|
461 | |
---|
462 | private: |
---|
463 | |
---|
464 | struct LinearItem { |
---|
465 | LinearItem(const Item& _item, int _value) |
---|
466 | : item(_item), value(_value) {} |
---|
467 | |
---|
468 | Item item; |
---|
469 | int value; |
---|
470 | |
---|
471 | int prev, next; |
---|
472 | }; |
---|
473 | |
---|
474 | ItemIntMap& index; |
---|
475 | std::vector<int> first; |
---|
476 | std::vector<LinearItem> data; |
---|
477 | mutable int maximal; |
---|
478 | |
---|
479 | }; // class LinearHeap |
---|
480 | |
---|
481 | } |
---|
482 | |
---|
483 | #endif |
---|