1 | /* -*- C++ -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2006 |
---|
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_RADIX_HEAP_H |
---|
20 | #define LEMON_RADIX_HEAP_H |
---|
21 | |
---|
22 | ///\ingroup auxdat |
---|
23 | ///\file |
---|
24 | ///\brief Radix Heap implementation. |
---|
25 | |
---|
26 | #include <vector> |
---|
27 | #include <lemon/error.h> |
---|
28 | |
---|
29 | namespace lemon { |
---|
30 | |
---|
31 | /// \brief Exception thrown by RadixHeap. |
---|
32 | /// |
---|
33 | /// This Exception is thrown when a smaller priority |
---|
34 | /// is inserted into the \e RadixHeap then the last time erased. |
---|
35 | /// \see RadixHeap |
---|
36 | /// \author Balazs Dezso |
---|
37 | |
---|
38 | class UnderFlowPriorityError : public RuntimeError { |
---|
39 | public: |
---|
40 | virtual const char* what() const throw() { |
---|
41 | return "lemon::UnderFlowPriorityError"; |
---|
42 | } |
---|
43 | }; |
---|
44 | |
---|
45 | /// \ingroup auxdata |
---|
46 | /// |
---|
47 | /// \brief A Radix Heap implementation. |
---|
48 | /// |
---|
49 | /// This class implements the \e radix \e heap data structure. A \e heap |
---|
50 | /// is a data structure for storing items with specified values called \e |
---|
51 | /// priorities in such a way that finding the item with minimum priority is |
---|
52 | /// efficient. This heap type can store only items with \e int priority. |
---|
53 | /// In a heap one can change the priority of an item, add or erase an |
---|
54 | /// item, but the priority cannot be decreased under the last removed |
---|
55 | /// item's priority. |
---|
56 | /// |
---|
57 | /// \param _Item Type of the items to be stored. |
---|
58 | /// \param _ItemIntMap A read and writable Item int map, used internally |
---|
59 | /// to handle the cross references. |
---|
60 | /// |
---|
61 | /// \see BinHeap |
---|
62 | /// \see Dijkstra |
---|
63 | /// \author Balazs Dezso |
---|
64 | |
---|
65 | template <typename _Item, typename _ItemIntMap> |
---|
66 | class RadixHeap { |
---|
67 | |
---|
68 | public: |
---|
69 | typedef _Item Item; |
---|
70 | typedef int Prio; |
---|
71 | typedef _ItemIntMap ItemIntMap; |
---|
72 | |
---|
73 | /// \brief Type to represent the items states. |
---|
74 | /// |
---|
75 | /// Each Item element have a state associated to it. It may be "in heap", |
---|
76 | /// "pre heap" or "post heap". The latter two are indifferent from the |
---|
77 | /// heap's point of view, but may be useful to the user. |
---|
78 | /// |
---|
79 | /// The ItemIntMap \e should be initialized in such way that it maps |
---|
80 | /// PRE_HEAP (-1) to any element to be put in the heap... |
---|
81 | enum state_enum { |
---|
82 | IN_HEAP = 0, |
---|
83 | PRE_HEAP = -1, |
---|
84 | POST_HEAP = -2 |
---|
85 | }; |
---|
86 | |
---|
87 | private: |
---|
88 | |
---|
89 | struct RadixItem { |
---|
90 | int prev, next, box; |
---|
91 | Item item; |
---|
92 | int prio; |
---|
93 | RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {} |
---|
94 | }; |
---|
95 | |
---|
96 | struct RadixBox { |
---|
97 | int first; |
---|
98 | int min, size; |
---|
99 | RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {} |
---|
100 | }; |
---|
101 | |
---|
102 | std::vector<RadixItem> data; |
---|
103 | std::vector<RadixBox> boxes; |
---|
104 | |
---|
105 | ItemIntMap &iim; |
---|
106 | |
---|
107 | |
---|
108 | public: |
---|
109 | /// \brief The constructor. |
---|
110 | /// |
---|
111 | /// The constructor. |
---|
112 | /// |
---|
113 | /// \param _iim It should be given to the constructor, since it is used |
---|
114 | /// internally to handle the cross references. The value of the map |
---|
115 | /// should be PRE_HEAP (-1) for each element. |
---|
116 | /// |
---|
117 | /// \param minimal The initial minimal value of the heap. |
---|
118 | /// \param capacity It determines the initial capacity of the heap. |
---|
119 | RadixHeap(ItemIntMap &_iim, int minimal = 0, int capacity = 0) |
---|
120 | : iim(_iim) { |
---|
121 | boxes.push_back(RadixBox(minimal, 1)); |
---|
122 | boxes.push_back(RadixBox(minimal + 1, 1)); |
---|
123 | while (lower(boxes.size() - 1, capacity + minimal - 1)) { |
---|
124 | extend(); |
---|
125 | } |
---|
126 | } |
---|
127 | |
---|
128 | /// The number of items stored in the heap. |
---|
129 | /// |
---|
130 | /// \brief Returns the number of items stored in the heap. |
---|
131 | int size() const { return data.size(); } |
---|
132 | /// \brief Checks if the heap stores no items. |
---|
133 | /// |
---|
134 | /// Returns \c true if and only if the heap stores no items. |
---|
135 | bool empty() const { return data.empty(); } |
---|
136 | |
---|
137 | /// \brief Make empty this heap. |
---|
138 | /// |
---|
139 | /// Make empty this heap. It does not change the cross reference |
---|
140 | /// map. If you want to reuse a heap what is not surely empty you |
---|
141 | /// should first clear the heap and after that you should set the |
---|
142 | /// cross reference map for each item to \c PRE_HEAP. |
---|
143 | void clear(int minimal = 0, int capacity = 0) { |
---|
144 | data.clear(); boxes.clear(); |
---|
145 | boxes.push_back(RadixBox(minimal, 1)); |
---|
146 | boxes.push_back(RadixBox(minimal + 1, 1)); |
---|
147 | while (lower(boxes.size() - 1, capacity + minimal - 1)) { |
---|
148 | extend(); |
---|
149 | } |
---|
150 | } |
---|
151 | |
---|
152 | private: |
---|
153 | |
---|
154 | bool upper(int box, Prio prio) { |
---|
155 | return prio < boxes[box].min; |
---|
156 | } |
---|
157 | |
---|
158 | bool lower(int box, Prio prio) { |
---|
159 | return prio >= boxes[box].min + boxes[box].size; |
---|
160 | } |
---|
161 | |
---|
162 | /// \brief Remove item from the box list. |
---|
163 | void remove(int index) { |
---|
164 | if (data[index].prev >= 0) { |
---|
165 | data[data[index].prev].next = data[index].next; |
---|
166 | } else { |
---|
167 | boxes[data[index].box].first = data[index].next; |
---|
168 | } |
---|
169 | if (data[index].next >= 0) { |
---|
170 | data[data[index].next].prev = data[index].prev; |
---|
171 | } |
---|
172 | } |
---|
173 | |
---|
174 | /// \brief Insert item into the box list. |
---|
175 | void insert(int box, int index) { |
---|
176 | if (boxes[box].first == -1) { |
---|
177 | boxes[box].first = index; |
---|
178 | data[index].next = data[index].prev = -1; |
---|
179 | } else { |
---|
180 | data[index].next = boxes[box].first; |
---|
181 | data[boxes[box].first].prev = index; |
---|
182 | data[index].prev = -1; |
---|
183 | boxes[box].first = index; |
---|
184 | } |
---|
185 | data[index].box = box; |
---|
186 | } |
---|
187 | |
---|
188 | /// \brief Add a new box to the box list. |
---|
189 | void extend() { |
---|
190 | int min = boxes.back().min + boxes.back().size; |
---|
191 | int size = 2 * boxes.back().size; |
---|
192 | boxes.push_back(RadixBox(min, size)); |
---|
193 | } |
---|
194 | |
---|
195 | /// \brief Move an item up into the proper box. |
---|
196 | void bubble_up(int index) { |
---|
197 | if (!lower(data[index].box, data[index].prio)) return; |
---|
198 | remove(index); |
---|
199 | int box = findUp(data[index].box, data[index].prio); |
---|
200 | insert(box, index); |
---|
201 | } |
---|
202 | |
---|
203 | /// \brief Find up the proper box for the item with the given prio. |
---|
204 | int findUp(int start, int prio) { |
---|
205 | while (lower(start, prio)) { |
---|
206 | if (++start == (int)boxes.size()) { |
---|
207 | extend(); |
---|
208 | } |
---|
209 | } |
---|
210 | return start; |
---|
211 | } |
---|
212 | |
---|
213 | /// \brief Move an item down into the proper box. |
---|
214 | void bubble_down(int index) { |
---|
215 | if (!upper(data[index].box, data[index].prio)) return; |
---|
216 | remove(index); |
---|
217 | int box = findDown(data[index].box, data[index].prio); |
---|
218 | insert(box, index); |
---|
219 | } |
---|
220 | |
---|
221 | /// \brief Find up the proper box for the item with the given prio. |
---|
222 | int findDown(int start, int prio) { |
---|
223 | while (upper(start, prio)) { |
---|
224 | if (--start < 0) throw UnderFlowPriorityError(); |
---|
225 | } |
---|
226 | return start; |
---|
227 | } |
---|
228 | |
---|
229 | /// \brief Find the first not empty box. |
---|
230 | int findFirst() { |
---|
231 | int first = 0; |
---|
232 | while (boxes[first].first == -1) ++first; |
---|
233 | return first; |
---|
234 | } |
---|
235 | |
---|
236 | /// \brief Gives back the minimal prio of the box. |
---|
237 | int minValue(int box) { |
---|
238 | int min = data[boxes[box].first].prio; |
---|
239 | for (int k = boxes[box].first; k != -1; k = data[k].next) { |
---|
240 | if (data[k].prio < min) min = data[k].prio; |
---|
241 | } |
---|
242 | return min; |
---|
243 | } |
---|
244 | |
---|
245 | /// \brief Rearrange the items of the heap and makes the |
---|
246 | /// first box not empty. |
---|
247 | void moveDown() { |
---|
248 | int box = findFirst(); |
---|
249 | if (box == 0) return; |
---|
250 | int min = minValue(box); |
---|
251 | for (int i = 0; i <= box; ++i) { |
---|
252 | boxes[i].min = min; |
---|
253 | min += boxes[i].size; |
---|
254 | } |
---|
255 | int curr = boxes[box].first, next; |
---|
256 | while (curr != -1) { |
---|
257 | next = data[curr].next; |
---|
258 | bubble_down(curr); |
---|
259 | curr = next; |
---|
260 | } |
---|
261 | } |
---|
262 | |
---|
263 | void relocate_last(int index) { |
---|
264 | if (index != (int)data.size() - 1) { |
---|
265 | data[index] = data.back(); |
---|
266 | if (data[index].prev != -1) { |
---|
267 | data[data[index].prev].next = index; |
---|
268 | } else { |
---|
269 | boxes[data[index].box].first = index; |
---|
270 | } |
---|
271 | if (data[index].next != -1) { |
---|
272 | data[data[index].next].prev = index; |
---|
273 | } |
---|
274 | iim[data[index].item] = index; |
---|
275 | } |
---|
276 | data.pop_back(); |
---|
277 | } |
---|
278 | |
---|
279 | public: |
---|
280 | |
---|
281 | /// \brief Insert an item into the heap with the given priority. |
---|
282 | /// |
---|
283 | /// Adds \c i to the heap with priority \c p. |
---|
284 | /// \param i The item to insert. |
---|
285 | /// \param p The priority of the item. |
---|
286 | void push(const Item &i, const Prio &p) { |
---|
287 | int n = data.size(); |
---|
288 | iim.set(i, n); |
---|
289 | data.push_back(RadixItem(i, p)); |
---|
290 | while (lower(boxes.size() - 1, p)) { |
---|
291 | extend(); |
---|
292 | } |
---|
293 | int box = findDown(boxes.size() - 1, p); |
---|
294 | insert(box, n); |
---|
295 | } |
---|
296 | |
---|
297 | /// \brief Returns the item with minimum priority. |
---|
298 | /// |
---|
299 | /// This method returns the item with minimum priority. |
---|
300 | /// \pre The heap must be nonempty. |
---|
301 | Item top() const { |
---|
302 | const_cast<RadixHeap<Item, ItemIntMap>&>(*this).moveDown(); |
---|
303 | return data[boxes[0].first].item; |
---|
304 | } |
---|
305 | |
---|
306 | /// \brief Returns the minimum priority. |
---|
307 | /// |
---|
308 | /// It returns the minimum priority. |
---|
309 | /// \pre The heap must be nonempty. |
---|
310 | Prio prio() const { |
---|
311 | const_cast<RadixHeap<Item, ItemIntMap>&>(*this).moveDown(); |
---|
312 | return data[boxes[0].first].prio; |
---|
313 | } |
---|
314 | |
---|
315 | /// \brief Deletes the item with minimum priority. |
---|
316 | /// |
---|
317 | /// This method deletes the item with minimum priority. |
---|
318 | /// \pre The heap must be non-empty. |
---|
319 | void pop() { |
---|
320 | moveDown(); |
---|
321 | int index = boxes[0].first; |
---|
322 | iim[data[index].item] = POST_HEAP; |
---|
323 | remove(index); |
---|
324 | relocate_last(index); |
---|
325 | } |
---|
326 | |
---|
327 | /// \brief Deletes \c i from the heap. |
---|
328 | /// |
---|
329 | /// This method deletes item \c i from the heap, if \c i was |
---|
330 | /// already stored in the heap. |
---|
331 | /// \param i The item to erase. |
---|
332 | void erase(const Item &i) { |
---|
333 | int index = iim[i]; |
---|
334 | iim[i] = POST_HEAP; |
---|
335 | remove(index); |
---|
336 | relocate_last(index); |
---|
337 | } |
---|
338 | |
---|
339 | /// \brief Returns the priority of \c i. |
---|
340 | /// |
---|
341 | /// This function returns the priority of item \c i. |
---|
342 | /// \pre \c i must be in the heap. |
---|
343 | /// \param i The item. |
---|
344 | Prio operator[](const Item &i) const { |
---|
345 | int idx = iim[i]; |
---|
346 | return data[idx].prio; |
---|
347 | } |
---|
348 | |
---|
349 | /// \brief \c i gets to the heap with priority \c p independently |
---|
350 | /// if \c i was already there. |
---|
351 | /// |
---|
352 | /// This method calls \ref push(\c i, \c p) if \c i is not stored |
---|
353 | /// in the heap and sets the priority of \c i to \c p otherwise. |
---|
354 | /// It may throw an \e UnderFlowPriorityException. |
---|
355 | /// \param i The item. |
---|
356 | /// \param p The priority. |
---|
357 | void set(const Item &i, const Prio &p) { |
---|
358 | int idx = iim[i]; |
---|
359 | if( idx < 0 ) { |
---|
360 | push(i, p); |
---|
361 | } |
---|
362 | else if( p >= data[idx].prio ) { |
---|
363 | data[idx].prio = p; |
---|
364 | bubble_up(idx); |
---|
365 | } else { |
---|
366 | data[idx].prio = p; |
---|
367 | bubble_down(idx); |
---|
368 | } |
---|
369 | } |
---|
370 | |
---|
371 | |
---|
372 | /// \brief Decreases the priority of \c i to \c p. |
---|
373 | /// |
---|
374 | /// This method decreases the priority of item \c i to \c p. |
---|
375 | /// \pre \c i must be stored in the heap with priority at least \c p, and |
---|
376 | /// \c should be greater or equal to the last removed item's priority. |
---|
377 | /// \param i The item. |
---|
378 | /// \param p The priority. |
---|
379 | void decrease(const Item &i, const Prio &p) { |
---|
380 | int idx = iim[i]; |
---|
381 | data[idx].prio = p; |
---|
382 | bubble_down(idx); |
---|
383 | } |
---|
384 | |
---|
385 | /// \brief Increases the priority of \c i to \c p. |
---|
386 | /// |
---|
387 | /// This method sets the priority of item \c i to \c p. |
---|
388 | /// \pre \c i must be stored in the heap with priority at most \c p |
---|
389 | /// \param i The item. |
---|
390 | /// \param p The priority. |
---|
391 | void increase(const Item &i, const Prio &p) { |
---|
392 | int idx = iim[i]; |
---|
393 | data[idx].prio = p; |
---|
394 | bubble_up(idx); |
---|
395 | } |
---|
396 | |
---|
397 | /// \brief Returns if \c item is in, has already been in, or has |
---|
398 | /// never been in the heap. |
---|
399 | /// |
---|
400 | /// This method returns PRE_HEAP if \c item has never been in the |
---|
401 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
---|
402 | /// otherwise. In the latter case it is possible that \c item will |
---|
403 | /// get back to the heap again. |
---|
404 | /// \param i The item. |
---|
405 | state_enum state(const Item &i) const { |
---|
406 | int s = iim[i]; |
---|
407 | if( s >= 0 ) s = 0; |
---|
408 | return state_enum(s); |
---|
409 | } |
---|
410 | |
---|
411 | /// \brief Sets the state of the \c item in the heap. |
---|
412 | /// |
---|
413 | /// Sets the state of the \c item in the heap. It can be used to |
---|
414 | /// manually clear the heap when it is important to achive the |
---|
415 | /// better time complexity. |
---|
416 | /// \param i The item. |
---|
417 | /// \param st The state. It should not be \c IN_HEAP. |
---|
418 | void state(const Item& i, state_enum st) { |
---|
419 | switch (st) { |
---|
420 | case POST_HEAP: |
---|
421 | case PRE_HEAP: |
---|
422 | if (state(i) == IN_HEAP) { |
---|
423 | erase(i); |
---|
424 | } |
---|
425 | iim[i] = st; |
---|
426 | break; |
---|
427 | case IN_HEAP: |
---|
428 | break; |
---|
429 | } |
---|
430 | } |
---|
431 | |
---|
432 | }; // class RadixHeap |
---|
433 | |
---|
434 | } // namespace lemon |
---|
435 | |
---|
436 | #endif // LEMON_RADIX_HEAP_H |
---|