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2 * lemon/radix_heap.h - Part of LEMON, a generic C++ optimization library
4 * Copyright (C) 2006 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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.
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
17 #ifndef LEMON_RADIX_HEAP_H
18 #define LEMON_RADIX_HEAP_H
22 ///\brief Radix Heap implementation.
25 #include <lemon/error.h>
29 /// \brief Exception thrown by RadixHeap.
31 /// This Exception is thrown when a smaller priority
32 /// is inserted into the \e RadixHeap then the last time erased.
34 /// \author Balazs Dezso
36 class UnderFlowPriorityError : public RuntimeError {
38 virtual const char* exceptionName() const {
39 return "lemon::UnderFlowPriorityError";
45 /// \brief A Radix Heap implementation.
47 /// This class implements the \e radix \e heap data structure. A \e heap
48 /// is a data structure for storing items with specified values called \e
49 /// priorities in such a way that finding the item with minimum priority is
50 /// efficient. This heap type can store only items with \e int priority.
51 /// In a heap one can change the priority of an item, add or erase an
52 /// item, but the priority cannot be decreased under the last removed
55 /// \param _Item Type of the items to be stored.
56 /// \param _ItemIntMap A read and writable Item int map, used internally
57 /// to handle the cross references.
61 /// \author Balazs Dezso
63 template <typename _Item, typename _ItemIntMap>
69 typedef _ItemIntMap ItemIntMap;
71 /// \brief Type to represent the items states.
73 /// Each Item element have a state associated to it. It may be "in heap",
74 /// "pre heap" or "post heap". The latter two are indifferent from the
75 /// heap's point of view, but may be useful to the user.
77 /// The ItemIntMap \e should be initialized in such way that it maps
78 /// PRE_HEAP (-1) to any element to be put in the heap...
91 RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {}
97 RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {}
100 std::vector<RadixItem> data;
101 std::vector<RadixBox> boxes;
107 /// \brief The constructor.
111 /// \param _iim It should be given to the constructor, since it is used
112 /// internally to handle the cross references. The value of the map
113 /// should be PRE_HEAP (-1) for each element.
115 /// \param minimal The initial minimal value of the heap.
116 /// \param capacity It determines the initial capacity of the heap.
117 RadixHeap(ItemIntMap &_iim, int minimal = 0, int capacity = 0)
119 boxes.push_back(RadixBox(minimal, 1));
120 boxes.push_back(RadixBox(minimal + 1, 1));
121 while (lower(boxes.size() - 1, capacity + minimal - 1)) {
126 /// The number of items stored in the heap.
128 /// \brief Returns the number of items stored in the heap.
129 int size() const { return data.size(); }
130 /// \brief Checks if the heap stores no items.
132 /// Returns \c true if and only if the heap stores no items.
133 bool empty() const { return data.empty(); }
135 /// \brief Make empty this heap.
137 /// Make empty this heap.
138 void clear(int minimal = 0, int capacity = 0) {
139 for (int i = 0; i < (int)data.size(); ++i) {
140 iim[data[i].item] = -2;
142 data.clear(); boxes.clear();
143 boxes.push_back(RadixBox(minimal, 1));
144 boxes.push_back(RadixBox(minimal + 1, 1));
145 while (lower(boxes.size() - 1, capacity + minimal - 1)) {
152 bool upper(int box, Prio prio) {
153 return prio < boxes[box].min;
156 bool lower(int box, Prio prio) {
157 return prio >= boxes[box].min + boxes[box].size;
160 /// \brief Remove item from the box list.
161 void remove(int index) {
162 if (data[index].prev >= 0) {
163 data[data[index].prev].next = data[index].next;
165 boxes[data[index].box].first = data[index].next;
167 if (data[index].next >= 0) {
168 data[data[index].next].prev = data[index].prev;
172 /// \brief Insert item into the box list.
173 void insert(int box, int index) {
174 if (boxes[box].first == -1) {
175 boxes[box].first = index;
176 data[index].next = data[index].prev = -1;
178 data[index].next = boxes[box].first;
179 data[boxes[box].first].prev = index;
180 data[index].prev = -1;
181 boxes[box].first = index;
183 data[index].box = box;
186 /// \brief Add a new box to the box list.
188 int min = boxes.back().min + boxes.back().size;
189 int size = 2 * boxes.back().size;
190 boxes.push_back(RadixBox(min, size));
193 /// \brief Move an item up into the proper box.
194 void bubble_up(int index) {
195 if (!lower(data[index].box, data[index].prio)) return;
197 int box = findUp(data[index].box, data[index].prio);
201 /// \brief Find up the proper box for the item with the given prio.
202 int findUp(int start, int prio) {
203 while (lower(start, prio)) {
204 if (++start == (int)boxes.size()) {
211 /// \brief Move an item down into the proper box.
212 void bubble_down(int index) {
213 if (!upper(data[index].box, data[index].prio)) return;
215 int box = findDown(data[index].box, data[index].prio);
219 /// \brief Find up the proper box for the item with the given prio.
220 int findDown(int start, int prio) {
221 while (upper(start, prio)) {
222 if (--start < 0) throw UnderFlowPriorityError();
227 /// \brief Find the first not empty box.
230 while (boxes[first].first == -1) ++first;
234 /// \brief Gives back the minimal prio of the box.
235 int minValue(int box) {
236 int min = data[boxes[box].first].prio;
237 for (int k = boxes[box].first; k != -1; k = data[k].next) {
238 if (data[k].prio < min) min = data[k].prio;
243 /// \brief Rearrange the items of the heap and makes the
244 /// first box not empty.
246 int box = findFirst();
247 if (box == 0) return;
248 int min = minValue(box);
249 for (int i = 0; i <= box; ++i) {
251 min += boxes[i].size;
253 int curr = boxes[box].first, next;
255 next = data[curr].next;
261 void relocate_last(int index) {
262 if (index != (int)data.size() - 1) {
263 data[index] = data.back();
264 if (data[index].prev != -1) {
265 data[data[index].prev].next = index;
267 boxes[data[index].box].first = index;
269 if (data[index].next != -1) {
270 data[data[index].next].prev = index;
272 iim[data[index].item] = index;
279 /// \brief Insert an item into the heap with the given priority.
281 /// Adds \c i to the heap with priority \c p.
282 /// \param i The item to insert.
283 /// \param p The priority of the item.
284 void push(const Item &i, const Prio &p) {
287 data.push_back(RadixItem(i, p));
288 while (lower(boxes.size() - 1, p)) {
291 int box = findDown(boxes.size() - 1, p);
295 /// \brief Returns the item with minimum priority.
297 /// This method returns the item with minimum priority.
298 /// \pre The heap must be nonempty.
300 const_cast<RadixHeap<Item, ItemIntMap>&>(*this).moveDown();
301 return data[boxes[0].first].item;
304 /// \brief Returns the minimum priority.
306 /// It returns the minimum priority.
307 /// \pre The heap must be nonempty.
309 const_cast<RadixHeap<Item, ItemIntMap>&>(*this).moveDown();
310 return data[boxes[0].first].prio;
313 /// \brief Deletes the item with minimum priority.
315 /// This method deletes the item with minimum priority.
316 /// \pre The heap must be non-empty.
319 int index = boxes[0].first;
320 iim[data[index].item] = POST_HEAP;
322 relocate_last(index);
325 /// \brief Deletes \c i from the heap.
327 /// This method deletes item \c i from the heap, if \c i was
328 /// already stored in the heap.
329 /// \param i The item to erase.
330 void erase(const Item &i) {
334 relocate_last(index);
337 /// \brief Returns the priority of \c i.
339 /// This function returns the priority of item \c i.
340 /// \pre \c i must be in the heap.
341 /// \param i The item.
342 Prio operator[](const Item &i) const {
344 return data[idx].prio;
347 /// \brief \c i gets to the heap with priority \c p independently
348 /// if \c i was already there.
350 /// This method calls \ref push(\c i, \c p) if \c i is not stored
351 /// in the heap and sets the priority of \c i to \c p otherwise.
352 /// It may throw an \e UnderFlowPriorityException.
353 /// \param i The item.
354 /// \param p The priority.
355 void set(const Item &i, const Prio &p) {
360 else if( p >= data[idx].prio ) {
370 /// \brief Decreases the priority of \c i to \c p.
372 /// This method decreases the priority of item \c i to \c p.
373 /// \pre \c i must be stored in the heap with priority at least \c p, and
374 /// \c should be greater or equal to the last removed item's priority.
375 /// \param i The item.
376 /// \param p The priority.
377 void decrease(const Item &i, const Prio &p) {
383 /// \brief Increases the priority of \c i to \c p.
385 /// This method sets the priority of item \c i to \c p.
386 /// \pre \c i must be stored in the heap with priority at most \c p
387 /// \param i The item.
388 /// \param p The priority.
389 void increase(const Item &i, const Prio &p) {
395 /// \brief Returns if \c item is in, has already been in, or has
396 /// never been in the heap.
398 /// This method returns PRE_HEAP if \c item has never been in the
399 /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
400 /// otherwise. In the latter case it is possible that \c item will
401 /// get back to the heap again.
402 /// \param i The item.
403 state_enum state(const Item &i) const {
406 return state_enum(s);
409 }; // class RadixHeap
413 #endif // LEMON_RADIX_HEAP_H