1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/radix_heap.h Mon May 23 04:48:14 2005 +0000
1.3 @@ -0,0 +1,412 @@
1.4 +/* -*- C++ -*-
1.5 + * lemon/radix_heap.h - Part of LEMON, a generic C++ optimization library
1.6 + *
1.7 + * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.8 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.9 + *
1.10 + * Permission to use, modify and distribute this software is granted
1.11 + * provided that this copyright notice appears in all copies. For
1.12 + * precise terms see the accompanying LICENSE file.
1.13 + *
1.14 + * This software is provided "AS IS" with no warranty of any kind,
1.15 + * express or implied, and with no claim as to its suitability for any
1.16 + * purpose.
1.17 + *
1.18 + */
1.19 +
1.20 +#ifndef LEMON_RADIX_HEAP_H
1.21 +#define LEMON_RADIX_HEAP_H
1.22 +
1.23 +///\ingroup auxdat
1.24 +///\file
1.25 +///\brief Radix Heap implementation.
1.26 +
1.27 +#include <vector>
1.28 +#include <lemon/error.h>
1.29 +
1.30 +namespace lemon {
1.31 +
1.32 + /// \addtogroup auxdat
1.33 + /// @{
1.34 +
1.35 + /// \brief Exception thrown by RadixHeap.
1.36 + ///
1.37 + /// This Exception is thrown when a smaller priority
1.38 + /// is inserted into the \e RadixHeap then the last time erased.
1.39 + /// \see RadixHeap
1.40 + /// \author Balazs Dezso
1.41 +
1.42 + class UnderFlowPriorityError : public RuntimeError {
1.43 + public:
1.44 + virtual const char* exceptionName() const {
1.45 + return "lemon::UnderFlowPriorityError";
1.46 + }
1.47 + };
1.48 +
1.49 + /// \brief A Radix Heap implementation.
1.50 + ///
1.51 + /// This class implements the \e radix \e heap data structure. A \e heap
1.52 + /// is a data structure for storing items with specified values called \e
1.53 + /// priorities in such a way that finding the item with minimum priority is
1.54 + /// efficient. This heap type can store only items with \e int priority.
1.55 + /// In a heap one can change the priority of an item, add or erase an
1.56 + /// item, but the priority cannot be decreased under the last removed
1.57 + /// item's priority.
1.58 + ///
1.59 + /// \param _Item Type of the items to be stored.
1.60 + /// \param _ItemIntMap A read and writable Item int map, used internally
1.61 + /// to handle the cross references.
1.62 + ///
1.63 + /// \see BinHeap
1.64 + /// \see Dijkstra
1.65 + /// \author Balazs Dezso
1.66 +
1.67 + template <typename _Item, typename _ItemIntMap>
1.68 + class RadixHeap {
1.69 +
1.70 + public:
1.71 + typedef _Item Item;
1.72 + typedef int Prio;
1.73 + typedef _ItemIntMap ItemIntMap;
1.74 +
1.75 + /// \brief Type to represent the items states.
1.76 + ///
1.77 + /// Each Item element have a state associated to it. It may be "in heap",
1.78 + /// "pre heap" or "post heap". The latter two are indifferent from the
1.79 + /// heap's point of view, but may be useful to the user.
1.80 + ///
1.81 + /// The ItemIntMap \e should be initialized in such way that it maps
1.82 + /// PRE_HEAP (-1) to any element to be put in the heap...
1.83 + enum state_enum {
1.84 + IN_HEAP = 0,
1.85 + PRE_HEAP = -1,
1.86 + POST_HEAP = -2
1.87 + };
1.88 +
1.89 + private:
1.90 +
1.91 + struct RadixItem {
1.92 + int prev, next, box;
1.93 + Item item;
1.94 + int prio;
1.95 + RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {}
1.96 + };
1.97 +
1.98 + struct RadixBox {
1.99 + int first;
1.100 + int min, size;
1.101 + RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {}
1.102 + };
1.103 +
1.104 + std::vector<RadixItem> data;
1.105 + std::vector<RadixBox> boxes;
1.106 +
1.107 + ItemIntMap &iim;
1.108 +
1.109 +
1.110 + public:
1.111 + /// \brief The constructor.
1.112 + ///
1.113 + /// The constructor.
1.114 + /// \param _iim should be given to the constructor, since it is used
1.115 + /// internally to handle the cross references. The value of the map
1.116 + /// should be PRE_HEAP (-1) for each element.
1.117 + explicit RadixHeap(ItemIntMap &_iim) : iim(_iim) {
1.118 + boxes.push_back(RadixBox(0, 1));
1.119 + boxes.push_back(RadixBox(1, 1));
1.120 + }
1.121 +
1.122 + /// \brief The constructor.
1.123 + ///
1.124 + /// The constructor.
1.125 + ///
1.126 + /// \param _iim It should be given to the constructor, since it is used
1.127 + /// internally to handle the cross references. The value of the map
1.128 + /// should be PRE_HEAP (-1) for each element.
1.129 + ///
1.130 + /// \param capacity It determines the initial capacity of the heap.
1.131 + RadixHeap(ItemIntMap &_iim, int capacity) : iim(_iim) {
1.132 + boxes.push_back(RadixBox(0, 1));
1.133 + boxes.push_back(RadixBox(1, 1));
1.134 + while (upper(boxes.back(), capacity)) {
1.135 + extend();
1.136 + }
1.137 + }
1.138 +
1.139 + /// The number of items stored in the heap.
1.140 + ///
1.141 + /// \brief Returns the number of items stored in the heap.
1.142 + int size() const { return data.size(); }
1.143 + /// \brief Checks if the heap stores no items.
1.144 + ///
1.145 + /// Returns \c true if and only if the heap stores no items.
1.146 + bool empty() const { return data.empty(); }
1.147 +
1.148 + private:
1.149 +
1.150 + bool upper(int box, Prio prio) {
1.151 + return prio < boxes[box].min;
1.152 + }
1.153 +
1.154 + bool lower(int box, Prio prio) {
1.155 + return prio >= boxes[box].min + boxes[box].size;
1.156 + }
1.157 +
1.158 + /// \brief Remove item from the box list.
1.159 + void remove(int index) {
1.160 + if (data[index].prev >= 0) {
1.161 + data[data[index].prev].next = data[index].next;
1.162 + } else {
1.163 + boxes[data[index].box].first = data[index].next;
1.164 + }
1.165 + if (data[index].next >= 0) {
1.166 + data[data[index].next].prev = data[index].prev;
1.167 + }
1.168 + }
1.169 +
1.170 + /// \brief Insert item into the box list.
1.171 + void insert(int box, int index) {
1.172 + if (boxes[box].first == -1) {
1.173 + boxes[box].first = index;
1.174 + data[index].next = data[index].prev = -1;
1.175 + } else {
1.176 + data[index].next = boxes[box].first;
1.177 + data[boxes[box].first].prev = index;
1.178 + data[index].prev = -1;
1.179 + boxes[box].first = index;
1.180 + }
1.181 + data[index].box = box;
1.182 + }
1.183 +
1.184 + /// \brief Add a new box to the box list.
1.185 + void extend() {
1.186 + int min = boxes.back().min + boxes.back().size;
1.187 + int size = 2 * boxes.back().size;
1.188 + boxes.push_back(RadixBox(min, size));
1.189 + }
1.190 +
1.191 + /// \brief Move an item up into the proper box.
1.192 + void bubble_up(int index) {
1.193 + if (!lower(data[index].box, data[index].prio)) return;
1.194 + remove(index);
1.195 + int box = findUp(data[index].box, data[index].prio);
1.196 + insert(box, index);
1.197 + }
1.198 +
1.199 + /// \brief Find up the proper box for the item with the given prio.
1.200 + int findUp(int start, int prio) {
1.201 + while (lower(start, prio)) {
1.202 + if (++start == (int)boxes.size()) {
1.203 + extend();
1.204 + }
1.205 + }
1.206 + return start;
1.207 + }
1.208 +
1.209 + /// \brief Move an item down into the proper box.
1.210 + void bubble_down(int index) {
1.211 + if (!upper(data[index].box, data[index].prio)) return;
1.212 + remove(index);
1.213 + int box = findDown(data[index].box, data[index].prio);
1.214 + insert(box, index);
1.215 + }
1.216 +
1.217 + /// \brief Find up the proper box for the item with the given prio.
1.218 + int findDown(int start, int prio) {
1.219 + while (upper(start, prio)) {
1.220 + if (--start < 0) throw UnderFlowPriorityError();
1.221 + }
1.222 + return start;
1.223 + }
1.224 +
1.225 + /// \brief Find the first not empty box.
1.226 + int findFirst() {
1.227 + int first = 0;
1.228 + while (boxes[first].first == -1) ++first;
1.229 + return first;
1.230 + }
1.231 +
1.232 + /// \brief Gives back the minimal prio of the box.
1.233 + int minValue(int box) {
1.234 + int min = data[boxes[box].first].prio;
1.235 + for (int k = boxes[box].first; k != -1; k = data[k].next) {
1.236 + if (data[k].prio < min) min = data[k].prio;
1.237 + }
1.238 + return min;
1.239 + }
1.240 +
1.241 + /// \brief Rearrange the items of the heap and makes the
1.242 + /// first box not empty.
1.243 + void moveDown() {
1.244 + int box = findFirst();
1.245 + if (box == 0) return;
1.246 + int min = minValue(box);
1.247 + for (int i = 0; i <= box; ++i) {
1.248 + boxes[i].min = min;
1.249 + min += boxes[i].size;
1.250 + }
1.251 + int curr = boxes[box].first, next;
1.252 + while (curr != -1) {
1.253 + next = data[curr].next;
1.254 + bubble_down(curr);
1.255 + curr = next;
1.256 + }
1.257 + }
1.258 +
1.259 + void relocate_last(int index) {
1.260 + if (index != (int)data.size() - 1) {
1.261 + data[index] = data.back();
1.262 + if (data[index].prev != -1) {
1.263 + data[data[index].prev].next = index;
1.264 + } else {
1.265 + boxes[data[index].box].first = index;
1.266 + }
1.267 + if (data[index].next != -1) {
1.268 + data[data[index].next].prev = index;
1.269 + }
1.270 + iim[data[index].item] = index;
1.271 + }
1.272 + data.pop_back();
1.273 + }
1.274 +
1.275 + public:
1.276 +
1.277 + /// \brief Insert an item into the heap with the given heap.
1.278 + ///
1.279 + /// Adds \c i to the heap with priority \c p.
1.280 + /// \param i The item to insert.
1.281 + /// \param p The priority of the item.
1.282 + void push(const Item &i, const Prio &p) {
1.283 + int n = data.size();
1.284 + iim.set(i, n);
1.285 + data.push_back(RadixItem(i, p));
1.286 + while (lower(boxes.size() - 1, p)) {
1.287 + extend();
1.288 + }
1.289 + int box = findDown(boxes.size() - 1, p);
1.290 + insert(box, n);
1.291 + }
1.292 +
1.293 + /// \brief Returns the item with minimum priority.
1.294 + ///
1.295 + /// This method returns the item with minimum priority.
1.296 + /// \pre The heap must be nonempty.
1.297 + Item top() const {
1.298 + const_cast<RadixHeap<Item, ItemIntMap>*>(this)->moveDown();
1.299 + return data[boxes[0].first].item;
1.300 + }
1.301 +
1.302 + /// \brief Returns the minimum priority.
1.303 + ///
1.304 + /// It returns the minimum priority.
1.305 + /// \pre The heap must be nonempty.
1.306 + Prio prio() const {
1.307 + const_cast<RadixHeap<Item, ItemIntMap>*>(this)->moveDown();
1.308 + return data[boxes[0].first].prio;
1.309 + }
1.310 +
1.311 + /// \brief Deletes the item with minimum priority.
1.312 + ///
1.313 + /// This method deletes the item with minimum priority.
1.314 + /// \pre The heap must be non-empty.
1.315 + void pop() {
1.316 + moveDown();
1.317 + int index = boxes[0].first;
1.318 + iim[data[index].item] = POST_HEAP;
1.319 + remove(index);
1.320 + relocate_last(index);
1.321 + }
1.322 +
1.323 + /// \brief Deletes \c i from the heap.
1.324 + ///
1.325 + /// This method deletes item \c i from the heap, if \c i was
1.326 + /// already stored in the heap.
1.327 + /// \param i The item to erase.
1.328 + void erase(const Item &i) {
1.329 + int index = iim[i];
1.330 + iim[i] = POST_HEAP;
1.331 + remove(index);
1.332 + relocate_last(index);
1.333 + }
1.334 +
1.335 + /// \brief Returns the priority of \c i.
1.336 + ///
1.337 + /// This function returns the priority of item \c i.
1.338 + /// \pre \c i must be in the heap.
1.339 + /// \param i The item.
1.340 + Prio operator[](const Item &i) const {
1.341 + int idx = iim[i];
1.342 + return data[idx].prio;
1.343 + }
1.344 +
1.345 + /// \brief \c i gets to the heap with priority \c p independently
1.346 + /// if \c i was already there.
1.347 + ///
1.348 + /// This method calls \ref push(\c i, \c p) if \c i is not stored
1.349 + /// in the heap and sets the priority of \c i to \c p otherwise.
1.350 + /// It may throw an \e UnderFlowPriorityException.
1.351 + /// \param i The item.
1.352 + /// \param p The priority.
1.353 + void set(const Item &i, const Prio &p) {
1.354 + int idx = iim[i];
1.355 + if( idx < 0 ) {
1.356 + push(i, p);
1.357 + }
1.358 + else if( p >= data[idx].prio ) {
1.359 + data[idx].prio = p;
1.360 + bubble_up(idx);
1.361 + } else {
1.362 + data[idx].prio = p;
1.363 + bubble_down(idx);
1.364 + }
1.365 + }
1.366 +
1.367 +
1.368 + /// \brief Decreases the priority of \c i to \c p.
1.369 + ///
1.370 + /// This method decreases the priority of item \c i to \c p.
1.371 + /// \pre \c i must be stored in the heap with priority at least \c p, and
1.372 + /// \c should be greater then the last removed item's priority.
1.373 + /// \param i The item.
1.374 + /// \param p The priority.
1.375 + void decrease(const Item &i, const Prio &p) {
1.376 + int idx = iim[i];
1.377 + data[idx].prio = p;
1.378 + bubble_down(idx);
1.379 + }
1.380 +
1.381 + /// \brief Increases the priority of \c i to \c p.
1.382 + ///
1.383 + /// This method sets the priority of item \c i to \c p.
1.384 + /// \pre \c i must be stored in the heap with priority at most \c
1.385 + /// p relative to \c Compare.
1.386 + /// \param i The item.
1.387 + /// \param p The priority.
1.388 + void increase(const Item &i, const Prio &p) {
1.389 + int idx = iim[i];
1.390 + data[idx].prio = p;
1.391 + bubble_up(idx);
1.392 + }
1.393 +
1.394 + /// \brief Returns if \c item is in, has already been in, or has
1.395 + /// never been in the heap.
1.396 + ///
1.397 + /// This method returns PRE_HEAP if \c item has never been in the
1.398 + /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
1.399 + /// otherwise. In the latter case it is possible that \c item will
1.400 + /// get back to the heap again.
1.401 + /// \param i The item.
1.402 + state_enum state(const Item &i) const {
1.403 + int s = iim[i];
1.404 + if( s >= 0 ) s = 0;
1.405 + return state_enum(s);
1.406 + }
1.407 +
1.408 + }; // class RadixHeap
1.409 +
1.410 +
1.411 + ///@}
1.412 +
1.413 +} // namespace lemon
1.414 +
1.415 +#endif // LEMON_RADIX_HEAP_H