1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/radix_heap.h Thu Jun 11 22:11:29 2009 +0200
1.3 @@ -0,0 +1,433 @@
1.4 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
1.5 + *
1.6 + * This file is a part of LEMON, a generic C++ optimization library.
1.7 + *
1.8 + * Copyright (C) 2003-2009
1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.11 + *
1.12 + * Permission to use, modify and distribute this software is granted
1.13 + * provided that this copyright notice appears in all copies. For
1.14 + * precise terms see the accompanying LICENSE file.
1.15 + *
1.16 + * This software is provided "AS IS" with no warranty of any kind,
1.17 + * express or implied, and with no claim as to its suitability for any
1.18 + * purpose.
1.19 + *
1.20 + */
1.21 +
1.22 +#ifndef LEMON_RADIX_HEAP_H
1.23 +#define LEMON_RADIX_HEAP_H
1.24 +
1.25 +///\ingroup auxdat
1.26 +///\file
1.27 +///\brief Radix Heap implementation.
1.28 +
1.29 +#include <vector>
1.30 +#include <lemon/error.h>
1.31 +
1.32 +namespace lemon {
1.33 +
1.34 +
1.35 + /// \ingroup auxdata
1.36 + ///
1.37 + /// \brief A Radix Heap implementation.
1.38 + ///
1.39 + /// This class implements the \e radix \e heap data structure. A \e heap
1.40 + /// is a data structure for storing items with specified values called \e
1.41 + /// priorities in such a way that finding the item with minimum priority is
1.42 + /// efficient. This heap type can store only items with \e int priority.
1.43 + /// In a heap one can change the priority of an item, add or erase an
1.44 + /// item, but the priority cannot be decreased under the last removed
1.45 + /// item's priority.
1.46 + ///
1.47 + /// \param _ItemIntMap A read and writable Item int map, used internally
1.48 + /// to handle the cross references.
1.49 + ///
1.50 + /// \see BinHeap
1.51 + /// \see Dijkstra
1.52 + template <typename _ItemIntMap>
1.53 + class RadixHeap {
1.54 +
1.55 + public:
1.56 + typedef typename _ItemIntMap::Key Item;
1.57 + typedef int Prio;
1.58 + typedef _ItemIntMap ItemIntMap;
1.59 +
1.60 + /// \brief Exception thrown by RadixHeap.
1.61 + ///
1.62 + /// This Exception is thrown when a smaller priority
1.63 + /// is inserted into the \e RadixHeap then the last time erased.
1.64 + /// \see RadixHeap
1.65 +
1.66 + class UnderFlowPriorityError : public Exception {
1.67 + public:
1.68 + virtual const char* what() const throw() {
1.69 + return "lemon::RadixHeap::UnderFlowPriorityError";
1.70 + }
1.71 + };
1.72 +
1.73 + /// \brief Type to represent the items states.
1.74 + ///
1.75 + /// Each Item element have a state associated to it. It may be "in heap",
1.76 + /// "pre heap" or "post heap". The latter two are indifferent from the
1.77 + /// heap's point of view, but may be useful to the user.
1.78 + ///
1.79 + /// The ItemIntMap \e should be initialized in such way that it maps
1.80 + /// PRE_HEAP (-1) to any element to be put in the heap...
1.81 + enum State {
1.82 + IN_HEAP = 0,
1.83 + PRE_HEAP = -1,
1.84 + POST_HEAP = -2
1.85 + };
1.86 +
1.87 + private:
1.88 +
1.89 + struct RadixItem {
1.90 + int prev, next, box;
1.91 + Item item;
1.92 + int prio;
1.93 + RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {}
1.94 + };
1.95 +
1.96 + struct RadixBox {
1.97 + int first;
1.98 + int min, size;
1.99 + RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {}
1.100 + };
1.101 +
1.102 + std::vector<RadixItem> data;
1.103 + std::vector<RadixBox> boxes;
1.104 +
1.105 + ItemIntMap &iim;
1.106 +
1.107 +
1.108 + public:
1.109 + /// \brief The constructor.
1.110 + ///
1.111 + /// The constructor.
1.112 + ///
1.113 + /// \param _iim It should be given to the constructor, since it is used
1.114 + /// internally to handle the cross references. The value of the map
1.115 + /// should be PRE_HEAP (-1) for each element.
1.116 + ///
1.117 + /// \param minimal The initial minimal value of the heap.
1.118 + /// \param capacity It determines the initial capacity of the heap.
1.119 + RadixHeap(ItemIntMap &_iim, int minimal = 0, int capacity = 0)
1.120 + : iim(_iim) {
1.121 + boxes.push_back(RadixBox(minimal, 1));
1.122 + boxes.push_back(RadixBox(minimal + 1, 1));
1.123 + while (lower(boxes.size() - 1, capacity + minimal - 1)) {
1.124 + extend();
1.125 + }
1.126 + }
1.127 +
1.128 + /// The number of items stored in the heap.
1.129 + ///
1.130 + /// \brief Returns the number of items stored in the heap.
1.131 + int size() const { return data.size(); }
1.132 + /// \brief Checks if the heap stores no items.
1.133 + ///
1.134 + /// Returns \c true if and only if the heap stores no items.
1.135 + bool empty() const { return data.empty(); }
1.136 +
1.137 + /// \brief Make empty this heap.
1.138 + ///
1.139 + /// Make empty this heap. It does not change the cross reference
1.140 + /// map. If you want to reuse a heap what is not surely empty you
1.141 + /// should first clear the heap and after that you should set the
1.142 + /// cross reference map for each item to \c PRE_HEAP.
1.143 + void clear(int minimal = 0, int capacity = 0) {
1.144 + data.clear(); boxes.clear();
1.145 + boxes.push_back(RadixBox(minimal, 1));
1.146 + boxes.push_back(RadixBox(minimal + 1, 1));
1.147 + while (lower(boxes.size() - 1, capacity + minimal - 1)) {
1.148 + extend();
1.149 + }
1.150 + }
1.151 +
1.152 + private:
1.153 +
1.154 + bool upper(int box, Prio pr) {
1.155 + return pr < boxes[box].min;
1.156 + }
1.157 +
1.158 + bool lower(int box, Prio pr) {
1.159 + return pr >= boxes[box].min + boxes[box].size;
1.160 + }
1.161 +
1.162 + /// \brief Remove item from the box list.
1.163 + void remove(int index) {
1.164 + if (data[index].prev >= 0) {
1.165 + data[data[index].prev].next = data[index].next;
1.166 + } else {
1.167 + boxes[data[index].box].first = data[index].next;
1.168 + }
1.169 + if (data[index].next >= 0) {
1.170 + data[data[index].next].prev = data[index].prev;
1.171 + }
1.172 + }
1.173 +
1.174 + /// \brief Insert item into the box list.
1.175 + void insert(int box, int index) {
1.176 + if (boxes[box].first == -1) {
1.177 + boxes[box].first = index;
1.178 + data[index].next = data[index].prev = -1;
1.179 + } else {
1.180 + data[index].next = boxes[box].first;
1.181 + data[boxes[box].first].prev = index;
1.182 + data[index].prev = -1;
1.183 + boxes[box].first = index;
1.184 + }
1.185 + data[index].box = box;
1.186 + }
1.187 +
1.188 + /// \brief Add a new box to the box list.
1.189 + void extend() {
1.190 + int min = boxes.back().min + boxes.back().size;
1.191 + int bs = 2 * boxes.back().size;
1.192 + boxes.push_back(RadixBox(min, bs));
1.193 + }
1.194 +
1.195 + /// \brief Move an item up into the proper box.
1.196 + void bubble_up(int index) {
1.197 + if (!lower(data[index].box, data[index].prio)) return;
1.198 + remove(index);
1.199 + int box = findUp(data[index].box, data[index].prio);
1.200 + insert(box, index);
1.201 + }
1.202 +
1.203 + /// \brief Find up the proper box for the item with the given prio.
1.204 + int findUp(int start, int pr) {
1.205 + while (lower(start, pr)) {
1.206 + if (++start == int(boxes.size())) {
1.207 + extend();
1.208 + }
1.209 + }
1.210 + return start;
1.211 + }
1.212 +
1.213 + /// \brief Move an item down into the proper box.
1.214 + void bubble_down(int index) {
1.215 + if (!upper(data[index].box, data[index].prio)) return;
1.216 + remove(index);
1.217 + int box = findDown(data[index].box, data[index].prio);
1.218 + insert(box, index);
1.219 + }
1.220 +
1.221 + /// \brief Find up the proper box for the item with the given prio.
1.222 + int findDown(int start, int pr) {
1.223 + while (upper(start, pr)) {
1.224 + if (--start < 0) throw UnderFlowPriorityError();
1.225 + }
1.226 + return start;
1.227 + }
1.228 +
1.229 + /// \brief Find the first not empty box.
1.230 + int findFirst() {
1.231 + int first = 0;
1.232 + while (boxes[first].first == -1) ++first;
1.233 + return first;
1.234 + }
1.235 +
1.236 + /// \brief Gives back the minimal prio of the box.
1.237 + int minValue(int box) {
1.238 + int min = data[boxes[box].first].prio;
1.239 + for (int k = boxes[box].first; k != -1; k = data[k].next) {
1.240 + if (data[k].prio < min) min = data[k].prio;
1.241 + }
1.242 + return min;
1.243 + }
1.244 +
1.245 + /// \brief Rearrange the items of the heap and makes the
1.246 + /// first box not empty.
1.247 + void moveDown() {
1.248 + int box = findFirst();
1.249 + if (box == 0) return;
1.250 + int min = minValue(box);
1.251 + for (int i = 0; i <= box; ++i) {
1.252 + boxes[i].min = min;
1.253 + min += boxes[i].size;
1.254 + }
1.255 + int curr = boxes[box].first, next;
1.256 + while (curr != -1) {
1.257 + next = data[curr].next;
1.258 + bubble_down(curr);
1.259 + curr = next;
1.260 + }
1.261 + }
1.262 +
1.263 + void relocate_last(int index) {
1.264 + if (index != int(data.size()) - 1) {
1.265 + data[index] = data.back();
1.266 + if (data[index].prev != -1) {
1.267 + data[data[index].prev].next = index;
1.268 + } else {
1.269 + boxes[data[index].box].first = index;
1.270 + }
1.271 + if (data[index].next != -1) {
1.272 + data[data[index].next].prev = index;
1.273 + }
1.274 + iim[data[index].item] = index;
1.275 + }
1.276 + data.pop_back();
1.277 + }
1.278 +
1.279 + public:
1.280 +
1.281 + /// \brief Insert an item into the heap with the given priority.
1.282 + ///
1.283 + /// Adds \c i to the heap with priority \c p.
1.284 + /// \param i The item to insert.
1.285 + /// \param p The priority of the item.
1.286 + void push(const Item &i, const Prio &p) {
1.287 + int n = data.size();
1.288 + iim.set(i, n);
1.289 + data.push_back(RadixItem(i, p));
1.290 + while (lower(boxes.size() - 1, p)) {
1.291 + extend();
1.292 + }
1.293 + int box = findDown(boxes.size() - 1, p);
1.294 + insert(box, n);
1.295 + }
1.296 +
1.297 + /// \brief Returns the item with minimum priority.
1.298 + ///
1.299 + /// This method returns the item with minimum priority.
1.300 + /// \pre The heap must be nonempty.
1.301 + Item top() const {
1.302 + const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown();
1.303 + return data[boxes[0].first].item;
1.304 + }
1.305 +
1.306 + /// \brief Returns the minimum priority.
1.307 + ///
1.308 + /// It returns the minimum priority.
1.309 + /// \pre The heap must be nonempty.
1.310 + Prio prio() const {
1.311 + const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown();
1.312 + return data[boxes[0].first].prio;
1.313 + }
1.314 +
1.315 + /// \brief Deletes the item with minimum priority.
1.316 + ///
1.317 + /// This method deletes the item with minimum priority.
1.318 + /// \pre The heap must be non-empty.
1.319 + void pop() {
1.320 + moveDown();
1.321 + int index = boxes[0].first;
1.322 + iim[data[index].item] = POST_HEAP;
1.323 + remove(index);
1.324 + relocate_last(index);
1.325 + }
1.326 +
1.327 + /// \brief Deletes \c i from the heap.
1.328 + ///
1.329 + /// This method deletes item \c i from the heap, if \c i was
1.330 + /// already stored in the heap.
1.331 + /// \param i The item to erase.
1.332 + void erase(const Item &i) {
1.333 + int index = iim[i];
1.334 + iim[i] = POST_HEAP;
1.335 + remove(index);
1.336 + relocate_last(index);
1.337 + }
1.338 +
1.339 + /// \brief Returns the priority of \c i.
1.340 + ///
1.341 + /// This function returns the priority of item \c i.
1.342 + /// \pre \c i must be in the heap.
1.343 + /// \param i The item.
1.344 + Prio operator[](const Item &i) const {
1.345 + int idx = iim[i];
1.346 + return data[idx].prio;
1.347 + }
1.348 +
1.349 + /// \brief \c i gets to the heap with priority \c p independently
1.350 + /// if \c i was already there.
1.351 + ///
1.352 + /// This method calls \ref push(\c i, \c p) if \c i is not stored
1.353 + /// in the heap and sets the priority of \c i to \c p otherwise.
1.354 + /// It may throw an \e UnderFlowPriorityException.
1.355 + /// \param i The item.
1.356 + /// \param p The priority.
1.357 + void set(const Item &i, const Prio &p) {
1.358 + int idx = iim[i];
1.359 + if( idx < 0 ) {
1.360 + push(i, p);
1.361 + }
1.362 + else if( p >= data[idx].prio ) {
1.363 + data[idx].prio = p;
1.364 + bubble_up(idx);
1.365 + } else {
1.366 + data[idx].prio = p;
1.367 + bubble_down(idx);
1.368 + }
1.369 + }
1.370 +
1.371 +
1.372 + /// \brief Decreases the priority of \c i to \c p.
1.373 + ///
1.374 + /// This method decreases the priority of item \c i to \c p.
1.375 + /// \pre \c i must be stored in the heap with priority at least \c p, and
1.376 + /// \c should be greater or equal to the last removed item's priority.
1.377 + /// \param i The item.
1.378 + /// \param p The priority.
1.379 + void decrease(const Item &i, const Prio &p) {
1.380 + int idx = iim[i];
1.381 + data[idx].prio = p;
1.382 + bubble_down(idx);
1.383 + }
1.384 +
1.385 + /// \brief Increases the priority of \c i to \c p.
1.386 + ///
1.387 + /// This method sets the priority of item \c i to \c p.
1.388 + /// \pre \c i must be stored in the heap with priority at most \c p
1.389 + /// \param i The item.
1.390 + /// \param p The priority.
1.391 + void increase(const Item &i, const Prio &p) {
1.392 + int idx = iim[i];
1.393 + data[idx].prio = p;
1.394 + bubble_up(idx);
1.395 + }
1.396 +
1.397 + /// \brief Returns if \c item is in, has already been in, or has
1.398 + /// never been in the heap.
1.399 + ///
1.400 + /// This method returns PRE_HEAP if \c item has never been in the
1.401 + /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
1.402 + /// otherwise. In the latter case it is possible that \c item will
1.403 + /// get back to the heap again.
1.404 + /// \param i The item.
1.405 + State state(const Item &i) const {
1.406 + int s = iim[i];
1.407 + if( s >= 0 ) s = 0;
1.408 + return State(s);
1.409 + }
1.410 +
1.411 + /// \brief Sets the state of the \c item in the heap.
1.412 + ///
1.413 + /// Sets the state of the \c item in the heap. It can be used to
1.414 + /// manually clear the heap when it is important to achive the
1.415 + /// better time complexity.
1.416 + /// \param i The item.
1.417 + /// \param st The state. It should not be \c IN_HEAP.
1.418 + void state(const Item& i, State st) {
1.419 + switch (st) {
1.420 + case POST_HEAP:
1.421 + case PRE_HEAP:
1.422 + if (state(i) == IN_HEAP) {
1.423 + erase(i);
1.424 + }
1.425 + iim[i] = st;
1.426 + break;
1.427 + case IN_HEAP:
1.428 + break;
1.429 + }
1.430 + }
1.431 +
1.432 + }; // class RadixHeap
1.433 +
1.434 +} // namespace lemon
1.435 +
1.436 +#endif // LEMON_RADIX_HEAP_H