1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/bucket_heap.h Thu Dec 10 17:10:25 2009 +0100
1.3 @@ -0,0 +1,567 @@
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_BUCKET_HEAP_H
1.23 +#define LEMON_BUCKET_HEAP_H
1.24 +
1.25 +///\ingroup auxdat
1.26 +///\file
1.27 +///\brief Bucket Heap implementation.
1.28 +
1.29 +#include <vector>
1.30 +#include <utility>
1.31 +#include <functional>
1.32 +
1.33 +namespace lemon {
1.34 +
1.35 + namespace _bucket_heap_bits {
1.36 +
1.37 + template <bool MIN>
1.38 + struct DirectionTraits {
1.39 + static bool less(int left, int right) {
1.40 + return left < right;
1.41 + }
1.42 + static void increase(int& value) {
1.43 + ++value;
1.44 + }
1.45 + };
1.46 +
1.47 + template <>
1.48 + struct DirectionTraits<false> {
1.49 + static bool less(int left, int right) {
1.50 + return left > right;
1.51 + }
1.52 + static void increase(int& value) {
1.53 + --value;
1.54 + }
1.55 + };
1.56 +
1.57 + }
1.58 +
1.59 + /// \ingroup auxdat
1.60 + ///
1.61 + /// \brief A Bucket Heap implementation.
1.62 + ///
1.63 + /// This class implements the \e bucket \e heap data structure. A \e heap
1.64 + /// is a data structure for storing items with specified values called \e
1.65 + /// priorities in such a way that finding the item with minimum priority is
1.66 + /// efficient. The bucket heap is very simple implementation, it can store
1.67 + /// only integer priorities and it stores for each priority in the
1.68 + /// \f$ [0..C) \f$ range a list of items. So it should be used only when
1.69 + /// the priorities are small. It is not intended to use as dijkstra heap.
1.70 + ///
1.71 + /// \param IM A read and write Item int map, used internally
1.72 + /// to handle the cross references.
1.73 + /// \param MIN If the given parameter is false then instead of the
1.74 + /// minimum value the maximum can be retrivied with the top() and
1.75 + /// prio() member functions.
1.76 + template <typename IM, bool MIN = true>
1.77 + class BucketHeap {
1.78 +
1.79 + public:
1.80 + /// \e
1.81 + typedef typename IM::Key Item;
1.82 + /// \e
1.83 + typedef int Prio;
1.84 + /// \e
1.85 + typedef std::pair<Item, Prio> Pair;
1.86 + /// \e
1.87 + typedef IM ItemIntMap;
1.88 +
1.89 + private:
1.90 +
1.91 + typedef _bucket_heap_bits::DirectionTraits<MIN> Direction;
1.92 +
1.93 + public:
1.94 +
1.95 + /// \brief Type to represent the items states.
1.96 + ///
1.97 + /// Each Item element have a state associated to it. It may be "in heap",
1.98 + /// "pre heap" or "post heap". The latter two are indifferent from the
1.99 + /// heap's point of view, but may be useful to the user.
1.100 + ///
1.101 + /// The item-int map must be initialized in such way that it assigns
1.102 + /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
1.103 + enum State {
1.104 + IN_HEAP = 0, ///< = 0.
1.105 + PRE_HEAP = -1, ///< = -1.
1.106 + POST_HEAP = -2 ///< = -2.
1.107 + };
1.108 +
1.109 + public:
1.110 + /// \brief The constructor.
1.111 + ///
1.112 + /// The constructor.
1.113 + /// \param map 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 + explicit BucketHeap(ItemIntMap &map) : _iim(map), _minimum(0) {}
1.117 +
1.118 + /// The number of items stored in the heap.
1.119 + ///
1.120 + /// \brief Returns the number of items stored in the heap.
1.121 + int size() const { return _data.size(); }
1.122 +
1.123 + /// \brief Checks if the heap stores no items.
1.124 + ///
1.125 + /// Returns \c true if and only if the heap stores no items.
1.126 + bool empty() const { return _data.empty(); }
1.127 +
1.128 + /// \brief Make empty this heap.
1.129 + ///
1.130 + /// Make empty this heap. It does not change the cross reference
1.131 + /// map. If you want to reuse a heap what is not surely empty you
1.132 + /// should first clear the heap and after that you should set the
1.133 + /// cross reference map for each item to \c PRE_HEAP.
1.134 + void clear() {
1.135 + _data.clear(); _first.clear(); _minimum = 0;
1.136 + }
1.137 +
1.138 + private:
1.139 +
1.140 + void relocate_last(int idx) {
1.141 + if (idx + 1 < int(_data.size())) {
1.142 + _data[idx] = _data.back();
1.143 + if (_data[idx].prev != -1) {
1.144 + _data[_data[idx].prev].next = idx;
1.145 + } else {
1.146 + _first[_data[idx].value] = idx;
1.147 + }
1.148 + if (_data[idx].next != -1) {
1.149 + _data[_data[idx].next].prev = idx;
1.150 + }
1.151 + _iim[_data[idx].item] = idx;
1.152 + }
1.153 + _data.pop_back();
1.154 + }
1.155 +
1.156 + void unlace(int idx) {
1.157 + if (_data[idx].prev != -1) {
1.158 + _data[_data[idx].prev].next = _data[idx].next;
1.159 + } else {
1.160 + _first[_data[idx].value] = _data[idx].next;
1.161 + }
1.162 + if (_data[idx].next != -1) {
1.163 + _data[_data[idx].next].prev = _data[idx].prev;
1.164 + }
1.165 + }
1.166 +
1.167 + void lace(int idx) {
1.168 + if (int(_first.size()) <= _data[idx].value) {
1.169 + _first.resize(_data[idx].value + 1, -1);
1.170 + }
1.171 + _data[idx].next = _first[_data[idx].value];
1.172 + if (_data[idx].next != -1) {
1.173 + _data[_data[idx].next].prev = idx;
1.174 + }
1.175 + _first[_data[idx].value] = idx;
1.176 + _data[idx].prev = -1;
1.177 + }
1.178 +
1.179 + public:
1.180 + /// \brief Insert a pair of item and priority into the heap.
1.181 + ///
1.182 + /// Adds \c p.first to the heap with priority \c p.second.
1.183 + /// \param p The pair to insert.
1.184 + void push(const Pair& p) {
1.185 + push(p.first, p.second);
1.186 + }
1.187 +
1.188 + /// \brief Insert an item into the heap with the given priority.
1.189 + ///
1.190 + /// Adds \c i to the heap with priority \c p.
1.191 + /// \param i The item to insert.
1.192 + /// \param p The priority of the item.
1.193 + void push(const Item &i, const Prio &p) {
1.194 + int idx = _data.size();
1.195 + _iim[i] = idx;
1.196 + _data.push_back(BucketItem(i, p));
1.197 + lace(idx);
1.198 + if (Direction::less(p, _minimum)) {
1.199 + _minimum = p;
1.200 + }
1.201 + }
1.202 +
1.203 + /// \brief Returns the item with minimum priority.
1.204 + ///
1.205 + /// This method returns the item with minimum priority.
1.206 + /// \pre The heap must be nonempty.
1.207 + Item top() const {
1.208 + while (_first[_minimum] == -1) {
1.209 + Direction::increase(_minimum);
1.210 + }
1.211 + return _data[_first[_minimum]].item;
1.212 + }
1.213 +
1.214 + /// \brief Returns the minimum priority.
1.215 + ///
1.216 + /// It returns the minimum priority.
1.217 + /// \pre The heap must be nonempty.
1.218 + Prio prio() const {
1.219 + while (_first[_minimum] == -1) {
1.220 + Direction::increase(_minimum);
1.221 + }
1.222 + return _minimum;
1.223 + }
1.224 +
1.225 + /// \brief Deletes the item with minimum priority.
1.226 + ///
1.227 + /// This method deletes the item with minimum priority from the heap.
1.228 + /// \pre The heap must be non-empty.
1.229 + void pop() {
1.230 + while (_first[_minimum] == -1) {
1.231 + Direction::increase(_minimum);
1.232 + }
1.233 + int idx = _first[_minimum];
1.234 + _iim[_data[idx].item] = -2;
1.235 + unlace(idx);
1.236 + relocate_last(idx);
1.237 + }
1.238 +
1.239 + /// \brief Deletes \c i from the heap.
1.240 + ///
1.241 + /// This method deletes item \c i from the heap, if \c i was
1.242 + /// already stored in the heap.
1.243 + /// \param i The item to erase.
1.244 + void erase(const Item &i) {
1.245 + int idx = _iim[i];
1.246 + _iim[_data[idx].item] = -2;
1.247 + unlace(idx);
1.248 + relocate_last(idx);
1.249 + }
1.250 +
1.251 +
1.252 + /// \brief Returns the priority of \c i.
1.253 + ///
1.254 + /// This function returns the priority of item \c i.
1.255 + /// \pre \c i must be in the heap.
1.256 + /// \param i The item.
1.257 + Prio operator[](const Item &i) const {
1.258 + int idx = _iim[i];
1.259 + return _data[idx].value;
1.260 + }
1.261 +
1.262 + /// \brief \c i gets to the heap with priority \c p independently
1.263 + /// if \c i was already there.
1.264 + ///
1.265 + /// This method calls \ref push(\c i, \c p) if \c i is not stored
1.266 + /// in the heap and sets the priority of \c i to \c p otherwise.
1.267 + /// \param i The item.
1.268 + /// \param p The priority.
1.269 + void set(const Item &i, const Prio &p) {
1.270 + int idx = _iim[i];
1.271 + if (idx < 0) {
1.272 + push(i, p);
1.273 + } else if (Direction::less(p, _data[idx].value)) {
1.274 + decrease(i, p);
1.275 + } else {
1.276 + increase(i, p);
1.277 + }
1.278 + }
1.279 +
1.280 + /// \brief Decreases the priority of \c i to \c p.
1.281 + ///
1.282 + /// This method decreases the priority of item \c i to \c p.
1.283 + /// \pre \c i must be stored in the heap with priority at least \c
1.284 + /// p relative to \c Compare.
1.285 + /// \param i The item.
1.286 + /// \param p The priority.
1.287 + void decrease(const Item &i, const Prio &p) {
1.288 + int idx = _iim[i];
1.289 + unlace(idx);
1.290 + _data[idx].value = p;
1.291 + if (Direction::less(p, _minimum)) {
1.292 + _minimum = p;
1.293 + }
1.294 + lace(idx);
1.295 + }
1.296 +
1.297 + /// \brief Increases the priority of \c i to \c p.
1.298 + ///
1.299 + /// This method sets the priority of item \c i to \c p.
1.300 + /// \pre \c i must be stored in the heap with priority at most \c
1.301 + /// p relative to \c Compare.
1.302 + /// \param i The item.
1.303 + /// \param p The priority.
1.304 + void increase(const Item &i, const Prio &p) {
1.305 + int idx = _iim[i];
1.306 + unlace(idx);
1.307 + _data[idx].value = p;
1.308 + lace(idx);
1.309 + }
1.310 +
1.311 + /// \brief Returns if \c item is in, has already been in, or has
1.312 + /// never been in the heap.
1.313 + ///
1.314 + /// This method returns PRE_HEAP if \c item has never been in the
1.315 + /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
1.316 + /// otherwise. In the latter case it is possible that \c item will
1.317 + /// get back to the heap again.
1.318 + /// \param i The item.
1.319 + State state(const Item &i) const {
1.320 + int idx = _iim[i];
1.321 + if (idx >= 0) idx = 0;
1.322 + return State(idx);
1.323 + }
1.324 +
1.325 + /// \brief Sets the state of the \c item in the heap.
1.326 + ///
1.327 + /// Sets the state of the \c item in the heap. It can be used to
1.328 + /// manually clear the heap when it is important to achive the
1.329 + /// better time complexity.
1.330 + /// \param i The item.
1.331 + /// \param st The state. It should not be \c IN_HEAP.
1.332 + void state(const Item& i, State st) {
1.333 + switch (st) {
1.334 + case POST_HEAP:
1.335 + case PRE_HEAP:
1.336 + if (state(i) == IN_HEAP) {
1.337 + erase(i);
1.338 + }
1.339 + _iim[i] = st;
1.340 + break;
1.341 + case IN_HEAP:
1.342 + break;
1.343 + }
1.344 + }
1.345 +
1.346 + private:
1.347 +
1.348 + struct BucketItem {
1.349 + BucketItem(const Item& _item, int _value)
1.350 + : item(_item), value(_value) {}
1.351 +
1.352 + Item item;
1.353 + int value;
1.354 +
1.355 + int prev, next;
1.356 + };
1.357 +
1.358 + ItemIntMap& _iim;
1.359 + std::vector<int> _first;
1.360 + std::vector<BucketItem> _data;
1.361 + mutable int _minimum;
1.362 +
1.363 + }; // class BucketHeap
1.364 +
1.365 + /// \ingroup auxdat
1.366 + ///
1.367 + /// \brief A Simplified Bucket Heap implementation.
1.368 + ///
1.369 + /// This class implements a simplified \e bucket \e heap data
1.370 + /// structure. It does not provide some functionality but it faster
1.371 + /// and simplier data structure than the BucketHeap. The main
1.372 + /// difference is that the BucketHeap stores for every key a double
1.373 + /// linked list while this class stores just simple lists. In the
1.374 + /// other way it does not support erasing each elements just the
1.375 + /// minimal and it does not supports key increasing, decreasing.
1.376 + ///
1.377 + /// \param IM A read and write Item int map, used internally
1.378 + /// to handle the cross references.
1.379 + /// \param MIN If the given parameter is false then instead of the
1.380 + /// minimum value the maximum can be retrivied with the top() and
1.381 + /// prio() member functions.
1.382 + ///
1.383 + /// \sa BucketHeap
1.384 + template <typename IM, bool MIN = true >
1.385 + class SimpleBucketHeap {
1.386 +
1.387 + public:
1.388 + typedef typename IM::Key Item;
1.389 + typedef int Prio;
1.390 + typedef std::pair<Item, Prio> Pair;
1.391 + typedef IM ItemIntMap;
1.392 +
1.393 + private:
1.394 +
1.395 + typedef _bucket_heap_bits::DirectionTraits<MIN> Direction;
1.396 +
1.397 + public:
1.398 +
1.399 + /// \brief Type to represent the items states.
1.400 + ///
1.401 + /// Each Item element have a state associated to it. It may be "in heap",
1.402 + /// "pre heap" or "post heap". The latter two are indifferent from the
1.403 + /// heap's point of view, but may be useful to the user.
1.404 + ///
1.405 + /// The item-int map must be initialized in such way that it assigns
1.406 + /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
1.407 + enum State {
1.408 + IN_HEAP = 0, ///< = 0.
1.409 + PRE_HEAP = -1, ///< = -1.
1.410 + POST_HEAP = -2 ///< = -2.
1.411 + };
1.412 +
1.413 + public:
1.414 +
1.415 + /// \brief The constructor.
1.416 + ///
1.417 + /// The constructor.
1.418 + /// \param map should be given to the constructor, since it is used
1.419 + /// internally to handle the cross references. The value of the map
1.420 + /// should be PRE_HEAP (-1) for each element.
1.421 + explicit SimpleBucketHeap(ItemIntMap &map)
1.422 + : _iim(map), _free(-1), _num(0), _minimum(0) {}
1.423 +
1.424 + /// \brief Returns the number of items stored in the heap.
1.425 + ///
1.426 + /// The number of items stored in the heap.
1.427 + int size() const { return _num; }
1.428 +
1.429 + /// \brief Checks if the heap stores no items.
1.430 + ///
1.431 + /// Returns \c true if and only if the heap stores no items.
1.432 + bool empty() const { return _num == 0; }
1.433 +
1.434 + /// \brief Make empty this heap.
1.435 + ///
1.436 + /// Make empty this heap. It does not change the cross reference
1.437 + /// map. If you want to reuse a heap what is not surely empty you
1.438 + /// should first clear the heap and after that you should set the
1.439 + /// cross reference map for each item to \c PRE_HEAP.
1.440 + void clear() {
1.441 + _data.clear(); _first.clear(); _free = -1; _num = 0; _minimum = 0;
1.442 + }
1.443 +
1.444 + /// \brief Insert a pair of item and priority into the heap.
1.445 + ///
1.446 + /// Adds \c p.first to the heap with priority \c p.second.
1.447 + /// \param p The pair to insert.
1.448 + void push(const Pair& p) {
1.449 + push(p.first, p.second);
1.450 + }
1.451 +
1.452 + /// \brief Insert an item into the heap with the given priority.
1.453 + ///
1.454 + /// Adds \c i to the heap with priority \c p.
1.455 + /// \param i The item to insert.
1.456 + /// \param p The priority of the item.
1.457 + void push(const Item &i, const Prio &p) {
1.458 + int idx;
1.459 + if (_free == -1) {
1.460 + idx = _data.size();
1.461 + _data.push_back(BucketItem(i));
1.462 + } else {
1.463 + idx = _free;
1.464 + _free = _data[idx].next;
1.465 + _data[idx].item = i;
1.466 + }
1.467 + _iim[i] = idx;
1.468 + if (p >= int(_first.size())) _first.resize(p + 1, -1);
1.469 + _data[idx].next = _first[p];
1.470 + _first[p] = idx;
1.471 + if (Direction::less(p, _minimum)) {
1.472 + _minimum = p;
1.473 + }
1.474 + ++_num;
1.475 + }
1.476 +
1.477 + /// \brief Returns the item with minimum priority.
1.478 + ///
1.479 + /// This method returns the item with minimum priority.
1.480 + /// \pre The heap must be nonempty.
1.481 + Item top() const {
1.482 + while (_first[_minimum] == -1) {
1.483 + Direction::increase(_minimum);
1.484 + }
1.485 + return _data[_first[_minimum]].item;
1.486 + }
1.487 +
1.488 + /// \brief Returns the minimum priority.
1.489 + ///
1.490 + /// It returns the minimum priority.
1.491 + /// \pre The heap must be nonempty.
1.492 + Prio prio() const {
1.493 + while (_first[_minimum] == -1) {
1.494 + Direction::increase(_minimum);
1.495 + }
1.496 + return _minimum;
1.497 + }
1.498 +
1.499 + /// \brief Deletes the item with minimum priority.
1.500 + ///
1.501 + /// This method deletes the item with minimum priority from the heap.
1.502 + /// \pre The heap must be non-empty.
1.503 + void pop() {
1.504 + while (_first[_minimum] == -1) {
1.505 + Direction::increase(_minimum);
1.506 + }
1.507 + int idx = _first[_minimum];
1.508 + _iim[_data[idx].item] = -2;
1.509 + _first[_minimum] = _data[idx].next;
1.510 + _data[idx].next = _free;
1.511 + _free = idx;
1.512 + --_num;
1.513 + }
1.514 +
1.515 + /// \brief Returns the priority of \c i.
1.516 + ///
1.517 + /// This function returns the priority of item \c i.
1.518 + /// \warning This operator is not a constant time function
1.519 + /// because it scans the whole data structure to find the proper
1.520 + /// value.
1.521 + /// \pre \c i must be in the heap.
1.522 + /// \param i The item.
1.523 + Prio operator[](const Item &i) const {
1.524 + for (int k = 0; k < _first.size(); ++k) {
1.525 + int idx = _first[k];
1.526 + while (idx != -1) {
1.527 + if (_data[idx].item == i) {
1.528 + return k;
1.529 + }
1.530 + idx = _data[idx].next;
1.531 + }
1.532 + }
1.533 + return -1;
1.534 + }
1.535 +
1.536 + /// \brief Returns if \c item is in, has already been in, or has
1.537 + /// never been in the heap.
1.538 + ///
1.539 + /// This method returns PRE_HEAP if \c item has never been in the
1.540 + /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
1.541 + /// otherwise. In the latter case it is possible that \c item will
1.542 + /// get back to the heap again.
1.543 + /// \param i The item.
1.544 + State state(const Item &i) const {
1.545 + int idx = _iim[i];
1.546 + if (idx >= 0) idx = 0;
1.547 + return State(idx);
1.548 + }
1.549 +
1.550 + private:
1.551 +
1.552 + struct BucketItem {
1.553 + BucketItem(const Item& _item)
1.554 + : item(_item) {}
1.555 +
1.556 + Item item;
1.557 + int next;
1.558 + };
1.559 +
1.560 + ItemIntMap& _iim;
1.561 + std::vector<int> _first;
1.562 + std::vector<BucketItem> _data;
1.563 + int _free, _num;
1.564 + mutable int _minimum;
1.565 +
1.566 + }; // class SimpleBucketHeap
1.567 +
1.568 +}
1.569 +
1.570 +#endif