1.1 --- a/lemon/fourary_heap.h Thu Jul 09 02:39:47 2009 +0200
1.2 +++ b/lemon/fourary_heap.h Thu Jul 09 04:07:08 2009 +0200
1.3 @@ -1,8 +1,8 @@
1.4 -/* -*- C++ -*-
1.5 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
1.6 *
1.7 - * This file is a part of LEMON, a generic C++ optimization library
1.8 + * This file is a part of LEMON, a generic C++ optimization library.
1.9 *
1.10 - * Copyright (C) 2003-2008
1.11 + * Copyright (C) 2003-2009
1.12 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.13 * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.14 *
1.15 @@ -19,159 +19,158 @@
1.16 #ifndef LEMON_FOURARY_HEAP_H
1.17 #define LEMON_FOURARY_HEAP_H
1.18
1.19 -///\ingroup auxdat
1.20 +///\ingroup heaps
1.21 ///\file
1.22 -///\brief 4ary Heap implementation.
1.23 +///\brief Fourary heap implementation.
1.24
1.25 -#include <iostream>
1.26 #include <vector>
1.27 #include <utility>
1.28 #include <functional>
1.29
1.30 namespace lemon {
1.31
1.32 - ///\ingroup auxdat
1.33 + /// \ingroup heaps
1.34 ///
1.35 - ///\brief A 4ary Heap implementation.
1.36 + ///\brief Fourary heap data structure.
1.37 ///
1.38 - ///This class implements the \e 4ary \e heap data structure. A \e heap
1.39 - ///is a data structure for storing items with specified values called \e
1.40 - ///priorities in such a way that finding the item with minimum priority is
1.41 - ///efficient. \c Compare specifies the ordering of the priorities. In a heap
1.42 - ///one can change the priority of an item, add or erase an item, etc.
1.43 + /// This class implements the \e fourary \e heap data structure.
1.44 + /// It fully conforms to the \ref concepts::Heap "heap concept".
1.45 ///
1.46 - ///\param _Prio Type of the priority of the items.
1.47 - ///\param _ItemIntMap A read and writable Item int map, used internally
1.48 - ///to handle the cross references.
1.49 - ///\param _Compare A class for the ordering of the priorities. The
1.50 - ///default is \c std::less<_Prio>.
1.51 + /// The fourary heap is a specialization of the \ref KaryHeap "K-ary heap"
1.52 + /// for <tt>K=4</tt>. It is similar to the \ref BinHeap "binary heap",
1.53 + /// but its nodes have at most four children, instead of two.
1.54 ///
1.55 - ///\sa FibHeap
1.56 - ///\sa Dijkstra
1.57 - ///\author Dorian Batha
1.58 + /// \tparam PR Type of the priorities of the items.
1.59 + /// \tparam IM A read-writable item map with \c int values, used
1.60 + /// internally to handle the cross references.
1.61 + /// \tparam CMP A functor class for comparing the priorities.
1.62 + /// The default is \c std::less<PR>.
1.63 + ///
1.64 + ///\sa BinHeap
1.65 + ///\sa KaryHeap
1.66 +#ifdef DOXYGEN
1.67 + template <typename PR, typename IM, typename CMP>
1.68 +#else
1.69 + template <typename PR, typename IM, typename CMP = std::less<PR> >
1.70 +#endif
1.71 + class FouraryHeap {
1.72 + public:
1.73 + /// Type of the item-int map.
1.74 + typedef IM ItemIntMap;
1.75 + /// Type of the priorities.
1.76 + typedef PR Prio;
1.77 + /// Type of the items stored in the heap.
1.78 + typedef typename ItemIntMap::Key Item;
1.79 + /// Type of the item-priority pairs.
1.80 + typedef std::pair<Item,Prio> Pair;
1.81 + /// Functor type for comparing the priorities.
1.82 + typedef CMP Compare;
1.83
1.84 - template <typename _Prio, typename _ItemIntMap,
1.85 - typename _Compare = std::less<_Prio> >
1.86 -
1.87 - class FouraryHeap {
1.88 -
1.89 - public:
1.90 - ///\e
1.91 - typedef _ItemIntMap ItemIntMap;
1.92 - ///\e
1.93 - typedef _Prio Prio;
1.94 - ///\e
1.95 - typedef typename ItemIntMap::Key Item;
1.96 - ///\e
1.97 - typedef std::pair<Item,Prio> Pair;
1.98 - ///\e
1.99 - typedef _Compare Compare;
1.100 -
1.101 - /// \brief Type to represent the items states.
1.102 + /// \brief Type to represent the states of the items.
1.103 ///
1.104 - /// Each Item element have a state associated to it. It may be "in heap",
1.105 - /// "pre heap" or "post heap". The latter two are indifferent from the
1.106 + /// Each item has a state associated to it. It can be "in heap",
1.107 + /// "pre-heap" or "post-heap". The latter two are indifferent from the
1.108 /// heap's point of view, but may be useful to the user.
1.109 ///
1.110 - /// The ItemIntMap \e should be initialized in such way that it maps
1.111 - /// PRE_HEAP (-1) to any element to be put in the heap...
1.112 + /// The item-int map must be initialized in such way that it assigns
1.113 + /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
1.114 enum State {
1.115 - IN_HEAP = 0,
1.116 - PRE_HEAP = -1,
1.117 - POST_HEAP = -2
1.118 + IN_HEAP = 0, ///< = 0.
1.119 + PRE_HEAP = -1, ///< = -1.
1.120 + POST_HEAP = -2 ///< = -2.
1.121 };
1.122
1.123 private:
1.124 - std::vector<Pair> data;
1.125 - Compare comp;
1.126 - ItemIntMap &iim;
1.127 + std::vector<Pair> _data;
1.128 + Compare _comp;
1.129 + ItemIntMap &_iim;
1.130
1.131 public:
1.132 - /// \brief The constructor.
1.133 + /// \brief Constructor.
1.134 ///
1.135 - /// The constructor.
1.136 - /// \param _iim should be given to the constructor, since it is used
1.137 - /// internally to handle the cross references. The value of the map
1.138 - /// should be PRE_HEAP (-1) for each element.
1.139 - explicit FouraryHeap(ItemIntMap &_iim) : iim(_iim) {}
1.140 + /// Constructor.
1.141 + /// \param map A map that assigns \c int values to the items.
1.142 + /// It is used internally to handle the cross references.
1.143 + /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
1.144 + explicit FouraryHeap(ItemIntMap &map) : _iim(map) {}
1.145
1.146 - /// \brief The constructor.
1.147 + /// \brief Constructor.
1.148 ///
1.149 - /// The constructor.
1.150 - /// \param _iim should be given to the constructor, since it is used
1.151 - /// internally to handle the cross references. The value of the map
1.152 - /// should be PRE_HEAP (-1) for each element.
1.153 + /// Constructor.
1.154 + /// \param map A map that assigns \c int values to the items.
1.155 + /// It is used internally to handle the cross references.
1.156 + /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
1.157 + /// \param comp The function object used for comparing the priorities.
1.158 + FouraryHeap(ItemIntMap &map, const Compare &comp)
1.159 + : _iim(map), _comp(comp) {}
1.160 +
1.161 + /// \brief The number of items stored in the heap.
1.162 ///
1.163 - /// \param _comp The comparator function object.
1.164 - FouraryHeap(ItemIntMap &_iim, const Compare &_comp)
1.165 - : iim(_iim), comp(_comp) {}
1.166 + /// This function returns the number of items stored in the heap.
1.167 + int size() const { return _data.size(); }
1.168
1.169 - /// The number of items stored in the heap.
1.170 + /// \brief Check if the heap is empty.
1.171 ///
1.172 - /// \brief Returns the number of items stored in the heap.
1.173 - int size() const { return data.size(); }
1.174 + /// This function returns \c true if the heap is empty.
1.175 + bool empty() const { return _data.empty(); }
1.176
1.177 - /// \brief Checks if the heap stores no items.
1.178 + /// \brief Make the heap empty.
1.179 ///
1.180 - /// Returns \c true if and only if the heap stores no items.
1.181 - bool empty() const { return data.empty(); }
1.182 -
1.183 - /// \brief Make empty this heap.
1.184 - ///
1.185 - /// Make empty this heap. It does not change the cross reference map.
1.186 - /// If you want to reuse what is not surely empty you should first clear
1.187 - /// the heap and after that you should set the cross reference map for
1.188 - /// each item to \c PRE_HEAP.
1.189 - void clear() { data.clear(); }
1.190 + /// This functon makes the heap empty.
1.191 + /// It does not change the cross reference map. If you want to reuse
1.192 + /// a heap that is not surely empty, you should first clear it and
1.193 + /// then you should set the cross reference map to \c PRE_HEAP
1.194 + /// for each item.
1.195 + void clear() { _data.clear(); }
1.196
1.197 private:
1.198 static int parent(int i) { return (i-1)/4; }
1.199 static int firstChild(int i) { return 4*i+1; }
1.200
1.201 bool less(const Pair &p1, const Pair &p2) const {
1.202 - return comp(p1.second, p2.second);
1.203 + return _comp(p1.second, p2.second);
1.204 }
1.205
1.206 - int find_min(const int child, const int length) {
1.207 + int findMin(const int child, const int length) {
1.208 int min=child;
1.209 if( child+3<length ) {
1.210 - if( less(data[child+3], data[min]) )
1.211 + if( less(_data[child+3], _data[min]) )
1.212 min=child+3;
1.213 - if( less(data[child+2], data[min]) )
1.214 + if( less(_data[child+2], _data[min]) )
1.215 min=child+2;
1.216 - if( less(data[child+1], data[min]) )
1.217 + if( less(_data[child+1], _data[min]) )
1.218 min=child+1;
1.219 }
1.220 else if( child+2<length ) {
1.221 - if( less(data[child+2], data[min]) )
1.222 + if( less(_data[child+2], _data[min]) )
1.223 min=child+2;
1.224 - if( less(data[child+1], data[min]) )
1.225 + if( less(_data[child+1], _data[min]) )
1.226 min=child+1;
1.227 }
1.228 else if( child+1<length ) {
1.229 - if( less(data[child+1], data[min]) )
1.230 + if( less(_data[child+1], _data[min]) )
1.231 min=child+1;
1.232 }
1.233 return min;
1.234 }
1.235
1.236 - void bubble_up(int hole, Pair p) {
1.237 + void bubbleUp(int hole, Pair p) {
1.238 int par = parent(hole);
1.239 - while( hole>0 && less(p,data[par]) ) {
1.240 - move(data[par],hole);
1.241 + while( hole>0 && less(p,_data[par]) ) {
1.242 + move(_data[par],hole);
1.243 hole = par;
1.244 par = parent(hole);
1.245 }
1.246 move(p, hole);
1.247 }
1.248
1.249 - void bubble_down(int hole, Pair p, int length) {
1.250 + void bubbleDown(int hole, Pair p, int length) {
1.251 int child = firstChild(hole);
1.252 while( child<length && length>1 ) {
1.253 - child = find_min(child,length);
1.254 - if( !less(data[child], p) )
1.255 + child = findMin(child,length);
1.256 + if( !less(_data[child], p) )
1.257 goto ok;
1.258 - move(data[child], hole);
1.259 + move(_data[child], hole);
1.260 hole = child;
1.261 child = firstChild(hole);
1.262 }
1.263 @@ -180,142 +179,143 @@
1.264 }
1.265
1.266 void move(const Pair &p, int i) {
1.267 - data[i] = p;
1.268 - iim.set(p.first, i);
1.269 + _data[i] = p;
1.270 + _iim.set(p.first, i);
1.271 }
1.272
1.273 public:
1.274 -
1.275 /// \brief Insert a pair of item and priority into the heap.
1.276 ///
1.277 - /// Adds \c p.first to the heap with priority \c p.second.
1.278 + /// This function inserts \c p.first to the heap with priority
1.279 + /// \c p.second.
1.280 /// \param p The pair to insert.
1.281 + /// \pre \c p.first must not be stored in the heap.
1.282 void push(const Pair &p) {
1.283 - int n = data.size();
1.284 - data.resize(n+1);
1.285 - bubble_up(n, p);
1.286 + int n = _data.size();
1.287 + _data.resize(n+1);
1.288 + bubbleUp(n, p);
1.289 }
1.290
1.291 - /// \brief Insert an item into the heap with the given heap.
1.292 + /// \brief Insert an item into the heap with the given priority.
1.293 ///
1.294 - /// Adds \c i to the heap with priority \c p.
1.295 + /// This function inserts the given item into the heap with the
1.296 + /// given priority.
1.297 /// \param i The item to insert.
1.298 /// \param p The priority of the item.
1.299 + /// \pre \e i must not be stored in the heap.
1.300 void push(const Item &i, const Prio &p) { push(Pair(i,p)); }
1.301
1.302 - /// \brief Returns the item with minimum priority relative to \c Compare.
1.303 + /// \brief Return the item having minimum priority.
1.304 ///
1.305 - /// This method returns the item with minimum priority relative to \c
1.306 - /// Compare.
1.307 - /// \pre The heap must be nonempty.
1.308 - Item top() const { return data[0].first; }
1.309 + /// This function returns the item having minimum priority.
1.310 + /// \pre The heap must be non-empty.
1.311 + Item top() const { return _data[0].first; }
1.312
1.313 - /// \brief Returns the minimum priority relative to \c Compare.
1.314 + /// \brief The minimum priority.
1.315 ///
1.316 - /// It returns the minimum priority relative to \c Compare.
1.317 - /// \pre The heap must be nonempty.
1.318 - Prio prio() const { return data[0].second; }
1.319 + /// This function returns the minimum priority.
1.320 + /// \pre The heap must be non-empty.
1.321 + Prio prio() const { return _data[0].second; }
1.322
1.323 - /// \brief Deletes the item with minimum priority relative to \c Compare.
1.324 + /// \brief Remove the item having minimum priority.
1.325 ///
1.326 - /// This method deletes the item with minimum priority relative to \c
1.327 - /// Compare from the heap.
1.328 + /// This function removes the item having minimum priority.
1.329 /// \pre The heap must be non-empty.
1.330 void pop() {
1.331 - int n = data.size()-1;
1.332 - iim.set(data[0].first, POST_HEAP);
1.333 - if (n>0) bubble_down(0, data[n], n);
1.334 - data.pop_back();
1.335 + int n = _data.size()-1;
1.336 + _iim.set(_data[0].first, POST_HEAP);
1.337 + if (n>0) bubbleDown(0, _data[n], n);
1.338 + _data.pop_back();
1.339 }
1.340
1.341 - /// \brief Deletes \c i from the heap.
1.342 + /// \brief Remove the given item from the heap.
1.343 ///
1.344 - /// This method deletes item \c i from the heap.
1.345 - /// \param i The item to erase.
1.346 - /// \pre The item should be in the heap.
1.347 + /// This function removes the given item from the heap if it is
1.348 + /// already stored.
1.349 + /// \param i The item to delete.
1.350 + /// \pre \e i must be in the heap.
1.351 void erase(const Item &i) {
1.352 - int h = iim[i];
1.353 - int n = data.size()-1;
1.354 - iim.set(data[h].first, POST_HEAP);
1.355 + int h = _iim[i];
1.356 + int n = _data.size()-1;
1.357 + _iim.set(_data[h].first, POST_HEAP);
1.358 if( h<n ) {
1.359 - if( less(data[parent(h)], data[n]) )
1.360 - bubble_down(h, data[n], n);
1.361 + if( less(_data[parent(h)], _data[n]) )
1.362 + bubbleDown(h, _data[n], n);
1.363 else
1.364 - bubble_up(h, data[n]);
1.365 + bubbleUp(h, _data[n]);
1.366 }
1.367 - data.pop_back();
1.368 + _data.pop_back();
1.369 }
1.370
1.371 - /// \brief Returns the priority of \c i.
1.372 + /// \brief The priority of the given item.
1.373 ///
1.374 - /// This function returns the priority of item \c i.
1.375 - /// \pre \c i must be in the heap.
1.376 + /// This function returns the priority of the given item.
1.377 /// \param i The item.
1.378 + /// \pre \e i must be in the heap.
1.379 Prio operator[](const Item &i) const {
1.380 - int idx = iim[i];
1.381 - return data[idx].second;
1.382 + int idx = _iim[i];
1.383 + return _data[idx].second;
1.384 }
1.385
1.386 - /// \brief \c i gets to the heap with priority \c p independently
1.387 - /// if \c i was already there.
1.388 + /// \brief Set the priority of an item or insert it, if it is
1.389 + /// not stored in the heap.
1.390 ///
1.391 - /// This method calls \ref push(\c i, \c p) if \c i is not stored
1.392 - /// in the heap and sets the priority of \c i to \c p otherwise.
1.393 + /// This method sets the priority of the given item if it is
1.394 + /// already stored in the heap. Otherwise it inserts the given
1.395 + /// item into the heap with the given priority.
1.396 /// \param i The item.
1.397 /// \param p The priority.
1.398 void set(const Item &i, const Prio &p) {
1.399 - int idx = iim[i];
1.400 + int idx = _iim[i];
1.401 if( idx < 0 )
1.402 push(i,p);
1.403 - else if( comp(p, data[idx].second) )
1.404 - bubble_up(idx, Pair(i,p));
1.405 + else if( _comp(p, _data[idx].second) )
1.406 + bubbleUp(idx, Pair(i,p));
1.407 else
1.408 - bubble_down(idx, Pair(i,p), data.size());
1.409 + bubbleDown(idx, Pair(i,p), _data.size());
1.410 }
1.411
1.412 - /// \brief Decreases the priority of \c i to \c p.
1.413 + /// \brief Decrease the priority of an item to the given value.
1.414 ///
1.415 - /// This method decreases the priority of item \c i to \c p.
1.416 - /// \pre \c i must be stored in the heap with priority at least \c
1.417 - /// p relative to \c Compare.
1.418 + /// This function decreases the priority of an item to the given value.
1.419 /// \param i The item.
1.420 /// \param p The priority.
1.421 + /// \pre \e i must be stored in the heap with priority at least \e p.
1.422 void decrease(const Item &i, const Prio &p) {
1.423 - int idx = iim[i];
1.424 - bubble_up(idx, Pair(i,p));
1.425 + int idx = _iim[i];
1.426 + bubbleUp(idx, Pair(i,p));
1.427 }
1.428
1.429 - /// \brief Increases the priority of \c i to \c p.
1.430 + /// \brief Increase the priority of an item to the given value.
1.431 ///
1.432 - /// This method sets the priority of item \c i to \c p.
1.433 - /// \pre \c i must be stored in the heap with priority at most \c
1.434 - /// p relative to \c Compare.
1.435 + /// This function increases the priority of an item to the given value.
1.436 /// \param i The item.
1.437 /// \param p The priority.
1.438 + /// \pre \e i must be stored in the heap with priority at most \e p.
1.439 void increase(const Item &i, const Prio &p) {
1.440 - int idx = iim[i];
1.441 - bubble_down(idx, Pair(i,p), data.size());
1.442 + int idx = _iim[i];
1.443 + bubbleDown(idx, Pair(i,p), _data.size());
1.444 }
1.445
1.446 - /// \brief Returns if \c item is in, has already been in, or has
1.447 - /// never been in the heap.
1.448 + /// \brief Return the state of an item.
1.449 ///
1.450 - /// This method returns PRE_HEAP if \c item has never been in the
1.451 - /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
1.452 - /// otherwise. In the latter case it is possible that \c item will
1.453 - /// get back to the heap again.
1.454 + /// This method returns \c PRE_HEAP if the given item has never
1.455 + /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
1.456 + /// and \c POST_HEAP otherwise.
1.457 + /// In the latter case it is possible that the item will get back
1.458 + /// to the heap again.
1.459 /// \param i The item.
1.460 State state(const Item &i) const {
1.461 - int s = iim[i];
1.462 + int s = _iim[i];
1.463 if (s>=0) s=0;
1.464 return State(s);
1.465 }
1.466
1.467 - /// \brief Sets the state of the \c item in the heap.
1.468 + /// \brief Set the state of an item in the heap.
1.469 ///
1.470 - /// Sets the state of the \c item in the heap. It can be used to
1.471 - /// manually clear the heap when it is important to achive the
1.472 - /// better time complexity.
1.473 + /// This function sets the state of the given item in the heap.
1.474 + /// It can be used to manually clear the heap when it is important
1.475 + /// to achive better time complexity.
1.476 /// \param i The item.
1.477 /// \param st The state. It should not be \c IN_HEAP.
1.478 void state(const Item& i, State st) {
1.479 @@ -323,24 +323,25 @@
1.480 case POST_HEAP:
1.481 case PRE_HEAP:
1.482 if (state(i) == IN_HEAP) erase(i);
1.483 - iim[i] = st;
1.484 + _iim[i] = st;
1.485 break;
1.486 case IN_HEAP:
1.487 break;
1.488 }
1.489 }
1.490
1.491 - /// \brief Replaces an item in the heap.
1.492 + /// \brief Replace an item in the heap.
1.493 ///
1.494 - /// The \c i item is replaced with \c j item. The \c i item should
1.495 - /// be in the heap, while the \c j should be out of the heap. The
1.496 - /// \c i item will out of the heap and \c j will be in the heap
1.497 - /// with the same prioriority as prevoiusly the \c i item.
1.498 + /// This function replaces item \c i with item \c j.
1.499 + /// Item \c i must be in the heap, while \c j must be out of the heap.
1.500 + /// After calling this method, item \c i will be out of the
1.501 + /// heap and \c j will be in the heap with the same prioriority
1.502 + /// as item \c i had before.
1.503 void replace(const Item& i, const Item& j) {
1.504 - int idx = iim[i];
1.505 - iim.set(i, iim[j]);
1.506 - iim.set(j, idx);
1.507 - data[idx].first = j;
1.508 + int idx = _iim[i];
1.509 + _iim.set(i, _iim[j]);
1.510 + _iim.set(j, idx);
1.511 + _data[idx].first = j;
1.512 }
1.513
1.514 }; // class FouraryHeap