1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/fib_heap.h Fri Sep 25 09:13:03 2009 +0200
1.3 @@ -0,0 +1,475 @@
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_FIB_HEAP_H
1.23 +#define LEMON_FIB_HEAP_H
1.24 +
1.25 +///\file
1.26 +///\ingroup heaps
1.27 +///\brief Fibonacci heap implementation.
1.28 +
1.29 +#include <vector>
1.30 +#include <utility>
1.31 +#include <functional>
1.32 +#include <lemon/math.h>
1.33 +
1.34 +namespace lemon {
1.35 +
1.36 + /// \ingroup heaps
1.37 + ///
1.38 + /// \brief Fibonacci heap data structure.
1.39 + ///
1.40 + /// This class implements the \e Fibonacci \e heap data structure.
1.41 + /// It fully conforms to the \ref concepts::Heap "heap concept".
1.42 + ///
1.43 + /// The methods \ref increase() and \ref erase() are not efficient in a
1.44 + /// Fibonacci heap. In case of many calls of these operations, it is
1.45 + /// better to use other heap structure, e.g. \ref BinHeap "binary heap".
1.46 + ///
1.47 + /// \tparam PR Type of the priorities of the items.
1.48 + /// \tparam IM A read-writable item map with \c int values, used
1.49 + /// internally to handle the cross references.
1.50 + /// \tparam CMP A functor class for comparing the priorities.
1.51 + /// The default is \c std::less<PR>.
1.52 +#ifdef DOXYGEN
1.53 + template <typename PR, typename IM, typename CMP>
1.54 +#else
1.55 + template <typename PR, typename IM, typename CMP = std::less<PR> >
1.56 +#endif
1.57 + class FibHeap {
1.58 + public:
1.59 +
1.60 + /// Type of the item-int map.
1.61 + typedef IM ItemIntMap;
1.62 + /// Type of the priorities.
1.63 + typedef PR Prio;
1.64 + /// Type of the items stored in the heap.
1.65 + typedef typename ItemIntMap::Key Item;
1.66 + /// Type of the item-priority pairs.
1.67 + typedef std::pair<Item,Prio> Pair;
1.68 + /// Functor type for comparing the priorities.
1.69 + typedef CMP Compare;
1.70 +
1.71 + private:
1.72 + class Store;
1.73 +
1.74 + std::vector<Store> _data;
1.75 + int _minimum;
1.76 + ItemIntMap &_iim;
1.77 + Compare _comp;
1.78 + int _num;
1.79 +
1.80 + public:
1.81 +
1.82 + /// \brief Type to represent the states of the items.
1.83 + ///
1.84 + /// Each item has a state associated to it. It can be "in heap",
1.85 + /// "pre-heap" or "post-heap". The latter two are indifferent from the
1.86 + /// heap's point of view, but may be useful to the user.
1.87 + ///
1.88 + /// The item-int map must be initialized in such way that it assigns
1.89 + /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
1.90 + enum State {
1.91 + IN_HEAP = 0, ///< = 0.
1.92 + PRE_HEAP = -1, ///< = -1.
1.93 + POST_HEAP = -2 ///< = -2.
1.94 + };
1.95 +
1.96 + /// \brief Constructor.
1.97 + ///
1.98 + /// Constructor.
1.99 + /// \param map A map that assigns \c int values to the items.
1.100 + /// It is used internally to handle the cross references.
1.101 + /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
1.102 + explicit FibHeap(ItemIntMap &map)
1.103 + : _minimum(0), _iim(map), _num() {}
1.104 +
1.105 + /// \brief Constructor.
1.106 + ///
1.107 + /// Constructor.
1.108 + /// \param map A map that assigns \c int values to the items.
1.109 + /// It is used internally to handle the cross references.
1.110 + /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
1.111 + /// \param comp The function object used for comparing the priorities.
1.112 + FibHeap(ItemIntMap &map, const Compare &comp)
1.113 + : _minimum(0), _iim(map), _comp(comp), _num() {}
1.114 +
1.115 + /// \brief The number of items stored in the heap.
1.116 + ///
1.117 + /// This function returns the number of items stored in the heap.
1.118 + int size() const { return _num; }
1.119 +
1.120 + /// \brief Check if the heap is empty.
1.121 + ///
1.122 + /// This function returns \c true if the heap is empty.
1.123 + bool empty() const { return _num==0; }
1.124 +
1.125 + /// \brief Make the heap empty.
1.126 + ///
1.127 + /// This functon makes the heap empty.
1.128 + /// It does not change the cross reference map. If you want to reuse
1.129 + /// a heap that is not surely empty, you should first clear it and
1.130 + /// then you should set the cross reference map to \c PRE_HEAP
1.131 + /// for each item.
1.132 + void clear() {
1.133 + _data.clear(); _minimum = 0; _num = 0;
1.134 + }
1.135 +
1.136 + /// \brief Insert an item into the heap with the given priority.
1.137 + ///
1.138 + /// This function inserts the given item into the heap with the
1.139 + /// given priority.
1.140 + /// \param item The item to insert.
1.141 + /// \param prio The priority of the item.
1.142 + /// \pre \e item must not be stored in the heap.
1.143 + void push (const Item& item, const Prio& prio) {
1.144 + int i=_iim[item];
1.145 + if ( i < 0 ) {
1.146 + int s=_data.size();
1.147 + _iim.set( item, s );
1.148 + Store st;
1.149 + st.name=item;
1.150 + _data.push_back(st);
1.151 + i=s;
1.152 + } else {
1.153 + _data[i].parent=_data[i].child=-1;
1.154 + _data[i].degree=0;
1.155 + _data[i].in=true;
1.156 + _data[i].marked=false;
1.157 + }
1.158 +
1.159 + if ( _num ) {
1.160 + _data[_data[_minimum].right_neighbor].left_neighbor=i;
1.161 + _data[i].right_neighbor=_data[_minimum].right_neighbor;
1.162 + _data[_minimum].right_neighbor=i;
1.163 + _data[i].left_neighbor=_minimum;
1.164 + if ( _comp( prio, _data[_minimum].prio) ) _minimum=i;
1.165 + } else {
1.166 + _data[i].right_neighbor=_data[i].left_neighbor=i;
1.167 + _minimum=i;
1.168 + }
1.169 + _data[i].prio=prio;
1.170 + ++_num;
1.171 + }
1.172 +
1.173 + /// \brief Return the item having minimum priority.
1.174 + ///
1.175 + /// This function returns the item having minimum priority.
1.176 + /// \pre The heap must be non-empty.
1.177 + Item top() const { return _data[_minimum].name; }
1.178 +
1.179 + /// \brief The minimum priority.
1.180 + ///
1.181 + /// This function returns the minimum priority.
1.182 + /// \pre The heap must be non-empty.
1.183 + Prio prio() const { return _data[_minimum].prio; }
1.184 +
1.185 + /// \brief Remove the item having minimum priority.
1.186 + ///
1.187 + /// This function removes the item having minimum priority.
1.188 + /// \pre The heap must be non-empty.
1.189 + void pop() {
1.190 + /*The first case is that there are only one root.*/
1.191 + if ( _data[_minimum].left_neighbor==_minimum ) {
1.192 + _data[_minimum].in=false;
1.193 + if ( _data[_minimum].degree!=0 ) {
1.194 + makeRoot(_data[_minimum].child);
1.195 + _minimum=_data[_minimum].child;
1.196 + balance();
1.197 + }
1.198 + } else {
1.199 + int right=_data[_minimum].right_neighbor;
1.200 + unlace(_minimum);
1.201 + _data[_minimum].in=false;
1.202 + if ( _data[_minimum].degree > 0 ) {
1.203 + int left=_data[_minimum].left_neighbor;
1.204 + int child=_data[_minimum].child;
1.205 + int last_child=_data[child].left_neighbor;
1.206 +
1.207 + makeRoot(child);
1.208 +
1.209 + _data[left].right_neighbor=child;
1.210 + _data[child].left_neighbor=left;
1.211 + _data[right].left_neighbor=last_child;
1.212 + _data[last_child].right_neighbor=right;
1.213 + }
1.214 + _minimum=right;
1.215 + balance();
1.216 + } // the case where there are more roots
1.217 + --_num;
1.218 + }
1.219 +
1.220 + /// \brief Remove the given item from the heap.
1.221 + ///
1.222 + /// This function removes the given item from the heap if it is
1.223 + /// already stored.
1.224 + /// \param item The item to delete.
1.225 + /// \pre \e item must be in the heap.
1.226 + void erase (const Item& item) {
1.227 + int i=_iim[item];
1.228 +
1.229 + if ( i >= 0 && _data[i].in ) {
1.230 + if ( _data[i].parent!=-1 ) {
1.231 + int p=_data[i].parent;
1.232 + cut(i,p);
1.233 + cascade(p);
1.234 + }
1.235 + _minimum=i; //As if its prio would be -infinity
1.236 + pop();
1.237 + }
1.238 + }
1.239 +
1.240 + /// \brief The priority of the given item.
1.241 + ///
1.242 + /// This function returns the priority of the given item.
1.243 + /// \param item The item.
1.244 + /// \pre \e item must be in the heap.
1.245 + Prio operator[](const Item& item) const {
1.246 + return _data[_iim[item]].prio;
1.247 + }
1.248 +
1.249 + /// \brief Set the priority of an item or insert it, if it is
1.250 + /// not stored in the heap.
1.251 + ///
1.252 + /// This method sets the priority of the given item if it is
1.253 + /// already stored in the heap. Otherwise it inserts the given
1.254 + /// item into the heap with the given priority.
1.255 + /// \param item The item.
1.256 + /// \param prio The priority.
1.257 + void set (const Item& item, const Prio& prio) {
1.258 + int i=_iim[item];
1.259 + if ( i >= 0 && _data[i].in ) {
1.260 + if ( _comp(prio, _data[i].prio) ) decrease(item, prio);
1.261 + if ( _comp(_data[i].prio, prio) ) increase(item, prio);
1.262 + } else push(item, prio);
1.263 + }
1.264 +
1.265 + /// \brief Decrease the priority of an item to the given value.
1.266 + ///
1.267 + /// This function decreases the priority of an item to the given value.
1.268 + /// \param item The item.
1.269 + /// \param prio The priority.
1.270 + /// \pre \e item must be stored in the heap with priority at least \e prio.
1.271 + void decrease (const Item& item, const Prio& prio) {
1.272 + int i=_iim[item];
1.273 + _data[i].prio=prio;
1.274 + int p=_data[i].parent;
1.275 +
1.276 + if ( p!=-1 && _comp(prio, _data[p].prio) ) {
1.277 + cut(i,p);
1.278 + cascade(p);
1.279 + }
1.280 + if ( _comp(prio, _data[_minimum].prio) ) _minimum=i;
1.281 + }
1.282 +
1.283 + /// \brief Increase the priority of an item to the given value.
1.284 + ///
1.285 + /// This function increases the priority of an item to the given value.
1.286 + /// \param item The item.
1.287 + /// \param prio The priority.
1.288 + /// \pre \e item must be stored in the heap with priority at most \e prio.
1.289 + void increase (const Item& item, const Prio& prio) {
1.290 + erase(item);
1.291 + push(item, prio);
1.292 + }
1.293 +
1.294 + /// \brief Return the state of an item.
1.295 + ///
1.296 + /// This method returns \c PRE_HEAP if the given item has never
1.297 + /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
1.298 + /// and \c POST_HEAP otherwise.
1.299 + /// In the latter case it is possible that the item will get back
1.300 + /// to the heap again.
1.301 + /// \param item The item.
1.302 + State state(const Item &item) const {
1.303 + int i=_iim[item];
1.304 + if( i>=0 ) {
1.305 + if ( _data[i].in ) i=0;
1.306 + else i=-2;
1.307 + }
1.308 + return State(i);
1.309 + }
1.310 +
1.311 + /// \brief Set the state of an item in the heap.
1.312 + ///
1.313 + /// This function sets the state of the given item in the heap.
1.314 + /// It can be used to manually clear the heap when it is important
1.315 + /// to achive better time complexity.
1.316 + /// \param i The item.
1.317 + /// \param st The state. It should not be \c IN_HEAP.
1.318 + void state(const Item& i, State st) {
1.319 + switch (st) {
1.320 + case POST_HEAP:
1.321 + case PRE_HEAP:
1.322 + if (state(i) == IN_HEAP) {
1.323 + erase(i);
1.324 + }
1.325 + _iim[i] = st;
1.326 + break;
1.327 + case IN_HEAP:
1.328 + break;
1.329 + }
1.330 + }
1.331 +
1.332 + private:
1.333 +
1.334 + void balance() {
1.335 +
1.336 + int maxdeg=int( std::floor( 2.08*log(double(_data.size()))))+1;
1.337 +
1.338 + std::vector<int> A(maxdeg,-1);
1.339 +
1.340 + /*
1.341 + *Recall that now minimum does not point to the minimum prio element.
1.342 + *We set minimum to this during balance().
1.343 + */
1.344 + int anchor=_data[_minimum].left_neighbor;
1.345 + int next=_minimum;
1.346 + bool end=false;
1.347 +
1.348 + do {
1.349 + int active=next;
1.350 + if ( anchor==active ) end=true;
1.351 + int d=_data[active].degree;
1.352 + next=_data[active].right_neighbor;
1.353 +
1.354 + while (A[d]!=-1) {
1.355 + if( _comp(_data[active].prio, _data[A[d]].prio) ) {
1.356 + fuse(active,A[d]);
1.357 + } else {
1.358 + fuse(A[d],active);
1.359 + active=A[d];
1.360 + }
1.361 + A[d]=-1;
1.362 + ++d;
1.363 + }
1.364 + A[d]=active;
1.365 + } while ( !end );
1.366 +
1.367 +
1.368 + while ( _data[_minimum].parent >=0 )
1.369 + _minimum=_data[_minimum].parent;
1.370 + int s=_minimum;
1.371 + int m=_minimum;
1.372 + do {
1.373 + if ( _comp(_data[s].prio, _data[_minimum].prio) ) _minimum=s;
1.374 + s=_data[s].right_neighbor;
1.375 + } while ( s != m );
1.376 + }
1.377 +
1.378 + void makeRoot(int c) {
1.379 + int s=c;
1.380 + do {
1.381 + _data[s].parent=-1;
1.382 + s=_data[s].right_neighbor;
1.383 + } while ( s != c );
1.384 + }
1.385 +
1.386 + void cut(int a, int b) {
1.387 + /*
1.388 + *Replacing a from the children of b.
1.389 + */
1.390 + --_data[b].degree;
1.391 +
1.392 + if ( _data[b].degree !=0 ) {
1.393 + int child=_data[b].child;
1.394 + if ( child==a )
1.395 + _data[b].child=_data[child].right_neighbor;
1.396 + unlace(a);
1.397 + }
1.398 +
1.399 +
1.400 + /*Lacing a to the roots.*/
1.401 + int right=_data[_minimum].right_neighbor;
1.402 + _data[_minimum].right_neighbor=a;
1.403 + _data[a].left_neighbor=_minimum;
1.404 + _data[a].right_neighbor=right;
1.405 + _data[right].left_neighbor=a;
1.406 +
1.407 + _data[a].parent=-1;
1.408 + _data[a].marked=false;
1.409 + }
1.410 +
1.411 + void cascade(int a) {
1.412 + if ( _data[a].parent!=-1 ) {
1.413 + int p=_data[a].parent;
1.414 +
1.415 + if ( _data[a].marked==false ) _data[a].marked=true;
1.416 + else {
1.417 + cut(a,p);
1.418 + cascade(p);
1.419 + }
1.420 + }
1.421 + }
1.422 +
1.423 + void fuse(int a, int b) {
1.424 + unlace(b);
1.425 +
1.426 + /*Lacing b under a.*/
1.427 + _data[b].parent=a;
1.428 +
1.429 + if (_data[a].degree==0) {
1.430 + _data[b].left_neighbor=b;
1.431 + _data[b].right_neighbor=b;
1.432 + _data[a].child=b;
1.433 + } else {
1.434 + int child=_data[a].child;
1.435 + int last_child=_data[child].left_neighbor;
1.436 + _data[child].left_neighbor=b;
1.437 + _data[b].right_neighbor=child;
1.438 + _data[last_child].right_neighbor=b;
1.439 + _data[b].left_neighbor=last_child;
1.440 + }
1.441 +
1.442 + ++_data[a].degree;
1.443 +
1.444 + _data[b].marked=false;
1.445 + }
1.446 +
1.447 + /*
1.448 + *It is invoked only if a has siblings.
1.449 + */
1.450 + void unlace(int a) {
1.451 + int leftn=_data[a].left_neighbor;
1.452 + int rightn=_data[a].right_neighbor;
1.453 + _data[leftn].right_neighbor=rightn;
1.454 + _data[rightn].left_neighbor=leftn;
1.455 + }
1.456 +
1.457 +
1.458 + class Store {
1.459 + friend class FibHeap;
1.460 +
1.461 + Item name;
1.462 + int parent;
1.463 + int left_neighbor;
1.464 + int right_neighbor;
1.465 + int child;
1.466 + int degree;
1.467 + bool marked;
1.468 + bool in;
1.469 + Prio prio;
1.470 +
1.471 + Store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
1.472 + };
1.473 + };
1.474 +
1.475 +} //namespace lemon
1.476 +
1.477 +#endif //LEMON_FIB_HEAP_H
1.478 +