1.1 --- a/lemon/fib_heap.h Thu Aug 20 20:34:30 2009 +0200
1.2 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000
1.3 @@ -1,468 +0,0 @@
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 auxdat
1.27 -///\brief Fibonacci Heap implementation.
1.28 -
1.29 -#include <vector>
1.30 -#include <functional>
1.31 -#include <lemon/math.h>
1.32 -
1.33 -namespace lemon {
1.34 -
1.35 - /// \ingroup auxdat
1.36 - ///
1.37 - ///\brief Fibonacci Heap.
1.38 - ///
1.39 - ///This class implements the \e Fibonacci \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. \c CMP specifies the ordering of the priorities. In a heap
1.43 - ///one can change the priority of an item, add or erase an item, etc.
1.44 - ///
1.45 - ///The methods \ref increase and \ref erase are not efficient in a Fibonacci
1.46 - ///heap. In case of many calls to these operations, it is better to use a
1.47 - ///\ref BinHeap "binary heap".
1.48 - ///
1.49 - ///\param PRIO Type of the priority of the items.
1.50 - ///\param IM A read and writable Item int map, used internally
1.51 - ///to handle the cross references.
1.52 - ///\param CMP A class for the ordering of the priorities. The
1.53 - ///default is \c std::less<PRIO>.
1.54 - ///
1.55 - ///\sa BinHeap
1.56 - ///\sa Dijkstra
1.57 -#ifdef DOXYGEN
1.58 - template <typename PRIO, typename IM, typename CMP>
1.59 -#else
1.60 - template <typename PRIO, typename IM, typename CMP = std::less<PRIO> >
1.61 -#endif
1.62 - class FibHeap {
1.63 - public:
1.64 - ///\e
1.65 - typedef IM ItemIntMap;
1.66 - ///\e
1.67 - typedef PRIO Prio;
1.68 - ///\e
1.69 - typedef typename ItemIntMap::Key Item;
1.70 - ///\e
1.71 - typedef std::pair<Item,Prio> Pair;
1.72 - ///\e
1.73 - typedef CMP Compare;
1.74 -
1.75 - private:
1.76 - class Store;
1.77 -
1.78 - std::vector<Store> _data;
1.79 - int _minimum;
1.80 - ItemIntMap &_iim;
1.81 - Compare _comp;
1.82 - int _num;
1.83 -
1.84 - public:
1.85 -
1.86 - /// \brief Type to represent the items states.
1.87 - ///
1.88 - /// Each Item element have a state associated to it. It may be "in heap",
1.89 - /// "pre heap" or "post heap". The latter two are indifferent from the
1.90 - /// heap's point of view, but may be useful to the user.
1.91 - ///
1.92 - /// The item-int map must be initialized in such way that it assigns
1.93 - /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
1.94 - enum State {
1.95 - IN_HEAP = 0, ///< = 0.
1.96 - PRE_HEAP = -1, ///< = -1.
1.97 - POST_HEAP = -2 ///< = -2.
1.98 - };
1.99 -
1.100 - /// \brief The constructor
1.101 - ///
1.102 - /// \c map should be given to the constructor, since it is
1.103 - /// used internally to handle the cross references.
1.104 - explicit FibHeap(ItemIntMap &map)
1.105 - : _minimum(0), _iim(map), _num() {}
1.106 -
1.107 - /// \brief The constructor
1.108 - ///
1.109 - /// \c map should be given to the constructor, since it is used
1.110 - /// internally to handle the cross references. \c comp is an
1.111 - /// object for ordering of 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 - /// Returns the number of items stored in the heap.
1.118 - int size() const { return _num; }
1.119 -
1.120 - /// \brief Checks if the heap stores no items.
1.121 - ///
1.122 - /// Returns \c true if and only if the heap stores no items.
1.123 - bool empty() const { return _num==0; }
1.124 -
1.125 - /// \brief Make empty this heap.
1.126 - ///
1.127 - /// Make empty this heap. It does not change the cross reference
1.128 - /// map. If you want to reuse a heap what is not surely empty you
1.129 - /// should first clear the heap and after that you should set the
1.130 - /// cross reference map for each item to \c PRE_HEAP.
1.131 - void clear() {
1.132 - _data.clear(); _minimum = 0; _num = 0;
1.133 - }
1.134 -
1.135 - /// \brief \c item gets to the heap with priority \c value independently
1.136 - /// if \c item was already there.
1.137 - ///
1.138 - /// This method calls \ref push(\c item, \c value) if \c item is not
1.139 - /// stored in the heap and it calls \ref decrease(\c item, \c value) or
1.140 - /// \ref increase(\c item, \c value) otherwise.
1.141 - void set (const Item& item, const Prio& value) {
1.142 - int i=_iim[item];
1.143 - if ( i >= 0 && _data[i].in ) {
1.144 - if ( _comp(value, _data[i].prio) ) decrease(item, value);
1.145 - if ( _comp(_data[i].prio, value) ) increase(item, value);
1.146 - } else push(item, value);
1.147 - }
1.148 -
1.149 - /// \brief Adds \c item to the heap with priority \c value.
1.150 - ///
1.151 - /// Adds \c item to the heap with priority \c value.
1.152 - /// \pre \c item must not be stored in the heap.
1.153 - void push (const Item& item, const Prio& value) {
1.154 - int i=_iim[item];
1.155 - if ( i < 0 ) {
1.156 - int s=_data.size();
1.157 - _iim.set( item, s );
1.158 - Store st;
1.159 - st.name=item;
1.160 - _data.push_back(st);
1.161 - i=s;
1.162 - } else {
1.163 - _data[i].parent=_data[i].child=-1;
1.164 - _data[i].degree=0;
1.165 - _data[i].in=true;
1.166 - _data[i].marked=false;
1.167 - }
1.168 -
1.169 - if ( _num ) {
1.170 - _data[_data[_minimum].right_neighbor].left_neighbor=i;
1.171 - _data[i].right_neighbor=_data[_minimum].right_neighbor;
1.172 - _data[_minimum].right_neighbor=i;
1.173 - _data[i].left_neighbor=_minimum;
1.174 - if ( _comp( value, _data[_minimum].prio) ) _minimum=i;
1.175 - } else {
1.176 - _data[i].right_neighbor=_data[i].left_neighbor=i;
1.177 - _minimum=i;
1.178 - }
1.179 - _data[i].prio=value;
1.180 - ++_num;
1.181 - }
1.182 -
1.183 - /// \brief Returns the item with minimum priority relative to \c Compare.
1.184 - ///
1.185 - /// This method returns the item with minimum priority relative to \c
1.186 - /// Compare.
1.187 - /// \pre The heap must be nonempty.
1.188 - Item top() const { return _data[_minimum].name; }
1.189 -
1.190 - /// \brief Returns the minimum priority relative to \c Compare.
1.191 - ///
1.192 - /// It returns the minimum priority relative to \c Compare.
1.193 - /// \pre The heap must be nonempty.
1.194 - const Prio& prio() const { return _data[_minimum].prio; }
1.195 -
1.196 - /// \brief Returns the priority of \c item.
1.197 - ///
1.198 - /// It returns the priority of \c item.
1.199 - /// \pre \c item must be in the heap.
1.200 - const Prio& operator[](const Item& item) const {
1.201 - return _data[_iim[item]].prio;
1.202 - }
1.203 -
1.204 - /// \brief Deletes the item with minimum priority relative to \c Compare.
1.205 - ///
1.206 - /// This method deletes the item with minimum priority relative to \c
1.207 - /// Compare from the heap.
1.208 - /// \pre The heap must be non-empty.
1.209 - void pop() {
1.210 - /*The first case is that there are only one root.*/
1.211 - if ( _data[_minimum].left_neighbor==_minimum ) {
1.212 - _data[_minimum].in=false;
1.213 - if ( _data[_minimum].degree!=0 ) {
1.214 - makeroot(_data[_minimum].child);
1.215 - _minimum=_data[_minimum].child;
1.216 - balance();
1.217 - }
1.218 - } else {
1.219 - int right=_data[_minimum].right_neighbor;
1.220 - unlace(_minimum);
1.221 - _data[_minimum].in=false;
1.222 - if ( _data[_minimum].degree > 0 ) {
1.223 - int left=_data[_minimum].left_neighbor;
1.224 - int child=_data[_minimum].child;
1.225 - int last_child=_data[child].left_neighbor;
1.226 -
1.227 - makeroot(child);
1.228 -
1.229 - _data[left].right_neighbor=child;
1.230 - _data[child].left_neighbor=left;
1.231 - _data[right].left_neighbor=last_child;
1.232 - _data[last_child].right_neighbor=right;
1.233 - }
1.234 - _minimum=right;
1.235 - balance();
1.236 - } // the case where there are more roots
1.237 - --_num;
1.238 - }
1.239 -
1.240 - /// \brief Deletes \c item from the heap.
1.241 - ///
1.242 - /// This method deletes \c item from the heap, if \c item was already
1.243 - /// stored in the heap. It is quite inefficient in Fibonacci heaps.
1.244 - void erase (const Item& item) {
1.245 - int i=_iim[item];
1.246 -
1.247 - if ( i >= 0 && _data[i].in ) {
1.248 - if ( _data[i].parent!=-1 ) {
1.249 - int p=_data[i].parent;
1.250 - cut(i,p);
1.251 - cascade(p);
1.252 - }
1.253 - _minimum=i; //As if its prio would be -infinity
1.254 - pop();
1.255 - }
1.256 - }
1.257 -
1.258 - /// \brief Decreases the priority of \c item to \c value.
1.259 - ///
1.260 - /// This method decreases the priority of \c item to \c value.
1.261 - /// \pre \c item must be stored in the heap with priority at least \c
1.262 - /// value relative to \c Compare.
1.263 - void decrease (Item item, const Prio& value) {
1.264 - int i=_iim[item];
1.265 - _data[i].prio=value;
1.266 - int p=_data[i].parent;
1.267 -
1.268 - if ( p!=-1 && _comp(value, _data[p].prio) ) {
1.269 - cut(i,p);
1.270 - cascade(p);
1.271 - }
1.272 - if ( _comp(value, _data[_minimum].prio) ) _minimum=i;
1.273 - }
1.274 -
1.275 - /// \brief Increases the priority of \c item to \c value.
1.276 - ///
1.277 - /// This method sets the priority of \c item to \c value. Though
1.278 - /// there is no precondition on the priority of \c item, this
1.279 - /// method should be used only if it is indeed necessary to increase
1.280 - /// (relative to \c Compare) the priority of \c item, because this
1.281 - /// method is inefficient.
1.282 - void increase (Item item, const Prio& value) {
1.283 - erase(item);
1.284 - push(item, value);
1.285 - }
1.286 -
1.287 -
1.288 - /// \brief Returns if \c item is in, has already been in, or has never
1.289 - /// been in the heap.
1.290 - ///
1.291 - /// This method returns PRE_HEAP if \c item has never been in the
1.292 - /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
1.293 - /// otherwise. In the latter case it is possible that \c item will
1.294 - /// get back to the heap again.
1.295 - State state(const Item &item) const {
1.296 - int i=_iim[item];
1.297 - if( i>=0 ) {
1.298 - if ( _data[i].in ) i=0;
1.299 - else i=-2;
1.300 - }
1.301 - return State(i);
1.302 - }
1.303 -
1.304 - /// \brief Sets the state of the \c item in the heap.
1.305 - ///
1.306 - /// Sets the state of the \c item in the heap. It can be used to
1.307 - /// manually clear the heap when it is important to achive the
1.308 - /// better time _complexity.
1.309 - /// \param i The item.
1.310 - /// \param st The state. It should not be \c IN_HEAP.
1.311 - void state(const Item& i, State st) {
1.312 - switch (st) {
1.313 - case POST_HEAP:
1.314 - case PRE_HEAP:
1.315 - if (state(i) == IN_HEAP) {
1.316 - erase(i);
1.317 - }
1.318 - _iim[i] = st;
1.319 - break;
1.320 - case IN_HEAP:
1.321 - break;
1.322 - }
1.323 - }
1.324 -
1.325 - private:
1.326 -
1.327 - void balance() {
1.328 -
1.329 - int maxdeg=int( std::floor( 2.08*log(double(_data.size()))))+1;
1.330 -
1.331 - std::vector<int> A(maxdeg,-1);
1.332 -
1.333 - /*
1.334 - *Recall that now minimum does not point to the minimum prio element.
1.335 - *We set minimum to this during balance().
1.336 - */
1.337 - int anchor=_data[_minimum].left_neighbor;
1.338 - int next=_minimum;
1.339 - bool end=false;
1.340 -
1.341 - do {
1.342 - int active=next;
1.343 - if ( anchor==active ) end=true;
1.344 - int d=_data[active].degree;
1.345 - next=_data[active].right_neighbor;
1.346 -
1.347 - while (A[d]!=-1) {
1.348 - if( _comp(_data[active].prio, _data[A[d]].prio) ) {
1.349 - fuse(active,A[d]);
1.350 - } else {
1.351 - fuse(A[d],active);
1.352 - active=A[d];
1.353 - }
1.354 - A[d]=-1;
1.355 - ++d;
1.356 - }
1.357 - A[d]=active;
1.358 - } while ( !end );
1.359 -
1.360 -
1.361 - while ( _data[_minimum].parent >=0 )
1.362 - _minimum=_data[_minimum].parent;
1.363 - int s=_minimum;
1.364 - int m=_minimum;
1.365 - do {
1.366 - if ( _comp(_data[s].prio, _data[_minimum].prio) ) _minimum=s;
1.367 - s=_data[s].right_neighbor;
1.368 - } while ( s != m );
1.369 - }
1.370 -
1.371 - void makeroot(int c) {
1.372 - int s=c;
1.373 - do {
1.374 - _data[s].parent=-1;
1.375 - s=_data[s].right_neighbor;
1.376 - } while ( s != c );
1.377 - }
1.378 -
1.379 - void cut(int a, int b) {
1.380 - /*
1.381 - *Replacing a from the children of b.
1.382 - */
1.383 - --_data[b].degree;
1.384 -
1.385 - if ( _data[b].degree !=0 ) {
1.386 - int child=_data[b].child;
1.387 - if ( child==a )
1.388 - _data[b].child=_data[child].right_neighbor;
1.389 - unlace(a);
1.390 - }
1.391 -
1.392 -
1.393 - /*Lacing a to the roots.*/
1.394 - int right=_data[_minimum].right_neighbor;
1.395 - _data[_minimum].right_neighbor=a;
1.396 - _data[a].left_neighbor=_minimum;
1.397 - _data[a].right_neighbor=right;
1.398 - _data[right].left_neighbor=a;
1.399 -
1.400 - _data[a].parent=-1;
1.401 - _data[a].marked=false;
1.402 - }
1.403 -
1.404 - void cascade(int a) {
1.405 - if ( _data[a].parent!=-1 ) {
1.406 - int p=_data[a].parent;
1.407 -
1.408 - if ( _data[a].marked==false ) _data[a].marked=true;
1.409 - else {
1.410 - cut(a,p);
1.411 - cascade(p);
1.412 - }
1.413 - }
1.414 - }
1.415 -
1.416 - void fuse(int a, int b) {
1.417 - unlace(b);
1.418 -
1.419 - /*Lacing b under a.*/
1.420 - _data[b].parent=a;
1.421 -
1.422 - if (_data[a].degree==0) {
1.423 - _data[b].left_neighbor=b;
1.424 - _data[b].right_neighbor=b;
1.425 - _data[a].child=b;
1.426 - } else {
1.427 - int child=_data[a].child;
1.428 - int last_child=_data[child].left_neighbor;
1.429 - _data[child].left_neighbor=b;
1.430 - _data[b].right_neighbor=child;
1.431 - _data[last_child].right_neighbor=b;
1.432 - _data[b].left_neighbor=last_child;
1.433 - }
1.434 -
1.435 - ++_data[a].degree;
1.436 -
1.437 - _data[b].marked=false;
1.438 - }
1.439 -
1.440 - /*
1.441 - *It is invoked only if a has siblings.
1.442 - */
1.443 - void unlace(int a) {
1.444 - int leftn=_data[a].left_neighbor;
1.445 - int rightn=_data[a].right_neighbor;
1.446 - _data[leftn].right_neighbor=rightn;
1.447 - _data[rightn].left_neighbor=leftn;
1.448 - }
1.449 -
1.450 -
1.451 - class Store {
1.452 - friend class FibHeap;
1.453 -
1.454 - Item name;
1.455 - int parent;
1.456 - int left_neighbor;
1.457 - int right_neighbor;
1.458 - int child;
1.459 - int degree;
1.460 - bool marked;
1.461 - bool in;
1.462 - Prio prio;
1.463 -
1.464 - Store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
1.465 - };
1.466 - };
1.467 -
1.468 -} //namespace lemon
1.469 -
1.470 -#endif //LEMON_FIB_HEAP_H
1.471 -