1.1 --- a/src/lemon/fib_heap.h Sat May 21 21:04:57 2005 +0000
1.2 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000
1.3 @@ -1,531 +0,0 @@
1.4 -/* -*- C++ -*-
1.5 - * src/lemon/fib_heap.h - Part of LEMON, a generic C++ optimization library
1.6 - *
1.7 - * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.8 - * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.9 - *
1.10 - * Permission to use, modify and distribute this software is granted
1.11 - * provided that this copyright notice appears in all copies. For
1.12 - * precise terms see the accompanying LICENSE file.
1.13 - *
1.14 - * This software is provided "AS IS" with no warranty of any kind,
1.15 - * express or implied, and with no claim as to its suitability for any
1.16 - * purpose.
1.17 - *
1.18 - */
1.19 -
1.20 -#ifndef LEMON_FIB_HEAP_H
1.21 -#define LEMON_FIB_HEAP_H
1.22 -
1.23 -///\file
1.24 -///\ingroup auxdat
1.25 -///\brief Fibonacci Heap implementation.
1.26 -
1.27 -#include <vector>
1.28 -#include <functional>
1.29 -#include <cmath>
1.30 -
1.31 -namespace lemon {
1.32 -
1.33 - /// \addtogroup auxdat
1.34 - /// @{
1.35 -
1.36 - /// Fibonacci Heap.
1.37 -
1.38 - ///This class implements the \e Fibonacci \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 - ///
1.44 - ///The methods \ref increase and \ref erase are not efficient in a Fibonacci
1.45 - ///heap. In case of many calls to these operations, it is better to use a
1.46 - ///\e binary \e heap.
1.47 - ///
1.48 - ///\param Item Type of the items to be stored.
1.49 - ///\param Prio Type of the priority of the items.
1.50 - ///\param ItemIntMap A read and writable Item int map, used internally
1.51 - ///to handle the cross references.
1.52 - ///\param Compare 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 - ///\author Jacint Szabo
1.58 -
1.59 -#ifdef DOXYGEN
1.60 - template <typename Item,
1.61 - typename Prio,
1.62 - typename ItemIntMap,
1.63 - typename Compare>
1.64 -#else
1.65 - template <typename Item,
1.66 - typename Prio,
1.67 - typename ItemIntMap,
1.68 - typename Compare = std::less<Prio> >
1.69 -#endif
1.70 - class FibHeap {
1.71 - public:
1.72 - typedef Prio PrioType;
1.73 -
1.74 - private:
1.75 - class store;
1.76 -
1.77 - std::vector<store> container;
1.78 - int minimum;
1.79 - ItemIntMap &iimap;
1.80 - Compare comp;
1.81 - int num_items;
1.82 -
1.83 - public:
1.84 - ///Status of the nodes
1.85 - enum state_enum {
1.86 - ///The node is in the heap
1.87 - IN_HEAP = 0,
1.88 - ///The node has never been in the heap
1.89 - PRE_HEAP = -1,
1.90 - ///The node was in the heap but it got out of it
1.91 - POST_HEAP = -2
1.92 - };
1.93 -
1.94 - ///The constructor
1.95 -
1.96 - /**
1.97 - \c _iimap should be given to the constructor, since it is
1.98 - used internally to handle the cross references.
1.99 - */
1.100 - explicit FibHeap(ItemIntMap &_iimap)
1.101 - : minimum(0), iimap(_iimap), num_items() {}
1.102 -
1.103 - ///The constructor
1.104 -
1.105 - /**
1.106 - \c _iimap should be given to the constructor, since it is used
1.107 - internally to handle the cross references. \c _comp is an
1.108 - object for ordering of the priorities.
1.109 - */
1.110 - FibHeap(ItemIntMap &_iimap, const Compare &_comp) : minimum(0),
1.111 - iimap(_iimap), comp(_comp), num_items() {}
1.112 -
1.113 - ///The number of items stored in the heap.
1.114 -
1.115 - /**
1.116 - Returns the number of items stored in the heap.
1.117 - */
1.118 - int size() const { return num_items; }
1.119 -
1.120 - ///Checks if the heap stores no items.
1.121 -
1.122 - /**
1.123 - Returns \c true if and only if the heap stores no items.
1.124 - */
1.125 - bool empty() const { return num_items==0; }
1.126 -
1.127 - ///\c item gets to the heap with priority \c value independently if \c item was already there.
1.128 -
1.129 - /**
1.130 - This method calls \ref push(\c item, \c value) if \c item is not
1.131 - stored in the heap and it calls \ref decrease(\c item, \c value) or
1.132 - \ref increase(\c item, \c value) otherwise.
1.133 - */
1.134 - void set (Item const item, PrioType const value);
1.135 -
1.136 - ///Adds \c item to the heap with priority \c value.
1.137 -
1.138 - /**
1.139 - Adds \c item to the heap with priority \c value.
1.140 - \pre \c item must not be stored in the heap.
1.141 - */
1.142 - void push (Item const item, PrioType const value);
1.143 -
1.144 - ///Returns the item with minimum priority relative to \c Compare.
1.145 -
1.146 - /**
1.147 - This method returns the item with minimum priority relative to \c
1.148 - Compare.
1.149 - \pre The heap must be nonempty.
1.150 - */
1.151 - Item top() const { return container[minimum].name; }
1.152 -
1.153 - ///Returns the minimum priority relative to \c Compare.
1.154 -
1.155 - /**
1.156 - It returns the minimum priority relative to \c Compare.
1.157 - \pre The heap must be nonempty.
1.158 - */
1.159 - PrioType prio() const { return container[minimum].prio; }
1.160 -
1.161 - ///Returns the priority of \c item.
1.162 -
1.163 - /**
1.164 - This function returns the priority of \c item.
1.165 - \pre \c item must be in the heap.
1.166 - */
1.167 - PrioType& operator[](const Item& item) {
1.168 - return container[iimap[item]].prio;
1.169 - }
1.170 -
1.171 - ///Returns the priority of \c item.
1.172 -
1.173 - /**
1.174 - It returns the priority of \c item.
1.175 - \pre \c item must be in the heap.
1.176 - */
1.177 - const PrioType& operator[](const Item& item) const {
1.178 - return container[iimap[item]].prio;
1.179 - }
1.180 -
1.181 -
1.182 - ///Deletes the item with minimum priority relative to \c Compare.
1.183 -
1.184 - /**
1.185 - This method deletes the item with minimum priority relative to \c
1.186 - Compare from the heap.
1.187 - \pre The heap must be non-empty.
1.188 - */
1.189 - void pop();
1.190 -
1.191 - ///Deletes \c item from the heap.
1.192 -
1.193 - /**
1.194 - This method deletes \c item from the heap, if \c item was already
1.195 - stored in the heap. It is quite inefficient in Fibonacci heaps.
1.196 - */
1.197 - void erase (const Item& item);
1.198 -
1.199 - ///Decreases the priority of \c item to \c value.
1.200 -
1.201 - /**
1.202 - This method decreases the priority of \c item to \c value.
1.203 - \pre \c item must be stored in the heap with priority at least \c
1.204 - value relative to \c Compare.
1.205 - */
1.206 - void decrease (Item item, PrioType const value);
1.207 -
1.208 - ///Increases the priority of \c item to \c value.
1.209 -
1.210 - /**
1.211 - This method sets the priority of \c item to \c value. Though
1.212 - there is no precondition on the priority of \c item, this
1.213 - method should be used only if it is indeed necessary to increase
1.214 - (relative to \c Compare) the priority of \c item, because this
1.215 - method is inefficient.
1.216 - */
1.217 - void increase (Item item, PrioType const value) {
1.218 - erase(item);
1.219 - push(item, value);
1.220 - }
1.221 -
1.222 -
1.223 - ///Returns if \c item is in, has already been in, or has never been in the heap.
1.224 -
1.225 - /**
1.226 - This method returns PRE_HEAP if \c item has never been in the
1.227 - heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
1.228 - otherwise. In the latter case it is possible that \c item will
1.229 - get back to the heap again.
1.230 - */
1.231 - state_enum state(const Item &item) const {
1.232 - int i=iimap[item];
1.233 - if( i>=0 ) {
1.234 - if ( container[i].in ) i=0;
1.235 - else i=-2;
1.236 - }
1.237 - return state_enum(i);
1.238 - }
1.239 -
1.240 - private:
1.241 -
1.242 - void balance();
1.243 - void makeroot(int c);
1.244 - void cut(int a, int b);
1.245 - void cascade(int a);
1.246 - void fuse(int a, int b);
1.247 - void unlace(int a);
1.248 -
1.249 -
1.250 - class store {
1.251 - friend class FibHeap;
1.252 -
1.253 - Item name;
1.254 - int parent;
1.255 - int left_neighbor;
1.256 - int right_neighbor;
1.257 - int child;
1.258 - int degree;
1.259 - bool marked;
1.260 - bool in;
1.261 - PrioType prio;
1.262 -
1.263 - store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
1.264 - };
1.265 - };
1.266 -
1.267 -
1.268 -
1.269 - // **********************************************************************
1.270 - // IMPLEMENTATIONS
1.271 - // **********************************************************************
1.272 -
1.273 - template <typename Item, typename Prio, typename ItemIntMap,
1.274 - typename Compare>
1.275 - void FibHeap<Item, Prio, ItemIntMap, Compare>::set
1.276 - (Item const item, PrioType const value)
1.277 - {
1.278 - int i=iimap[item];
1.279 - if ( i >= 0 && container[i].in ) {
1.280 - if ( comp(value, container[i].prio) ) decrease(item, value);
1.281 - if ( comp(container[i].prio, value) ) increase(item, value);
1.282 - } else push(item, value);
1.283 - }
1.284 -
1.285 - template <typename Item, typename Prio, typename ItemIntMap,
1.286 - typename Compare>
1.287 - void FibHeap<Item, Prio, ItemIntMap, Compare>::push
1.288 - (Item const item, PrioType const value) {
1.289 - int i=iimap[item];
1.290 - if ( i < 0 ) {
1.291 - int s=container.size();
1.292 - iimap.set( item, s );
1.293 - store st;
1.294 - st.name=item;
1.295 - container.push_back(st);
1.296 - i=s;
1.297 - } else {
1.298 - container[i].parent=container[i].child=-1;
1.299 - container[i].degree=0;
1.300 - container[i].in=true;
1.301 - container[i].marked=false;
1.302 - }
1.303 -
1.304 - if ( num_items ) {
1.305 - container[container[minimum].right_neighbor].left_neighbor=i;
1.306 - container[i].right_neighbor=container[minimum].right_neighbor;
1.307 - container[minimum].right_neighbor=i;
1.308 - container[i].left_neighbor=minimum;
1.309 - if ( comp( value, container[minimum].prio) ) minimum=i;
1.310 - } else {
1.311 - container[i].right_neighbor=container[i].left_neighbor=i;
1.312 - minimum=i;
1.313 - }
1.314 - container[i].prio=value;
1.315 - ++num_items;
1.316 - }
1.317 -
1.318 - template <typename Item, typename Prio, typename ItemIntMap,
1.319 - typename Compare>
1.320 - void FibHeap<Item, Prio, ItemIntMap, Compare>::pop() {
1.321 - /*The first case is that there are only one root.*/
1.322 - if ( container[minimum].left_neighbor==minimum ) {
1.323 - container[minimum].in=false;
1.324 - if ( container[minimum].degree!=0 ) {
1.325 - makeroot(container[minimum].child);
1.326 - minimum=container[minimum].child;
1.327 - balance();
1.328 - }
1.329 - } else {
1.330 - int right=container[minimum].right_neighbor;
1.331 - unlace(minimum);
1.332 - container[minimum].in=false;
1.333 - if ( container[minimum].degree > 0 ) {
1.334 - int left=container[minimum].left_neighbor;
1.335 - int child=container[minimum].child;
1.336 - int last_child=container[child].left_neighbor;
1.337 -
1.338 - makeroot(child);
1.339 -
1.340 - container[left].right_neighbor=child;
1.341 - container[child].left_neighbor=left;
1.342 - container[right].left_neighbor=last_child;
1.343 - container[last_child].right_neighbor=right;
1.344 - }
1.345 - minimum=right;
1.346 - balance();
1.347 - } // the case where there are more roots
1.348 - --num_items;
1.349 - }
1.350 -
1.351 -
1.352 - template <typename Item, typename Prio, typename ItemIntMap,
1.353 - typename Compare>
1.354 - void FibHeap<Item, Prio, ItemIntMap, Compare>::erase
1.355 - (const Item& item) {
1.356 - int i=iimap[item];
1.357 -
1.358 - if ( i >= 0 && container[i].in ) {
1.359 - if ( container[i].parent!=-1 ) {
1.360 - int p=container[i].parent;
1.361 - cut(i,p);
1.362 - cascade(p);
1.363 - }
1.364 - minimum=i; //As if its prio would be -infinity
1.365 - pop();
1.366 - }
1.367 - }
1.368 -
1.369 - template <typename Item, typename Prio, typename ItemIntMap,
1.370 - typename Compare>
1.371 - void FibHeap<Item, Prio, ItemIntMap, Compare>::decrease
1.372 - (Item item, PrioType const value) {
1.373 - int i=iimap[item];
1.374 - container[i].prio=value;
1.375 - int p=container[i].parent;
1.376 -
1.377 - if ( p!=-1 && comp(value, container[p].prio) ) {
1.378 - cut(i,p);
1.379 - cascade(p);
1.380 - }
1.381 - if ( comp(value, container[minimum].prio) ) minimum=i;
1.382 - }
1.383 -
1.384 -
1.385 - template <typename Item, typename Prio, typename ItemIntMap,
1.386 - typename Compare>
1.387 - void FibHeap<Item, Prio, ItemIntMap, Compare>::balance() {
1.388 -
1.389 - int maxdeg=int( std::floor( 2.08*log(double(container.size()))))+1;
1.390 -
1.391 - std::vector<int> A(maxdeg,-1);
1.392 -
1.393 - /*
1.394 - *Recall that now minimum does not point to the minimum prio element.
1.395 - *We set minimum to this during balance().
1.396 - */
1.397 - int anchor=container[minimum].left_neighbor;
1.398 - int next=minimum;
1.399 - bool end=false;
1.400 -
1.401 - do {
1.402 - int active=next;
1.403 - if ( anchor==active ) end=true;
1.404 - int d=container[active].degree;
1.405 - next=container[active].right_neighbor;
1.406 -
1.407 - while (A[d]!=-1) {
1.408 - if( comp(container[active].prio, container[A[d]].prio) ) {
1.409 - fuse(active,A[d]);
1.410 - } else {
1.411 - fuse(A[d],active);
1.412 - active=A[d];
1.413 - }
1.414 - A[d]=-1;
1.415 - ++d;
1.416 - }
1.417 - A[d]=active;
1.418 - } while ( !end );
1.419 -
1.420 -
1.421 - while ( container[minimum].parent >=0 ) minimum=container[minimum].parent;
1.422 - int s=minimum;
1.423 - int m=minimum;
1.424 - do {
1.425 - if ( comp(container[s].prio, container[minimum].prio) ) minimum=s;
1.426 - s=container[s].right_neighbor;
1.427 - } while ( s != m );
1.428 - }
1.429 -
1.430 - template <typename Item, typename Prio, typename ItemIntMap,
1.431 - typename Compare>
1.432 - void FibHeap<Item, Prio, ItemIntMap, Compare>::makeroot
1.433 - (int c) {
1.434 - int s=c;
1.435 - do {
1.436 - container[s].parent=-1;
1.437 - s=container[s].right_neighbor;
1.438 - } while ( s != c );
1.439 - }
1.440 -
1.441 -
1.442 - template <typename Item, typename Prio, typename ItemIntMap,
1.443 - typename Compare>
1.444 - void FibHeap<Item, Prio, ItemIntMap, Compare>::cut
1.445 - (int a, int b) {
1.446 - /*
1.447 - *Replacing a from the children of b.
1.448 - */
1.449 - --container[b].degree;
1.450 -
1.451 - if ( container[b].degree !=0 ) {
1.452 - int child=container[b].child;
1.453 - if ( child==a )
1.454 - container[b].child=container[child].right_neighbor;
1.455 - unlace(a);
1.456 - }
1.457 -
1.458 -
1.459 - /*Lacing a to the roots.*/
1.460 - int right=container[minimum].right_neighbor;
1.461 - container[minimum].right_neighbor=a;
1.462 - container[a].left_neighbor=minimum;
1.463 - container[a].right_neighbor=right;
1.464 - container[right].left_neighbor=a;
1.465 -
1.466 - container[a].parent=-1;
1.467 - container[a].marked=false;
1.468 - }
1.469 -
1.470 -
1.471 - template <typename Item, typename Prio, typename ItemIntMap,
1.472 - typename Compare>
1.473 - void FibHeap<Item, Prio, ItemIntMap, Compare>::cascade
1.474 - (int a)
1.475 - {
1.476 - if ( container[a].parent!=-1 ) {
1.477 - int p=container[a].parent;
1.478 -
1.479 - if ( container[a].marked==false ) container[a].marked=true;
1.480 - else {
1.481 - cut(a,p);
1.482 - cascade(p);
1.483 - }
1.484 - }
1.485 - }
1.486 -
1.487 -
1.488 - template <typename Item, typename Prio, typename ItemIntMap,
1.489 - typename Compare>
1.490 - void FibHeap<Item, Prio, ItemIntMap, Compare>::fuse
1.491 - (int a, int b) {
1.492 - unlace(b);
1.493 -
1.494 - /*Lacing b under a.*/
1.495 - container[b].parent=a;
1.496 -
1.497 - if (container[a].degree==0) {
1.498 - container[b].left_neighbor=b;
1.499 - container[b].right_neighbor=b;
1.500 - container[a].child=b;
1.501 - } else {
1.502 - int child=container[a].child;
1.503 - int last_child=container[child].left_neighbor;
1.504 - container[child].left_neighbor=b;
1.505 - container[b].right_neighbor=child;
1.506 - container[last_child].right_neighbor=b;
1.507 - container[b].left_neighbor=last_child;
1.508 - }
1.509 -
1.510 - ++container[a].degree;
1.511 -
1.512 - container[b].marked=false;
1.513 - }
1.514 -
1.515 -
1.516 - /*
1.517 - *It is invoked only if a has siblings.
1.518 - */
1.519 - template <typename Item, typename Prio, typename ItemIntMap,
1.520 - typename Compare>
1.521 - void FibHeap<Item, Prio, ItemIntMap, Compare>::unlace
1.522 - (int a) {
1.523 - int leftn=container[a].left_neighbor;
1.524 - int rightn=container[a].right_neighbor;
1.525 - container[leftn].right_neighbor=rightn;
1.526 - container[rightn].left_neighbor=leftn;
1.527 - }
1.528 -
1.529 - ///@}
1.530 -
1.531 -} //namespace lemon
1.532 -
1.533 -#endif //LEMON_FIB_HEAP_H
1.534 -