1.1 --- a/src/hugo/fib_heap.h Wed Sep 29 14:12:26 2004 +0000
1.2 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000
1.3 @@ -1,510 +0,0 @@
1.4 -/* -*- C++ -*-
1.5 - * src/hugo/fib_heap.h - Part of HUGOlib, a generic C++ optimization library
1.6 - *
1.7 - * Copyright (C) 2004 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.8 - * (Egervary Combinatorial Optimization Research Group, 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 HUGO_FIB_HEAP_H
1.21 -#define HUGO_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 <math.h>
1.30 -
1.31 -namespace hugo {
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, for the usage of
1.51 - ///the heap.
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 - ///\author Jacint Szabo
1.56 -
1.57 -#ifdef DOXYGEN
1.58 - template <typename Item,
1.59 - typename Prio,
1.60 - typename ItemIntMap,
1.61 - typename Compare>
1.62 -#else
1.63 - template <typename Item,
1.64 - typename Prio,
1.65 - typename ItemIntMap,
1.66 - typename Compare = std::less<Prio> >
1.67 -#endif
1.68 - class FibHeap {
1.69 - public:
1.70 - typedef Prio PrioType;
1.71 -
1.72 - private:
1.73 - class store;
1.74 -
1.75 - std::vector<store> container;
1.76 - int minimum;
1.77 - ItemIntMap &iimap;
1.78 - Compare comp;
1.79 - int num_items;
1.80 -
1.81 - public:
1.82 - enum state_enum {
1.83 - IN_HEAP = 0,
1.84 - PRE_HEAP = -1,
1.85 - POST_HEAP = -2
1.86 - };
1.87 -
1.88 - FibHeap(ItemIntMap &_iimap) : minimum(0), iimap(_iimap), num_items() {}
1.89 - FibHeap(ItemIntMap &_iimap, const Compare &_comp) : minimum(0),
1.90 - iimap(_iimap), comp(_comp), num_items() {}
1.91 -
1.92 - ///The number of items stored in the heap.
1.93 -
1.94 - /**
1.95 - Returns the number of items stored in the heap.
1.96 - */
1.97 - int size() const { return num_items; }
1.98 -
1.99 - ///Checks if the heap stores no items.
1.100 -
1.101 - /**
1.102 - Returns \c true if and only if the heap stores no items.
1.103 - */
1.104 - bool empty() const { return num_items==0; }
1.105 -
1.106 - ///\c item gets to the heap with priority \c value independently if \c item was already there.
1.107 -
1.108 - /**
1.109 - This method calls \ref push(\c item, \c value) if \c item is not
1.110 - stored in the heap and it calls \ref decrease(\c item, \c value) or
1.111 - \ref increase(\c item, \c value) otherwise.
1.112 - */
1.113 - void set (Item const item, PrioType const value);
1.114 -
1.115 - ///Adds \c item to the heap with priority \c value.
1.116 -
1.117 - /**
1.118 - Adds \c item to the heap with priority \c value.
1.119 - \pre \c item must not be stored in the heap.
1.120 - */
1.121 - void push (Item const item, PrioType const value);
1.122 -
1.123 - ///Returns the item with minimum priority relative to \c Compare.
1.124 -
1.125 - /**
1.126 - This method returns the item with minimum priority relative to \c
1.127 - Compare.
1.128 - \pre The heap must be nonempty.
1.129 - */
1.130 - Item top() const { return container[minimum].name; }
1.131 -
1.132 - ///Returns the minimum priority relative to \c Compare.
1.133 -
1.134 - /**
1.135 - It returns the minimum priority relative to \c Compare.
1.136 - \pre The heap must be nonempty.
1.137 - */
1.138 - PrioType prio() const { return container[minimum].prio; }
1.139 -
1.140 - ///Returns the priority of \c item.
1.141 -
1.142 - /**
1.143 - This function returns the priority of \c item.
1.144 - \pre \c item must be in the heap.
1.145 - */
1.146 - PrioType& operator[](const Item& item) {
1.147 - return container[iimap[item]].prio;
1.148 - }
1.149 -
1.150 - ///Returns the priority of \c item.
1.151 -
1.152 - /**
1.153 - It returns the priority of \c item.
1.154 - \pre \c item must be in the heap.
1.155 - */
1.156 - const PrioType& operator[](const Item& item) const {
1.157 - return container[iimap[item]].prio;
1.158 - }
1.159 -
1.160 -
1.161 - ///Deletes the item with minimum priority relative to \c Compare.
1.162 -
1.163 - /**
1.164 - This method deletes the item with minimum priority relative to \c
1.165 - Compare from the heap.
1.166 - \pre The heap must be non-empty.
1.167 - */
1.168 - void pop();
1.169 -
1.170 - ///Deletes \c item from the heap.
1.171 -
1.172 - /**
1.173 - This method deletes \c item from the heap, if \c item was already
1.174 - stored in the heap. It is quite inefficient in Fibonacci heaps.
1.175 - */
1.176 - void erase (const Item& item);
1.177 -
1.178 - ///Decreases the priority of \c item to \c value.
1.179 -
1.180 - /**
1.181 - This method decreases the priority of \c item to \c value.
1.182 - \pre \c item must be stored in the heap with priority at least \c
1.183 - value relative to \c Compare.
1.184 - */
1.185 - void decrease (Item item, PrioType const value);
1.186 -
1.187 - ///Increases the priority of \c item to \c value.
1.188 -
1.189 - /**
1.190 - This method sets the priority of \c item to \c value. Though
1.191 - there is no precondition on the priority of \c item, this
1.192 - method should be used only if it is indeed necessary to increase
1.193 - (relative to \c Compare) the priority of \c item, because this
1.194 - method is inefficient.
1.195 - */
1.196 - void increase (Item item, PrioType const value) {
1.197 - erase(item);
1.198 - push(item, value);
1.199 - }
1.200 -
1.201 -
1.202 - ///Returns if \c item is in, has already been in, or has never been in the heap.
1.203 -
1.204 - /**
1.205 - This method returns PRE_HEAP if \c item has never been in the
1.206 - heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
1.207 - otherwise. In the latter case it is possible that \c item will
1.208 - get back to the heap again.
1.209 - */
1.210 - state_enum state(const Item &item) const {
1.211 - int i=iimap[item];
1.212 - if( i>=0 ) {
1.213 - if ( container[i].in ) i=0;
1.214 - else i=-2;
1.215 - }
1.216 - return state_enum(i);
1.217 - }
1.218 -
1.219 - private:
1.220 -
1.221 - void balance();
1.222 - void makeroot(int c);
1.223 - void cut(int a, int b);
1.224 - void cascade(int a);
1.225 - void fuse(int a, int b);
1.226 - void unlace(int a);
1.227 -
1.228 -
1.229 - class store {
1.230 - friend class FibHeap;
1.231 -
1.232 - Item name;
1.233 - int parent;
1.234 - int left_neighbor;
1.235 - int right_neighbor;
1.236 - int child;
1.237 - int degree;
1.238 - bool marked;
1.239 - bool in;
1.240 - PrioType prio;
1.241 -
1.242 - store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
1.243 - };
1.244 - };
1.245 -
1.246 -
1.247 -
1.248 - // **********************************************************************
1.249 - // IMPLEMENTATIONS
1.250 - // **********************************************************************
1.251 -
1.252 - template <typename Item, typename Prio, typename ItemIntMap,
1.253 - typename Compare>
1.254 - void FibHeap<Item, Prio, ItemIntMap, Compare>::set
1.255 - (Item const item, PrioType const value)
1.256 - {
1.257 - int i=iimap[item];
1.258 - if ( i >= 0 && container[i].in ) {
1.259 - if ( comp(value, container[i].prio) ) decrease(item, value);
1.260 - if ( comp(container[i].prio, value) ) increase(item, value);
1.261 - } else push(item, value);
1.262 - }
1.263 -
1.264 - template <typename Item, typename Prio, typename ItemIntMap,
1.265 - typename Compare>
1.266 - void FibHeap<Item, Prio, ItemIntMap, Compare>::push
1.267 - (Item const item, PrioType const value) {
1.268 - int i=iimap[item];
1.269 - if ( i < 0 ) {
1.270 - int s=container.size();
1.271 - iimap.set( item, s );
1.272 - store st;
1.273 - st.name=item;
1.274 - container.push_back(st);
1.275 - i=s;
1.276 - } else {
1.277 - container[i].parent=container[i].child=-1;
1.278 - container[i].degree=0;
1.279 - container[i].in=true;
1.280 - container[i].marked=false;
1.281 - }
1.282 -
1.283 - if ( num_items ) {
1.284 - container[container[minimum].right_neighbor].left_neighbor=i;
1.285 - container[i].right_neighbor=container[minimum].right_neighbor;
1.286 - container[minimum].right_neighbor=i;
1.287 - container[i].left_neighbor=minimum;
1.288 - if ( comp( value, container[minimum].prio) ) minimum=i;
1.289 - } else {
1.290 - container[i].right_neighbor=container[i].left_neighbor=i;
1.291 - minimum=i;
1.292 - }
1.293 - container[i].prio=value;
1.294 - ++num_items;
1.295 - }
1.296 -
1.297 - template <typename Item, typename Prio, typename ItemIntMap,
1.298 - typename Compare>
1.299 - void FibHeap<Item, Prio, ItemIntMap, Compare>::pop() {
1.300 - /*The first case is that there are only one root.*/
1.301 - if ( container[minimum].left_neighbor==minimum ) {
1.302 - container[minimum].in=false;
1.303 - if ( container[minimum].degree!=0 ) {
1.304 - makeroot(container[minimum].child);
1.305 - minimum=container[minimum].child;
1.306 - balance();
1.307 - }
1.308 - } else {
1.309 - int right=container[minimum].right_neighbor;
1.310 - unlace(minimum);
1.311 - container[minimum].in=false;
1.312 - if ( container[minimum].degree > 0 ) {
1.313 - int left=container[minimum].left_neighbor;
1.314 - int child=container[minimum].child;
1.315 - int last_child=container[child].left_neighbor;
1.316 -
1.317 - makeroot(child);
1.318 -
1.319 - container[left].right_neighbor=child;
1.320 - container[child].left_neighbor=left;
1.321 - container[right].left_neighbor=last_child;
1.322 - container[last_child].right_neighbor=right;
1.323 - }
1.324 - minimum=right;
1.325 - balance();
1.326 - } // the case where there are more roots
1.327 - --num_items;
1.328 - }
1.329 -
1.330 -
1.331 - template <typename Item, typename Prio, typename ItemIntMap,
1.332 - typename Compare>
1.333 - void FibHeap<Item, Prio, ItemIntMap, Compare>::erase
1.334 - (const Item& item) {
1.335 - int i=iimap[item];
1.336 -
1.337 - if ( i >= 0 && container[i].in ) {
1.338 - if ( container[i].parent!=-1 ) {
1.339 - int p=container[i].parent;
1.340 - cut(i,p);
1.341 - cascade(p);
1.342 - }
1.343 - minimum=i; //As if its prio would be -infinity
1.344 - pop();
1.345 - }
1.346 - }
1.347 -
1.348 - template <typename Item, typename Prio, typename ItemIntMap,
1.349 - typename Compare>
1.350 - void FibHeap<Item, Prio, ItemIntMap, Compare>::decrease
1.351 - (Item item, PrioType const value) {
1.352 - int i=iimap[item];
1.353 - container[i].prio=value;
1.354 - int p=container[i].parent;
1.355 -
1.356 - if ( p!=-1 && comp(value, container[p].prio) ) {
1.357 - cut(i,p);
1.358 - cascade(p);
1.359 - }
1.360 - if ( comp(value, container[minimum].prio) ) minimum=i;
1.361 - }
1.362 -
1.363 -
1.364 - template <typename Item, typename Prio, typename ItemIntMap,
1.365 - typename Compare>
1.366 - void FibHeap<Item, Prio, ItemIntMap, Compare>::balance() {
1.367 -
1.368 - int maxdeg=int( floor( 2.08*log(double(container.size()))))+1;
1.369 -
1.370 - std::vector<int> A(maxdeg,-1);
1.371 -
1.372 - /*
1.373 - *Recall that now minimum does not point to the minimum prio element.
1.374 - *We set minimum to this during balance().
1.375 - */
1.376 - int anchor=container[minimum].left_neighbor;
1.377 - int next=minimum;
1.378 - bool end=false;
1.379 -
1.380 - do {
1.381 - int active=next;
1.382 - if ( anchor==active ) end=true;
1.383 - int d=container[active].degree;
1.384 - next=container[active].right_neighbor;
1.385 -
1.386 - while (A[d]!=-1) {
1.387 - if( comp(container[active].prio, container[A[d]].prio) ) {
1.388 - fuse(active,A[d]);
1.389 - } else {
1.390 - fuse(A[d],active);
1.391 - active=A[d];
1.392 - }
1.393 - A[d]=-1;
1.394 - ++d;
1.395 - }
1.396 - A[d]=active;
1.397 - } while ( !end );
1.398 -
1.399 -
1.400 - while ( container[minimum].parent >=0 ) minimum=container[minimum].parent;
1.401 - int s=minimum;
1.402 - int m=minimum;
1.403 - do {
1.404 - if ( comp(container[s].prio, container[minimum].prio) ) minimum=s;
1.405 - s=container[s].right_neighbor;
1.406 - } while ( s != m );
1.407 - }
1.408 -
1.409 - template <typename Item, typename Prio, typename ItemIntMap,
1.410 - typename Compare>
1.411 - void FibHeap<Item, Prio, ItemIntMap, Compare>::makeroot
1.412 - (int c) {
1.413 - int s=c;
1.414 - do {
1.415 - container[s].parent=-1;
1.416 - s=container[s].right_neighbor;
1.417 - } while ( s != c );
1.418 - }
1.419 -
1.420 -
1.421 - template <typename Item, typename Prio, typename ItemIntMap,
1.422 - typename Compare>
1.423 - void FibHeap<Item, Prio, ItemIntMap, Compare>::cut
1.424 - (int a, int b) {
1.425 - /*
1.426 - *Replacing a from the children of b.
1.427 - */
1.428 - --container[b].degree;
1.429 -
1.430 - if ( container[b].degree !=0 ) {
1.431 - int child=container[b].child;
1.432 - if ( child==a )
1.433 - container[b].child=container[child].right_neighbor;
1.434 - unlace(a);
1.435 - }
1.436 -
1.437 -
1.438 - /*Lacing a to the roots.*/
1.439 - int right=container[minimum].right_neighbor;
1.440 - container[minimum].right_neighbor=a;
1.441 - container[a].left_neighbor=minimum;
1.442 - container[a].right_neighbor=right;
1.443 - container[right].left_neighbor=a;
1.444 -
1.445 - container[a].parent=-1;
1.446 - container[a].marked=false;
1.447 - }
1.448 -
1.449 -
1.450 - template <typename Item, typename Prio, typename ItemIntMap,
1.451 - typename Compare>
1.452 - void FibHeap<Item, Prio, ItemIntMap, Compare>::cascade
1.453 - (int a)
1.454 - {
1.455 - if ( container[a].parent!=-1 ) {
1.456 - int p=container[a].parent;
1.457 -
1.458 - if ( container[a].marked==false ) container[a].marked=true;
1.459 - else {
1.460 - cut(a,p);
1.461 - cascade(p);
1.462 - }
1.463 - }
1.464 - }
1.465 -
1.466 -
1.467 - template <typename Item, typename Prio, typename ItemIntMap,
1.468 - typename Compare>
1.469 - void FibHeap<Item, Prio, ItemIntMap, Compare>::fuse
1.470 - (int a, int b) {
1.471 - unlace(b);
1.472 -
1.473 - /*Lacing b under a.*/
1.474 - container[b].parent=a;
1.475 -
1.476 - if (container[a].degree==0) {
1.477 - container[b].left_neighbor=b;
1.478 - container[b].right_neighbor=b;
1.479 - container[a].child=b;
1.480 - } else {
1.481 - int child=container[a].child;
1.482 - int last_child=container[child].left_neighbor;
1.483 - container[child].left_neighbor=b;
1.484 - container[b].right_neighbor=child;
1.485 - container[last_child].right_neighbor=b;
1.486 - container[b].left_neighbor=last_child;
1.487 - }
1.488 -
1.489 - ++container[a].degree;
1.490 -
1.491 - container[b].marked=false;
1.492 - }
1.493 -
1.494 -
1.495 - /*
1.496 - *It is invoked only if a has siblings.
1.497 - */
1.498 - template <typename Item, typename Prio, typename ItemIntMap,
1.499 - typename Compare>
1.500 - void FibHeap<Item, Prio, ItemIntMap, Compare>::unlace
1.501 - (int a) {
1.502 - int leftn=container[a].left_neighbor;
1.503 - int rightn=container[a].right_neighbor;
1.504 - container[leftn].right_neighbor=rightn;
1.505 - container[rightn].left_neighbor=leftn;
1.506 - }
1.507 -
1.508 - ///@}
1.509 -
1.510 -} //namespace hugo
1.511 -
1.512 -#endif //HUGO_FIB_HEAP_H
1.513 -