1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/src/lemon/fib_heap.h Wed Sep 29 15:30:04 2004 +0000
1.3 @@ -0,0 +1,510 @@
1.4 +/* -*- C++ -*-
1.5 + * src/lemon/fib_heap.h - Part of LEMON, 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 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 <math.h>
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, 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 lemon
1.511 +
1.512 +#endif //LEMON_FIB_HEAP_H
1.513 +