Small bug fixes.
3 * This file is a part of LEMON, a generic C++ optimization library
5 * Copyright (C) 2003-2007
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
19 #ifndef LEMON_FIB_HEAP_H
20 #define LEMON_FIB_HEAP_H
24 ///\brief Fibonacci Heap implementation.
36 ///This class implements the \e Fibonacci \e heap data structure. A \e heap
37 ///is a data structure for storing items with specified values called \e
38 ///priorities in such a way that finding the item with minimum priority is
39 ///efficient. \c Compare specifies the ordering of the priorities. In a heap
40 ///one can change the priority of an item, add or erase an item, etc.
42 ///The methods \ref increase and \ref erase are not efficient in a Fibonacci
43 ///heap. In case of many calls to these operations, it is better to use a
46 ///\param Prio Type of the priority of the items.
47 ///\param ItemIntMap A read and writable Item int map, used internally
48 ///to handle the cross references.
49 ///\param Compare A class for the ordering of the priorities. The
50 ///default is \c std::less<Prio>.
54 ///\author Jacint Szabo
57 template <typename Prio,
61 template <typename Prio,
63 typename Compare = std::less<Prio> >
67 typedef typename ItemIntMap::Key Item;
68 typedef Prio PrioType;
73 std::vector<store> container;
80 ///Status of the nodes
82 ///The node is in the heap
84 ///The node has never been in the heap
86 ///The node was in the heap but it got out of it
90 /// \brief The constructor
92 /// \c _iimap should be given to the constructor, since it is
93 /// used internally to handle the cross references.
94 explicit FibHeap(ItemIntMap &_iimap)
95 : minimum(0), iimap(_iimap), num_items() {}
97 /// \brief The constructor
99 /// \c _iimap should be given to the constructor, since it is used
100 /// internally to handle the cross references. \c _comp is an
101 /// object for ordering of the priorities.
102 FibHeap(ItemIntMap &_iimap, const Compare &_comp) : minimum(0),
103 iimap(_iimap), comp(_comp), num_items() {}
105 /// \brief The number of items stored in the heap.
107 /// Returns the number of items stored in the heap.
108 int size() const { return num_items; }
110 /// \brief Checks if the heap stores no items.
112 /// Returns \c true if and only if the heap stores no items.
113 bool empty() const { return num_items==0; }
115 /// \brief Make empty this heap.
117 /// Make empty this heap. It does not change the cross reference
118 /// map. If you want to reuse a heap what is not surely empty you
119 /// should first clear the heap and after that you should set the
120 /// cross reference map for each item to \c PRE_HEAP.
122 container.clear(); minimum = 0; num_items = 0;
125 /// \brief \c item gets to the heap with priority \c value independently
126 /// if \c item was already there.
128 /// This method calls \ref push(\c item, \c value) if \c item is not
129 /// stored in the heap and it calls \ref decrease(\c item, \c value) or
130 /// \ref increase(\c item, \c value) otherwise.
131 void set (Item const item, PrioType const value);
133 /// \brief Adds \c item to the heap with priority \c value.
135 /// Adds \c item to the heap with priority \c value.
136 /// \pre \c item must not be stored in the heap.
137 void push (Item const item, PrioType const value);
139 /// \brief Returns the item with minimum priority relative to \c Compare.
141 /// This method returns the item with minimum priority relative to \c
143 /// \pre The heap must be nonempty.
144 Item top() const { return container[minimum].name; }
146 /// \brief Returns the minimum priority relative to \c Compare.
148 /// It returns the minimum priority relative to \c Compare.
149 /// \pre The heap must be nonempty.
150 PrioType prio() const { return container[minimum].prio; }
152 /// \brief Returns the priority of \c item.
154 /// This function returns the priority of \c item.
155 /// \pre \c item must be in the heap.
156 PrioType& operator[](const Item& item) {
157 return container[iimap[item]].prio;
160 /// \brief Returns the priority of \c item.
162 /// It returns the priority of \c item.
163 /// \pre \c item must be in the heap.
164 const PrioType& operator[](const Item& item) const {
165 return container[iimap[item]].prio;
169 /// \brief Deletes the item with minimum priority relative to \c Compare.
171 /// This method deletes the item with minimum priority relative to \c
172 /// Compare from the heap.
173 /// \pre The heap must be non-empty.
176 /// \brief Deletes \c item from the heap.
178 /// This method deletes \c item from the heap, if \c item was already
179 /// stored in the heap. It is quite inefficient in Fibonacci heaps.
180 void erase (const Item& item);
182 /// \brief Decreases the priority of \c item to \c value.
184 /// This method decreases the priority of \c item to \c value.
185 /// \pre \c item must be stored in the heap with priority at least \c
186 /// value relative to \c Compare.
187 void decrease (Item item, PrioType const value);
189 /// \brief Increases the priority of \c item to \c value.
191 /// This method sets the priority of \c item to \c value. Though
192 /// there is no precondition on the priority of \c item, this
193 /// method should be used only if it is indeed necessary to increase
194 /// (relative to \c Compare) the priority of \c item, because this
195 /// method is inefficient.
196 void increase (Item item, PrioType const value) {
202 /// \brief Returns if \c item is in, has already been in, or has never
203 /// been in the heap.
205 /// This method returns PRE_HEAP if \c item has never been in the
206 /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
207 /// otherwise. In the latter case it is possible that \c item will
208 /// get back to the heap again.
209 state_enum state(const Item &item) const {
212 if ( container[i].in ) i=0;
215 return state_enum(i);
218 /// \brief Sets the state of the \c item in the heap.
220 /// Sets the state of the \c item in the heap. It can be used to
221 /// manually clear the heap when it is important to achive the
222 /// better time complexity.
223 /// \param i The item.
224 /// \param st The state. It should not be \c IN_HEAP.
225 void state(const Item& i, state_enum st) {
229 if (state(i) == IN_HEAP) {
242 void makeroot(int c);
243 void cut(int a, int b);
245 void fuse(int a, int b);
250 friend class FibHeap;
262 store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
268 // **********************************************************************
270 // **********************************************************************
272 template <typename Prio, typename ItemIntMap,
274 void FibHeap<Prio, ItemIntMap, Compare>::set
275 (Item const item, PrioType const value)
278 if ( i >= 0 && container[i].in ) {
279 if ( comp(value, container[i].prio) ) decrease(item, value);
280 if ( comp(container[i].prio, value) ) increase(item, value);
281 } else push(item, value);
284 template <typename Prio, typename ItemIntMap,
286 void FibHeap<Prio, ItemIntMap, Compare>::push
287 (Item const item, PrioType const value) {
290 int s=container.size();
291 iimap.set( item, s );
294 container.push_back(st);
297 container[i].parent=container[i].child=-1;
298 container[i].degree=0;
299 container[i].in=true;
300 container[i].marked=false;
304 container[container[minimum].right_neighbor].left_neighbor=i;
305 container[i].right_neighbor=container[minimum].right_neighbor;
306 container[minimum].right_neighbor=i;
307 container[i].left_neighbor=minimum;
308 if ( comp( value, container[minimum].prio) ) minimum=i;
310 container[i].right_neighbor=container[i].left_neighbor=i;
313 container[i].prio=value;
317 template <typename Prio, typename ItemIntMap,
319 void FibHeap<Prio, ItemIntMap, Compare>::pop() {
320 /*The first case is that there are only one root.*/
321 if ( container[minimum].left_neighbor==minimum ) {
322 container[minimum].in=false;
323 if ( container[minimum].degree!=0 ) {
324 makeroot(container[minimum].child);
325 minimum=container[minimum].child;
329 int right=container[minimum].right_neighbor;
331 container[minimum].in=false;
332 if ( container[minimum].degree > 0 ) {
333 int left=container[minimum].left_neighbor;
334 int child=container[minimum].child;
335 int last_child=container[child].left_neighbor;
339 container[left].right_neighbor=child;
340 container[child].left_neighbor=left;
341 container[right].left_neighbor=last_child;
342 container[last_child].right_neighbor=right;
346 } // the case where there are more roots
351 template <typename Prio, typename ItemIntMap,
353 void FibHeap<Prio, ItemIntMap, Compare>::erase
357 if ( i >= 0 && container[i].in ) {
358 if ( container[i].parent!=-1 ) {
359 int p=container[i].parent;
363 minimum=i; //As if its prio would be -infinity
368 template <typename Prio, typename ItemIntMap,
370 void FibHeap<Prio, ItemIntMap, Compare>::decrease
371 (Item item, PrioType const value) {
373 container[i].prio=value;
374 int p=container[i].parent;
376 if ( p!=-1 && comp(value, container[p].prio) ) {
380 if ( comp(value, container[minimum].prio) ) minimum=i;
384 template <typename Prio, typename ItemIntMap,
386 void FibHeap<Prio, ItemIntMap, Compare>::balance() {
388 int maxdeg=int( std::floor( 2.08*log(double(container.size()))))+1;
390 std::vector<int> A(maxdeg,-1);
393 *Recall that now minimum does not point to the minimum prio element.
394 *We set minimum to this during balance().
396 int anchor=container[minimum].left_neighbor;
402 if ( anchor==active ) end=true;
403 int d=container[active].degree;
404 next=container[active].right_neighbor;
407 if( comp(container[active].prio, container[A[d]].prio) ) {
420 while ( container[minimum].parent >=0 ) minimum=container[minimum].parent;
424 if ( comp(container[s].prio, container[minimum].prio) ) minimum=s;
425 s=container[s].right_neighbor;
429 template <typename Prio, typename ItemIntMap,
431 void FibHeap<Prio, ItemIntMap, Compare>::makeroot
435 container[s].parent=-1;
436 s=container[s].right_neighbor;
441 template <typename Prio, typename ItemIntMap,
443 void FibHeap<Prio, ItemIntMap, Compare>::cut
446 *Replacing a from the children of b.
448 --container[b].degree;
450 if ( container[b].degree !=0 ) {
451 int child=container[b].child;
453 container[b].child=container[child].right_neighbor;
458 /*Lacing a to the roots.*/
459 int right=container[minimum].right_neighbor;
460 container[minimum].right_neighbor=a;
461 container[a].left_neighbor=minimum;
462 container[a].right_neighbor=right;
463 container[right].left_neighbor=a;
465 container[a].parent=-1;
466 container[a].marked=false;
470 template <typename Prio, typename ItemIntMap,
472 void FibHeap<Prio, ItemIntMap, Compare>::cascade
475 if ( container[a].parent!=-1 ) {
476 int p=container[a].parent;
478 if ( container[a].marked==false ) container[a].marked=true;
487 template <typename Prio, typename ItemIntMap,
489 void FibHeap<Prio, ItemIntMap, Compare>::fuse
493 /*Lacing b under a.*/
494 container[b].parent=a;
496 if (container[a].degree==0) {
497 container[b].left_neighbor=b;
498 container[b].right_neighbor=b;
499 container[a].child=b;
501 int child=container[a].child;
502 int last_child=container[child].left_neighbor;
503 container[child].left_neighbor=b;
504 container[b].right_neighbor=child;
505 container[last_child].right_neighbor=b;
506 container[b].left_neighbor=last_child;
509 ++container[a].degree;
511 container[b].marked=false;
516 *It is invoked only if a has siblings.
518 template <typename Prio, typename ItemIntMap,
520 void FibHeap<Prio, ItemIntMap, Compare>::unlace
522 int leftn=container[a].left_neighbor;
523 int rightn=container[a].right_neighbor;
524 container[leftn].right_neighbor=rightn;
525 container[rightn].left_neighbor=leftn;
531 #endif //LEMON_FIB_HEAP_H