COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/fib_heap.h @ 682:bb8c4cd57900

Last change on this file since 682:bb8c4cd57900 was 681:532697c9fa53, checked in by Balazs Dezso <deba@…>, 11 years ago

Port remaining heaps from SVN -r 3509 (#50)

File size: 13.5 KB
Line 
1/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library.
4 *
5 * Copyright (C) 2003-2009
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
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.
12 *
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
15 * purpose.
16 *
17 */
18
19#ifndef LEMON_FIB_HEAP_H
20#define LEMON_FIB_HEAP_H
21
22///\file
23///\ingroup auxdat
24///\brief Fibonacci Heap implementation.
25
26#include <vector>
27#include <functional>
28#include <lemon/math.h>
29
30namespace lemon {
31
32  /// \ingroup auxdat
33  ///
34  ///\brief Fibonacci Heap.
35  ///
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.
41  ///
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
44  ///\ref BinHeap "binary heap".
45  ///
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>.
51  ///
52  ///\sa BinHeap
53  ///\sa Dijkstra
54#ifdef DOXYGEN
55  template <typename _Prio,
56            typename _ItemIntMap,
57            typename _Compare>
58#else
59  template <typename _Prio,
60            typename _ItemIntMap,
61            typename _Compare = std::less<_Prio> >
62#endif
63  class FibHeap {
64  public:
65    ///\e
66    typedef _ItemIntMap ItemIntMap;
67    ///\e
68    typedef _Prio Prio;
69    ///\e
70    typedef typename ItemIntMap::Key Item;
71    ///\e
72    typedef std::pair<Item,Prio> Pair;
73    ///\e
74    typedef _Compare Compare;
75
76  private:
77    class store;
78
79    std::vector<store> container;
80    int minimum;
81    ItemIntMap &iimap;
82    Compare comp;
83    int num_items;
84
85  public:
86    ///Status of the nodes
87    enum State {
88      ///The node is in the heap
89      IN_HEAP = 0,
90      ///The node has never been in the heap
91      PRE_HEAP = -1,
92      ///The node was in the heap but it got out of it
93      POST_HEAP = -2
94    };
95
96    /// \brief The constructor
97    ///
98    /// \c _iimap should be given to the constructor, since it is
99    ///   used internally to handle the cross references.
100    explicit FibHeap(ItemIntMap &_iimap)
101      : minimum(0), iimap(_iimap), num_items() {}
102
103    /// \brief The constructor
104    ///
105    /// \c _iimap should be given to the constructor, since it is used
106    /// internally to handle the cross references. \c _comp is an
107    /// object for ordering of the priorities.
108    FibHeap(ItemIntMap &_iimap, const Compare &_comp)
109      : minimum(0), iimap(_iimap), comp(_comp), num_items() {}
110
111    /// \brief The number of items stored in the heap.
112    ///
113    /// Returns the number of items stored in the heap.
114    int size() const { return num_items; }
115
116    /// \brief Checks if the heap stores no items.
117    ///
118    ///   Returns \c true if and only if the heap stores no items.
119    bool empty() const { return num_items==0; }
120
121    /// \brief Make empty this heap.
122    ///
123    /// Make empty this heap. It does not change the cross reference
124    /// map.  If you want to reuse a heap what is not surely empty you
125    /// should first clear the heap and after that you should set the
126    /// cross reference map for each item to \c PRE_HEAP.
127    void clear() {
128      container.clear(); minimum = 0; num_items = 0;
129    }
130
131    /// \brief \c item gets to the heap with priority \c value independently
132    /// if \c item was already there.
133    ///
134    /// This method calls \ref push(\c item, \c value) if \c item is not
135    /// stored in the heap and it calls \ref decrease(\c item, \c value) or
136    /// \ref increase(\c item, \c value) otherwise.
137    void set (const Item& item, const Prio& value) {
138      int i=iimap[item];
139      if ( i >= 0 && container[i].in ) {
140        if ( comp(value, container[i].prio) ) decrease(item, value);
141        if ( comp(container[i].prio, value) ) increase(item, value);
142      } else push(item, value);
143    }
144
145    /// \brief Adds \c item to the heap with priority \c value.
146    ///
147    /// Adds \c item to the heap with priority \c value.
148    /// \pre \c item must not be stored in the heap.
149    void push (const Item& item, const Prio& value) {
150      int i=iimap[item];
151      if ( i < 0 ) {
152        int s=container.size();
153        iimap.set( item, s );
154        store st;
155        st.name=item;
156        container.push_back(st);
157        i=s;
158      } else {
159        container[i].parent=container[i].child=-1;
160        container[i].degree=0;
161        container[i].in=true;
162        container[i].marked=false;
163      }
164
165      if ( num_items ) {
166        container[container[minimum].right_neighbor].left_neighbor=i;
167        container[i].right_neighbor=container[minimum].right_neighbor;
168        container[minimum].right_neighbor=i;
169        container[i].left_neighbor=minimum;
170        if ( comp( value, container[minimum].prio) ) minimum=i;
171      } else {
172        container[i].right_neighbor=container[i].left_neighbor=i;
173        minimum=i;
174      }
175      container[i].prio=value;
176      ++num_items;
177    }
178
179    /// \brief Returns the item with minimum priority relative to \c Compare.
180    ///
181    /// This method returns the item with minimum priority relative to \c
182    /// Compare.
183    /// \pre The heap must be nonempty.
184    Item top() const { return container[minimum].name; }
185
186    /// \brief Returns the minimum priority relative to \c Compare.
187    ///
188    /// It returns the minimum priority relative to \c Compare.
189    /// \pre The heap must be nonempty.
190    const Prio& prio() const { return container[minimum].prio; }
191
192    /// \brief Returns the priority of \c item.
193    ///
194    /// It returns the priority of \c item.
195    /// \pre \c item must be in the heap.
196    const Prio& operator[](const Item& item) const {
197      return container[iimap[item]].prio;
198    }
199
200    /// \brief Deletes the item with minimum priority relative to \c Compare.
201    ///
202    /// This method deletes the item with minimum priority relative to \c
203    /// Compare from the heap.
204    /// \pre The heap must be non-empty.
205    void pop() {
206      /*The first case is that there are only one root.*/
207      if ( container[minimum].left_neighbor==minimum ) {
208        container[minimum].in=false;
209        if ( container[minimum].degree!=0 ) {
210          makeroot(container[minimum].child);
211          minimum=container[minimum].child;
212          balance();
213        }
214      } else {
215        int right=container[minimum].right_neighbor;
216        unlace(minimum);
217        container[minimum].in=false;
218        if ( container[minimum].degree > 0 ) {
219          int left=container[minimum].left_neighbor;
220          int child=container[minimum].child;
221          int last_child=container[child].left_neighbor;
222
223          makeroot(child);
224
225          container[left].right_neighbor=child;
226          container[child].left_neighbor=left;
227          container[right].left_neighbor=last_child;
228          container[last_child].right_neighbor=right;
229        }
230        minimum=right;
231        balance();
232      } // the case where there are more roots
233      --num_items;
234    }
235
236    /// \brief Deletes \c item from the heap.
237    ///
238    /// This method deletes \c item from the heap, if \c item was already
239    /// stored in the heap. It is quite inefficient in Fibonacci heaps.
240    void erase (const Item& item) {
241      int i=iimap[item];
242
243      if ( i >= 0 && container[i].in ) {
244        if ( container[i].parent!=-1 ) {
245          int p=container[i].parent;
246          cut(i,p);
247          cascade(p);
248        }
249        minimum=i;     //As if its prio would be -infinity
250        pop();
251      }
252    }
253
254    /// \brief Decreases the priority of \c item to \c value.
255    ///
256    /// This method decreases the priority of \c item to \c value.
257    /// \pre \c item must be stored in the heap with priority at least \c
258    ///   value relative to \c Compare.
259    void decrease (Item item, const Prio& value) {
260      int i=iimap[item];
261      container[i].prio=value;
262      int p=container[i].parent;
263
264      if ( p!=-1 && comp(value, container[p].prio) ) {
265        cut(i,p);
266        cascade(p);
267      }
268      if ( comp(value, container[minimum].prio) ) minimum=i;
269    }
270
271    /// \brief Increases the priority of \c item to \c value.
272    ///
273    /// This method sets the priority of \c item to \c value. Though
274    /// there is no precondition on the priority of \c item, this
275    /// method should be used only if it is indeed necessary to increase
276    /// (relative to \c Compare) the priority of \c item, because this
277    /// method is inefficient.
278    void increase (Item item, const Prio& value) {
279      erase(item);
280      push(item, value);
281    }
282
283
284    /// \brief Returns if \c item is in, has already been in, or has never
285    /// been in the heap.
286    ///
287    /// This method returns PRE_HEAP if \c item has never been in the
288    /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
289    /// otherwise. In the latter case it is possible that \c item will
290    /// get back to the heap again.
291    State state(const Item &item) const {
292      int i=iimap[item];
293      if( i>=0 ) {
294        if ( container[i].in ) i=0;
295        else i=-2;
296      }
297      return State(i);
298    }
299
300    /// \brief Sets the state of the \c item in the heap.
301    ///
302    /// Sets the state of the \c item in the heap. It can be used to
303    /// manually clear the heap when it is important to achive the
304    /// better time complexity.
305    /// \param i The item.
306    /// \param st The state. It should not be \c IN_HEAP.
307    void state(const Item& i, State st) {
308      switch (st) {
309      case POST_HEAP:
310      case PRE_HEAP:
311        if (state(i) == IN_HEAP) {
312          erase(i);
313        }
314        iimap[i] = st;
315        break;
316      case IN_HEAP:
317        break;
318      }
319    }
320
321  private:
322
323    void balance() {
324
325      int maxdeg=int( std::floor( 2.08*log(double(container.size()))))+1;
326
327      std::vector<int> A(maxdeg,-1);
328
329      /*
330       *Recall that now minimum does not point to the minimum prio element.
331       *We set minimum to this during balance().
332       */
333      int anchor=container[minimum].left_neighbor;
334      int next=minimum;
335      bool end=false;
336
337      do {
338        int active=next;
339        if ( anchor==active ) end=true;
340        int d=container[active].degree;
341        next=container[active].right_neighbor;
342
343        while (A[d]!=-1) {
344          if( comp(container[active].prio, container[A[d]].prio) ) {
345            fuse(active,A[d]);
346          } else {
347            fuse(A[d],active);
348            active=A[d];
349          }
350          A[d]=-1;
351          ++d;
352        }
353        A[d]=active;
354      } while ( !end );
355
356
357      while ( container[minimum].parent >=0 )
358        minimum=container[minimum].parent;
359      int s=minimum;
360      int m=minimum;
361      do {
362        if ( comp(container[s].prio, container[minimum].prio) ) minimum=s;
363        s=container[s].right_neighbor;
364      } while ( s != m );
365    }
366
367    void makeroot(int c) {
368      int s=c;
369      do {
370        container[s].parent=-1;
371        s=container[s].right_neighbor;
372      } while ( s != c );
373    }
374
375    void cut(int a, int b) {
376      /*
377       *Replacing a from the children of b.
378       */
379      --container[b].degree;
380
381      if ( container[b].degree !=0 ) {
382        int child=container[b].child;
383        if ( child==a )
384          container[b].child=container[child].right_neighbor;
385        unlace(a);
386      }
387
388
389      /*Lacing a to the roots.*/
390      int right=container[minimum].right_neighbor;
391      container[minimum].right_neighbor=a;
392      container[a].left_neighbor=minimum;
393      container[a].right_neighbor=right;
394      container[right].left_neighbor=a;
395
396      container[a].parent=-1;
397      container[a].marked=false;
398    }
399
400    void cascade(int a) {
401      if ( container[a].parent!=-1 ) {
402        int p=container[a].parent;
403
404        if ( container[a].marked==false ) container[a].marked=true;
405        else {
406          cut(a,p);
407          cascade(p);
408        }
409      }
410    }
411
412    void fuse(int a, int b) {
413      unlace(b);
414
415      /*Lacing b under a.*/
416      container[b].parent=a;
417
418      if (container[a].degree==0) {
419        container[b].left_neighbor=b;
420        container[b].right_neighbor=b;
421        container[a].child=b;
422      } else {
423        int child=container[a].child;
424        int last_child=container[child].left_neighbor;
425        container[child].left_neighbor=b;
426        container[b].right_neighbor=child;
427        container[last_child].right_neighbor=b;
428        container[b].left_neighbor=last_child;
429      }
430
431      ++container[a].degree;
432
433      container[b].marked=false;
434    }
435
436    /*
437     *It is invoked only if a has siblings.
438     */
439    void unlace(int a) {
440      int leftn=container[a].left_neighbor;
441      int rightn=container[a].right_neighbor;
442      container[leftn].right_neighbor=rightn;
443      container[rightn].left_neighbor=leftn;
444    }
445
446
447    class store {
448      friend class FibHeap;
449
450      Item name;
451      int parent;
452      int left_neighbor;
453      int right_neighbor;
454      int child;
455      int degree;
456      bool marked;
457      bool in;
458      Prio prio;
459
460      store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
461    };
462  };
463
464} //namespace lemon
465
466#endif //LEMON_FIB_HEAP_H
467
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