COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/fib_heap.h @ 1753:98d83dd56c1d

Last change on this file since 1753:98d83dd56c1d was 1753:98d83dd56c1d, checked in by Balazs Dezso, 14 years ago

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1/* -*- C++ -*-
2 * lemon/fib_heap.h - Part of LEMON, a generic C++ optimization library
3 *
4 * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5 * (Egervary Research Group on Combinatorial Optimization, EGRES).
6 *
7 * Permission to use, modify and distribute this software is granted
8 * provided that this copyright notice appears in all copies. For
9 * precise terms see the accompanying LICENSE file.
10 *
11 * This software is provided "AS IS" with no warranty of any kind,
12 * express or implied, and with no claim as to its suitability for any
13 * purpose.
14 *
15 */
16
17#ifndef LEMON_FIB_HEAP_H
18#define LEMON_FIB_HEAP_H
19
20///\file
21///\ingroup auxdat
22///\brief Fibonacci Heap implementation.
23
24#include <vector>
25#include <functional>
26#include <cmath>
27
28namespace lemon {
29 
30  /// \addtogroup auxdat
31  /// @{
32
33  /// Fibonacci Heap.
34
35  ///This class implements the \e Fibonacci \e heap data structure. A \e heap
36  ///is a data structure for storing items with specified values called \e
37  ///priorities in such a way that finding the item with minimum priority is
38  ///efficient. \c Compare specifies the ordering of the priorities. In a heap
39  ///one can change the priority of an item, add or erase an item, etc.
40  ///
41  ///The methods \ref increase and \ref erase are not efficient in a Fibonacci
42  ///heap. In case of many calls to these operations, it is better to use a
43  ///\e binary \e heap.
44  ///
45  ///\param Item Type of the items to be stored. 
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  ///\author Jacint Szabo
55 
56#ifdef DOXYGEN
57  template <typename Item,
58            typename Prio,
59            typename ItemIntMap,
60            typename Compare>
61#else
62  template <typename Item,
63            typename Prio,
64            typename ItemIntMap,
65            typename Compare = std::less<Prio> >
66#endif
67  class FibHeap {
68  public:     
69    typedef Prio PrioType;
70   
71  private:
72    class store;
73   
74    std::vector<store> container;
75    int minimum;
76    ItemIntMap &iimap;
77    Compare comp;
78    int num_items;
79   
80  public:
81    ///Status of the nodes
82    enum state_enum {
83      ///The node is in the heap
84      IN_HEAP = 0,
85      ///The node has never been in the heap
86      PRE_HEAP = -1,
87      ///The node was in the heap but it got out of it
88      POST_HEAP = -2
89    };
90   
91    /// \brief The constructor
92    ///
93    /// \c _iimap should be given to the constructor, since it is
94    ///   used internally to handle the cross references.
95    explicit FibHeap(ItemIntMap &_iimap)
96      : minimum(0), iimap(_iimap), num_items() {}
97 
98    /// \brief The constructor
99    ///
100    /// \c _iimap should be given to the constructor, since it is used
101    /// internally to handle the cross references. \c _comp is an
102    /// object for ordering of the priorities.
103    FibHeap(ItemIntMap &_iimap, const Compare &_comp) : minimum(0),
104                  iimap(_iimap), comp(_comp), num_items() {}
105   
106    /// \brief The number of items stored in the heap.
107    ///
108    /// Returns the number of items stored in the heap.
109    int size() const { return num_items; }
110
111    /// \brief Checks if the heap stores no items.
112    ///
113    ///   Returns \c true if and only if the heap stores no items.
114    bool empty() const { return num_items==0; }
115
116    /// \brief Make empty this heap.
117    ///
118    /// Make empty this heap.
119    void clear() {
120      if (num_items != 0) {
121        for (int i = 0; i < (int)container.size(); ++i) {
122          iimap[container[i].name] = -2;
123        }
124      }
125      container.clear(); minimum = 0; num_items = 0;
126    }
127
128    /// \brief \c item gets to the heap with priority \c value independently
129    /// if \c item was already there.
130    ///
131    /// This method calls \ref push(\c item, \c value) if \c item is not
132    /// stored in the heap and it calls \ref decrease(\c item, \c value) or
133    /// \ref increase(\c item, \c value) otherwise.
134    void set (Item const item, PrioType const value);
135   
136    /// \brief Adds \c item to the heap with priority \c value.
137    ///   
138    /// Adds \c item to the heap with priority \c value.
139    /// \pre \c item must not be stored in the heap.
140    void push (Item const item, PrioType const value);
141   
142    /// \brief Returns the item with minimum priority relative to \c Compare.
143    ///
144    /// This method returns the item with minimum priority relative to \c
145    /// Compare. 
146    /// \pre The heap must be nonempty. 
147    Item top() const { return container[minimum].name; }
148
149    /// \brief Returns the minimum priority relative to \c Compare.
150    ///
151    /// It returns the minimum priority relative to \c Compare.
152    /// \pre The heap must be nonempty.
153    PrioType prio() const { return container[minimum].prio; }
154   
155    /// \brief Returns the priority of \c item.
156    ///
157    /// This function returns the priority of \c item.
158    /// \pre \c item must be in the heap.
159    PrioType& operator[](const Item& item) {
160      return container[iimap[item]].prio;
161    }
162   
163    /// \brief Returns the priority of \c item.
164    ///
165    /// It returns the priority of \c item.
166    /// \pre \c item must be in the heap.
167    const PrioType& operator[](const Item& item) const {
168      return container[iimap[item]].prio;
169    }
170
171
172    /// \brief Deletes the item with minimum priority relative to \c Compare.
173    ///
174    /// This method deletes the item with minimum priority relative to \c
175    /// Compare from the heap. 
176    /// \pre The heap must be non-empty. 
177    void pop();
178
179    /// \brief Deletes \c item from the heap.
180    ///
181    /// This method deletes \c item from the heap, if \c item was already
182    /// stored in the heap. It is quite inefficient in Fibonacci heaps.
183    void erase (const Item& item);
184
185    /// \brief Decreases the priority of \c item to \c value.
186    ///
187    /// This method decreases the priority of \c item to \c value.
188    /// \pre \c item must be stored in the heap with priority at least \c
189    ///   value relative to \c Compare.
190    void decrease (Item item, PrioType const value);
191
192    /// \brief Increases the priority of \c item to \c value.
193    ///
194    /// This method sets the priority of \c item to \c value. Though
195    /// there is no precondition on the priority of \c item, this
196    /// method should be used only if it is indeed necessary to increase
197    /// (relative to \c Compare) the priority of \c item, because this
198    /// method is inefficient.
199    void increase (Item item, PrioType const value) {
200      erase(item);
201      push(item, value);
202    }
203
204
205    /// \brief Returns if \c item is in, has already been in, or has never
206    /// been in the heap.
207    ///
208    /// This method returns PRE_HEAP if \c item has never been in the
209    /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
210    /// otherwise. In the latter case it is possible that \c item will
211    /// get back to the heap again.
212    state_enum state(const Item &item) const {
213      int i=iimap[item];
214      if( i>=0 ) {
215        if ( container[i].in ) i=0;
216        else i=-2;
217      }
218      return state_enum(i);
219    }   
220   
221  private:
222   
223    void balance();
224    void makeroot(int c);
225    void cut(int a, int b);
226    void cascade(int a);
227    void fuse(int a, int b);
228    void unlace(int a);
229
230
231    class store {
232      friend class FibHeap;
233     
234      Item name;
235      int parent;
236      int left_neighbor;
237      int right_neighbor;
238      int child;
239      int degree; 
240      bool marked;
241      bool in;
242      PrioType prio;
243     
244      store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
245    };
246  };   
247 
248
249
250    // **********************************************************************
251    //  IMPLEMENTATIONS
252    // **********************************************************************
253   
254  template <typename Item, typename Prio, typename ItemIntMap,
255    typename Compare>
256  void FibHeap<Item, Prio, ItemIntMap, Compare>::set
257  (Item const item, PrioType const value)
258  {
259    int i=iimap[item];
260    if ( i >= 0 && container[i].in ) {
261      if ( comp(value, container[i].prio) ) decrease(item, value);
262      if ( comp(container[i].prio, value) ) increase(item, value);
263    } else push(item, value);
264  }
265   
266  template <typename Item, typename Prio, typename ItemIntMap,
267    typename Compare>
268  void FibHeap<Item, Prio, ItemIntMap, Compare>::push
269  (Item const item, PrioType const value) {
270      int i=iimap[item];     
271      if ( i < 0 ) {
272        int s=container.size();
273        iimap.set( item, s );   
274        store st;
275        st.name=item;
276        container.push_back(st);
277        i=s;
278      } else {
279        container[i].parent=container[i].child=-1;
280        container[i].degree=0;
281        container[i].in=true;
282        container[i].marked=false;
283      }
284
285      if ( num_items ) {
286        container[container[minimum].right_neighbor].left_neighbor=i;
287        container[i].right_neighbor=container[minimum].right_neighbor;
288        container[minimum].right_neighbor=i;
289        container[i].left_neighbor=minimum;
290        if ( comp( value, container[minimum].prio) ) minimum=i;
291      } else {
292        container[i].right_neighbor=container[i].left_neighbor=i;
293        minimum=i;     
294      }
295      container[i].prio=value;
296      ++num_items;
297    }
298   
299  template <typename Item, typename Prio, typename ItemIntMap,
300    typename Compare>
301  void FibHeap<Item, Prio, ItemIntMap, Compare>::pop() {
302      /*The first case is that there are only one root.*/
303      if ( container[minimum].left_neighbor==minimum ) {
304        container[minimum].in=false;
305        if ( container[minimum].degree!=0 ) {
306          makeroot(container[minimum].child);
307          minimum=container[minimum].child;
308          balance();
309        }
310      } else {
311        int right=container[minimum].right_neighbor;
312        unlace(minimum);
313        container[minimum].in=false;
314        if ( container[minimum].degree > 0 ) {
315          int left=container[minimum].left_neighbor;
316          int child=container[minimum].child;
317          int last_child=container[child].left_neighbor;
318       
319          makeroot(child);
320         
321          container[left].right_neighbor=child;
322          container[child].left_neighbor=left;
323          container[right].left_neighbor=last_child;
324          container[last_child].right_neighbor=right;
325        }
326        minimum=right;
327        balance();
328      } // the case where there are more roots
329      --num_items;   
330    }
331
332
333  template <typename Item, typename Prio, typename ItemIntMap,
334    typename Compare>
335  void FibHeap<Item, Prio, ItemIntMap, Compare>::erase
336  (const Item& item) {
337      int i=iimap[item];
338     
339      if ( i >= 0 && container[i].in ) {       
340        if ( container[i].parent!=-1 ) {
341          int p=container[i].parent;
342          cut(i,p);         
343          cascade(p);
344        }
345        minimum=i;     //As if its prio would be -infinity
346        pop();
347      }
348  }
349   
350  template <typename Item, typename Prio, typename ItemIntMap,
351    typename Compare>
352  void FibHeap<Item, Prio, ItemIntMap, Compare>::decrease
353  (Item item, PrioType const value) {
354      int i=iimap[item];
355      container[i].prio=value;
356      int p=container[i].parent;
357     
358      if ( p!=-1 && comp(value, container[p].prio) ) {
359        cut(i,p);           
360        cascade(p);
361      }     
362      if ( comp(value, container[minimum].prio) ) minimum=i;
363  }
364 
365
366  template <typename Item, typename Prio, typename ItemIntMap,
367    typename Compare>
368  void FibHeap<Item, Prio, ItemIntMap, Compare>::balance() {     
369
370    int maxdeg=int( std::floor( 2.08*log(double(container.size()))))+1;
371 
372    std::vector<int> A(maxdeg,-1);
373   
374    /*
375     *Recall that now minimum does not point to the minimum prio element.
376     *We set minimum to this during balance().
377     */
378    int anchor=container[minimum].left_neighbor;
379    int next=minimum;
380    bool end=false;
381       
382       do {
383        int active=next;
384        if ( anchor==active ) end=true;
385        int d=container[active].degree;
386        next=container[active].right_neighbor;
387
388        while (A[d]!=-1) {       
389          if( comp(container[active].prio, container[A[d]].prio) ) {
390            fuse(active,A[d]);
391          } else {
392            fuse(A[d],active);
393            active=A[d];
394          }
395          A[d]=-1;
396          ++d;
397        }       
398        A[d]=active;
399       } while ( !end );
400
401
402       while ( container[minimum].parent >=0 ) minimum=container[minimum].parent;
403       int s=minimum;
404       int m=minimum;
405       do { 
406         if ( comp(container[s].prio, container[minimum].prio) ) minimum=s;
407         s=container[s].right_neighbor;
408       } while ( s != m );
409    }
410
411  template <typename Item, typename Prio, typename ItemIntMap,
412    typename Compare>
413  void FibHeap<Item, Prio, ItemIntMap, Compare>::makeroot
414  (int c) {
415      int s=c;
416      do { 
417        container[s].parent=-1;
418        s=container[s].right_neighbor;
419      } while ( s != c );
420    }
421 
422 
423  template <typename Item, typename Prio, typename ItemIntMap,
424    typename Compare>
425  void FibHeap<Item, Prio, ItemIntMap, Compare>::cut
426  (int a, int b) {   
427    /*
428     *Replacing a from the children of b.
429     */
430    --container[b].degree;
431   
432    if ( container[b].degree !=0 ) {
433      int child=container[b].child;
434      if ( child==a )
435        container[b].child=container[child].right_neighbor;
436      unlace(a);
437    }
438   
439   
440    /*Lacing a to the roots.*/
441    int right=container[minimum].right_neighbor;
442    container[minimum].right_neighbor=a;
443    container[a].left_neighbor=minimum;
444    container[a].right_neighbor=right;
445    container[right].left_neighbor=a;
446   
447    container[a].parent=-1;
448    container[a].marked=false;
449  }
450 
451
452  template <typename Item, typename Prio, typename ItemIntMap,
453    typename Compare>
454  void FibHeap<Item, Prio, ItemIntMap, Compare>::cascade
455  (int a)
456    {
457      if ( container[a].parent!=-1 ) {
458        int p=container[a].parent;
459       
460        if ( container[a].marked==false ) container[a].marked=true;
461        else {
462          cut(a,p);
463          cascade(p);
464        }
465      }
466    }
467
468
469  template <typename Item, typename Prio, typename ItemIntMap,
470    typename Compare>
471  void FibHeap<Item, Prio, ItemIntMap, Compare>::fuse
472  (int a, int b) {
473      unlace(b);
474     
475      /*Lacing b under a.*/
476      container[b].parent=a;
477
478      if (container[a].degree==0) {
479        container[b].left_neighbor=b;
480        container[b].right_neighbor=b;
481        container[a].child=b;   
482      } else {
483        int child=container[a].child;
484        int last_child=container[child].left_neighbor;
485        container[child].left_neighbor=b;
486        container[b].right_neighbor=child;
487        container[last_child].right_neighbor=b;
488        container[b].left_neighbor=last_child;
489      }
490
491      ++container[a].degree;
492     
493      container[b].marked=false;
494    }
495
496 
497  /*
498   *It is invoked only if a has siblings.
499   */
500  template <typename Item, typename Prio, typename ItemIntMap,
501    typename Compare>
502  void FibHeap<Item, Prio, ItemIntMap, Compare>::unlace
503  (int a) {     
504      int leftn=container[a].left_neighbor;
505      int rightn=container[a].right_neighbor;
506      container[leftn].right_neighbor=rightn;
507      container[rightn].left_neighbor=leftn;
508  }
509 
510  ///@}
511
512} //namespace lemon
513
514#endif //LEMON_FIB_HEAP_H
515
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