COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/fib_heap.h @ 1906:7fa90b66ca9e

Last change on this file since 1906:7fa90b66ca9e was 1906:7fa90b66ca9e, checked in by Balazs Dezso, 14 years ago

Omitting warnings

File size: 15.0 KB
Line 
1/* -*- C++ -*-
2 * lemon/fib_heap.h - Part of LEMON, a generic C++ optimization library
3 *
4 * Copyright (C) 2006 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  /// \ingroup auxdat
31
32  /// Fibonacci Heap.
33
34  ///This class implements the \e Fibonacci \e heap data structure. A \e heap
35  ///is a data structure for storing items with specified values called \e
36  ///priorities in such a way that finding the item with minimum priority is
37  ///efficient. \c Compare specifies the ordering of the priorities. In a heap
38  ///one can change the priority of an item, add or erase an item, etc.
39  ///
40  ///The methods \ref increase and \ref erase are not efficient in a Fibonacci
41  ///heap. In case of many calls to these operations, it is better to use a
42  ///\e binary \e heap.
43  ///
44  ///\param Item Type of the items to be stored. 
45  ///\param Prio Type of the priority of the items.
46  ///\param ItemIntMap A read and writable Item int map, used internally
47  ///to handle the cross references.
48  ///\param Compare A class for the ordering of the priorities. The
49  ///default is \c std::less<Prio>.
50  ///
51  ///\sa BinHeap
52  ///\sa Dijkstra
53  ///\author Jacint Szabo
54 
55#ifdef DOXYGEN
56  template <typename Item,
57            typename Prio,
58            typename ItemIntMap,
59            typename Compare>
60#else
61  template <typename Item,
62            typename Prio,
63            typename ItemIntMap,
64            typename Compare = std::less<Prio> >
65#endif
66  class FibHeap {
67  public:     
68    typedef Prio PrioType;
69   
70  private:
71    class store;
72   
73    std::vector<store> container;
74    int minimum;
75    ItemIntMap &iimap;
76    Compare comp;
77    int num_items;
78   
79  public:
80    ///Status of the nodes
81    enum state_enum {
82      ///The node is in the heap
83      IN_HEAP = 0,
84      ///The node has never been in the heap
85      PRE_HEAP = -1,
86      ///The node was in the heap but it got out of it
87      POST_HEAP = -2
88    };
89   
90    /// \brief The constructor
91    ///
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() {}
96 
97    /// \brief The constructor
98    ///
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() {}
104   
105    /// \brief The number of items stored in the heap.
106    ///
107    /// Returns the number of items stored in the heap.
108    int size() const { return num_items; }
109
110    /// \brief Checks if the heap stores no items.
111    ///
112    ///   Returns \c true if and only if the heap stores no items.
113    bool empty() const { return num_items==0; }
114
115    /// \brief Make empty this heap.
116    ///
117    /// Make empty this heap.
118    void clear() {
119      if (num_items != 0) {
120        for (int i = 0; i < (int)container.size(); ++i) {
121          iimap[container[i].name] = -2;
122        }
123      }
124      container.clear(); minimum = 0; num_items = 0;
125    }
126
127    /// \brief \c item gets to the heap with priority \c value independently
128    /// if \c item was already there.
129    ///
130    /// This method calls \ref push(\c item, \c value) if \c item is not
131    /// stored in the heap and it calls \ref decrease(\c item, \c value) or
132    /// \ref increase(\c item, \c value) otherwise.
133    void set (Item const item, PrioType const value);
134   
135    /// \brief Adds \c item to the heap with priority \c value.
136    ///   
137    /// Adds \c item to the heap with priority \c value.
138    /// \pre \c item must not be stored in the heap.
139    void push (Item const item, PrioType const value);
140   
141    /// \brief Returns the item with minimum priority relative to \c Compare.
142    ///
143    /// This method returns the item with minimum priority relative to \c
144    /// Compare. 
145    /// \pre The heap must be nonempty. 
146    Item top() const { return container[minimum].name; }
147
148    /// \brief Returns the minimum priority relative to \c Compare.
149    ///
150    /// It returns the minimum priority relative to \c Compare.
151    /// \pre The heap must be nonempty.
152    PrioType prio() const { return container[minimum].prio; }
153   
154    /// \brief Returns the priority of \c item.
155    ///
156    /// This function returns the priority of \c item.
157    /// \pre \c item must be in the heap.
158    PrioType& operator[](const Item& item) {
159      return container[iimap[item]].prio;
160    }
161   
162    /// \brief Returns the priority of \c item.
163    ///
164    /// It returns the priority of \c item.
165    /// \pre \c item must be in the heap.
166    const PrioType& operator[](const Item& item) const {
167      return container[iimap[item]].prio;
168    }
169
170
171    /// \brief Deletes the item with minimum priority relative to \c Compare.
172    ///
173    /// This method deletes the item with minimum priority relative to \c
174    /// Compare from the heap. 
175    /// \pre The heap must be non-empty. 
176    void pop();
177
178    /// \brief Deletes \c item from the heap.
179    ///
180    /// This method deletes \c item from the heap, if \c item was already
181    /// stored in the heap. It is quite inefficient in Fibonacci heaps.
182    void erase (const Item& item);
183
184    /// \brief Decreases the priority of \c item to \c value.
185    ///
186    /// This method decreases the priority of \c item to \c value.
187    /// \pre \c item must be stored in the heap with priority at least \c
188    ///   value relative to \c Compare.
189    void decrease (Item item, PrioType const value);
190
191    /// \brief Increases the priority of \c item to \c value.
192    ///
193    /// This method sets the priority of \c item to \c value. Though
194    /// there is no precondition on the priority of \c item, this
195    /// method should be used only if it is indeed necessary to increase
196    /// (relative to \c Compare) the priority of \c item, because this
197    /// method is inefficient.
198    void increase (Item item, PrioType const value) {
199      erase(item);
200      push(item, value);
201    }
202
203
204    /// \brief Returns if \c item is in, has already been in, or has never
205    /// been in the heap.
206    ///
207    /// This method returns PRE_HEAP if \c item has never been in the
208    /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
209    /// otherwise. In the latter case it is possible that \c item will
210    /// get back to the heap again.
211    state_enum state(const Item &item) const {
212      int i=iimap[item];
213      if( i>=0 ) {
214        if ( container[i].in ) i=0;
215        else i=-2;
216      }
217      return state_enum(i);
218    }   
219
220    /// \brief Sets the state of the \c item in the heap.
221    ///
222    /// Sets the state of the \c item in the heap. It can be used to
223    /// manually clear the heap when it is important to achive the
224    /// better time complexity.
225    /// \param i The item.
226    /// \param st The state. It should not be \c IN_HEAP.
227    void state(const Item& i, state_enum st) {
228      switch (st) {
229      case POST_HEAP:
230      case PRE_HEAP:
231        if (state(i) == IN_HEAP) {
232          erase(i);
233        }
234        iimap[i] = st;
235        break;
236      case IN_HEAP:
237        break;
238      }
239    }
240   
241  private:
242   
243    void balance();
244    void makeroot(int c);
245    void cut(int a, int b);
246    void cascade(int a);
247    void fuse(int a, int b);
248    void unlace(int a);
249
250
251    class store {
252      friend class FibHeap;
253     
254      Item name;
255      int parent;
256      int left_neighbor;
257      int right_neighbor;
258      int child;
259      int degree; 
260      bool marked;
261      bool in;
262      PrioType prio;
263     
264      store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
265    };
266  };   
267 
268
269
270    // **********************************************************************
271    //  IMPLEMENTATIONS
272    // **********************************************************************
273   
274  template <typename Item, typename Prio, typename ItemIntMap,
275    typename Compare>
276  void FibHeap<Item, Prio, ItemIntMap, Compare>::set
277  (Item const item, PrioType const value)
278  {
279    int i=iimap[item];
280    if ( i >= 0 && container[i].in ) {
281      if ( comp(value, container[i].prio) ) decrease(item, value);
282      if ( comp(container[i].prio, value) ) increase(item, value);
283    } else push(item, value);
284  }
285   
286  template <typename Item, typename Prio, typename ItemIntMap,
287    typename Compare>
288  void FibHeap<Item, Prio, ItemIntMap, Compare>::push
289  (Item const item, PrioType const value) {
290      int i=iimap[item];     
291      if ( i < 0 ) {
292        int s=container.size();
293        iimap.set( item, s );   
294        store st;
295        st.name=item;
296        container.push_back(st);
297        i=s;
298      } else {
299        container[i].parent=container[i].child=-1;
300        container[i].degree=0;
301        container[i].in=true;
302        container[i].marked=false;
303      }
304
305      if ( num_items ) {
306        container[container[minimum].right_neighbor].left_neighbor=i;
307        container[i].right_neighbor=container[minimum].right_neighbor;
308        container[minimum].right_neighbor=i;
309        container[i].left_neighbor=minimum;
310        if ( comp( value, container[minimum].prio) ) minimum=i;
311      } else {
312        container[i].right_neighbor=container[i].left_neighbor=i;
313        minimum=i;     
314      }
315      container[i].prio=value;
316      ++num_items;
317    }
318   
319  template <typename Item, typename Prio, typename ItemIntMap,
320    typename Compare>
321  void FibHeap<Item, Prio, ItemIntMap, Compare>::pop() {
322      /*The first case is that there are only one root.*/
323      if ( container[minimum].left_neighbor==minimum ) {
324        container[minimum].in=false;
325        if ( container[minimum].degree!=0 ) {
326          makeroot(container[minimum].child);
327          minimum=container[minimum].child;
328          balance();
329        }
330      } else {
331        int right=container[minimum].right_neighbor;
332        unlace(minimum);
333        container[minimum].in=false;
334        if ( container[minimum].degree > 0 ) {
335          int left=container[minimum].left_neighbor;
336          int child=container[minimum].child;
337          int last_child=container[child].left_neighbor;
338       
339          makeroot(child);
340         
341          container[left].right_neighbor=child;
342          container[child].left_neighbor=left;
343          container[right].left_neighbor=last_child;
344          container[last_child].right_neighbor=right;
345        }
346        minimum=right;
347        balance();
348      } // the case where there are more roots
349      --num_items;   
350    }
351
352
353  template <typename Item, typename Prio, typename ItemIntMap,
354    typename Compare>
355  void FibHeap<Item, Prio, ItemIntMap, Compare>::erase
356  (const Item& item) {
357      int i=iimap[item];
358     
359      if ( i >= 0 && container[i].in ) {       
360        if ( container[i].parent!=-1 ) {
361          int p=container[i].parent;
362          cut(i,p);         
363          cascade(p);
364        }
365        minimum=i;     //As if its prio would be -infinity
366        pop();
367      }
368  }
369   
370  template <typename Item, typename Prio, typename ItemIntMap,
371    typename Compare>
372  void FibHeap<Item, Prio, ItemIntMap, Compare>::decrease
373  (Item item, PrioType const value) {
374      int i=iimap[item];
375      container[i].prio=value;
376      int p=container[i].parent;
377     
378      if ( p!=-1 && comp(value, container[p].prio) ) {
379        cut(i,p);           
380        cascade(p);
381      }     
382      if ( comp(value, container[minimum].prio) ) minimum=i;
383  }
384 
385
386  template <typename Item, typename Prio, typename ItemIntMap,
387    typename Compare>
388  void FibHeap<Item, Prio, ItemIntMap, Compare>::balance() {     
389
390    int maxdeg=int( std::floor( 2.08*log(double(container.size()))))+1;
391 
392    std::vector<int> A(maxdeg,-1);
393   
394    /*
395     *Recall that now minimum does not point to the minimum prio element.
396     *We set minimum to this during balance().
397     */
398    int anchor=container[minimum].left_neighbor;
399    int next=minimum;
400    bool end=false;
401       
402       do {
403        int active=next;
404        if ( anchor==active ) end=true;
405        int d=container[active].degree;
406        next=container[active].right_neighbor;
407
408        while (A[d]!=-1) {       
409          if( comp(container[active].prio, container[A[d]].prio) ) {
410            fuse(active,A[d]);
411          } else {
412            fuse(A[d],active);
413            active=A[d];
414          }
415          A[d]=-1;
416          ++d;
417        }       
418        A[d]=active;
419       } while ( !end );
420
421
422       while ( container[minimum].parent >=0 ) minimum=container[minimum].parent;
423       int s=minimum;
424       int m=minimum;
425       do { 
426         if ( comp(container[s].prio, container[minimum].prio) ) minimum=s;
427         s=container[s].right_neighbor;
428       } while ( s != m );
429    }
430
431  template <typename Item, typename Prio, typename ItemIntMap,
432    typename Compare>
433  void FibHeap<Item, Prio, ItemIntMap, Compare>::makeroot
434  (int c) {
435      int s=c;
436      do { 
437        container[s].parent=-1;
438        s=container[s].right_neighbor;
439      } while ( s != c );
440    }
441 
442 
443  template <typename Item, typename Prio, typename ItemIntMap,
444    typename Compare>
445  void FibHeap<Item, Prio, ItemIntMap, Compare>::cut
446  (int a, int b) {   
447    /*
448     *Replacing a from the children of b.
449     */
450    --container[b].degree;
451   
452    if ( container[b].degree !=0 ) {
453      int child=container[b].child;
454      if ( child==a )
455        container[b].child=container[child].right_neighbor;
456      unlace(a);
457    }
458   
459   
460    /*Lacing a to the roots.*/
461    int right=container[minimum].right_neighbor;
462    container[minimum].right_neighbor=a;
463    container[a].left_neighbor=minimum;
464    container[a].right_neighbor=right;
465    container[right].left_neighbor=a;
466   
467    container[a].parent=-1;
468    container[a].marked=false;
469  }
470 
471
472  template <typename Item, typename Prio, typename ItemIntMap,
473    typename Compare>
474  void FibHeap<Item, Prio, ItemIntMap, Compare>::cascade
475  (int a)
476    {
477      if ( container[a].parent!=-1 ) {
478        int p=container[a].parent;
479       
480        if ( container[a].marked==false ) container[a].marked=true;
481        else {
482          cut(a,p);
483          cascade(p);
484        }
485      }
486    }
487
488
489  template <typename Item, typename Prio, typename ItemIntMap,
490    typename Compare>
491  void FibHeap<Item, Prio, ItemIntMap, Compare>::fuse
492  (int a, int b) {
493      unlace(b);
494     
495      /*Lacing b under a.*/
496      container[b].parent=a;
497
498      if (container[a].degree==0) {
499        container[b].left_neighbor=b;
500        container[b].right_neighbor=b;
501        container[a].child=b;   
502      } else {
503        int child=container[a].child;
504        int last_child=container[child].left_neighbor;
505        container[child].left_neighbor=b;
506        container[b].right_neighbor=child;
507        container[last_child].right_neighbor=b;
508        container[b].left_neighbor=last_child;
509      }
510
511      ++container[a].degree;
512     
513      container[b].marked=false;
514    }
515
516 
517  /*
518   *It is invoked only if a has siblings.
519   */
520  template <typename Item, typename Prio, typename ItemIntMap,
521    typename Compare>
522  void FibHeap<Item, Prio, ItemIntMap, Compare>::unlace
523  (int a) {     
524      int leftn=container[a].left_neighbor;
525      int rightn=container[a].right_neighbor;
526      container[leftn].right_neighbor=rightn;
527      container[rightn].left_neighbor=leftn;
528  }
529 
530
531} //namespace lemon
532
533#endif //LEMON_FIB_HEAP_H
534
Note: See TracBrowser for help on using the repository browser.