COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/fib_heap.h @ 1717:75fe24093ded

Last change on this file since 1717:75fe24093ded was 1717:75fe24093ded, checked in by Balazs Dezso, 14 years ago

Added clear function to heaps and concept

File size: 14.5 KB
Line 
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      for (int i = 0; i < (int)container.size(); ++i) {
121        iimap[container[i].name] = -2;
122      }
123      container.clear(); minimum = 0; num_items = 0;
124    }
125
126    /// \brief \c item gets to the heap with priority \c value independently
127    /// if \c item was already there.
128    ///
129    /// This method calls \ref push(\c item, \c value) if \c item is not
130    /// stored in the heap and it calls \ref decrease(\c item, \c value) or
131    /// \ref increase(\c item, \c value) otherwise.
132    void set (Item const item, PrioType const value);
133   
134    /// \brief Adds \c item to the heap with priority \c value.
135    ///   
136    /// Adds \c item to the heap with priority \c value.
137    /// \pre \c item must not be stored in the heap.
138    void push (Item const item, PrioType const value);
139   
140    /// \brief Returns the item with minimum priority relative to \c Compare.
141    ///
142    /// This method returns the item with minimum priority relative to \c
143    /// Compare. 
144    /// \pre The heap must be nonempty. 
145    Item top() const { return container[minimum].name; }
146
147    /// \brief Returns the minimum priority relative to \c Compare.
148    ///
149    /// It returns the minimum priority relative to \c Compare.
150    /// \pre The heap must be nonempty.
151    PrioType prio() const { return container[minimum].prio; }
152   
153    /// \brief Returns the priority of \c item.
154    ///
155    /// This function returns the priority of \c item.
156    /// \pre \c item must be in the heap.
157    PrioType& operator[](const Item& item) {
158      return container[iimap[item]].prio;
159    }
160   
161    /// \brief Returns the priority of \c item.
162    ///
163    /// It returns the priority of \c item.
164    /// \pre \c item must be in the heap.
165    const PrioType& operator[](const Item& item) const {
166      return container[iimap[item]].prio;
167    }
168
169
170    /// \brief Deletes the item with minimum priority relative to \c Compare.
171    ///
172    /// This method deletes the item with minimum priority relative to \c
173    /// Compare from the heap. 
174    /// \pre The heap must be non-empty. 
175    void pop();
176
177    /// \brief Deletes \c item from the heap.
178    ///
179    /// This method deletes \c item from the heap, if \c item was already
180    /// stored in the heap. It is quite inefficient in Fibonacci heaps.
181    void erase (const Item& item);
182
183    /// \brief Decreases the priority of \c item to \c value.
184    ///
185    /// This method decreases the priority of \c item to \c value.
186    /// \pre \c item must be stored in the heap with priority at least \c
187    ///   value relative to \c Compare.
188    void decrease (Item item, PrioType const value);
189
190    /// \brief Increases the priority of \c item to \c value.
191    ///
192    /// This method sets the priority of \c item to \c value. Though
193    /// there is no precondition on the priority of \c item, this
194    /// method should be used only if it is indeed necessary to increase
195    /// (relative to \c Compare) the priority of \c item, because this
196    /// method is inefficient.
197    void increase (Item item, PrioType const value) {
198      erase(item);
199      push(item, value);
200    }
201
202
203    /// \brief Returns if \c item is in, has already been in, or has never
204    /// been in the heap.
205    ///
206    /// This method returns PRE_HEAP if \c item has never been in the
207    /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
208    /// otherwise. In the latter case it is possible that \c item will
209    /// get back to the heap again.
210    state_enum state(const Item &item) const {
211      int i=iimap[item];
212      if( i>=0 ) {
213        if ( container[i].in ) i=0;
214        else i=-2;
215      }
216      return state_enum(i);
217    }   
218   
219  private:
220   
221    void balance();
222    void makeroot(int c);
223    void cut(int a, int b);
224    void cascade(int a);
225    void fuse(int a, int b);
226    void unlace(int a);
227
228
229    class store {
230      friend class FibHeap;
231     
232      Item name;
233      int parent;
234      int left_neighbor;
235      int right_neighbor;
236      int child;
237      int degree; 
238      bool marked;
239      bool in;
240      PrioType prio;
241     
242      store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
243    };
244  };   
245 
246
247
248    // **********************************************************************
249    //  IMPLEMENTATIONS
250    // **********************************************************************
251   
252  template <typename Item, typename Prio, typename ItemIntMap,
253    typename Compare>
254  void FibHeap<Item, Prio, ItemIntMap, Compare>::set
255  (Item const item, PrioType const value)
256  {
257    int i=iimap[item];
258    if ( i >= 0 && container[i].in ) {
259      if ( comp(value, container[i].prio) ) decrease(item, value);
260      if ( comp(container[i].prio, value) ) increase(item, value);
261    } else push(item, value);
262  }
263   
264  template <typename Item, typename Prio, typename ItemIntMap,
265    typename Compare>
266  void FibHeap<Item, Prio, ItemIntMap, Compare>::push
267  (Item const item, PrioType const value) {
268      int i=iimap[item];     
269      if ( i < 0 ) {
270        int s=container.size();
271        iimap.set( item, s );   
272        store st;
273        st.name=item;
274        container.push_back(st);
275        i=s;
276      } else {
277        container[i].parent=container[i].child=-1;
278        container[i].degree=0;
279        container[i].in=true;
280        container[i].marked=false;
281      }
282
283      if ( num_items ) {
284        container[container[minimum].right_neighbor].left_neighbor=i;
285        container[i].right_neighbor=container[minimum].right_neighbor;
286        container[minimum].right_neighbor=i;
287        container[i].left_neighbor=minimum;
288        if ( comp( value, container[minimum].prio) ) minimum=i;
289      } else {
290        container[i].right_neighbor=container[i].left_neighbor=i;
291        minimum=i;     
292      }
293      container[i].prio=value;
294      ++num_items;
295    }
296   
297  template <typename Item, typename Prio, typename ItemIntMap,
298    typename Compare>
299  void FibHeap<Item, Prio, ItemIntMap, Compare>::pop() {
300      /*The first case is that there are only one root.*/
301      if ( container[minimum].left_neighbor==minimum ) {
302        container[minimum].in=false;
303        if ( container[minimum].degree!=0 ) {
304          makeroot(container[minimum].child);
305          minimum=container[minimum].child;
306          balance();
307        }
308      } else {
309        int right=container[minimum].right_neighbor;
310        unlace(minimum);
311        container[minimum].in=false;
312        if ( container[minimum].degree > 0 ) {
313          int left=container[minimum].left_neighbor;
314          int child=container[minimum].child;
315          int last_child=container[child].left_neighbor;
316       
317          makeroot(child);
318         
319          container[left].right_neighbor=child;
320          container[child].left_neighbor=left;
321          container[right].left_neighbor=last_child;
322          container[last_child].right_neighbor=right;
323        }
324        minimum=right;
325        balance();
326      } // the case where there are more roots
327      --num_items;   
328    }
329
330
331  template <typename Item, typename Prio, typename ItemIntMap,
332    typename Compare>
333  void FibHeap<Item, Prio, ItemIntMap, Compare>::erase
334  (const Item& item) {
335      int i=iimap[item];
336     
337      if ( i >= 0 && container[i].in ) {       
338        if ( container[i].parent!=-1 ) {
339          int p=container[i].parent;
340          cut(i,p);         
341          cascade(p);
342        }
343        minimum=i;     //As if its prio would be -infinity
344        pop();
345      }
346  }
347   
348  template <typename Item, typename Prio, typename ItemIntMap,
349    typename Compare>
350  void FibHeap<Item, Prio, ItemIntMap, Compare>::decrease
351  (Item item, PrioType const value) {
352      int i=iimap[item];
353      container[i].prio=value;
354      int p=container[i].parent;
355     
356      if ( p!=-1 && comp(value, container[p].prio) ) {
357        cut(i,p);           
358        cascade(p);
359      }     
360      if ( comp(value, container[minimum].prio) ) minimum=i;
361  }
362 
363
364  template <typename Item, typename Prio, typename ItemIntMap,
365    typename Compare>
366  void FibHeap<Item, Prio, ItemIntMap, Compare>::balance() {     
367
368    int maxdeg=int( std::floor( 2.08*log(double(container.size()))))+1;
369 
370    std::vector<int> A(maxdeg,-1);
371   
372    /*
373     *Recall that now minimum does not point to the minimum prio element.
374     *We set minimum to this during balance().
375     */
376    int anchor=container[minimum].left_neighbor;
377    int next=minimum;
378    bool end=false;
379       
380       do {
381        int active=next;
382        if ( anchor==active ) end=true;
383        int d=container[active].degree;
384        next=container[active].right_neighbor;
385
386        while (A[d]!=-1) {       
387          if( comp(container[active].prio, container[A[d]].prio) ) {
388            fuse(active,A[d]);
389          } else {
390            fuse(A[d],active);
391            active=A[d];
392          }
393          A[d]=-1;
394          ++d;
395        }       
396        A[d]=active;
397       } while ( !end );
398
399
400       while ( container[minimum].parent >=0 ) minimum=container[minimum].parent;
401       int s=minimum;
402       int m=minimum;
403       do { 
404         if ( comp(container[s].prio, container[minimum].prio) ) minimum=s;
405         s=container[s].right_neighbor;
406       } while ( s != m );
407    }
408
409  template <typename Item, typename Prio, typename ItemIntMap,
410    typename Compare>
411  void FibHeap<Item, Prio, ItemIntMap, Compare>::makeroot
412  (int c) {
413      int s=c;
414      do { 
415        container[s].parent=-1;
416        s=container[s].right_neighbor;
417      } while ( s != c );
418    }
419 
420 
421  template <typename Item, typename Prio, typename ItemIntMap,
422    typename Compare>
423  void FibHeap<Item, Prio, ItemIntMap, Compare>::cut
424  (int a, int b) {   
425    /*
426     *Replacing a from the children of b.
427     */
428    --container[b].degree;
429   
430    if ( container[b].degree !=0 ) {
431      int child=container[b].child;
432      if ( child==a )
433        container[b].child=container[child].right_neighbor;
434      unlace(a);
435    }
436   
437   
438    /*Lacing a to the roots.*/
439    int right=container[minimum].right_neighbor;
440    container[minimum].right_neighbor=a;
441    container[a].left_neighbor=minimum;
442    container[a].right_neighbor=right;
443    container[right].left_neighbor=a;
444   
445    container[a].parent=-1;
446    container[a].marked=false;
447  }
448 
449
450  template <typename Item, typename Prio, typename ItemIntMap,
451    typename Compare>
452  void FibHeap<Item, Prio, ItemIntMap, Compare>::cascade
453  (int a)
454    {
455      if ( container[a].parent!=-1 ) {
456        int p=container[a].parent;
457       
458        if ( container[a].marked==false ) container[a].marked=true;
459        else {
460          cut(a,p);
461          cascade(p);
462        }
463      }
464    }
465
466
467  template <typename Item, typename Prio, typename ItemIntMap,
468    typename Compare>
469  void FibHeap<Item, Prio, ItemIntMap, Compare>::fuse
470  (int a, int b) {
471      unlace(b);
472     
473      /*Lacing b under a.*/
474      container[b].parent=a;
475
476      if (container[a].degree==0) {
477        container[b].left_neighbor=b;
478        container[b].right_neighbor=b;
479        container[a].child=b;   
480      } else {
481        int child=container[a].child;
482        int last_child=container[child].left_neighbor;
483        container[child].left_neighbor=b;
484        container[b].right_neighbor=child;
485        container[last_child].right_neighbor=b;
486        container[b].left_neighbor=last_child;
487      }
488
489      ++container[a].degree;
490     
491      container[b].marked=false;
492    }
493
494 
495  /*
496   *It is invoked only if a has siblings.
497   */
498  template <typename Item, typename Prio, typename ItemIntMap,
499    typename Compare>
500  void FibHeap<Item, Prio, ItemIntMap, Compare>::unlace
501  (int a) {     
502      int leftn=container[a].left_neighbor;
503      int rightn=container[a].right_neighbor;
504      container[leftn].right_neighbor=rightn;
505      container[rightn].left_neighbor=leftn;
506  }
507 
508  ///@}
509
510} //namespace lemon
511
512#endif //LEMON_FIB_HEAP_H
513
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