COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/fib_heap.h @ 1852:ffa7c6e96330

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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  /// \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  private:
221   
222    void balance();
223    void makeroot(int c);
224    void cut(int a, int b);
225    void cascade(int a);
226    void fuse(int a, int b);
227    void unlace(int a);
228
229
230    class store {
231      friend class FibHeap;
232     
233      Item name;
234      int parent;
235      int left_neighbor;
236      int right_neighbor;
237      int child;
238      int degree; 
239      bool marked;
240      bool in;
241      PrioType prio;
242     
243      store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
244    };
245  };   
246 
247
248
249    // **********************************************************************
250    //  IMPLEMENTATIONS
251    // **********************************************************************
252   
253  template <typename Item, typename Prio, typename ItemIntMap,
254    typename Compare>
255  void FibHeap<Item, Prio, ItemIntMap, Compare>::set
256  (Item const item, PrioType const value)
257  {
258    int i=iimap[item];
259    if ( i >= 0 && container[i].in ) {
260      if ( comp(value, container[i].prio) ) decrease(item, value);
261      if ( comp(container[i].prio, value) ) increase(item, value);
262    } else push(item, value);
263  }
264   
265  template <typename Item, typename Prio, typename ItemIntMap,
266    typename Compare>
267  void FibHeap<Item, Prio, ItemIntMap, Compare>::push
268  (Item const item, PrioType const value) {
269      int i=iimap[item];     
270      if ( i < 0 ) {
271        int s=container.size();
272        iimap.set( item, s );   
273        store st;
274        st.name=item;
275        container.push_back(st);
276        i=s;
277      } else {
278        container[i].parent=container[i].child=-1;
279        container[i].degree=0;
280        container[i].in=true;
281        container[i].marked=false;
282      }
283
284      if ( num_items ) {
285        container[container[minimum].right_neighbor].left_neighbor=i;
286        container[i].right_neighbor=container[minimum].right_neighbor;
287        container[minimum].right_neighbor=i;
288        container[i].left_neighbor=minimum;
289        if ( comp( value, container[minimum].prio) ) minimum=i;
290      } else {
291        container[i].right_neighbor=container[i].left_neighbor=i;
292        minimum=i;     
293      }
294      container[i].prio=value;
295      ++num_items;
296    }
297   
298  template <typename Item, typename Prio, typename ItemIntMap,
299    typename Compare>
300  void FibHeap<Item, Prio, ItemIntMap, Compare>::pop() {
301      /*The first case is that there are only one root.*/
302      if ( container[minimum].left_neighbor==minimum ) {
303        container[minimum].in=false;
304        if ( container[minimum].degree!=0 ) {
305          makeroot(container[minimum].child);
306          minimum=container[minimum].child;
307          balance();
308        }
309      } else {
310        int right=container[minimum].right_neighbor;
311        unlace(minimum);
312        container[minimum].in=false;
313        if ( container[minimum].degree > 0 ) {
314          int left=container[minimum].left_neighbor;
315          int child=container[minimum].child;
316          int last_child=container[child].left_neighbor;
317       
318          makeroot(child);
319         
320          container[left].right_neighbor=child;
321          container[child].left_neighbor=left;
322          container[right].left_neighbor=last_child;
323          container[last_child].right_neighbor=right;
324        }
325        minimum=right;
326        balance();
327      } // the case where there are more roots
328      --num_items;   
329    }
330
331
332  template <typename Item, typename Prio, typename ItemIntMap,
333    typename Compare>
334  void FibHeap<Item, Prio, ItemIntMap, Compare>::erase
335  (const Item& item) {
336      int i=iimap[item];
337     
338      if ( i >= 0 && container[i].in ) {       
339        if ( container[i].parent!=-1 ) {
340          int p=container[i].parent;
341          cut(i,p);         
342          cascade(p);
343        }
344        minimum=i;     //As if its prio would be -infinity
345        pop();
346      }
347  }
348   
349  template <typename Item, typename Prio, typename ItemIntMap,
350    typename Compare>
351  void FibHeap<Item, Prio, ItemIntMap, Compare>::decrease
352  (Item item, PrioType const value) {
353      int i=iimap[item];
354      container[i].prio=value;
355      int p=container[i].parent;
356     
357      if ( p!=-1 && comp(value, container[p].prio) ) {
358        cut(i,p);           
359        cascade(p);
360      }     
361      if ( comp(value, container[minimum].prio) ) minimum=i;
362  }
363 
364
365  template <typename Item, typename Prio, typename ItemIntMap,
366    typename Compare>
367  void FibHeap<Item, Prio, ItemIntMap, Compare>::balance() {     
368
369    int maxdeg=int( std::floor( 2.08*log(double(container.size()))))+1;
370 
371    std::vector<int> A(maxdeg,-1);
372   
373    /*
374     *Recall that now minimum does not point to the minimum prio element.
375     *We set minimum to this during balance().
376     */
377    int anchor=container[minimum].left_neighbor;
378    int next=minimum;
379    bool end=false;
380       
381       do {
382        int active=next;
383        if ( anchor==active ) end=true;
384        int d=container[active].degree;
385        next=container[active].right_neighbor;
386
387        while (A[d]!=-1) {       
388          if( comp(container[active].prio, container[A[d]].prio) ) {
389            fuse(active,A[d]);
390          } else {
391            fuse(A[d],active);
392            active=A[d];
393          }
394          A[d]=-1;
395          ++d;
396        }       
397        A[d]=active;
398       } while ( !end );
399
400
401       while ( container[minimum].parent >=0 ) minimum=container[minimum].parent;
402       int s=minimum;
403       int m=minimum;
404       do { 
405         if ( comp(container[s].prio, container[minimum].prio) ) minimum=s;
406         s=container[s].right_neighbor;
407       } while ( s != m );
408    }
409
410  template <typename Item, typename Prio, typename ItemIntMap,
411    typename Compare>
412  void FibHeap<Item, Prio, ItemIntMap, Compare>::makeroot
413  (int c) {
414      int s=c;
415      do { 
416        container[s].parent=-1;
417        s=container[s].right_neighbor;
418      } while ( s != c );
419    }
420 
421 
422  template <typename Item, typename Prio, typename ItemIntMap,
423    typename Compare>
424  void FibHeap<Item, Prio, ItemIntMap, Compare>::cut
425  (int a, int b) {   
426    /*
427     *Replacing a from the children of b.
428     */
429    --container[b].degree;
430   
431    if ( container[b].degree !=0 ) {
432      int child=container[b].child;
433      if ( child==a )
434        container[b].child=container[child].right_neighbor;
435      unlace(a);
436    }
437   
438   
439    /*Lacing a to the roots.*/
440    int right=container[minimum].right_neighbor;
441    container[minimum].right_neighbor=a;
442    container[a].left_neighbor=minimum;
443    container[a].right_neighbor=right;
444    container[right].left_neighbor=a;
445   
446    container[a].parent=-1;
447    container[a].marked=false;
448  }
449 
450
451  template <typename Item, typename Prio, typename ItemIntMap,
452    typename Compare>
453  void FibHeap<Item, Prio, ItemIntMap, Compare>::cascade
454  (int a)
455    {
456      if ( container[a].parent!=-1 ) {
457        int p=container[a].parent;
458       
459        if ( container[a].marked==false ) container[a].marked=true;
460        else {
461          cut(a,p);
462          cascade(p);
463        }
464      }
465    }
466
467
468  template <typename Item, typename Prio, typename ItemIntMap,
469    typename Compare>
470  void FibHeap<Item, Prio, ItemIntMap, Compare>::fuse
471  (int a, int b) {
472      unlace(b);
473     
474      /*Lacing b under a.*/
475      container[b].parent=a;
476
477      if (container[a].degree==0) {
478        container[b].left_neighbor=b;
479        container[b].right_neighbor=b;
480        container[a].child=b;   
481      } else {
482        int child=container[a].child;
483        int last_child=container[child].left_neighbor;
484        container[child].left_neighbor=b;
485        container[b].right_neighbor=child;
486        container[last_child].right_neighbor=b;
487        container[b].left_neighbor=last_child;
488      }
489
490      ++container[a].degree;
491     
492      container[b].marked=false;
493    }
494
495 
496  /*
497   *It is invoked only if a has siblings.
498   */
499  template <typename Item, typename Prio, typename ItemIntMap,
500    typename Compare>
501  void FibHeap<Item, Prio, ItemIntMap, Compare>::unlace
502  (int a) {     
503      int leftn=container[a].left_neighbor;
504      int rightn=container[a].right_neighbor;
505      container[leftn].right_neighbor=rightn;
506      container[rightn].left_neighbor=leftn;
507  }
508 
509
510} //namespace lemon
511
512#endif //LEMON_FIB_HEAP_H
513
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