COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/fib_heap.h @ 2546:b5eba564bb60

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1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2007
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 <cmath>
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  ///\e binary \e 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  ///\author Jacint Szabo
55 
56#ifdef DOXYGEN
57  template <typename Prio,
58            typename ItemIntMap,
59            typename Compare>
60#else
61  template <typename Prio,
62            typename ItemIntMap,
63            typename Compare = std::less<Prio> >
64#endif
65  class FibHeap {
66  public:
67    typedef typename ItemIntMap::Key Item;
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. It does not change the cross reference
118    /// map.  If you want to reuse a heap what is not surely empty you
119    /// should first clear the heap and after that you should set the
120    /// cross reference map for each item to \c PRE_HEAP.
121    void clear() {
122      container.clear(); minimum = 0; num_items = 0;
123    }
124
125    /// \brief \c item gets to the heap with priority \c value independently
126    /// if \c item was already there.
127    ///
128    /// This method calls \ref push(\c item, \c value) if \c item is not
129    /// stored in the heap and it calls \ref decrease(\c item, \c value) or
130    /// \ref increase(\c item, \c value) otherwise.
131    void set (Item const item, PrioType const value);
132   
133    /// \brief Adds \c item to the heap with priority \c value.
134    ///   
135    /// Adds \c item to the heap with priority \c value.
136    /// \pre \c item must not be stored in the heap.
137    void push (Item const item, PrioType const value);
138   
139    /// \brief Returns the item with minimum priority relative to \c Compare.
140    ///
141    /// This method returns the item with minimum priority relative to \c
142    /// Compare. 
143    /// \pre The heap must be nonempty. 
144    Item top() const { return container[minimum].name; }
145
146    /// \brief Returns the minimum priority relative to \c Compare.
147    ///
148    /// It returns the minimum priority relative to \c Compare.
149    /// \pre The heap must be nonempty.
150    PrioType prio() const { return container[minimum].prio; }
151   
152    /// \brief Returns the priority of \c item.
153    ///
154    /// This function returns the priority of \c item.
155    /// \pre \c item must be in the heap.
156    PrioType& operator[](const Item& item) {
157      return container[iimap[item]].prio;
158    }
159   
160    /// \brief Returns the priority of \c item.
161    ///
162    /// It returns the priority of \c item.
163    /// \pre \c item must be in the heap.
164    const PrioType& operator[](const Item& item) const {
165      return container[iimap[item]].prio;
166    }
167
168
169    /// \brief Deletes the item with minimum priority relative to \c Compare.
170    ///
171    /// This method deletes the item with minimum priority relative to \c
172    /// Compare from the heap. 
173    /// \pre The heap must be non-empty. 
174    void pop();
175
176    /// \brief Deletes \c item from the heap.
177    ///
178    /// This method deletes \c item from the heap, if \c item was already
179    /// stored in the heap. It is quite inefficient in Fibonacci heaps.
180    void erase (const Item& item);
181
182    /// \brief Decreases the priority of \c item to \c value.
183    ///
184    /// This method decreases the priority of \c item to \c value.
185    /// \pre \c item must be stored in the heap with priority at least \c
186    ///   value relative to \c Compare.
187    void decrease (Item item, PrioType const value);
188
189    /// \brief Increases the priority of \c item to \c value.
190    ///
191    /// This method sets the priority of \c item to \c value. Though
192    /// there is no precondition on the priority of \c item, this
193    /// method should be used only if it is indeed necessary to increase
194    /// (relative to \c Compare) the priority of \c item, because this
195    /// method is inefficient.
196    void increase (Item item, PrioType const value) {
197      erase(item);
198      push(item, value);
199    }
200
201
202    /// \brief Returns if \c item is in, has already been in, or has never
203    /// been in the heap.
204    ///
205    /// This method returns PRE_HEAP if \c item has never been in the
206    /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
207    /// otherwise. In the latter case it is possible that \c item will
208    /// get back to the heap again.
209    state_enum state(const Item &item) const {
210      int i=iimap[item];
211      if( i>=0 ) {
212        if ( container[i].in ) i=0;
213        else i=-2;
214      }
215      return state_enum(i);
216    }   
217
218    /// \brief Sets the state of the \c item in the heap.
219    ///
220    /// Sets the state of the \c item in the heap. It can be used to
221    /// manually clear the heap when it is important to achive the
222    /// better time complexity.
223    /// \param i The item.
224    /// \param st The state. It should not be \c IN_HEAP.
225    void state(const Item& i, state_enum st) {
226      switch (st) {
227      case POST_HEAP:
228      case PRE_HEAP:
229        if (state(i) == IN_HEAP) {
230          erase(i);
231        }
232        iimap[i] = st;
233        break;
234      case IN_HEAP:
235        break;
236      }
237    }
238   
239  private:
240   
241    void balance();
242    void makeroot(int c);
243    void cut(int a, int b);
244    void cascade(int a);
245    void fuse(int a, int b);
246    void unlace(int a);
247
248
249    class store {
250      friend class FibHeap;
251     
252      Item name;
253      int parent;
254      int left_neighbor;
255      int right_neighbor;
256      int child;
257      int degree; 
258      bool marked;
259      bool in;
260      PrioType prio;
261     
262      store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
263    };
264  };   
265 
266
267
268    // **********************************************************************
269    //  IMPLEMENTATIONS
270    // **********************************************************************
271   
272  template <typename Prio, typename ItemIntMap,
273    typename Compare>
274  void FibHeap<Prio, ItemIntMap, Compare>::set
275  (Item const item, PrioType const value)
276  {
277    int i=iimap[item];
278    if ( i >= 0 && container[i].in ) {
279      if ( comp(value, container[i].prio) ) decrease(item, value);
280      if ( comp(container[i].prio, value) ) increase(item, value);
281    } else push(item, value);
282  }
283   
284  template <typename Prio, typename ItemIntMap,
285    typename Compare>
286  void FibHeap<Prio, ItemIntMap, Compare>::push
287  (Item const item, PrioType const value) {
288      int i=iimap[item];     
289      if ( i < 0 ) {
290        int s=container.size();
291        iimap.set( item, s );   
292        store st;
293        st.name=item;
294        container.push_back(st);
295        i=s;
296      } else {
297        container[i].parent=container[i].child=-1;
298        container[i].degree=0;
299        container[i].in=true;
300        container[i].marked=false;
301      }
302
303      if ( num_items ) {
304        container[container[minimum].right_neighbor].left_neighbor=i;
305        container[i].right_neighbor=container[minimum].right_neighbor;
306        container[minimum].right_neighbor=i;
307        container[i].left_neighbor=minimum;
308        if ( comp( value, container[minimum].prio) ) minimum=i;
309      } else {
310        container[i].right_neighbor=container[i].left_neighbor=i;
311        minimum=i;     
312      }
313      container[i].prio=value;
314      ++num_items;
315    }
316   
317  template <typename Prio, typename ItemIntMap,
318    typename Compare>
319  void FibHeap<Prio, ItemIntMap, Compare>::pop() {
320      /*The first case is that there are only one root.*/
321      if ( container[minimum].left_neighbor==minimum ) {
322        container[minimum].in=false;
323        if ( container[minimum].degree!=0 ) {
324          makeroot(container[minimum].child);
325          minimum=container[minimum].child;
326          balance();
327        }
328      } else {
329        int right=container[minimum].right_neighbor;
330        unlace(minimum);
331        container[minimum].in=false;
332        if ( container[minimum].degree > 0 ) {
333          int left=container[minimum].left_neighbor;
334          int child=container[minimum].child;
335          int last_child=container[child].left_neighbor;
336       
337          makeroot(child);
338         
339          container[left].right_neighbor=child;
340          container[child].left_neighbor=left;
341          container[right].left_neighbor=last_child;
342          container[last_child].right_neighbor=right;
343        }
344        minimum=right;
345        balance();
346      } // the case where there are more roots
347      --num_items;   
348    }
349
350
351  template <typename Prio, typename ItemIntMap,
352    typename Compare>
353  void FibHeap<Prio, ItemIntMap, Compare>::erase
354  (const Item& item) {
355      int i=iimap[item];
356     
357      if ( i >= 0 && container[i].in ) {       
358        if ( container[i].parent!=-1 ) {
359          int p=container[i].parent;
360          cut(i,p);         
361          cascade(p);
362        }
363        minimum=i;     //As if its prio would be -infinity
364        pop();
365      }
366  }
367   
368  template <typename Prio, typename ItemIntMap,
369    typename Compare>
370  void FibHeap<Prio, ItemIntMap, Compare>::decrease
371  (Item item, PrioType const value) {
372      int i=iimap[item];
373      container[i].prio=value;
374      int p=container[i].parent;
375     
376      if ( p!=-1 && comp(value, container[p].prio) ) {
377        cut(i,p);           
378        cascade(p);
379      }     
380      if ( comp(value, container[minimum].prio) ) minimum=i;
381  }
382 
383
384  template <typename Prio, typename ItemIntMap,
385    typename Compare>
386  void FibHeap<Prio, ItemIntMap, Compare>::balance() {     
387
388    int maxdeg=int( std::floor( 2.08*log(double(container.size()))))+1;
389 
390    std::vector<int> A(maxdeg,-1);
391   
392    /*
393     *Recall that now minimum does not point to the minimum prio element.
394     *We set minimum to this during balance().
395     */
396    int anchor=container[minimum].left_neighbor;
397    int next=minimum;
398    bool end=false;
399       
400       do {
401        int active=next;
402        if ( anchor==active ) end=true;
403        int d=container[active].degree;
404        next=container[active].right_neighbor;
405
406        while (A[d]!=-1) {       
407          if( comp(container[active].prio, container[A[d]].prio) ) {
408            fuse(active,A[d]);
409          } else {
410            fuse(A[d],active);
411            active=A[d];
412          }
413          A[d]=-1;
414          ++d;
415        }       
416        A[d]=active;
417       } while ( !end );
418
419
420       while ( container[minimum].parent >=0 ) minimum=container[minimum].parent;
421       int s=minimum;
422       int m=minimum;
423       do { 
424         if ( comp(container[s].prio, container[minimum].prio) ) minimum=s;
425         s=container[s].right_neighbor;
426       } while ( s != m );
427    }
428
429  template <typename Prio, typename ItemIntMap,
430    typename Compare>
431  void FibHeap<Prio, ItemIntMap, Compare>::makeroot
432  (int c) {
433      int s=c;
434      do { 
435        container[s].parent=-1;
436        s=container[s].right_neighbor;
437      } while ( s != c );
438    }
439 
440 
441  template <typename Prio, typename ItemIntMap,
442    typename Compare>
443  void FibHeap<Prio, ItemIntMap, Compare>::cut
444  (int a, int b) {   
445    /*
446     *Replacing a from the children of b.
447     */
448    --container[b].degree;
449   
450    if ( container[b].degree !=0 ) {
451      int child=container[b].child;
452      if ( child==a )
453        container[b].child=container[child].right_neighbor;
454      unlace(a);
455    }
456   
457   
458    /*Lacing a to the roots.*/
459    int right=container[minimum].right_neighbor;
460    container[minimum].right_neighbor=a;
461    container[a].left_neighbor=minimum;
462    container[a].right_neighbor=right;
463    container[right].left_neighbor=a;
464   
465    container[a].parent=-1;
466    container[a].marked=false;
467  }
468 
469
470  template <typename Prio, typename ItemIntMap,
471    typename Compare>
472  void FibHeap<Prio, ItemIntMap, Compare>::cascade
473  (int a)
474    {
475      if ( container[a].parent!=-1 ) {
476        int p=container[a].parent;
477       
478        if ( container[a].marked==false ) container[a].marked=true;
479        else {
480          cut(a,p);
481          cascade(p);
482        }
483      }
484    }
485
486
487  template <typename Prio, typename ItemIntMap,
488    typename Compare>
489  void FibHeap<Prio, ItemIntMap, Compare>::fuse
490  (int a, int b) {
491      unlace(b);
492     
493      /*Lacing b under a.*/
494      container[b].parent=a;
495
496      if (container[a].degree==0) {
497        container[b].left_neighbor=b;
498        container[b].right_neighbor=b;
499        container[a].child=b;   
500      } else {
501        int child=container[a].child;
502        int last_child=container[child].left_neighbor;
503        container[child].left_neighbor=b;
504        container[b].right_neighbor=child;
505        container[last_child].right_neighbor=b;
506        container[b].left_neighbor=last_child;
507      }
508
509      ++container[a].degree;
510     
511      container[b].marked=false;
512    }
513
514 
515  /*
516   *It is invoked only if a has siblings.
517   */
518  template <typename Prio, typename ItemIntMap,
519    typename Compare>
520  void FibHeap<Prio, ItemIntMap, Compare>::unlace
521  (int a) {     
522      int leftn=container[a].left_neighbor;
523      int rightn=container[a].right_neighbor;
524      container[leftn].right_neighbor=rightn;
525      container[rightn].left_neighbor=leftn;
526  }
527 
528
529} //namespace lemon
530
531#endif //LEMON_FIB_HEAP_H
532
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