COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/fib_heap.h @ 2049:a9933b493198

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1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2006
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  /// 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 Item Type of the items to be stored. 
47  ///\param Prio Type of the priority of the items.
48  ///\param ItemIntMap A read and writable Item int map, used internally
49  ///to handle the cross references.
50  ///\param Compare A class for the ordering of the priorities. The
51  ///default is \c std::less<Prio>.
52  ///
53  ///\sa BinHeap
54  ///\sa Dijkstra
55  ///\author Jacint Szabo
56 
57#ifdef DOXYGEN
58  template <typename Item,
59            typename Prio,
60            typename ItemIntMap,
61            typename Compare>
62#else
63  template <typename Item,
64            typename Prio,
65            typename ItemIntMap,
66            typename Compare = std::less<Prio> >
67#endif
68  class FibHeap {
69  public:     
70    typedef Prio PrioType;
71   
72  private:
73    class store;
74   
75    std::vector<store> container;
76    int minimum;
77    ItemIntMap &iimap;
78    Compare comp;
79    int num_items;
80   
81  public:
82    ///Status of the nodes
83    enum state_enum {
84      ///The node is in the heap
85      IN_HEAP = 0,
86      ///The node has never been in the heap
87      PRE_HEAP = -1,
88      ///The node was in the heap but it got out of it
89      POST_HEAP = -2
90    };
91   
92    /// \brief The constructor
93    ///
94    /// \c _iimap should be given to the constructor, since it is
95    ///   used internally to handle the cross references.
96    explicit FibHeap(ItemIntMap &_iimap)
97      : minimum(0), iimap(_iimap), num_items() {}
98 
99    /// \brief The constructor
100    ///
101    /// \c _iimap should be given to the constructor, since it is used
102    /// internally to handle the cross references. \c _comp is an
103    /// object for ordering of the priorities.
104    FibHeap(ItemIntMap &_iimap, const Compare &_comp) : minimum(0),
105                  iimap(_iimap), comp(_comp), num_items() {}
106   
107    /// \brief The number of items stored in the heap.
108    ///
109    /// Returns the number of items stored in the heap.
110    int size() const { return num_items; }
111
112    /// \brief Checks if the heap stores no items.
113    ///
114    ///   Returns \c true if and only if the heap stores no items.
115    bool empty() const { return num_items==0; }
116
117    /// \brief Make empty this heap.
118    ///
119    /// Make empty this heap.
120    void clear() {
121      if (num_items != 0) {
122        for (int i = 0; i < (int)container.size(); ++i) {
123          iimap[container[i].name] = -2;
124        }
125      }
126      container.clear(); minimum = 0; num_items = 0;
127    }
128
129    /// \brief \c item gets to the heap with priority \c value independently
130    /// if \c item was already there.
131    ///
132    /// This method calls \ref push(\c item, \c value) if \c item is not
133    /// stored in the heap and it calls \ref decrease(\c item, \c value) or
134    /// \ref increase(\c item, \c value) otherwise.
135    void set (Item const item, PrioType const value);
136   
137    /// \brief Adds \c item to the heap with priority \c value.
138    ///   
139    /// Adds \c item to the heap with priority \c value.
140    /// \pre \c item must not be stored in the heap.
141    void push (Item const item, PrioType const value);
142   
143    /// \brief Returns the item with minimum priority relative to \c Compare.
144    ///
145    /// This method returns the item with minimum priority relative to \c
146    /// Compare. 
147    /// \pre The heap must be nonempty. 
148    Item top() const { return container[minimum].name; }
149
150    /// \brief Returns the minimum priority relative to \c Compare.
151    ///
152    /// It returns the minimum priority relative to \c Compare.
153    /// \pre The heap must be nonempty.
154    PrioType prio() const { return container[minimum].prio; }
155   
156    /// \brief Returns the priority of \c item.
157    ///
158    /// This function returns the priority of \c item.
159    /// \pre \c item must be in the heap.
160    PrioType& operator[](const Item& item) {
161      return container[iimap[item]].prio;
162    }
163   
164    /// \brief Returns the priority of \c item.
165    ///
166    /// It returns the priority of \c item.
167    /// \pre \c item must be in the heap.
168    const PrioType& operator[](const Item& item) const {
169      return container[iimap[item]].prio;
170    }
171
172
173    /// \brief Deletes the item with minimum priority relative to \c Compare.
174    ///
175    /// This method deletes the item with minimum priority relative to \c
176    /// Compare from the heap. 
177    /// \pre The heap must be non-empty. 
178    void pop();
179
180    /// \brief Deletes \c item from the heap.
181    ///
182    /// This method deletes \c item from the heap, if \c item was already
183    /// stored in the heap. It is quite inefficient in Fibonacci heaps.
184    void erase (const Item& item);
185
186    /// \brief Decreases the priority of \c item to \c value.
187    ///
188    /// This method decreases the priority of \c item to \c value.
189    /// \pre \c item must be stored in the heap with priority at least \c
190    ///   value relative to \c Compare.
191    void decrease (Item item, PrioType const value);
192
193    /// \brief Increases the priority of \c item to \c value.
194    ///
195    /// This method sets the priority of \c item to \c value. Though
196    /// there is no precondition on the priority of \c item, this
197    /// method should be used only if it is indeed necessary to increase
198    /// (relative to \c Compare) the priority of \c item, because this
199    /// method is inefficient.
200    void increase (Item item, PrioType const value) {
201      erase(item);
202      push(item, value);
203    }
204
205
206    /// \brief Returns if \c item is in, has already been in, or has never
207    /// been in the heap.
208    ///
209    /// This method returns PRE_HEAP if \c item has never been in the
210    /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
211    /// otherwise. In the latter case it is possible that \c item will
212    /// get back to the heap again.
213    state_enum state(const Item &item) const {
214      int i=iimap[item];
215      if( i>=0 ) {
216        if ( container[i].in ) i=0;
217        else i=-2;
218      }
219      return state_enum(i);
220    }   
221
222    /// \brief Sets the state of the \c item in the heap.
223    ///
224    /// Sets the state of the \c item in the heap. It can be used to
225    /// manually clear the heap when it is important to achive the
226    /// better time complexity.
227    /// \param i The item.
228    /// \param st The state. It should not be \c IN_HEAP.
229    void state(const Item& i, state_enum st) {
230      switch (st) {
231      case POST_HEAP:
232      case PRE_HEAP:
233        if (state(i) == IN_HEAP) {
234          erase(i);
235        }
236        iimap[i] = st;
237        break;
238      case IN_HEAP:
239        break;
240      }
241    }
242   
243  private:
244   
245    void balance();
246    void makeroot(int c);
247    void cut(int a, int b);
248    void cascade(int a);
249    void fuse(int a, int b);
250    void unlace(int a);
251
252
253    class store {
254      friend class FibHeap;
255     
256      Item name;
257      int parent;
258      int left_neighbor;
259      int right_neighbor;
260      int child;
261      int degree; 
262      bool marked;
263      bool in;
264      PrioType prio;
265     
266      store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
267    };
268  };   
269 
270
271
272    // **********************************************************************
273    //  IMPLEMENTATIONS
274    // **********************************************************************
275   
276  template <typename Item, typename Prio, typename ItemIntMap,
277    typename Compare>
278  void FibHeap<Item, Prio, ItemIntMap, Compare>::set
279  (Item const item, PrioType const value)
280  {
281    int i=iimap[item];
282    if ( i >= 0 && container[i].in ) {
283      if ( comp(value, container[i].prio) ) decrease(item, value);
284      if ( comp(container[i].prio, value) ) increase(item, value);
285    } else push(item, value);
286  }
287   
288  template <typename Item, typename Prio, typename ItemIntMap,
289    typename Compare>
290  void FibHeap<Item, Prio, ItemIntMap, Compare>::push
291  (Item const item, PrioType const value) {
292      int i=iimap[item];     
293      if ( i < 0 ) {
294        int s=container.size();
295        iimap.set( item, s );   
296        store st;
297        st.name=item;
298        container.push_back(st);
299        i=s;
300      } else {
301        container[i].parent=container[i].child=-1;
302        container[i].degree=0;
303        container[i].in=true;
304        container[i].marked=false;
305      }
306
307      if ( num_items ) {
308        container[container[minimum].right_neighbor].left_neighbor=i;
309        container[i].right_neighbor=container[minimum].right_neighbor;
310        container[minimum].right_neighbor=i;
311        container[i].left_neighbor=minimum;
312        if ( comp( value, container[minimum].prio) ) minimum=i;
313      } else {
314        container[i].right_neighbor=container[i].left_neighbor=i;
315        minimum=i;     
316      }
317      container[i].prio=value;
318      ++num_items;
319    }
320   
321  template <typename Item, typename Prio, typename ItemIntMap,
322    typename Compare>
323  void FibHeap<Item, Prio, ItemIntMap, Compare>::pop() {
324      /*The first case is that there are only one root.*/
325      if ( container[minimum].left_neighbor==minimum ) {
326        container[minimum].in=false;
327        if ( container[minimum].degree!=0 ) {
328          makeroot(container[minimum].child);
329          minimum=container[minimum].child;
330          balance();
331        }
332      } else {
333        int right=container[minimum].right_neighbor;
334        unlace(minimum);
335        container[minimum].in=false;
336        if ( container[minimum].degree > 0 ) {
337          int left=container[minimum].left_neighbor;
338          int child=container[minimum].child;
339          int last_child=container[child].left_neighbor;
340       
341          makeroot(child);
342         
343          container[left].right_neighbor=child;
344          container[child].left_neighbor=left;
345          container[right].left_neighbor=last_child;
346          container[last_child].right_neighbor=right;
347        }
348        minimum=right;
349        balance();
350      } // the case where there are more roots
351      --num_items;   
352    }
353
354
355  template <typename Item, typename Prio, typename ItemIntMap,
356    typename Compare>
357  void FibHeap<Item, Prio, ItemIntMap, Compare>::erase
358  (const Item& item) {
359      int i=iimap[item];
360     
361      if ( i >= 0 && container[i].in ) {       
362        if ( container[i].parent!=-1 ) {
363          int p=container[i].parent;
364          cut(i,p);         
365          cascade(p);
366        }
367        minimum=i;     //As if its prio would be -infinity
368        pop();
369      }
370  }
371   
372  template <typename Item, typename Prio, typename ItemIntMap,
373    typename Compare>
374  void FibHeap<Item, Prio, ItemIntMap, Compare>::decrease
375  (Item item, PrioType const value) {
376      int i=iimap[item];
377      container[i].prio=value;
378      int p=container[i].parent;
379     
380      if ( p!=-1 && comp(value, container[p].prio) ) {
381        cut(i,p);           
382        cascade(p);
383      }     
384      if ( comp(value, container[minimum].prio) ) minimum=i;
385  }
386 
387
388  template <typename Item, typename Prio, typename ItemIntMap,
389    typename Compare>
390  void FibHeap<Item, Prio, ItemIntMap, Compare>::balance() {     
391
392    int maxdeg=int( std::floor( 2.08*log(double(container.size()))))+1;
393 
394    std::vector<int> A(maxdeg,-1);
395   
396    /*
397     *Recall that now minimum does not point to the minimum prio element.
398     *We set minimum to this during balance().
399     */
400    int anchor=container[minimum].left_neighbor;
401    int next=minimum;
402    bool end=false;
403       
404       do {
405        int active=next;
406        if ( anchor==active ) end=true;
407        int d=container[active].degree;
408        next=container[active].right_neighbor;
409
410        while (A[d]!=-1) {       
411          if( comp(container[active].prio, container[A[d]].prio) ) {
412            fuse(active,A[d]);
413          } else {
414            fuse(A[d],active);
415            active=A[d];
416          }
417          A[d]=-1;
418          ++d;
419        }       
420        A[d]=active;
421       } while ( !end );
422
423
424       while ( container[minimum].parent >=0 ) minimum=container[minimum].parent;
425       int s=minimum;
426       int m=minimum;
427       do { 
428         if ( comp(container[s].prio, container[minimum].prio) ) minimum=s;
429         s=container[s].right_neighbor;
430       } while ( s != m );
431    }
432
433  template <typename Item, typename Prio, typename ItemIntMap,
434    typename Compare>
435  void FibHeap<Item, Prio, ItemIntMap, Compare>::makeroot
436  (int c) {
437      int s=c;
438      do { 
439        container[s].parent=-1;
440        s=container[s].right_neighbor;
441      } while ( s != c );
442    }
443 
444 
445  template <typename Item, typename Prio, typename ItemIntMap,
446    typename Compare>
447  void FibHeap<Item, Prio, ItemIntMap, Compare>::cut
448  (int a, int b) {   
449    /*
450     *Replacing a from the children of b.
451     */
452    --container[b].degree;
453   
454    if ( container[b].degree !=0 ) {
455      int child=container[b].child;
456      if ( child==a )
457        container[b].child=container[child].right_neighbor;
458      unlace(a);
459    }
460   
461   
462    /*Lacing a to the roots.*/
463    int right=container[minimum].right_neighbor;
464    container[minimum].right_neighbor=a;
465    container[a].left_neighbor=minimum;
466    container[a].right_neighbor=right;
467    container[right].left_neighbor=a;
468   
469    container[a].parent=-1;
470    container[a].marked=false;
471  }
472 
473
474  template <typename Item, typename Prio, typename ItemIntMap,
475    typename Compare>
476  void FibHeap<Item, Prio, ItemIntMap, Compare>::cascade
477  (int a)
478    {
479      if ( container[a].parent!=-1 ) {
480        int p=container[a].parent;
481       
482        if ( container[a].marked==false ) container[a].marked=true;
483        else {
484          cut(a,p);
485          cascade(p);
486        }
487      }
488    }
489
490
491  template <typename Item, typename Prio, typename ItemIntMap,
492    typename Compare>
493  void FibHeap<Item, Prio, ItemIntMap, Compare>::fuse
494  (int a, int b) {
495      unlace(b);
496     
497      /*Lacing b under a.*/
498      container[b].parent=a;
499
500      if (container[a].degree==0) {
501        container[b].left_neighbor=b;
502        container[b].right_neighbor=b;
503        container[a].child=b;   
504      } else {
505        int child=container[a].child;
506        int last_child=container[child].left_neighbor;
507        container[child].left_neighbor=b;
508        container[b].right_neighbor=child;
509        container[last_child].right_neighbor=b;
510        container[b].left_neighbor=last_child;
511      }
512
513      ++container[a].degree;
514     
515      container[b].marked=false;
516    }
517
518 
519  /*
520   *It is invoked only if a has siblings.
521   */
522  template <typename Item, typename Prio, typename ItemIntMap,
523    typename Compare>
524  void FibHeap<Item, Prio, ItemIntMap, Compare>::unlace
525  (int a) {     
526      int leftn=container[a].left_neighbor;
527      int rightn=container[a].right_neighbor;
528      container[leftn].right_neighbor=rightn;
529      container[rightn].left_neighbor=leftn;
530  }
531 
532
533} //namespace lemon
534
535#endif //LEMON_FIB_HEAP_H
536
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