COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/fib_heap.h

Last change on this file was 2569:12c2c5c4330b, checked in by Alpar Juttner, 12 years ago

#include<cmath> -> #include<lemon/math.h>

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1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2008
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 <lemon/math.h>
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  ///\ref BinHeap "binary 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 _ItemIntMap ItemIntMap;
68    typedef _Prio Prio;
69    typedef typename ItemIntMap::Key Item;
70    typedef std::pair<Item,Prio> Pair;
71    typedef _Compare Compare;
72   
73  private:
74    class store;
75   
76    std::vector<store> container;
77    int minimum;
78    ItemIntMap &iimap;
79    Compare comp;
80    int num_items;
81   
82  public:
83    ///Status of the nodes
84    enum State {
85      ///The node is in the heap
86      IN_HEAP = 0,
87      ///The node has never been in the heap
88      PRE_HEAP = -1,
89      ///The node was in the heap but it got out of it
90      POST_HEAP = -2
91    };
92   
93    /// \brief The constructor
94    ///
95    /// \c _iimap should be given to the constructor, since it is
96    ///   used internally to handle the cross references.
97    explicit FibHeap(ItemIntMap &_iimap)
98      : minimum(0), iimap(_iimap), num_items() {}
99 
100    /// \brief The constructor
101    ///
102    /// \c _iimap should be given to the constructor, since it is used
103    /// internally to handle the cross references. \c _comp is an
104    /// object for ordering of the priorities.
105    FibHeap(ItemIntMap &_iimap, const Compare &_comp)
106      : minimum(0), iimap(_iimap), comp(_comp), num_items() {}
107   
108    /// \brief The number of items stored in the heap.
109    ///
110    /// Returns the number of items stored in the heap.
111    int size() const { return num_items; }
112
113    /// \brief Checks if the heap stores no items.
114    ///
115    ///   Returns \c true if and only if the heap stores no items.
116    bool empty() const { return num_items==0; }
117
118    /// \brief Make empty this heap.
119    ///
120    /// Make empty this heap. It does not change the cross reference
121    /// map.  If you want to reuse a heap what is not surely empty you
122    /// should first clear the heap and after that you should set the
123    /// cross reference map for each item to \c PRE_HEAP.
124    void clear() {
125      container.clear(); minimum = 0; num_items = 0;
126    }
127
128    /// \brief \c item gets to the heap with priority \c value independently
129    /// if \c item was already there.
130    ///
131    /// This method calls \ref push(\c item, \c value) if \c item is not
132    /// stored in the heap and it calls \ref decrease(\c item, \c value) or
133    /// \ref increase(\c item, \c value) otherwise.
134    void set (const Item& item, const Prio& value) {
135      int i=iimap[item];
136      if ( i >= 0 && container[i].in ) {
137        if ( comp(value, container[i].prio) ) decrease(item, value);
138        if ( comp(container[i].prio, value) ) increase(item, value);
139      } else push(item, value);
140    }
141   
142    /// \brief Adds \c item to the heap with priority \c value.
143    ///   
144    /// Adds \c item to the heap with priority \c value.
145    /// \pre \c item must not be stored in the heap.
146    void push (const Item& item, const Prio& value) {
147      int i=iimap[item];     
148      if ( i < 0 ) {
149        int s=container.size();
150        iimap.set( item, s );   
151        store st;
152        st.name=item;
153        container.push_back(st);
154        i=s;
155      } else {
156        container[i].parent=container[i].child=-1;
157        container[i].degree=0;
158        container[i].in=true;
159        container[i].marked=false;
160      }
161
162      if ( num_items ) {
163        container[container[minimum].right_neighbor].left_neighbor=i;
164        container[i].right_neighbor=container[minimum].right_neighbor;
165        container[minimum].right_neighbor=i;
166        container[i].left_neighbor=minimum;
167        if ( comp( value, container[minimum].prio) ) minimum=i;
168      } else {
169        container[i].right_neighbor=container[i].left_neighbor=i;
170        minimum=i;     
171      }
172      container[i].prio=value;
173      ++num_items;
174    }
175   
176    /// \brief Returns the item with minimum priority relative to \c Compare.
177    ///
178    /// This method returns the item with minimum priority relative to \c
179    /// Compare. 
180    /// \pre The heap must be nonempty. 
181    Item top() const { return container[minimum].name; }
182
183    /// \brief Returns the minimum priority relative to \c Compare.
184    ///
185    /// It returns the minimum priority relative to \c Compare.
186    /// \pre The heap must be nonempty.
187    const Prio& prio() const { return container[minimum].prio; }
188       
189    /// \brief Returns the priority of \c item.
190    ///
191    /// It returns the priority of \c item.
192    /// \pre \c item must be in the heap.
193    const Prio& operator[](const Item& item) const {
194      return container[iimap[item]].prio;
195    }
196
197    /// \brief Deletes the item with minimum priority relative to \c Compare.
198    ///
199    /// This method deletes the item with minimum priority relative to \c
200    /// Compare from the heap. 
201    /// \pre The heap must be non-empty. 
202    void pop() {
203      /*The first case is that there are only one root.*/
204      if ( container[minimum].left_neighbor==minimum ) {
205        container[minimum].in=false;
206        if ( container[minimum].degree!=0 ) {
207          makeroot(container[minimum].child);
208          minimum=container[minimum].child;
209          balance();
210        }
211      } else {
212        int right=container[minimum].right_neighbor;
213        unlace(minimum);
214        container[minimum].in=false;
215        if ( container[minimum].degree > 0 ) {
216          int left=container[minimum].left_neighbor;
217          int child=container[minimum].child;
218          int last_child=container[child].left_neighbor;
219         
220          makeroot(child);
221         
222          container[left].right_neighbor=child;
223          container[child].left_neighbor=left;
224          container[right].left_neighbor=last_child;
225          container[last_child].right_neighbor=right;
226        }
227        minimum=right;
228        balance();
229      } // the case where there are more roots
230      --num_items;   
231    }
232
233    /// \brief Deletes \c item from the heap.
234    ///
235    /// This method deletes \c item from the heap, if \c item was already
236    /// stored in the heap. It is quite inefficient in Fibonacci heaps.
237    void erase (const Item& item) {
238      int i=iimap[item];
239     
240      if ( i >= 0 && container[i].in ) {       
241        if ( container[i].parent!=-1 ) {
242          int p=container[i].parent;
243          cut(i,p);         
244          cascade(p);
245        }
246        minimum=i;     //As if its prio would be -infinity
247        pop();
248      }
249    }
250
251    /// \brief Decreases the priority of \c item to \c value.
252    ///
253    /// This method decreases the priority of \c item to \c value.
254    /// \pre \c item must be stored in the heap with priority at least \c
255    ///   value relative to \c Compare.
256    void decrease (Item item, const Prio& value) {
257      int i=iimap[item];
258      container[i].prio=value;
259      int p=container[i].parent;
260     
261      if ( p!=-1 && comp(value, container[p].prio) ) {
262        cut(i,p);           
263        cascade(p);
264      }     
265      if ( comp(value, container[minimum].prio) ) minimum=i;
266    }
267
268    /// \brief Increases the priority of \c item to \c value.
269    ///
270    /// This method sets the priority of \c item to \c value. Though
271    /// there is no precondition on the priority of \c item, this
272    /// method should be used only if it is indeed necessary to increase
273    /// (relative to \c Compare) the priority of \c item, because this
274    /// method is inefficient.
275    void increase (Item item, const Prio& value) {
276      erase(item);
277      push(item, value);
278    }
279
280
281    /// \brief Returns if \c item is in, has already been in, or has never
282    /// been in the heap.
283    ///
284    /// This method returns PRE_HEAP if \c item has never been in the
285    /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
286    /// otherwise. In the latter case it is possible that \c item will
287    /// get back to the heap again.
288    State state(const Item &item) const {
289      int i=iimap[item];
290      if( i>=0 ) {
291        if ( container[i].in ) i=0;
292        else i=-2;
293      }
294      return State(i);
295    }   
296
297    /// \brief Sets the state of the \c item in the heap.
298    ///
299    /// Sets the state of the \c item in the heap. It can be used to
300    /// manually clear the heap when it is important to achive the
301    /// better time complexity.
302    /// \param i The item.
303    /// \param st The state. It should not be \c IN_HEAP.
304    void state(const Item& i, State st) {
305      switch (st) {
306      case POST_HEAP:
307      case PRE_HEAP:
308        if (state(i) == IN_HEAP) {
309          erase(i);
310        }
311        iimap[i] = st;
312        break;
313      case IN_HEAP:
314        break;
315      }
316    }
317   
318  private:
319   
320    void balance() {
321
322      int maxdeg=int( std::floor( 2.08*log(double(container.size()))))+1;
323 
324      std::vector<int> A(maxdeg,-1);
325   
326      /*
327       *Recall that now minimum does not point to the minimum prio element.
328       *We set minimum to this during balance().
329       */
330      int anchor=container[minimum].left_neighbor;
331      int next=minimum;
332      bool end=false;
333       
334      do {
335        int active=next;
336        if ( anchor==active ) end=true;
337        int d=container[active].degree;
338        next=container[active].right_neighbor;
339
340        while (A[d]!=-1) {       
341          if( comp(container[active].prio, container[A[d]].prio) ) {
342            fuse(active,A[d]);
343          } else {
344            fuse(A[d],active);
345            active=A[d];
346          }
347          A[d]=-1;
348          ++d;
349        }       
350        A[d]=active;
351      } while ( !end );
352
353
354      while ( container[minimum].parent >=0 )
355        minimum=container[minimum].parent;
356      int s=minimum;
357      int m=minimum;
358      do { 
359        if ( comp(container[s].prio, container[minimum].prio) ) minimum=s;
360        s=container[s].right_neighbor;
361      } while ( s != m );
362    }
363
364    void makeroot(int c) {
365      int s=c;
366      do { 
367        container[s].parent=-1;
368        s=container[s].right_neighbor;
369      } while ( s != c );
370    }
371
372    void cut(int a, int b) {
373      /*
374       *Replacing a from the children of b.
375       */
376      --container[b].degree;
377   
378      if ( container[b].degree !=0 ) {
379        int child=container[b].child;
380        if ( child==a )
381          container[b].child=container[child].right_neighbor;
382        unlace(a);
383      }
384   
385   
386      /*Lacing a to the roots.*/
387      int right=container[minimum].right_neighbor;
388      container[minimum].right_neighbor=a;
389      container[a].left_neighbor=minimum;
390      container[a].right_neighbor=right;
391      container[right].left_neighbor=a;
392   
393      container[a].parent=-1;
394      container[a].marked=false;
395    }
396
397    void cascade(int a) {
398      if ( container[a].parent!=-1 ) {
399        int p=container[a].parent;
400       
401        if ( container[a].marked==false ) container[a].marked=true;
402        else {
403          cut(a,p);
404          cascade(p);
405        }
406      }
407    }
408
409    void fuse(int a, int b) {
410      unlace(b);
411     
412      /*Lacing b under a.*/
413      container[b].parent=a;
414
415      if (container[a].degree==0) {
416        container[b].left_neighbor=b;
417        container[b].right_neighbor=b;
418        container[a].child=b;   
419      } else {
420        int child=container[a].child;
421        int last_child=container[child].left_neighbor;
422        container[child].left_neighbor=b;
423        container[b].right_neighbor=child;
424        container[last_child].right_neighbor=b;
425        container[b].left_neighbor=last_child;
426      }
427
428      ++container[a].degree;
429     
430      container[b].marked=false;
431    }
432
433    /*
434     *It is invoked only if a has siblings.
435     */
436    void unlace(int a) {
437      int leftn=container[a].left_neighbor;
438      int rightn=container[a].right_neighbor;
439      container[leftn].right_neighbor=rightn;
440      container[rightn].left_neighbor=leftn;
441    }
442
443
444    class store {
445      friend class FibHeap;
446     
447      Item name;
448      int parent;
449      int left_neighbor;
450      int right_neighbor;
451      int child;
452      int degree; 
453      bool marked;
454      bool in;
455      Prio prio;
456     
457      store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
458    };
459  };   
460
461} //namespace lemon
462
463#endif //LEMON_FIB_HEAP_H
464
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