COIN-OR::LEMON - Graph Library

source: lemon/lemon/binom_heap.h @ 749:bdc7dfc8c054

Last change on this file since 749:bdc7dfc8c054 was 748:d1a9224f1e30, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Add fourary, k-ary, pairing and binomial heaps (#301)
These structures were implemented by Dorian Batha.

File size: 14.6 KB
Line 
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_BINOM_HEAP_H
20#define LEMON_BINOM_HEAP_H
21
22///\file
23///\ingroup auxdat
24///\brief Binomial Heap implementation.
25
26#include <vector>
27#include <functional>
28#include <lemon/math.h>
29#include <lemon/counter.h>
30
31namespace lemon {
32
33  /// \ingroup auxdat
34  ///
35  ///\brief Binomial Heap.
36  ///
37  ///This class implements the \e Binomial \e heap data structure. A \e heap
38  ///is a data structure for storing items with specified values called \e
39  ///priorities in such a way that finding the item with minimum priority is
40  ///efficient. \c Compare specifies the ordering of the priorities. In a heap
41  ///one can change the priority of an item, add or erase an item, etc.
42  ///
43  ///The methods \ref increase and \ref erase are not efficient in a Binomial
44  ///heap. In case of many calls to these operations, it is better to use a
45  ///\ref BinHeap "binary heap".
46  ///
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 Dorian Batha
56
57#ifdef DOXYGEN
58  template <typename _Prio,
59            typename _ItemIntMap,
60            typename _Compare>
61#else
62  template <typename _Prio,
63            typename _ItemIntMap,
64            typename _Compare = std::less<_Prio> >
65#endif
66  class BinomHeap {
67  public:
68    typedef _ItemIntMap ItemIntMap;
69    typedef _Prio Prio;
70    typedef typename ItemIntMap::Key Item;
71    typedef std::pair<Item,Prio> Pair;
72    typedef _Compare Compare;
73
74  private:
75    class store;
76
77    std::vector<store> container;
78    int minimum, head;
79    ItemIntMap &iimap;
80    Compare comp;
81    int num_items;
82
83  public:
84    ///Status of the nodes
85    enum State {
86      ///The node is in the heap
87      IN_HEAP = 0,
88      ///The node has never been in the heap
89      PRE_HEAP = -1,
90      ///The node was in the heap but it got out of it
91      POST_HEAP = -2
92    };
93
94    /// \brief The constructor
95    ///
96    /// \c _iimap should be given to the constructor, since it is
97    ///   used internally to handle the cross references.
98    explicit BinomHeap(ItemIntMap &_iimap)
99      : minimum(0), head(-1), iimap(_iimap), num_items() {}
100
101    /// \brief The constructor
102    ///
103    /// \c _iimap should be given to the constructor, since it is used
104    /// internally to handle the cross references. \c _comp is an
105    /// object for ordering of the priorities.
106    BinomHeap(ItemIntMap &_iimap, const Compare &_comp)
107      : minimum(0), head(-1), iimap(_iimap), comp(_comp), num_items() {}
108
109    /// \brief The number of items stored in the heap.
110    ///
111    /// Returns the number of items stored in the heap.
112    int size() const { return num_items; }
113
114    /// \brief Checks if the heap stores no items.
115    ///
116    ///   Returns \c true if and only if the heap stores no items.
117    bool empty() const { return num_items==0; }
118
119    /// \brief Make empty this heap.
120    ///
121    /// Make empty this heap. It does not change the cross reference
122    /// map.  If you want to reuse a heap what is not surely empty you
123    /// should first clear the heap and after that you should set the
124    /// cross reference map for each item to \c PRE_HEAP.
125    void clear() {
126      container.clear(); minimum=0; num_items=0; head=-1;
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 (const Item& item, const Prio& value) {
136      int i=iimap[item];
137      if ( i >= 0 && container[i].in ) {
138        if ( comp(value, container[i].prio) ) decrease(item, value);
139        if ( comp(container[i].prio, value) ) increase(item, value);
140      } else push(item, value);
141    }
142
143    /// \brief Adds \c item to the heap with priority \c value.
144    ///
145    /// Adds \c item to the heap with priority \c value.
146    /// \pre \c item must not be stored in the heap.
147    void push (const Item& item, const Prio& value) {
148      int i=iimap[item];
149      if ( i<0 ) {
150        int s=container.size();
151        iimap.set( item,s );
152        store st;
153        st.name=item;
154        container.push_back(st);
155        i=s;
156      }
157      else {
158        container[i].parent=container[i].right_neighbor=container[i].child=-1;
159        container[i].degree=0;
160        container[i].in=true;
161      }
162      container[i].prio=value;
163
164      if( 0==num_items ) { head=i; minimum=i; }
165      else { merge(i); }
166
167      minimum = find_min();
168
169      ++num_items;
170    }
171
172    /// \brief Returns the item with minimum priority relative to \c Compare.
173    ///
174    /// This method returns the item with minimum priority relative to \c
175    /// Compare.
176    /// \pre The heap must be nonempty.
177    Item top() const { return container[minimum].name; }
178
179    /// \brief Returns the minimum priority relative to \c Compare.
180    ///
181    /// It returns the minimum priority relative to \c Compare.
182    /// \pre The heap must be nonempty.
183    const Prio& prio() const { return container[minimum].prio; }
184
185    /// \brief Returns the priority of \c item.
186    ///
187    /// It returns the priority of \c item.
188    /// \pre \c item must be in the heap.
189    const Prio& operator[](const Item& item) const {
190      return container[iimap[item]].prio;
191    }
192
193    /// \brief Deletes the item with minimum priority relative to \c Compare.
194    ///
195    /// This method deletes the item with minimum priority relative to \c
196    /// Compare from the heap.
197    /// \pre The heap must be non-empty.
198    void pop() {
199      container[minimum].in=false;
200
201      int head_child=-1;
202      if ( container[minimum].child!=-1 ) {
203        int child=container[minimum].child;
204        int neighb;
205        int prev=-1;
206        while( child!=-1 ) {
207          neighb=container[child].right_neighbor;
208          container[child].parent=-1;
209          container[child].right_neighbor=prev;
210          head_child=child;
211          prev=child;
212          child=neighb;
213        }
214      }
215
216      // The first case is that there are only one root.
217      if ( -1==container[head].right_neighbor ) {
218        head=head_child;
219      }
220      // The case where there are more roots.
221      else {
222        if( head!=minimum )  { unlace(minimum); }
223        else { head=container[head].right_neighbor; }
224
225        merge(head_child);
226      }
227      minimum=find_min();
228      --num_items;
229    }
230
231    /// \brief Deletes \c item from the heap.
232    ///
233    /// This method deletes \c item from the heap, if \c item was already
234    /// stored in the heap. It is quite inefficient in Binomial heaps.
235    void erase (const Item& item) {
236      int i=iimap[item];
237      if ( i >= 0 && container[i].in ) {
238        decrease( item, container[minimum].prio-1 );
239        pop();
240      }
241    }
242
243    /// \brief Decreases the priority of \c item to \c value.
244    ///
245    /// This method decreases the priority of \c item to \c value.
246    /// \pre \c item must be stored in the heap with priority at least \c
247    ///   value relative to \c Compare.
248    void decrease (Item item, const Prio& value) {
249      int i=iimap[item];
250
251      if( comp( value,container[i].prio ) ) {
252        container[i].prio=value;
253
254        int p_loc=container[i].parent, loc=i;
255        int parent, child, neighb;
256
257        while( -1!=p_loc && comp(container[loc].prio,container[p_loc].prio) ) {
258
259          // parent set for other loc_child
260          child=container[loc].child;
261          while( -1!=child ) {
262            container[child].parent=p_loc;
263            child=container[child].right_neighbor;
264          }
265
266          // parent set for other p_loc_child
267          child=container[p_loc].child;
268          while( -1!=child ) {
269            container[child].parent=loc;
270            child=container[child].right_neighbor;
271          }
272
273          child=container[p_loc].child;
274          container[p_loc].child=container[loc].child;
275          if( child==loc )
276            child=p_loc;
277          container[loc].child=child;
278
279          // left_neighb set for p_loc
280          if( container[loc].child!=p_loc ) {
281            while( container[child].right_neighbor!=loc )
282              child=container[child].right_neighbor;
283            container[child].right_neighbor=p_loc;
284          }
285
286          // left_neighb set for loc
287          parent=container[p_loc].parent;
288          if( -1!=parent ) child=container[parent].child;
289          else child=head;
290
291          if( child!=p_loc ) {
292            while( container[child].right_neighbor!=p_loc )
293              child=container[child].right_neighbor;
294            container[child].right_neighbor=loc;
295          }
296
297          neighb=container[p_loc].right_neighbor;
298          container[p_loc].right_neighbor=container[loc].right_neighbor;
299          container[loc].right_neighbor=neighb;
300
301          container[p_loc].parent=loc;
302          container[loc].parent=parent;
303
304          if( -1!=parent && container[parent].child==p_loc )
305            container[parent].child=loc;
306
307          /*if new parent will be the first root*/
308          if( head==p_loc )
309            head=loc;
310
311          p_loc=container[loc].parent;
312        }
313      }
314      if( comp(value,container[minimum].prio) ) {
315        minimum=i;
316      }
317    }
318
319    /// \brief Increases the priority of \c item to \c value.
320    ///
321    /// This method sets the priority of \c item to \c value. Though
322    /// there is no precondition on the priority of \c item, this
323    /// method should be used only if it is indeed necessary to increase
324    /// (relative to \c Compare) the priority of \c item, because this
325    /// method is inefficient.
326    void increase (Item item, const Prio& value) {
327      erase(item);
328      push(item, value);
329    }
330
331
332    /// \brief Returns if \c item is in, has already been in, or has never
333    /// been in the heap.
334    ///
335    /// This method returns PRE_HEAP if \c item has never been in the
336    /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
337    /// otherwise. In the latter case it is possible that \c item will
338    /// get back to the heap again.
339    State state(const Item &item) const {
340      int i=iimap[item];
341      if( i>=0 ) {
342        if ( container[i].in ) i=0;
343        else i=-2;
344      }
345      return State(i);
346    }
347
348    /// \brief Sets the state of the \c item in the heap.
349    ///
350    /// Sets the state of the \c item in the heap. It can be used to
351    /// manually clear the heap when it is important to achive the
352    /// better time complexity.
353    /// \param i The item.
354    /// \param st The state. It should not be \c IN_HEAP.
355    void state(const Item& i, State st) {
356      switch (st) {
357      case POST_HEAP:
358      case PRE_HEAP:
359        if (state(i) == IN_HEAP) {
360          erase(i);
361        }
362        iimap[i] = st;
363        break;
364      case IN_HEAP:
365        break;
366      }
367    }
368
369  private:
370    int find_min() {
371      int min_loc=-1, min_val;
372      int x=head;
373      if( x!=-1 ) {
374        min_val=container[x].prio;
375        min_loc=x;
376        x=container[x].right_neighbor;
377
378        while( x!=-1 ) {
379          if( comp( container[x].prio,min_val ) ) {
380            min_val=container[x].prio;
381            min_loc=x;
382          }
383          x=container[x].right_neighbor;
384        }
385      }
386      return min_loc;
387    }
388
389    void merge(int a) {
390      interleave(a);
391
392      int x=head;
393      if( -1!=x ) {
394        int x_prev=-1, x_next=container[x].right_neighbor;
395        while( -1!=x_next ) {
396          if( container[x].degree!=container[x_next].degree || ( -1!=container[x_next].right_neighbor && container[container[x_next].right_neighbor].degree==container[x].degree ) ) {
397            x_prev=x;
398            x=x_next;
399          }
400          else {
401            if( comp(container[x].prio,container[x_next].prio) ) {
402              container[x].right_neighbor=container[x_next].right_neighbor;
403              fuse(x_next,x);
404            }
405            else {
406              if( -1==x_prev ) { head=x_next; }
407              else {
408                container[x_prev].right_neighbor=x_next;
409              }
410              fuse(x,x_next);
411              x=x_next;
412            }
413          }
414          x_next=container[x].right_neighbor;
415        }
416      }
417    }
418
419    void interleave(int a) {
420      int other=-1, head_other=-1;
421
422      while( -1!=a || -1!=head ) {
423        if( -1==a ) {
424          if( -1==head_other ) {
425            head_other=head;
426          }
427          else {
428            container[other].right_neighbor=head;
429          }
430          head=-1;
431        }
432        else if( -1==head ) {
433          if( -1==head_other ) {
434            head_other=a;
435          }
436          else {
437            container[other].right_neighbor=a;
438          }
439          a=-1;
440        }
441        else {
442          if( container[a].degree<container[head].degree ) {
443            if( -1==head_other ) {
444              head_other=a;
445            }
446            else {
447              container[other].right_neighbor=a;
448            }
449            other=a;
450            a=container[a].right_neighbor;
451          }
452          else {
453            if( -1==head_other ) {
454              head_other=head;
455            }
456            else {
457              container[other].right_neighbor=head;
458            }
459            other=head;
460            head=container[head].right_neighbor;
461          }
462        }
463      }
464      head=head_other;
465    }
466
467    // Lacing a under b
468    void fuse(int a, int b) {
469      container[a].parent=b;
470      container[a].right_neighbor=container[b].child;
471      container[b].child=a;
472
473      ++container[b].degree;
474    }
475
476    // It is invoked only if a has siblings.
477    void unlace(int a) {
478      int neighb=container[a].right_neighbor;
479      int other=head;
480
481      while( container[other].right_neighbor!=a )
482        other=container[other].right_neighbor;
483      container[other].right_neighbor=neighb;
484    }
485
486  private:
487
488    class store {
489      friend class BinomHeap;
490
491      Item name;
492      int parent;
493      int right_neighbor;
494      int child;
495      int degree;
496      bool in;
497      Prio prio;
498
499      store() : parent(-1), right_neighbor(-1), child(-1), degree(0), in(true) {}
500    };
501  };
502
503} //namespace lemon
504
505#endif //LEMON_BINOM_HEAP_H
506
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