COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/fourary_heap.h @ 839:f3bc4e9b5f3a

Last change on this file since 839:f3bc4e9b5f3a was 706:9314d9339475, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Smarter bubbleDown() in K-ary heaps (#301)

File size: 10.7 KB
Line 
1/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library.
4 *
5 * Copyright (C) 2003-2009
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_FOURARY_HEAP_H
20#define LEMON_FOURARY_HEAP_H
21
22///\ingroup heaps
23///\file
24///\brief Fourary heap implementation.
25
26#include <vector>
27#include <utility>
28#include <functional>
29
30namespace lemon {
31
32  /// \ingroup heaps
33  ///
34  ///\brief Fourary heap data structure.
35  ///
36  /// This class implements the \e fourary \e heap data structure.
37  /// It fully conforms to the \ref concepts::Heap "heap concept".
38  ///
39  /// The fourary heap is a specialization of the \ref KaryHeap "K-ary heap"
40  /// for <tt>K=4</tt>. It is similar to the \ref BinHeap "binary heap",
41  /// but its nodes have at most four children, instead of two.
42  ///
43  /// \tparam PR Type of the priorities of the items.
44  /// \tparam IM A read-writable item map with \c int values, used
45  /// internally to handle the cross references.
46  /// \tparam CMP A functor class for comparing the priorities.
47  /// The default is \c std::less<PR>.
48  ///
49  ///\sa BinHeap
50  ///\sa KaryHeap
51#ifdef DOXYGEN
52  template <typename PR, typename IM, typename CMP>
53#else
54  template <typename PR, typename IM, typename CMP = std::less<PR> >
55#endif
56  class FouraryHeap {
57  public:
58    /// Type of the item-int map.
59    typedef IM ItemIntMap;
60    /// Type of the priorities.
61    typedef PR Prio;
62    /// Type of the items stored in the heap.
63    typedef typename ItemIntMap::Key Item;
64    /// Type of the item-priority pairs.
65    typedef std::pair<Item,Prio> Pair;
66    /// Functor type for comparing the priorities.
67    typedef CMP Compare;
68
69    /// \brief Type to represent the states of the items.
70    ///
71    /// Each item has a state associated to it. It can be "in heap",
72    /// "pre-heap" or "post-heap". The latter two are indifferent from the
73    /// heap's point of view, but may be useful to the user.
74    ///
75    /// The item-int map must be initialized in such way that it assigns
76    /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
77    enum State {
78      IN_HEAP = 0,    ///< = 0.
79      PRE_HEAP = -1,  ///< = -1.
80      POST_HEAP = -2  ///< = -2.
81    };
82
83  private:
84    std::vector<Pair> _data;
85    Compare _comp;
86    ItemIntMap &_iim;
87
88  public:
89    /// \brief Constructor.
90    ///
91    /// Constructor.
92    /// \param map A map that assigns \c int values to the items.
93    /// It is used internally to handle the cross references.
94    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
95    explicit FouraryHeap(ItemIntMap &map) : _iim(map) {}
96
97    /// \brief Constructor.
98    ///
99    /// Constructor.
100    /// \param map A map that assigns \c int values to the items.
101    /// It is used internally to handle the cross references.
102    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
103    /// \param comp The function object used for comparing the priorities.
104    FouraryHeap(ItemIntMap &map, const Compare &comp)
105      : _iim(map), _comp(comp) {}
106
107    /// \brief The number of items stored in the heap.
108    ///
109    /// This function returns the number of items stored in the heap.
110    int size() const { return _data.size(); }
111
112    /// \brief Check if the heap is empty.
113    ///
114    /// This function returns \c true if the heap is empty.
115    bool empty() const { return _data.empty(); }
116
117    /// \brief Make the heap empty.
118    ///
119    /// This functon makes the heap empty.
120    /// It does not change the cross reference map. If you want to reuse
121    /// a heap that is not surely empty, you should first clear it and
122    /// then you should set the cross reference map to \c PRE_HEAP
123    /// for each item.
124    void clear() { _data.clear(); }
125
126  private:
127    static int parent(int i) { return (i-1)/4; }
128    static int firstChild(int i) { return 4*i+1; }
129
130    bool less(const Pair &p1, const Pair &p2) const {
131      return _comp(p1.second, p2.second);
132    }
133
134    void bubbleUp(int hole, Pair p) {
135      int par = parent(hole);
136      while( hole>0 && less(p,_data[par]) ) {
137        move(_data[par],hole);
138        hole = par;
139        par = parent(hole);
140      }
141      move(p, hole);
142    }
143
144    void bubbleDown(int hole, Pair p, int length) {
145      if( length>1 ) {
146        int child = firstChild(hole);
147        while( child+3<length ) {
148          int min=child;
149          if( less(_data[++child], _data[min]) ) min=child;
150          if( less(_data[++child], _data[min]) ) min=child;
151          if( less(_data[++child], _data[min]) ) min=child;
152          if( !less(_data[min], p) )
153            goto ok;
154          move(_data[min], hole);
155          hole = min;
156          child = firstChild(hole);
157        }
158        if ( child<length ) {
159          int min = child;
160          if( ++child<length && less(_data[child], _data[min]) ) min=child;
161          if( ++child<length && less(_data[child], _data[min]) ) min=child;
162          if( less(_data[min], p) ) {
163            move(_data[min], hole);
164            hole = min;
165          }
166        }
167      }
168    ok:
169      move(p, hole);
170    }
171
172    void move(const Pair &p, int i) {
173      _data[i] = p;
174      _iim.set(p.first, i);
175    }
176
177  public:
178    /// \brief Insert a pair of item and priority into the heap.
179    ///
180    /// This function inserts \c p.first to the heap with priority
181    /// \c p.second.
182    /// \param p The pair to insert.
183    /// \pre \c p.first must not be stored in the heap.
184    void push(const Pair &p) {
185      int n = _data.size();
186      _data.resize(n+1);
187      bubbleUp(n, p);
188    }
189
190    /// \brief Insert an item into the heap with the given priority.
191    ///
192    /// This function inserts the given item into the heap with the
193    /// given priority.
194    /// \param i The item to insert.
195    /// \param p The priority of the item.
196    /// \pre \e i must not be stored in the heap.
197    void push(const Item &i, const Prio &p) { push(Pair(i,p)); }
198
199    /// \brief Return the item having minimum priority.
200    ///
201    /// This function returns the item having minimum priority.
202    /// \pre The heap must be non-empty.
203    Item top() const { return _data[0].first; }
204
205    /// \brief The minimum priority.
206    ///
207    /// This function returns the minimum priority.
208    /// \pre The heap must be non-empty.
209    Prio prio() const { return _data[0].second; }
210
211    /// \brief Remove the item having minimum priority.
212    ///
213    /// This function removes the item having minimum priority.
214    /// \pre The heap must be non-empty.
215    void pop() {
216      int n = _data.size()-1;
217      _iim.set(_data[0].first, POST_HEAP);
218      if (n>0) bubbleDown(0, _data[n], n);
219      _data.pop_back();
220    }
221
222    /// \brief Remove the given item from the heap.
223    ///
224    /// This function removes the given item from the heap if it is
225    /// already stored.
226    /// \param i The item to delete.
227    /// \pre \e i must be in the heap.
228    void erase(const Item &i) {
229      int h = _iim[i];
230      int n = _data.size()-1;
231      _iim.set(_data[h].first, POST_HEAP);
232      if( h<n ) {
233        if( less(_data[parent(h)], _data[n]) )
234          bubbleDown(h, _data[n], n);
235        else
236          bubbleUp(h, _data[n]);
237      }
238      _data.pop_back();
239    }
240
241    /// \brief The priority of the given item.
242    ///
243    /// This function returns the priority of the given item.
244    /// \param i The item.
245    /// \pre \e i must be in the heap.
246    Prio operator[](const Item &i) const {
247      int idx = _iim[i];
248      return _data[idx].second;
249    }
250
251    /// \brief Set the priority of an item or insert it, if it is
252    /// not stored in the heap.
253    ///
254    /// This method sets the priority of the given item if it is
255    /// already stored in the heap. Otherwise it inserts the given
256    /// item into the heap with the given priority.
257    /// \param i The item.
258    /// \param p The priority.
259    void set(const Item &i, const Prio &p) {
260      int idx = _iim[i];
261      if( idx < 0 )
262        push(i,p);
263      else if( _comp(p, _data[idx].second) )
264        bubbleUp(idx, Pair(i,p));
265      else
266        bubbleDown(idx, Pair(i,p), _data.size());
267    }
268
269    /// \brief Decrease the priority of an item to the given value.
270    ///
271    /// This function decreases the priority of an item to the given value.
272    /// \param i The item.
273    /// \param p The priority.
274    /// \pre \e i must be stored in the heap with priority at least \e p.
275    void decrease(const Item &i, const Prio &p) {
276      int idx = _iim[i];
277      bubbleUp(idx, Pair(i,p));
278    }
279
280    /// \brief Increase the priority of an item to the given value.
281    ///
282    /// This function increases the priority of an item to the given value.
283    /// \param i The item.
284    /// \param p The priority.
285    /// \pre \e i must be stored in the heap with priority at most \e p.
286    void increase(const Item &i, const Prio &p) {
287      int idx = _iim[i];
288      bubbleDown(idx, Pair(i,p), _data.size());
289    }
290
291    /// \brief Return the state of an item.
292    ///
293    /// This method returns \c PRE_HEAP if the given item has never
294    /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
295    /// and \c POST_HEAP otherwise.
296    /// In the latter case it is possible that the item will get back
297    /// to the heap again.
298    /// \param i The item.
299    State state(const Item &i) const {
300      int s = _iim[i];
301      if (s>=0) s=0;
302      return State(s);
303    }
304
305    /// \brief Set the state of an item in the heap.
306    ///
307    /// This function sets the state of the given item in the heap.
308    /// It can be used to manually clear the heap when it is important
309    /// to achive better time complexity.
310    /// \param i The item.
311    /// \param st The state. It should not be \c IN_HEAP.
312    void state(const Item& i, State st) {
313      switch (st) {
314        case POST_HEAP:
315        case PRE_HEAP:
316          if (state(i) == IN_HEAP) erase(i);
317          _iim[i] = st;
318          break;
319        case IN_HEAP:
320          break;
321      }
322    }
323
324    /// \brief Replace an item in the heap.
325    ///
326    /// This function replaces item \c i with item \c j.
327    /// Item \c i must be in the heap, while \c j must be out of the heap.
328    /// After calling this method, item \c i will be out of the
329    /// heap and \c j will be in the heap with the same prioriority
330    /// as item \c i had before.
331    void replace(const Item& i, const Item& j) {
332      int idx = _iim[i];
333      _iim.set(i, _iim[j]);
334      _iim.set(j, idx);
335      _data[idx].first = j;
336    }
337
338  }; // class FouraryHeap
339
340} // namespace lemon
341
342#endif // LEMON_FOURARY_HEAP_H
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