COIN-OR::LEMON - Graph Library

source: lemon/lemon/dheap.h @ 929:65a0521e744e

Last change on this file since 929:65a0521e744e was 929:65a0521e744e, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Rename heap structures (#301)

File size: 11.0 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_DHEAP_H
20#define LEMON_DHEAP_H
21
22///\ingroup heaps
23///\file
24///\brief D-ary heap implementation.
25
26#include <vector>
27#include <utility>
28#include <functional>
29
30namespace lemon {
31
32  /// \ingroup heaps
33  ///
34  ///\brief D-ary heap data structure.
35  ///
36  /// This class implements the \e D-ary \e heap data structure.
37  /// It fully conforms to the \ref concepts::Heap "heap concept".
38  ///
39  /// The \ref DHeap "D-ary heap" is a generalization of the
40  /// \ref BinHeap "binary heap" structure, its nodes have at most
41  /// \c D children, instead of two.
42  /// \ref BinHeap and \ref QuadHeap are specialized implementations
43  /// of this structure for <tt>D=2</tt> and <tt>D=4</tt>, respectively.
44  ///
45  /// \tparam PR Type of the priorities of the items.
46  /// \tparam IM A read-writable item map with \c int values, used
47  /// internally to handle the cross references.
48  /// \tparam D The degree of the heap, each node have at most \e D
49  /// children. The default is 16. Powers of two are suggested to use
50  /// so that the multiplications and divisions needed to traverse the
51  /// nodes of the heap could be performed faster.
52  /// \tparam CMP A functor class for comparing the priorities.
53  /// The default is \c std::less<PR>.
54  ///
55  ///\sa BinHeap
56  ///\sa FouraryHeap
57#ifdef DOXYGEN
58  template <typename PR, typename IM, int D, typename CMP>
59#else
60  template <typename PR, typename IM, int D = 16,
61            typename CMP = std::less<PR> >
62#endif
63  class DHeap {
64  public:
65    /// Type of the item-int map.
66    typedef IM ItemIntMap;
67    /// Type of the priorities.
68    typedef PR Prio;
69    /// Type of the items stored in the heap.
70    typedef typename ItemIntMap::Key Item;
71    /// Type of the item-priority pairs.
72    typedef std::pair<Item,Prio> Pair;
73    /// Functor type for comparing the priorities.
74    typedef CMP Compare;
75
76    /// \brief Type to represent the states of the items.
77    ///
78    /// Each item has a state associated to it. It can be "in heap",
79    /// "pre-heap" or "post-heap". The latter two are indifferent from the
80    /// heap's point of view, but may be useful to the user.
81    ///
82    /// The item-int map must be initialized in such way that it assigns
83    /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
84    enum State {
85      IN_HEAP = 0,    ///< = 0.
86      PRE_HEAP = -1,  ///< = -1.
87      POST_HEAP = -2  ///< = -2.
88    };
89
90  private:
91    std::vector<Pair> _data;
92    Compare _comp;
93    ItemIntMap &_iim;
94
95  public:
96    /// \brief Constructor.
97    ///
98    /// Constructor.
99    /// \param map A map that assigns \c int values to the items.
100    /// It is used internally to handle the cross references.
101    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
102    explicit DHeap(ItemIntMap &map) : _iim(map) {}
103
104    /// \brief Constructor.
105    ///
106    /// Constructor.
107    /// \param map A map that assigns \c int values to the items.
108    /// It is used internally to handle the cross references.
109    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
110    /// \param comp The function object used for comparing the priorities.
111    DHeap(ItemIntMap &map, const Compare &comp)
112      : _iim(map), _comp(comp) {}
113
114    /// \brief The number of items stored in the heap.
115    ///
116    /// This function returns the number of items stored in the heap.
117    int size() const { return _data.size(); }
118
119    /// \brief Check if the heap is empty.
120    ///
121    /// This function returns \c true if the heap is empty.
122    bool empty() const { return _data.empty(); }
123
124    /// \brief Make the heap empty.
125    ///
126    /// This functon makes the heap empty.
127    /// It does not change the cross reference map. If you want to reuse
128    /// a heap that is not surely empty, you should first clear it and
129    /// then you should set the cross reference map to \c PRE_HEAP
130    /// for each item.
131    void clear() { _data.clear(); }
132
133  private:
134    int parent(int i) { return (i-1)/D; }
135    int firstChild(int i) { return D*i+1; }
136
137    bool less(const Pair &p1, const Pair &p2) const {
138      return _comp(p1.second, p2.second);
139    }
140
141    void bubbleUp(int hole, Pair p) {
142      int par = parent(hole);
143      while( hole>0 && less(p,_data[par]) ) {
144        move(_data[par],hole);
145        hole = par;
146        par = parent(hole);
147      }
148      move(p, hole);
149    }
150
151    void bubbleDown(int hole, Pair p, int length) {
152      if( length>1 ) {
153        int child = firstChild(hole);
154        while( child+D<=length ) {
155          int min=child;
156          for (int i=1; i<D; ++i) {
157            if( less(_data[child+i], _data[min]) )
158              min=child+i;
159          }
160          if( !less(_data[min], p) )
161            goto ok;
162          move(_data[min], hole);
163          hole = min;
164          child = firstChild(hole);
165        }
166        if ( child<length ) {
167          int min = child;
168          while (++child < length) {
169            if( less(_data[child], _data[min]) )
170              min=child;
171          }
172          if( less(_data[min], p) ) {
173            move(_data[min], hole);
174            hole = min;
175          }
176        }
177      }
178    ok:
179      move(p, hole);
180    }
181
182    void move(const Pair &p, int i) {
183      _data[i] = p;
184      _iim.set(p.first, i);
185    }
186
187  public:
188    /// \brief Insert a pair of item and priority into the heap.
189    ///
190    /// This function inserts \c p.first to the heap with priority
191    /// \c p.second.
192    /// \param p The pair to insert.
193    /// \pre \c p.first must not be stored in the heap.
194    void push(const Pair &p) {
195      int n = _data.size();
196      _data.resize(n+1);
197      bubbleUp(n, p);
198    }
199
200    /// \brief Insert an item into the heap with the given priority.
201    ///
202    /// This function inserts the given item into the heap with the
203    /// given priority.
204    /// \param i The item to insert.
205    /// \param p The priority of the item.
206    /// \pre \e i must not be stored in the heap.
207    void push(const Item &i, const Prio &p) { push(Pair(i,p)); }
208
209    /// \brief Return the item having minimum priority.
210    ///
211    /// This function returns the item having minimum priority.
212    /// \pre The heap must be non-empty.
213    Item top() const { return _data[0].first; }
214
215    /// \brief The minimum priority.
216    ///
217    /// This function returns the minimum priority.
218    /// \pre The heap must be non-empty.
219    Prio prio() const { return _data[0].second; }
220
221    /// \brief Remove the item having minimum priority.
222    ///
223    /// This function removes the item having minimum priority.
224    /// \pre The heap must be non-empty.
225    void pop() {
226      int n = _data.size()-1;
227      _iim.set(_data[0].first, POST_HEAP);
228      if (n>0) bubbleDown(0, _data[n], n);
229      _data.pop_back();
230    }
231
232    /// \brief Remove the given item from the heap.
233    ///
234    /// This function removes the given item from the heap if it is
235    /// already stored.
236    /// \param i The item to delete.
237    /// \pre \e i must be in the heap.
238    void erase(const Item &i) {
239      int h = _iim[i];
240      int n = _data.size()-1;
241      _iim.set(_data[h].first, POST_HEAP);
242      if( h<n ) {
243        if( less(_data[parent(h)], _data[n]) )
244          bubbleDown(h, _data[n], n);
245        else
246          bubbleUp(h, _data[n]);
247      }
248      _data.pop_back();
249    }
250
251    /// \brief The priority of the given item.
252    ///
253    /// This function returns the priority of the given item.
254    /// \param i The item.
255    /// \pre \e i must be in the heap.
256    Prio operator[](const Item &i) const {
257      int idx = _iim[i];
258      return _data[idx].second;
259    }
260
261    /// \brief Set the priority of an item or insert it, if it is
262    /// not stored in the heap.
263    ///
264    /// This method sets the priority of the given item if it is
265    /// already stored in the heap. Otherwise it inserts the given
266    /// item into the heap with the given priority.
267    /// \param i The item.
268    /// \param p The priority.
269    void set(const Item &i, const Prio &p) {
270      int idx = _iim[i];
271      if( idx<0 )
272        push(i,p);
273      else if( _comp(p, _data[idx].second) )
274        bubbleUp(idx, Pair(i,p));
275      else
276        bubbleDown(idx, Pair(i,p), _data.size());
277    }
278
279    /// \brief Decrease the priority of an item to the given value.
280    ///
281    /// This function decreases the priority of an item to the given value.
282    /// \param i The item.
283    /// \param p The priority.
284    /// \pre \e i must be stored in the heap with priority at least \e p.
285    void decrease(const Item &i, const Prio &p) {
286      int idx = _iim[i];
287      bubbleUp(idx, Pair(i,p));
288    }
289
290    /// \brief Increase the priority of an item to the given value.
291    ///
292    /// This function increases the priority of an item to the given value.
293    /// \param i The item.
294    /// \param p The priority.
295    /// \pre \e i must be stored in the heap with priority at most \e p.
296    void increase(const Item &i, const Prio &p) {
297      int idx = _iim[i];
298      bubbleDown(idx, Pair(i,p), _data.size());
299    }
300
301    /// \brief Return the state of an item.
302    ///
303    /// This method returns \c PRE_HEAP if the given item has never
304    /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
305    /// and \c POST_HEAP otherwise.
306    /// In the latter case it is possible that the item will get back
307    /// to the heap again.
308    /// \param i The item.
309    State state(const Item &i) const {
310      int s = _iim[i];
311      if (s>=0) s=0;
312      return State(s);
313    }
314
315    /// \brief Set the state of an item in the heap.
316    ///
317    /// This function sets the state of the given item in the heap.
318    /// It can be used to manually clear the heap when it is important
319    /// to achive better time complexity.
320    /// \param i The item.
321    /// \param st The state. It should not be \c IN_HEAP.
322    void state(const Item& i, State st) {
323      switch (st) {
324        case POST_HEAP:
325        case PRE_HEAP:
326          if (state(i) == IN_HEAP) erase(i);
327          _iim[i] = st;
328          break;
329        case IN_HEAP:
330          break;
331      }
332    }
333
334    /// \brief Replace an item in the heap.
335    ///
336    /// This function replaces item \c i with item \c j.
337    /// Item \c i must be in the heap, while \c j must be out of the heap.
338    /// After calling this method, item \c i will be out of the
339    /// heap and \c j will be in the heap with the same prioriority
340    /// as item \c i had before.
341    void replace(const Item& i, const Item& j) {
342      int idx=_iim[i];
343      _iim.set(i, _iim[j]);
344      _iim.set(j, idx);
345      _data[idx].first=j;
346    }
347
348  }; // class DHeap
349
350} // namespace lemon
351
352#endif // LEMON_DHEAP_H
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