COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/fourary_heap.h @ 705:39a5b48bcace

Last change on this file since 705:39a5b48bcace was 705:39a5b48bcace, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Small improvements in heap implementations (#301)

File size: 10.9 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    int findMin(const int child, const int length) {
135      int min=child;
136      if( child+3<length ) {
137        if( less(_data[child+3], _data[min]) )
138          min=child+3;
139        if( less(_data[child+2], _data[min]) )
140          min=child+2;
141        if( less(_data[child+1], _data[min]) )
142          min=child+1;
143      }
144      else if( child+2<length ) {
145        if( less(_data[child+2], _data[min]) )
146          min=child+2;
147        if( less(_data[child+1], _data[min]) )
148          min=child+1;
149      }
150      else if( child+1<length ) {
151        if( less(_data[child+1], _data[min]) )
152          min=child+1;
153      }
154      return min;
155    }
156
157    void bubbleUp(int hole, Pair p) {
158      int par = parent(hole);
159      while( hole>0 && less(p,_data[par]) ) {
160        move(_data[par],hole);
161        hole = par;
162        par = parent(hole);
163      }
164      move(p, hole);
165    }
166
167    void bubbleDown(int hole, Pair p, int length) {
168      if( length>1 ) {
169        int child = firstChild(hole);
170        while( child<length ) {
171          child = findMin(child, length);
172          if( !less(_data[child], p) )
173            goto ok;
174          move(_data[child], hole);
175          hole = child;
176          child = firstChild(hole);
177        }
178      }
179    ok:
180      move(p, hole);
181    }
182
183    void move(const Pair &p, int i) {
184      _data[i] = p;
185      _iim.set(p.first, i);
186    }
187
188  public:
189    /// \brief Insert a pair of item and priority into the heap.
190    ///
191    /// This function inserts \c p.first to the heap with priority
192    /// \c p.second.
193    /// \param p The pair to insert.
194    /// \pre \c p.first must not be stored in the heap.
195    void push(const Pair &p) {
196      int n = _data.size();
197      _data.resize(n+1);
198      bubbleUp(n, p);
199    }
200
201    /// \brief Insert an item into the heap with the given priority.
202    ///
203    /// This function inserts the given item into the heap with the
204    /// given priority.
205    /// \param i The item to insert.
206    /// \param p The priority of the item.
207    /// \pre \e i must not be stored in the heap.
208    void push(const Item &i, const Prio &p) { push(Pair(i,p)); }
209
210    /// \brief Return the item having minimum priority.
211    ///
212    /// This function returns the item having minimum priority.
213    /// \pre The heap must be non-empty.
214    Item top() const { return _data[0].first; }
215
216    /// \brief The minimum priority.
217    ///
218    /// This function returns the minimum priority.
219    /// \pre The heap must be non-empty.
220    Prio prio() const { return _data[0].second; }
221
222    /// \brief Remove the item having minimum priority.
223    ///
224    /// This function removes the item having minimum priority.
225    /// \pre The heap must be non-empty.
226    void pop() {
227      int n = _data.size()-1;
228      _iim.set(_data[0].first, POST_HEAP);
229      if (n>0) bubbleDown(0, _data[n], n);
230      _data.pop_back();
231    }
232
233    /// \brief Remove the given item from the heap.
234    ///
235    /// This function removes the given item from the heap if it is
236    /// already stored.
237    /// \param i The item to delete.
238    /// \pre \e i must be in the heap.
239    void erase(const Item &i) {
240      int h = _iim[i];
241      int n = _data.size()-1;
242      _iim.set(_data[h].first, POST_HEAP);
243      if( h<n ) {
244        if( less(_data[parent(h)], _data[n]) )
245          bubbleDown(h, _data[n], n);
246        else
247          bubbleUp(h, _data[n]);
248      }
249      _data.pop_back();
250    }
251
252    /// \brief The priority of the given item.
253    ///
254    /// This function returns the priority of the given item.
255    /// \param i The item.
256    /// \pre \e i must be in the heap.
257    Prio operator[](const Item &i) const {
258      int idx = _iim[i];
259      return _data[idx].second;
260    }
261
262    /// \brief Set the priority of an item or insert it, if it is
263    /// not stored in the heap.
264    ///
265    /// This method sets the priority of the given item if it is
266    /// already stored in the heap. Otherwise it inserts the given
267    /// item into the heap with the given priority.
268    /// \param i The item.
269    /// \param p The priority.
270    void set(const Item &i, const Prio &p) {
271      int idx = _iim[i];
272      if( idx < 0 )
273        push(i,p);
274      else if( _comp(p, _data[idx].second) )
275        bubbleUp(idx, Pair(i,p));
276      else
277        bubbleDown(idx, Pair(i,p), _data.size());
278    }
279
280    /// \brief Decrease the priority of an item to the given value.
281    ///
282    /// This function decreases 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 least \e p.
286    void decrease(const Item &i, const Prio &p) {
287      int idx = _iim[i];
288      bubbleUp(idx, Pair(i,p));
289    }
290
291    /// \brief Increase the priority of an item to the given value.
292    ///
293    /// This function increases the priority of an item to the given value.
294    /// \param i The item.
295    /// \param p The priority.
296    /// \pre \e i must be stored in the heap with priority at most \e p.
297    void increase(const Item &i, const Prio &p) {
298      int idx = _iim[i];
299      bubbleDown(idx, Pair(i,p), _data.size());
300    }
301
302    /// \brief Return the state of an item.
303    ///
304    /// This method returns \c PRE_HEAP if the given item has never
305    /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
306    /// and \c POST_HEAP otherwise.
307    /// In the latter case it is possible that the item will get back
308    /// to the heap again.
309    /// \param i The item.
310    State state(const Item &i) const {
311      int s = _iim[i];
312      if (s>=0) s=0;
313      return State(s);
314    }
315
316    /// \brief Set the state of an item in the heap.
317    ///
318    /// This function sets the state of the given item in the heap.
319    /// It can be used to manually clear the heap when it is important
320    /// to achive better time complexity.
321    /// \param i The item.
322    /// \param st The state. It should not be \c IN_HEAP.
323    void state(const Item& i, State st) {
324      switch (st) {
325        case POST_HEAP:
326        case PRE_HEAP:
327          if (state(i) == IN_HEAP) erase(i);
328          _iim[i] = st;
329          break;
330        case IN_HEAP:
331          break;
332      }
333    }
334
335    /// \brief Replace an item in the heap.
336    ///
337    /// This function replaces item \c i with item \c j.
338    /// Item \c i must be in the heap, while \c j must be out of the heap.
339    /// After calling this method, item \c i will be out of the
340    /// heap and \c j will be in the heap with the same prioriority
341    /// as item \c i had before.
342    void replace(const Item& i, const Item& j) {
343      int idx = _iim[i];
344      _iim.set(i, _iim[j]);
345      _iim.set(j, idx);
346      _data[idx].first = j;
347    }
348
349  }; // class FouraryHeap
350
351} // namespace lemon
352
353#endif // LEMON_FOURARY_HEAP_H
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