COIN-OR::LEMON - Graph Library

source: lemon/lemon/quad_heap.h @ 1298:a78e5b779b69

Last change on this file since 1298:a78e5b779b69 was 929:65a0521e744e, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Rename heap structures (#301)

File size: 10.8 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_QUAD_HEAP_H
20#define LEMON_QUAD_HEAP_H
21
22///\ingroup heaps
23///\file
24///\brief Fourary (quaternary) heap implementation.
25
26#include <vector>
27#include <utility>
28#include <functional>
29
30namespace lemon {
31
32  /// \ingroup heaps
33  ///
34  ///\brief Fourary (quaternary) heap data structure.
35  ///
36  /// This class implements the \e Fourary (\e quaternary) \e heap
37  /// data structure.
38  /// It fully conforms to the \ref concepts::Heap "heap concept".
39  ///
40  /// The fourary heap is a specialization of the \ref DHeap "D-ary heap"
41  /// for <tt>D=4</tt>. It is similar to the \ref BinHeap "binary heap",
42  /// but its nodes have at most four children, instead of two.
43  ///
44  /// \tparam PR Type of the priorities of the items.
45  /// \tparam IM A read-writable item map with \c int values, used
46  /// internally to handle the cross references.
47  /// \tparam CMP A functor class for comparing the priorities.
48  /// The default is \c std::less<PR>.
49  ///
50  ///\sa BinHeap
51  ///\sa DHeap
52#ifdef DOXYGEN
53  template <typename PR, typename IM, typename CMP>
54#else
55  template <typename PR, typename IM, typename CMP = std::less<PR> >
56#endif
57  class QuadHeap {
58  public:
59    /// Type of the item-int map.
60    typedef IM ItemIntMap;
61    /// Type of the priorities.
62    typedef PR Prio;
63    /// Type of the items stored in the heap.
64    typedef typename ItemIntMap::Key Item;
65    /// Type of the item-priority pairs.
66    typedef std::pair<Item,Prio> Pair;
67    /// Functor type for comparing the priorities.
68    typedef CMP Compare;
69
70    /// \brief Type to represent the states of the items.
71    ///
72    /// Each item has a state associated to it. It can be "in heap",
73    /// "pre-heap" or "post-heap". The latter two are indifferent from the
74    /// heap's point of view, but may be useful to the user.
75    ///
76    /// The item-int map must be initialized in such way that it assigns
77    /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
78    enum State {
79      IN_HEAP = 0,    ///< = 0.
80      PRE_HEAP = -1,  ///< = -1.
81      POST_HEAP = -2  ///< = -2.
82    };
83
84  private:
85    std::vector<Pair> _data;
86    Compare _comp;
87    ItemIntMap &_iim;
88
89  public:
90    /// \brief Constructor.
91    ///
92    /// Constructor.
93    /// \param map A map that assigns \c int values to the items.
94    /// It is used internally to handle the cross references.
95    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
96    explicit QuadHeap(ItemIntMap &map) : _iim(map) {}
97
98    /// \brief Constructor.
99    ///
100    /// Constructor.
101    /// \param map A map that assigns \c int values to the items.
102    /// It is used internally to handle the cross references.
103    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
104    /// \param comp The function object used for comparing the priorities.
105    QuadHeap(ItemIntMap &map, const Compare &comp)
106      : _iim(map), _comp(comp) {}
107
108    /// \brief The number of items stored in the heap.
109    ///
110    /// This function returns the number of items stored in the heap.
111    int size() const { return _data.size(); }
112
113    /// \brief Check if the heap is empty.
114    ///
115    /// This function returns \c true if the heap is empty.
116    bool empty() const { return _data.empty(); }
117
118    /// \brief Make the heap empty.
119    ///
120    /// This functon makes the heap empty.
121    /// It does not change the cross reference map. If you want to reuse
122    /// a heap that is not surely empty, you should first clear it and
123    /// then you should set the cross reference map to \c PRE_HEAP
124    /// for each item.
125    void clear() { _data.clear(); }
126
127  private:
128    static int parent(int i) { return (i-1)/4; }
129    static int firstChild(int i) { return 4*i+1; }
130
131    bool less(const Pair &p1, const Pair &p2) const {
132      return _comp(p1.second, p2.second);
133    }
134
135    void bubbleUp(int hole, Pair p) {
136      int par = parent(hole);
137      while( hole>0 && less(p,_data[par]) ) {
138        move(_data[par],hole);
139        hole = par;
140        par = parent(hole);
141      }
142      move(p, hole);
143    }
144
145    void bubbleDown(int hole, Pair p, int length) {
146      if( length>1 ) {
147        int child = firstChild(hole);
148        while( child+3<length ) {
149          int min=child;
150          if( less(_data[++child], _data[min]) ) min=child;
151          if( less(_data[++child], _data[min]) ) min=child;
152          if( less(_data[++child], _data[min]) ) min=child;
153          if( !less(_data[min], p) )
154            goto ok;
155          move(_data[min], hole);
156          hole = min;
157          child = firstChild(hole);
158        }
159        if ( child<length ) {
160          int min = child;
161          if( ++child<length && less(_data[child], _data[min]) ) min=child;
162          if( ++child<length && less(_data[child], _data[min]) ) min=child;
163          if( less(_data[min], p) ) {
164            move(_data[min], hole);
165            hole = min;
166          }
167        }
168      }
169    ok:
170      move(p, hole);
171    }
172
173    void move(const Pair &p, int i) {
174      _data[i] = p;
175      _iim.set(p.first, i);
176    }
177
178  public:
179    /// \brief Insert a pair of item and priority into the heap.
180    ///
181    /// This function inserts \c p.first to the heap with priority
182    /// \c p.second.
183    /// \param p The pair to insert.
184    /// \pre \c p.first must not be stored in the heap.
185    void push(const Pair &p) {
186      int n = _data.size();
187      _data.resize(n+1);
188      bubbleUp(n, p);
189    }
190
191    /// \brief Insert an item into the heap with the given priority.
192    ///
193    /// This function inserts the given item into the heap with the
194    /// given priority.
195    /// \param i The item to insert.
196    /// \param p The priority of the item.
197    /// \pre \e i must not be stored in the heap.
198    void push(const Item &i, const Prio &p) { push(Pair(i,p)); }
199
200    /// \brief Return the item having minimum priority.
201    ///
202    /// This function returns the item having minimum priority.
203    /// \pre The heap must be non-empty.
204    Item top() const { return _data[0].first; }
205
206    /// \brief The minimum priority.
207    ///
208    /// This function returns the minimum priority.
209    /// \pre The heap must be non-empty.
210    Prio prio() const { return _data[0].second; }
211
212    /// \brief Remove the item having minimum priority.
213    ///
214    /// This function removes the item having minimum priority.
215    /// \pre The heap must be non-empty.
216    void pop() {
217      int n = _data.size()-1;
218      _iim.set(_data[0].first, POST_HEAP);
219      if (n>0) bubbleDown(0, _data[n], n);
220      _data.pop_back();
221    }
222
223    /// \brief Remove the given item from the heap.
224    ///
225    /// This function removes the given item from the heap if it is
226    /// already stored.
227    /// \param i The item to delete.
228    /// \pre \e i must be in the heap.
229    void erase(const Item &i) {
230      int h = _iim[i];
231      int n = _data.size()-1;
232      _iim.set(_data[h].first, POST_HEAP);
233      if( h<n ) {
234        if( less(_data[parent(h)], _data[n]) )
235          bubbleDown(h, _data[n], n);
236        else
237          bubbleUp(h, _data[n]);
238      }
239      _data.pop_back();
240    }
241
242    /// \brief The priority of the given item.
243    ///
244    /// This function returns the priority of the given item.
245    /// \param i The item.
246    /// \pre \e i must be in the heap.
247    Prio operator[](const Item &i) const {
248      int idx = _iim[i];
249      return _data[idx].second;
250    }
251
252    /// \brief Set the priority of an item or insert it, if it is
253    /// not stored in the heap.
254    ///
255    /// This method sets the priority of the given item if it is
256    /// already stored in the heap. Otherwise it inserts the given
257    /// item into the heap with the given priority.
258    /// \param i The item.
259    /// \param p The priority.
260    void set(const Item &i, const Prio &p) {
261      int idx = _iim[i];
262      if( idx < 0 )
263        push(i,p);
264      else if( _comp(p, _data[idx].second) )
265        bubbleUp(idx, Pair(i,p));
266      else
267        bubbleDown(idx, Pair(i,p), _data.size());
268    }
269
270    /// \brief Decrease the priority of an item to the given value.
271    ///
272    /// This function decreases the priority of an item to the given value.
273    /// \param i The item.
274    /// \param p The priority.
275    /// \pre \e i must be stored in the heap with priority at least \e p.
276    void decrease(const Item &i, const Prio &p) {
277      int idx = _iim[i];
278      bubbleUp(idx, Pair(i,p));
279    }
280
281    /// \brief Increase the priority of an item to the given value.
282    ///
283    /// This function increases the priority of an item to the given value.
284    /// \param i The item.
285    /// \param p The priority.
286    /// \pre \e i must be stored in the heap with priority at most \e p.
287    void increase(const Item &i, const Prio &p) {
288      int idx = _iim[i];
289      bubbleDown(idx, Pair(i,p), _data.size());
290    }
291
292    /// \brief Return the state of an item.
293    ///
294    /// This method returns \c PRE_HEAP if the given item has never
295    /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
296    /// and \c POST_HEAP otherwise.
297    /// In the latter case it is possible that the item will get back
298    /// to the heap again.
299    /// \param i The item.
300    State state(const Item &i) const {
301      int s = _iim[i];
302      if (s>=0) s=0;
303      return State(s);
304    }
305
306    /// \brief Set the state of an item in the heap.
307    ///
308    /// This function sets the state of the given item in the heap.
309    /// It can be used to manually clear the heap when it is important
310    /// to achive better time complexity.
311    /// \param i The item.
312    /// \param st The state. It should not be \c IN_HEAP.
313    void state(const Item& i, State st) {
314      switch (st) {
315        case POST_HEAP:
316        case PRE_HEAP:
317          if (state(i) == IN_HEAP) erase(i);
318          _iim[i] = st;
319          break;
320        case IN_HEAP:
321          break;
322      }
323    }
324
325    /// \brief Replace an item in the heap.
326    ///
327    /// This function replaces item \c i with item \c j.
328    /// Item \c i must be in the heap, while \c j must be out of the heap.
329    /// After calling this method, item \c i will be out of the
330    /// heap and \c j will be in the heap with the same prioriority
331    /// as item \c i had before.
332    void replace(const Item& i, const Item& j) {
333      int idx = _iim[i];
334      _iim.set(i, _iim[j]);
335      _iim.set(j, idx);
336      _data[idx].first = j;
337    }
338
339  }; // class QuadHeap
340
341} // namespace lemon
342
343#endif // LEMON_FOURARY_HEAP_H
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