COIN-OR::LEMON - Graph Library

source: lemon/lemon/fourary_heap.h @ 750:bb3392fe91f2

Last change on this file since 750:bb3392fe91f2 was 750:bb3392fe91f2, checked in by Peter Kovacs <kpeter@…>, 10 years ago

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