COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/bin_heap.h @ 2391:14a343be7a5a

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1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2007
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_BIN_HEAP_H
20#define LEMON_BIN_HEAP_H
21
22///\ingroup auxdat
23///\file
24///\brief Binary Heap implementation.
25
26#include <vector>
27#include <utility>
28#include <functional>
29
30namespace lemon {
31
32  /// \ingroup auxdat
33
34  /// A Binary Heap implementation.
35 
36  ///This class implements the \e binary \e heap data structure. A \e heap
37  ///is a data structure for storing items with specified values called \e
38  ///priorities in such a way that finding the item with minimum priority is
39  ///efficient. \c Compare specifies the ordering of the priorities. In a heap
40  ///one can change the priority of an item, add or erase an item, etc.
41  ///
42  ///\param Prio Type of the priority of the items.
43  ///\param ItemIntMap A read and writable Item int map, used internally
44  ///to handle the cross references.
45  ///\param Compare A class for the ordering of the priorities. The
46  ///default is \c std::less<Prio>.
47  ///
48  ///\sa FibHeap
49  ///\sa Dijkstra
50  template <typename Prio, typename ItemIntMap,
51            typename Compare = std::less<Prio> >
52  class BinHeap {
53
54  public:
55    typedef typename ItemIntMap::Key         ItemType;
56    typedef Prio                             PrioType;
57    typedef std::pair<ItemType,PrioType>     PairType;
58    typedef ItemIntMap                       ItemIntMapType;
59    typedef Compare                          PrioCompare;
60
61    /// \brief Type to represent the items states.
62    ///
63    /// Each Item element have a state associated to it. It may be "in heap",
64    /// "pre heap" or "post heap". The latter two are indifferent from the
65    /// heap's point of view, but may be useful to the user.
66    ///
67    /// The ItemIntMap \e should be initialized in such way that it maps
68    /// PRE_HEAP (-1) to any element to be put in the heap...
69    enum state_enum {
70      IN_HEAP = 0,
71      PRE_HEAP = -1,
72      POST_HEAP = -2
73    };
74
75  private:
76    std::vector<PairType> data;
77    Compare comp;
78    ItemIntMap &iim;
79
80  public:
81    /// \brief The constructor.
82    ///
83    /// The constructor.
84    /// \param _iim should be given to the constructor, since it is used
85    /// internally to handle the cross references. The value of the map
86    /// should be PRE_HEAP (-1) for each element.
87    explicit BinHeap(ItemIntMap &_iim) : iim(_iim) {}
88   
89    /// \brief The constructor.
90    ///
91    /// The constructor.
92    /// \param _iim should be given to the constructor, since it is used
93    /// internally to handle the cross references. The value of the map
94    /// should be PRE_HEAP (-1) for each element.
95    ///
96    /// \param _comp The comparator function object.
97    BinHeap(ItemIntMap &_iim, const Compare &_comp)
98      : iim(_iim), comp(_comp) {}
99
100
101    /// The number of items stored in the heap.
102    ///
103    /// \brief Returns the number of items stored in the heap.
104    int size() const { return data.size(); }
105   
106    /// \brief Checks if the heap stores no items.
107    ///
108    /// Returns \c true if and only if the heap stores no items.
109    bool empty() const { return data.empty(); }
110
111    /// \brief Make empty this heap.
112    ///
113    /// Make empty this heap. It does not change the cross reference map.
114    /// If you want to reuse what is not surely empty you should first clear
115    /// the heap and after that you should set the cross reference map for
116    /// each item to \c PRE_HEAP.
117    void clear() {
118      data.clear();
119    }
120
121  private:
122    static int parent(int i) { return (i-1)/2; }
123    static int second_child(int i) { return 2*i+2; }
124    bool less(const PairType &p1, const PairType &p2) const {
125      return comp(p1.second, p2.second);
126    }
127
128    int bubble_up(int hole, PairType p);
129    int bubble_down(int hole, PairType p, int length);
130
131    void move(const PairType &p, int i) {
132      data[i] = p;
133      iim.set(p.first, i);
134    }
135
136    void rmidx(int h) {
137      int n = data.size()-1;
138      if( h>=0 && h<=n ) {
139        iim.set(data[h].first, POST_HEAP);
140        if ( h<n ) {
141          bubble_down(h, data[n], n);
142        }
143        data.pop_back();
144      }
145    }
146
147  public:
148    /// \brief Insert a pair of item and priority into the heap.
149    ///
150    /// Adds \c p.first to the heap with priority \c p.second.
151    /// \param p The pair to insert.
152    void push(const PairType &p) {
153      int n = data.size();
154      data.resize(n+1);
155      bubble_up(n, p);
156    }
157
158    /// \brief Insert an item into the heap with the given heap.
159    ///   
160    /// Adds \c i to the heap with priority \c p.
161    /// \param i The item to insert.
162    /// \param p The priority of the item.
163    void push(const ItemType &i, const Prio &p) { push(PairType(i,p)); }
164
165    /// \brief Returns the item with minimum priority relative to \c Compare.
166    ///
167    /// This method returns the item with minimum priority relative to \c
168    /// Compare. 
169    /// \pre The heap must be nonempty. 
170    ItemType top() const {
171      return data[0].first;
172    }
173
174    /// \brief Returns the minimum priority relative to \c Compare.
175    ///
176    /// It returns the minimum priority relative to \c Compare.
177    /// \pre The heap must be nonempty.
178    Prio prio() const {
179      return data[0].second;
180    }
181
182    /// \brief Deletes the item with minimum priority relative to \c Compare.
183    ///
184    /// This method deletes the item with minimum priority relative to \c
185    /// Compare from the heap. 
186    /// \pre The heap must be non-empty. 
187    void pop() {
188      rmidx(0);
189    }
190
191    /// \brief Deletes \c i from the heap.
192    ///
193    /// This method deletes item \c i from the heap, if \c i was
194    /// already stored in the heap.
195    /// \param i The item to erase.
196    void erase(const ItemType &i) {
197      rmidx(iim[i]);
198    }
199
200   
201    /// \brief Returns the priority of \c i.
202    ///
203    /// This function returns the priority of item \c i. 
204    /// \pre \c i must be in the heap.
205    /// \param i The item.
206    Prio operator[](const ItemType &i) const {
207      int idx = iim[i];
208      return data[idx].second;
209    }
210
211    /// \brief \c i gets to the heap with priority \c p independently
212    /// if \c i was already there.
213    ///
214    /// This method calls \ref push(\c i, \c p) if \c i is not stored
215    /// in the heap and sets the priority of \c i to \c p otherwise.
216    /// \param i The item.
217    /// \param p The priority.
218    void set(const ItemType &i, const Prio &p) {
219      int idx = iim[i];
220      if( idx < 0 ) {
221        push(i,p);
222      }
223      else if( comp(p, data[idx].second) ) {
224        bubble_up(idx, PairType(i,p));
225      }
226      else {
227        bubble_down(idx, PairType(i,p), data.size());
228      }
229    }
230
231    /// \brief Decreases the priority of \c i to \c p.
232
233    /// This method decreases the priority of item \c i to \c p.
234    /// \pre \c i must be stored in the heap with priority at least \c
235    /// p relative to \c Compare.
236    /// \param i The item.
237    /// \param p The priority.
238    void decrease(const ItemType &i, const Prio &p) {
239      int idx = iim[i];
240      bubble_up(idx, PairType(i,p));
241    }
242   
243    /// \brief Increases the priority of \c i to \c p.
244    ///
245    /// This method sets the priority of item \c i to \c p.
246    /// \pre \c i must be stored in the heap with priority at most \c
247    /// p relative to \c Compare.
248    /// \param i The item.
249    /// \param p The priority.
250    void increase(const ItemType &i, const Prio &p) {
251      int idx = iim[i];
252      bubble_down(idx, PairType(i,p), data.size());
253    }
254
255    /// \brief Returns if \c item is in, has already been in, or has
256    /// never been in the heap.
257    ///
258    /// This method returns PRE_HEAP if \c item has never been in the
259    /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
260    /// otherwise. In the latter case it is possible that \c item will
261    /// get back to the heap again.
262    /// \param i The item.
263    state_enum state(const ItemType &i) const {
264      int s = iim[i];
265      if( s>=0 )
266        s=0;
267      return state_enum(s);
268    }
269
270    /// \brief Sets the state of the \c item in the heap.
271    ///
272    /// Sets the state of the \c item in the heap. It can be used to
273    /// manually clear the heap when it is important to achive the
274    /// better time complexity.
275    /// \param i The item.
276    /// \param st The state. It should not be \c IN_HEAP.
277    void state(const ItemType& i, state_enum st) {
278      switch (st) {
279      case POST_HEAP:
280      case PRE_HEAP:
281        if (state(i) == IN_HEAP) {
282          erase(i);
283        }
284        iim[i] = st;
285        break;
286      case IN_HEAP:
287        break;
288      }
289    }
290
291  }; // class BinHeap
292
293 
294  template <typename V, typename M, typename C>
295  int BinHeap<V,M,C>::bubble_up(int hole, PairType p) {
296    int par = parent(hole);
297    while( hole>0 && less(p,data[par]) ) {
298      move(data[par],hole);
299      hole = par;
300      par = parent(hole);
301    }
302    move(p, hole);
303    return hole;
304  }
305
306  template <typename V, typename M, typename C>
307  int BinHeap<V,M,C>::bubble_down(int hole, PairType p, int length) {
308    int child = second_child(hole);
309    while(child < length) {
310      if( less(data[child-1], data[child]) ) {
311        --child;
312      }
313      if( !less(data[child], p) )
314        goto ok;
315      move(data[child], hole);
316      hole = child;
317      child = second_child(hole);
318    }
319    child--;
320    if( child<length && less(data[child], p) ) {
321      move(data[child], hole);
322      hole=child;
323    }
324  ok:
325    move(p, hole);
326    return hole;
327  }
328
329
330} // namespace lemon
331
332#endif // LEMON_BIN_HEAP_H
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