COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/radix_heap.h @ 1834:0a14e1ae45a1

Last change on this file since 1834:0a14e1ae45a1 was 1834:0a14e1ae45a1, checked in by Balazs Dezso, 14 years ago

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1/* -*- C++ -*-
2 * lemon/radix_heap.h - Part of LEMON, a generic C++ optimization library
3 *
4 * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5 * (Egervary Research Group on Combinatorial Optimization, EGRES).
6 *
7 * Permission to use, modify and distribute this software is granted
8 * provided that this copyright notice appears in all copies. For
9 * precise terms see the accompanying LICENSE file.
10 *
11 * This software is provided "AS IS" with no warranty of any kind,
12 * express or implied, and with no claim as to its suitability for any
13 * purpose.
14 *
15 */
16
17#ifndef LEMON_RADIX_HEAP_H
18#define LEMON_RADIX_HEAP_H
19
20///\ingroup auxdat
21///\file
22///\brief Radix Heap implementation.
23
24#include <vector>
25#include <lemon/error.h>
26
27namespace lemon {
28
29  /// \brief Exception thrown by RadixHeap.
30  /// 
31  /// This Exception is thrown when a smaller priority
32  /// is inserted into the \e RadixHeap then the last time erased.
33  /// \see RadixHeap
34  /// \author Balazs Dezso
35
36  class UnderFlowPriorityError : public RuntimeError {
37  public:
38    virtual const char* exceptionName() const {
39      return "lemon::UnderFlowPriorityError";
40    } 
41  };
42
43  /// \ingroup auxdata
44  ///
45  /// \brief A Radix Heap implementation.
46  ///
47  /// This class implements the \e radix \e heap data structure. A \e heap
48  /// is a data structure for storing items with specified values called \e
49  /// priorities in such a way that finding the item with minimum priority is
50  /// efficient. This heap type can store only items with \e int priority.
51  /// In a heap one can change the priority of an item, add or erase an
52  /// item, but the priority cannot be decreased under the last removed
53  /// item's priority.
54  ///
55  /// \param _Item Type of the items to be stored. 
56  /// \param _ItemIntMap A read and writable Item int map, used internally
57  /// to handle the cross references.
58  ///
59  /// \see BinHeap
60  /// \see Dijkstra
61  /// \author Balazs Dezso
62
63  template <typename _Item, typename _ItemIntMap>
64  class RadixHeap {
65
66  public:
67    typedef _Item Item;
68    typedef int Prio;
69    typedef _ItemIntMap ItemIntMap;
70
71    /// \brief Type to represent the items states.
72    ///
73    /// Each Item element have a state associated to it. It may be "in heap",
74    /// "pre heap" or "post heap". The latter two are indifferent from the
75    /// heap's point of view, but may be useful to the user.
76    ///
77    /// The ItemIntMap \e should be initialized in such way that it maps
78    /// PRE_HEAP (-1) to any element to be put in the heap...
79    enum state_enum {
80      IN_HEAP = 0,
81      PRE_HEAP = -1,
82      POST_HEAP = -2
83    };
84
85  private:
86   
87    struct RadixItem {
88      int prev, next, box;
89      Item item;
90      int prio;
91      RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {}
92    };
93
94    struct RadixBox {
95      int first;
96      int min, size;
97      RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {}
98    };
99
100    std::vector<RadixItem> data;
101    std::vector<RadixBox> boxes;
102
103    ItemIntMap &iim;
104
105
106  public:
107    /// \brief The constructor.
108    ///
109    /// The constructor.
110    ///
111    /// \param _iim It should be given to the constructor, since it is used
112    /// internally to handle the cross references. The value of the map
113    /// should be PRE_HEAP (-1) for each element.
114    ///
115    /// \param minimal The initial minimal value of the heap.
116    /// \param capacity It determines the initial capacity of the heap.
117    RadixHeap(ItemIntMap &_iim, int minimal = 0, int capacity = 0)
118      : iim(_iim) {
119      boxes.push_back(RadixBox(minimal, 1));
120      boxes.push_back(RadixBox(minimal + 1, 1));
121      while (lower(boxes.size() - 1, capacity + minimal - 1)) {
122        extend();
123      }
124    }
125
126    /// The number of items stored in the heap.
127    ///
128    /// \brief Returns the number of items stored in the heap.
129    int size() const { return data.size(); }
130    /// \brief Checks if the heap stores no items.
131    ///
132    /// Returns \c true if and only if the heap stores no items.
133    bool empty() const { return data.empty(); }
134
135    /// \brief Make empty this heap.
136    ///
137    /// Make empty this heap.
138    void clear(int minimal = 0, int capacity = 0) {
139      for (int i = 0; i < (int)data.size(); ++i) {
140        iim[data[i].item] = -2;
141      }
142      data.clear(); boxes.clear();
143      boxes.push_back(RadixBox(minimal, 1));
144      boxes.push_back(RadixBox(minimal + 1, 1));
145      while (lower(boxes.size() - 1, capacity + minimal - 1)) {
146        extend();
147      }
148    }
149
150  private:
151
152    bool upper(int box, Prio prio) {
153      return prio < boxes[box].min;
154    }
155
156    bool lower(int box, Prio prio) {
157      return prio >= boxes[box].min + boxes[box].size;
158    }
159
160    /// \brief Remove item from the box list.
161    void remove(int index) {
162      if (data[index].prev >= 0) {
163        data[data[index].prev].next = data[index].next;
164      } else {
165        boxes[data[index].box].first = data[index].next;
166      }
167      if (data[index].next >= 0) {
168        data[data[index].next].prev = data[index].prev;
169      }
170    }
171
172    /// \brief Insert item into the box list.
173    void insert(int box, int index) {
174      if (boxes[box].first == -1) {
175        boxes[box].first = index;
176        data[index].next = data[index].prev = -1;
177      } else {
178        data[index].next = boxes[box].first;
179        data[boxes[box].first].prev = index;
180        data[index].prev = -1;
181        boxes[box].first = index;
182      }
183      data[index].box = box;
184    }
185
186    /// \brief Add a new box to the box list.
187    void extend() {
188      int min = boxes.back().min + boxes.back().size;
189      int size = 2 * boxes.back().size;
190      boxes.push_back(RadixBox(min, size));
191    }
192
193    /// \brief Move an item up into the proper box.
194    void bubble_up(int index) {
195      if (!lower(data[index].box, data[index].prio)) return;
196      remove(index);
197      int box = findUp(data[index].box, data[index].prio);
198      insert(box, index);     
199    }
200
201    /// \brief Find up the proper box for the item with the given prio.
202    int findUp(int start, int prio) {
203      while (lower(start, prio)) {
204        if (++start == (int)boxes.size()) {
205          extend();
206        }
207      }
208      return start;
209    }
210
211    /// \brief Move an item down into the proper box.
212    void bubble_down(int index) {
213      if (!upper(data[index].box, data[index].prio)) return;
214      remove(index);
215      int box = findDown(data[index].box, data[index].prio);
216      insert(box, index);
217    }
218
219    /// \brief Find up the proper box for the item with the given prio.
220    int findDown(int start, int prio) {
221      while (upper(start, prio)) {
222        if (--start < 0) throw UnderFlowPriorityError();
223      }
224      return start;
225    }
226
227    /// \brief Find the first not empty box.
228    int findFirst() {
229      int first = 0;
230      while (boxes[first].first == -1) ++first;
231      return first;
232    }
233
234    /// \brief Gives back the minimal prio of the box.
235    int minValue(int box) {
236      int min = data[boxes[box].first].prio;
237      for (int k = boxes[box].first; k != -1; k = data[k].next) {
238        if (data[k].prio < min) min = data[k].prio;
239      }
240      return min;
241    }
242
243    /// \brief Rearrange the items of the heap and makes the
244    /// first box not empty.
245    void moveDown() {
246      int box = findFirst();
247      if (box == 0) return;
248      int min = minValue(box);
249      for (int i = 0; i <= box; ++i) {
250        boxes[i].min = min;
251        min += boxes[i].size;
252      }
253      int curr = boxes[box].first, next;
254      while (curr != -1) {
255        next = data[curr].next;
256        bubble_down(curr);
257        curr = next;
258      }     
259    }
260
261    void relocate_last(int index) {
262      if (index != (int)data.size() - 1) {
263        data[index] = data.back();
264        if (data[index].prev != -1) {
265          data[data[index].prev].next = index;
266        } else {
267          boxes[data[index].box].first = index;
268        }
269        if (data[index].next != -1) {
270          data[data[index].next].prev = index;
271        }
272        iim[data[index].item] = index;
273      }
274      data.pop_back();
275    }
276
277  public:
278
279    /// \brief Insert an item into the heap with the given priority.
280    ///   
281    /// Adds \c i to the heap with priority \c p.
282    /// \param i The item to insert.
283    /// \param p The priority of the item.
284    void push(const Item &i, const Prio &p) {
285      int n = data.size();
286      iim.set(i, n);
287      data.push_back(RadixItem(i, p));
288      while (lower(boxes.size() - 1, p)) {
289        extend();
290      }
291      int box = findDown(boxes.size() - 1, p);
292      insert(box, n);
293    }
294
295    /// \brief Returns the item with minimum priority.
296    ///
297    /// This method returns the item with minimum priority. 
298    /// \pre The heap must be nonempty. 
299    Item top() const {
300      const_cast<RadixHeap<Item, ItemIntMap>&>(*this).moveDown();
301      return data[boxes[0].first].item;
302    }
303
304    /// \brief Returns the minimum priority.
305    ///
306    /// It returns the minimum priority.
307    /// \pre The heap must be nonempty.
308    Prio prio() const {
309      const_cast<RadixHeap<Item, ItemIntMap>&>(*this).moveDown();
310      return data[boxes[0].first].prio;
311     }
312
313    /// \brief Deletes the item with minimum priority.
314    ///
315    /// This method deletes the item with minimum priority.
316    /// \pre The heap must be non-empty. 
317    void pop() {
318      moveDown();
319      int index = boxes[0].first;
320      iim[data[index].item] = POST_HEAP;
321      remove(index);
322      relocate_last(index);
323    }
324
325    /// \brief Deletes \c i from the heap.
326    ///
327    /// This method deletes item \c i from the heap, if \c i was
328    /// already stored in the heap.
329    /// \param i The item to erase.
330    void erase(const Item &i) {
331      int index = iim[i];
332      iim[i] = POST_HEAP;
333      remove(index);
334      relocate_last(index);
335   }
336
337    /// \brief Returns the priority of \c i.
338    ///
339    /// This function returns the priority of item \c i. 
340    /// \pre \c i must be in the heap.
341    /// \param i The item.
342    Prio operator[](const Item &i) const {
343      int idx = iim[i];
344      return data[idx].prio;
345    }
346
347    /// \brief \c i gets to the heap with priority \c p independently
348    /// if \c i was already there.
349    ///
350    /// This method calls \ref push(\c i, \c p) if \c i is not stored
351    /// in the heap and sets the priority of \c i to \c p otherwise.
352    /// It may throw an \e UnderFlowPriorityException.
353    /// \param i The item.
354    /// \param p The priority.
355    void set(const Item &i, const Prio &p) {
356      int idx = iim[i];
357      if( idx < 0 ) {
358        push(i, p);
359      }
360      else if( p >= data[idx].prio ) {
361        data[idx].prio = p;
362        bubble_up(idx);
363      } else {
364        data[idx].prio = p;
365        bubble_down(idx);
366      }
367    }
368
369
370    /// \brief Decreases the priority of \c i to \c p.
371    ///
372    /// This method decreases the priority of item \c i to \c p.
373    /// \pre \c i must be stored in the heap with priority at least \c p, and
374    /// \c should be greater or equal to the last removed item's priority.
375    /// \param i The item.
376    /// \param p The priority.
377    void decrease(const Item &i, const Prio &p) {
378      int idx = iim[i];
379      data[idx].prio = p;
380      bubble_down(idx);
381    }
382
383    /// \brief Increases the priority of \c i to \c p.
384    ///
385    /// This method sets the priority of item \c i to \c p.
386    /// \pre \c i must be stored in the heap with priority at most \c p
387    /// \param i The item.
388    /// \param p The priority.
389    void increase(const Item &i, const Prio &p) {
390      int idx = iim[i];
391      data[idx].prio = p;
392      bubble_up(idx);
393    }
394
395    /// \brief Returns if \c item is in, has already been in, or has
396    /// never been in the heap.
397    ///
398    /// This method returns PRE_HEAP if \c item has never been in the
399    /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
400    /// otherwise. In the latter case it is possible that \c item will
401    /// get back to the heap again.
402    /// \param i The item.
403    state_enum state(const Item &i) const {
404      int s = iim[i];
405      if( s >= 0 ) s = 0;
406      return state_enum(s);
407    }
408
409  }; // class RadixHeap
410
411} // namespace lemon
412
413#endif // LEMON_RADIX_HEAP_H
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