|
1 /* -*- C++ -*- |
|
2 * |
|
3 * This file is a part of LEMON, a generic C++ optimization library |
|
4 * |
|
5 * Copyright (C) 2003-2008 |
|
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 auxdat |
|
23 ///\file |
|
24 ///\brief 4ary Heap implementation. |
|
25 |
|
26 #include <iostream> |
|
27 #include <vector> |
|
28 #include <utility> |
|
29 #include <functional> |
|
30 |
|
31 namespace lemon { |
|
32 |
|
33 ///\ingroup auxdat |
|
34 /// |
|
35 ///\brief A 4ary Heap implementation. |
|
36 /// |
|
37 ///This class implements the \e 4ary \e heap data structure. A \e heap |
|
38 ///is a data structure for storing items with specified values called \e |
|
39 ///priorities in such a way that finding the item with minimum priority is |
|
40 ///efficient. \c Compare specifies the ordering of the priorities. In a heap |
|
41 ///one can change the priority of an item, add or erase an item, etc. |
|
42 /// |
|
43 ///\param _Prio Type of the priority of the items. |
|
44 ///\param _ItemIntMap A read and writable Item int map, used internally |
|
45 ///to handle the cross references. |
|
46 ///\param _Compare A class for the ordering of the priorities. The |
|
47 ///default is \c std::less<_Prio>. |
|
48 /// |
|
49 ///\sa FibHeap |
|
50 ///\sa Dijkstra |
|
51 ///\author Dorian Batha |
|
52 |
|
53 template <typename _Prio, typename _ItemIntMap, |
|
54 typename _Compare = std::less<_Prio> > |
|
55 |
|
56 class FouraryHeap { |
|
57 |
|
58 public: |
|
59 ///\e |
|
60 typedef _ItemIntMap ItemIntMap; |
|
61 ///\e |
|
62 typedef _Prio Prio; |
|
63 ///\e |
|
64 typedef typename ItemIntMap::Key Item; |
|
65 ///\e |
|
66 typedef std::pair<Item,Prio> Pair; |
|
67 ///\e |
|
68 typedef _Compare Compare; |
|
69 |
|
70 /// \brief Type to represent the items states. |
|
71 /// |
|
72 /// Each Item element have a state associated to it. It may 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 ItemIntMap \e should be initialized in such way that it maps |
|
77 /// PRE_HEAP (-1) to any element to be put in the heap... |
|
78 enum State { |
|
79 IN_HEAP = 0, |
|
80 PRE_HEAP = -1, |
|
81 POST_HEAP = -2 |
|
82 }; |
|
83 |
|
84 private: |
|
85 std::vector<Pair> data; |
|
86 Compare comp; |
|
87 ItemIntMap &iim; |
|
88 |
|
89 public: |
|
90 /// \brief The constructor. |
|
91 /// |
|
92 /// The constructor. |
|
93 /// \param _iim should be given to the constructor, since it is used |
|
94 /// internally to handle the cross references. The value of the map |
|
95 /// should be PRE_HEAP (-1) for each element. |
|
96 explicit FouraryHeap(ItemIntMap &_iim) : iim(_iim) {} |
|
97 |
|
98 /// \brief The constructor. |
|
99 /// |
|
100 /// The constructor. |
|
101 /// \param _iim should be given to the constructor, since it is used |
|
102 /// internally to handle the cross references. The value of the map |
|
103 /// should be PRE_HEAP (-1) for each element. |
|
104 /// |
|
105 /// \param _comp The comparator function object. |
|
106 FouraryHeap(ItemIntMap &_iim, const Compare &_comp) |
|
107 : iim(_iim), comp(_comp) {} |
|
108 |
|
109 /// The number of items stored in the heap. |
|
110 /// |
|
111 /// \brief Returns the number of items stored in the heap. |
|
112 int size() const { return data.size(); } |
|
113 |
|
114 /// \brief Checks if the heap stores no items. |
|
115 /// |
|
116 /// Returns \c true if and only if the heap stores no items. |
|
117 bool empty() const { return data.empty(); } |
|
118 |
|
119 /// \brief Make empty this heap. |
|
120 /// |
|
121 /// Make empty this heap. It does not change the cross reference map. |
|
122 /// If you want to reuse what is not surely empty you should first clear |
|
123 /// the heap and after that you should set the cross reference map for |
|
124 /// each item to \c PRE_HEAP. |
|
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 int find_min(const int child, const int length) { |
|
136 int min=child; |
|
137 if( child+3<length ) { |
|
138 if( less(data[child+3], data[min]) ) |
|
139 min=child+3; |
|
140 if( less(data[child+2], data[min]) ) |
|
141 min=child+2; |
|
142 if( less(data[child+1], data[min]) ) |
|
143 min=child+1; |
|
144 } |
|
145 else if( child+2<length ) { |
|
146 if( less(data[child+2], data[min]) ) |
|
147 min=child+2; |
|
148 if( less(data[child+1], data[min]) ) |
|
149 min=child+1; |
|
150 } |
|
151 else if( child+1<length ) { |
|
152 if( less(data[child+1], data[min]) ) |
|
153 min=child+1; |
|
154 } |
|
155 return min; |
|
156 } |
|
157 |
|
158 void bubble_up(int hole, Pair p) { |
|
159 int par = parent(hole); |
|
160 while( hole>0 && less(p,data[par]) ) { |
|
161 move(data[par],hole); |
|
162 hole = par; |
|
163 par = parent(hole); |
|
164 } |
|
165 move(p, hole); |
|
166 } |
|
167 |
|
168 void bubble_down(int hole, Pair p, int length) { |
|
169 int child = firstChild(hole); |
|
170 while( child<length && length>1 ) { |
|
171 child = find_min(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 ok: |
|
179 move(p, hole); |
|
180 } |
|
181 |
|
182 void move(const Pair &p, int i) { |
|
183 data[i] = p; |
|
184 iim.set(p.first, i); |
|
185 } |
|
186 |
|
187 public: |
|
188 |
|
189 /// \brief Insert a pair of item and priority into the heap. |
|
190 /// |
|
191 /// Adds \c p.first to the heap with priority \c p.second. |
|
192 /// \param p The pair to insert. |
|
193 void push(const Pair &p) { |
|
194 int n = data.size(); |
|
195 data.resize(n+1); |
|
196 bubble_up(n, p); |
|
197 } |
|
198 |
|
199 /// \brief Insert an item into the heap with the given heap. |
|
200 /// |
|
201 /// Adds \c i to the heap with priority \c p. |
|
202 /// \param i The item to insert. |
|
203 /// \param p The priority of the item. |
|
204 void push(const Item &i, const Prio &p) { push(Pair(i,p)); } |
|
205 |
|
206 /// \brief Returns the item with minimum priority relative to \c Compare. |
|
207 /// |
|
208 /// This method returns the item with minimum priority relative to \c |
|
209 /// Compare. |
|
210 /// \pre The heap must be nonempty. |
|
211 Item top() const { return data[0].first; } |
|
212 |
|
213 /// \brief Returns the minimum priority relative to \c Compare. |
|
214 /// |
|
215 /// It returns the minimum priority relative to \c Compare. |
|
216 /// \pre The heap must be nonempty. |
|
217 Prio prio() const { return data[0].second; } |
|
218 |
|
219 /// \brief Deletes the item with minimum priority relative to \c Compare. |
|
220 /// |
|
221 /// This method deletes the item with minimum priority relative to \c |
|
222 /// Compare from the heap. |
|
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) bubble_down(0, data[n], n); |
|
228 data.pop_back(); |
|
229 } |
|
230 |
|
231 /// \brief Deletes \c i from the heap. |
|
232 /// |
|
233 /// This method deletes item \c i from the heap. |
|
234 /// \param i The item to erase. |
|
235 /// \pre The item should be in the heap. |
|
236 void erase(const Item &i) { |
|
237 int h = iim[i]; |
|
238 int n = data.size()-1; |
|
239 iim.set(data[h].first, POST_HEAP); |
|
240 if( h<n ) { |
|
241 if( less(data[parent(h)], data[n]) ) |
|
242 bubble_down(h, data[n], n); |
|
243 else |
|
244 bubble_up(h, data[n]); |
|
245 } |
|
246 data.pop_back(); |
|
247 } |
|
248 |
|
249 /// \brief Returns the priority of \c i. |
|
250 /// |
|
251 /// This function returns the priority of item \c i. |
|
252 /// \pre \c i must be in the heap. |
|
253 /// \param i The item. |
|
254 Prio operator[](const Item &i) const { |
|
255 int idx = iim[i]; |
|
256 return data[idx].second; |
|
257 } |
|
258 |
|
259 /// \brief \c i gets to the heap with priority \c p independently |
|
260 /// if \c i was already there. |
|
261 /// |
|
262 /// This method calls \ref push(\c i, \c p) if \c i is not stored |
|
263 /// in the heap and sets the priority of \c i to \c p otherwise. |
|
264 /// \param i The item. |
|
265 /// \param p The priority. |
|
266 void set(const Item &i, const Prio &p) { |
|
267 int idx = iim[i]; |
|
268 if( idx < 0 ) |
|
269 push(i,p); |
|
270 else if( comp(p, data[idx].second) ) |
|
271 bubble_up(idx, Pair(i,p)); |
|
272 else |
|
273 bubble_down(idx, Pair(i,p), data.size()); |
|
274 } |
|
275 |
|
276 /// \brief Decreases the priority of \c i to \c p. |
|
277 /// |
|
278 /// This method decreases the priority of item \c i to \c p. |
|
279 /// \pre \c i must be stored in the heap with priority at least \c |
|
280 /// p relative to \c Compare. |
|
281 /// \param i The item. |
|
282 /// \param p The priority. |
|
283 void decrease(const Item &i, const Prio &p) { |
|
284 int idx = iim[i]; |
|
285 bubble_up(idx, Pair(i,p)); |
|
286 } |
|
287 |
|
288 /// \brief Increases the priority of \c i to \c p. |
|
289 /// |
|
290 /// This method sets the priority of item \c i to \c p. |
|
291 /// \pre \c i must be stored in the heap with priority at most \c |
|
292 /// p relative to \c Compare. |
|
293 /// \param i The item. |
|
294 /// \param p The priority. |
|
295 void increase(const Item &i, const Prio &p) { |
|
296 int idx = iim[i]; |
|
297 bubble_down(idx, Pair(i,p), data.size()); |
|
298 } |
|
299 |
|
300 /// \brief Returns if \c item is in, has already been in, or has |
|
301 /// never been in the heap. |
|
302 /// |
|
303 /// This method returns PRE_HEAP if \c item has never been in the |
|
304 /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
|
305 /// otherwise. In the latter case it is possible that \c item will |
|
306 /// get back 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 Sets the state of the \c item in the heap. |
|
315 /// |
|
316 /// Sets the state of the \c item in the heap. It can be used to |
|
317 /// manually clear the heap when it is important to achive the |
|
318 /// 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 Replaces an item in the heap. |
|
334 /// |
|
335 /// The \c i item is replaced with \c j item. The \c i item should |
|
336 /// be in the heap, while the \c j should be out of the heap. The |
|
337 /// \c i item will out of the heap and \c j will be in the heap |
|
338 /// with the same prioriority as prevoiusly the \c i item. |
|
339 void replace(const Item& i, const Item& j) { |
|
340 int idx = iim[i]; |
|
341 iim.set(i, iim[j]); |
|
342 iim.set(j, idx); |
|
343 data[idx].first = j; |
|
344 } |
|
345 |
|
346 }; // class FouraryHeap |
|
347 |
|
348 } // namespace lemon |
|
349 |
|
350 #endif // LEMON_FOURARY_HEAP_H |