Line data Source code
1 : /*-------------------------------------------------------------------------
2 : *
3 : * binaryheap.c
4 : * A simple binary heap implementation
5 : *
6 : * Portions Copyright (c) 2012-2017, PostgreSQL Global Development Group
7 : *
8 : * IDENTIFICATION
9 : * src/backend/lib/binaryheap.c
10 : *
11 : *-------------------------------------------------------------------------
12 : */
13 :
14 : #include "postgres.h"
15 :
16 : #include <math.h>
17 :
18 : #include "lib/binaryheap.h"
19 :
20 : static void sift_down(binaryheap *heap, int node_off);
21 : static void sift_up(binaryheap *heap, int node_off);
22 : static inline void swap_nodes(binaryheap *heap, int a, int b);
23 :
24 : /*
25 : * binaryheap_allocate
26 : *
27 : * Returns a pointer to a newly-allocated heap that has the capacity to
28 : * store the given number of nodes, with the heap property defined by
29 : * the given comparator function, which will be invoked with the additional
30 : * argument specified by 'arg'.
31 : */
32 : binaryheap *
33 50 : binaryheap_allocate(int capacity, binaryheap_comparator compare, void *arg)
34 : {
35 : int sz;
36 : binaryheap *heap;
37 :
38 50 : sz = offsetof(binaryheap, bh_nodes) + sizeof(Datum) * capacity;
39 50 : heap = (binaryheap *) palloc(sz);
40 50 : heap->bh_space = capacity;
41 50 : heap->bh_compare = compare;
42 50 : heap->bh_arg = arg;
43 :
44 50 : heap->bh_size = 0;
45 50 : heap->bh_has_heap_property = true;
46 :
47 50 : return heap;
48 : }
49 :
50 : /*
51 : * binaryheap_reset
52 : *
53 : * Resets the heap to an empty state, losing its data content but not the
54 : * parameters passed at allocation.
55 : */
56 : void
57 9 : binaryheap_reset(binaryheap *heap)
58 : {
59 9 : heap->bh_size = 0;
60 9 : heap->bh_has_heap_property = true;
61 9 : }
62 :
63 : /*
64 : * binaryheap_free
65 : *
66 : * Releases memory used by the given binaryheap.
67 : */
68 : void
69 8 : binaryheap_free(binaryheap *heap)
70 : {
71 8 : pfree(heap);
72 8 : }
73 :
74 : /*
75 : * These utility functions return the offset of the left child, right
76 : * child, and parent of the node at the given index, respectively.
77 : *
78 : * The heap is represented as an array of nodes, with the root node
79 : * stored at index 0. The left child of node i is at index 2*i+1, and
80 : * the right child at 2*i+2. The parent of node i is at index (i-1)/2.
81 : */
82 :
83 : static inline int
84 8349 : left_offset(int i)
85 : {
86 8349 : return 2 * i + 1;
87 : }
88 :
89 : static inline int
90 8349 : right_offset(int i)
91 : {
92 8349 : return 2 * i + 2;
93 : }
94 :
95 : static inline int
96 28 : parent_offset(int i)
97 : {
98 28 : return (i - 1) / 2;
99 : }
100 :
101 : /*
102 : * binaryheap_add_unordered
103 : *
104 : * Adds the given datum to the end of the heap's list of nodes in O(1) without
105 : * preserving the heap property. This is a convenience to add elements quickly
106 : * to a new heap. To obtain a valid heap, one must call binaryheap_build()
107 : * afterwards.
108 : */
109 : void
110 61 : binaryheap_add_unordered(binaryheap *heap, Datum d)
111 : {
112 61 : if (heap->bh_size >= heap->bh_space)
113 0 : elog(ERROR, "out of binary heap slots");
114 61 : heap->bh_has_heap_property = false;
115 61 : heap->bh_nodes[heap->bh_size] = d;
116 61 : heap->bh_size++;
117 61 : }
118 :
119 : /*
120 : * binaryheap_build
121 : *
122 : * Assembles a valid heap in O(n) from the nodes added by
123 : * binaryheap_add_unordered(). Not needed otherwise.
124 : */
125 : void
126 28 : binaryheap_build(binaryheap *heap)
127 : {
128 : int i;
129 :
130 61 : for (i = parent_offset(heap->bh_size - 1); i >= 0; i--)
131 33 : sift_down(heap, i);
132 28 : heap->bh_has_heap_property = true;
133 28 : }
134 :
135 : /*
136 : * binaryheap_add
137 : *
138 : * Adds the given datum to the heap in O(log n) time, while preserving
139 : * the heap property.
140 : */
141 : void
142 0 : binaryheap_add(binaryheap *heap, Datum d)
143 : {
144 0 : if (heap->bh_size >= heap->bh_space)
145 0 : elog(ERROR, "out of binary heap slots");
146 0 : heap->bh_nodes[heap->bh_size] = d;
147 0 : heap->bh_size++;
148 0 : sift_up(heap, heap->bh_size - 1);
149 0 : }
150 :
151 : /*
152 : * binaryheap_first
153 : *
154 : * Returns a pointer to the first (root, topmost) node in the heap
155 : * without modifying the heap. The caller must ensure that this
156 : * routine is not used on an empty heap. Always O(1).
157 : */
158 : Datum
159 8344 : binaryheap_first(binaryheap *heap)
160 : {
161 8344 : Assert(!binaryheap_empty(heap) && heap->bh_has_heap_property);
162 8344 : return heap->bh_nodes[0];
163 : }
164 :
165 : /*
166 : * binaryheap_remove_first
167 : *
168 : * Removes the first (root, topmost) node in the heap and returns a
169 : * pointer to it after rebalancing the heap. The caller must ensure
170 : * that this routine is not used on an empty heap. O(log n) worst
171 : * case.
172 : */
173 : Datum
174 28 : binaryheap_remove_first(binaryheap *heap)
175 : {
176 28 : Assert(!binaryheap_empty(heap) && heap->bh_has_heap_property);
177 :
178 28 : if (heap->bh_size == 1)
179 : {
180 15 : heap->bh_size--;
181 15 : return heap->bh_nodes[0];
182 : }
183 :
184 : /*
185 : * Swap the root and last nodes, decrease the size of the heap (i.e.
186 : * remove the former root node) and sift the new root node down to its
187 : * correct position.
188 : */
189 13 : swap_nodes(heap, 0, heap->bh_size - 1);
190 13 : heap->bh_size--;
191 13 : sift_down(heap, 0);
192 :
193 13 : return heap->bh_nodes[heap->bh_size];
194 : }
195 :
196 : /*
197 : * binaryheap_replace_first
198 : *
199 : * Replace the topmost element of a non-empty heap, preserving the heap
200 : * property. O(1) in the best case, or O(log n) if it must fall back to
201 : * sifting the new node down.
202 : */
203 : void
204 8212 : binaryheap_replace_first(binaryheap *heap, Datum d)
205 : {
206 8212 : Assert(!binaryheap_empty(heap) && heap->bh_has_heap_property);
207 :
208 8212 : heap->bh_nodes[0] = d;
209 :
210 8212 : if (heap->bh_size > 1)
211 7989 : sift_down(heap, 0);
212 8212 : }
213 :
214 : /*
215 : * Swap the contents of two nodes.
216 : */
217 : static inline void
218 327 : swap_nodes(binaryheap *heap, int a, int b)
219 : {
220 : Datum swap;
221 :
222 327 : swap = heap->bh_nodes[a];
223 327 : heap->bh_nodes[a] = heap->bh_nodes[b];
224 327 : heap->bh_nodes[b] = swap;
225 327 : }
226 :
227 : /*
228 : * Sift a node up to the highest position it can hold according to the
229 : * comparator.
230 : */
231 : static void
232 0 : sift_up(binaryheap *heap, int node_off)
233 : {
234 0 : while (node_off != 0)
235 : {
236 : int cmp;
237 : int parent_off;
238 :
239 : /*
240 : * If this node is smaller than its parent, the heap condition is
241 : * satisfied, and we're done.
242 : */
243 0 : parent_off = parent_offset(node_off);
244 0 : cmp = heap->bh_compare(heap->bh_nodes[node_off],
245 : heap->bh_nodes[parent_off],
246 : heap->bh_arg);
247 0 : if (cmp <= 0)
248 0 : break;
249 :
250 : /*
251 : * Otherwise, swap the node and its parent and go on to check the
252 : * node's new parent.
253 : */
254 0 : swap_nodes(heap, node_off, parent_off);
255 0 : node_off = parent_off;
256 : }
257 0 : }
258 :
259 : /*
260 : * Sift a node down from its current position to satisfy the heap
261 : * property.
262 : */
263 : static void
264 8349 : sift_down(binaryheap *heap, int node_off)
265 : {
266 : while (true)
267 : {
268 8349 : int left_off = left_offset(node_off);
269 8349 : int right_off = right_offset(node_off);
270 8349 : int swap_off = 0;
271 :
272 : /* Is the left child larger than the parent? */
273 16373 : if (left_off < heap->bh_size &&
274 8024 : heap->bh_compare(heap->bh_nodes[node_off],
275 : heap->bh_nodes[left_off],
276 : heap->bh_arg) < 0)
277 306 : swap_off = left_off;
278 :
279 : /* Is the right child larger than the parent? */
280 8420 : if (right_off < heap->bh_size &&
281 71 : heap->bh_compare(heap->bh_nodes[node_off],
282 : heap->bh_nodes[right_off],
283 : heap->bh_arg) < 0)
284 : {
285 : /* swap with the larger child */
286 38 : if (!swap_off ||
287 15 : heap->bh_compare(heap->bh_nodes[left_off],
288 : heap->bh_nodes[right_off],
289 : heap->bh_arg) < 0)
290 16 : swap_off = right_off;
291 : }
292 :
293 : /*
294 : * If we didn't find anything to swap, the heap condition is
295 : * satisfied, and we're done.
296 : */
297 8349 : if (!swap_off)
298 8035 : break;
299 :
300 : /*
301 : * Otherwise, swap the node with the child that violates the heap
302 : * property; then go on to check its children.
303 : */
304 314 : swap_nodes(heap, swap_off, node_off);
305 314 : node_off = swap_off;
306 314 : }
307 8035 : }
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