1 /* Copyright (c) 2013, Ben Noordhuis <info@bnoordhuis.nl>
2 *
3 * Permission to use, copy, modify, and/or distribute this software for any
4 * purpose with or without fee is hereby granted, provided that the above
5 * copyright notice and this permission notice appear in all copies.
6 *
7 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
8 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
9 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
10 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
11 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
12 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
13 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
14 */
15
16 #ifndef UV_SRC_HEAP_H_
17 #define UV_SRC_HEAP_H_
18
19 #include <stddef.h> /* NULL */
20
21 #if defined(__GNUC__)
22 # define HEAP_EXPORT(declaration) __attribute__((unused)) static declaration
23 #else
24 # define HEAP_EXPORT(declaration) static declaration
25 #endif
26
27 struct heap_node {
28 struct heap_node* left;
29 struct heap_node* right;
30 struct heap_node* parent;
31 };
32
33 /* A binary min heap. The usual properties hold: the root is the lowest
34 * element in the set, the height of the tree is at most log2(nodes) and
35 * it's always a complete binary tree.
36 *
37 * The heap function try hard to detect corrupted tree nodes at the cost
38 * of a minor reduction in performance. Compile with -DNDEBUG to disable.
39 */
40 struct heap {
41 struct heap_node* min;
42 unsigned int nelts;
43 };
44
45 /* Return non-zero if a < b. */
46 typedef int (*heap_compare_fn)(const struct heap_node* a,
47 const struct heap_node* b);
48
49 /* Public functions. */
50 HEAP_EXPORT(void heap_init(struct heap* heap));
51 HEAP_EXPORT(struct heap_node* heap_min(const struct heap* heap));
52 HEAP_EXPORT(void heap_insert(struct heap* heap,
53 struct heap_node* newnode,
54 heap_compare_fn less_than));
55 HEAP_EXPORT(void heap_remove(struct heap* heap,
56 struct heap_node* node,
57 heap_compare_fn less_than));
58 HEAP_EXPORT(void heap_dequeue(struct heap* heap, heap_compare_fn less_than));
59
60 /* Implementation follows. */
61
HEAP_EXPORT(void heap_init (struct heap * heap))62 HEAP_EXPORT(void heap_init(struct heap* heap)) {
63 heap->min = NULL;
64 heap->nelts = 0;
65 }
66
HEAP_EXPORT(struct heap_node * heap_min (const struct heap * heap))67 HEAP_EXPORT(struct heap_node* heap_min(const struct heap* heap)) {
68 return heap->min;
69 }
70
71 /* Swap parent with child. Child moves closer to the root, parent moves away. */
heap_node_swap(struct heap * heap,struct heap_node * parent,struct heap_node * child)72 static void heap_node_swap(struct heap* heap,
73 struct heap_node* parent,
74 struct heap_node* child) {
75 struct heap_node* sibling;
76 struct heap_node t;
77
78 t = *parent;
79 *parent = *child;
80 *child = t;
81
82 parent->parent = child;
83 if (child->left == child) {
84 child->left = parent;
85 sibling = child->right;
86 } else {
87 child->right = parent;
88 sibling = child->left;
89 }
90 if (sibling != NULL)
91 sibling->parent = child;
92
93 if (parent->left != NULL)
94 parent->left->parent = parent;
95 if (parent->right != NULL)
96 parent->right->parent = parent;
97
98 if (child->parent == NULL)
99 heap->min = child;
100 else if (child->parent->left == parent)
101 child->parent->left = child;
102 else
103 child->parent->right = child;
104 }
105
HEAP_EXPORT(void heap_insert (struct heap * heap,struct heap_node * newnode,heap_compare_fn less_than))106 HEAP_EXPORT(void heap_insert(struct heap* heap,
107 struct heap_node* newnode,
108 heap_compare_fn less_than)) {
109 struct heap_node** parent;
110 struct heap_node** child;
111 unsigned int path;
112 unsigned int n;
113 unsigned int k;
114
115 newnode->left = NULL;
116 newnode->right = NULL;
117 newnode->parent = NULL;
118
119 /* Calculate the path from the root to the insertion point. This is a min
120 * heap so we always insert at the left-most free node of the bottom row.
121 */
122 path = 0;
123 for (k = 0, n = 1 + heap->nelts; n >= 2; k += 1, n /= 2)
124 path = (path << 1) | (n & 1);
125
126 /* Now traverse the heap using the path we calculated in the previous step. */
127 parent = child = &heap->min;
128 while (k > 0) {
129 parent = child;
130 if (path & 1)
131 child = &(*child)->right;
132 else
133 child = &(*child)->left;
134 path >>= 1;
135 k -= 1;
136 }
137
138 /* Insert the new node. */
139 newnode->parent = *parent;
140 *child = newnode;
141 heap->nelts += 1;
142
143 /* Walk up the tree and check at each node if the heap property holds.
144 * It's a min heap so parent < child must be true.
145 */
146 while (newnode->parent != NULL && less_than(newnode, newnode->parent))
147 heap_node_swap(heap, newnode->parent, newnode);
148 }
149
HEAP_EXPORT(void heap_remove (struct heap * heap,struct heap_node * node,heap_compare_fn less_than))150 HEAP_EXPORT(void heap_remove(struct heap* heap,
151 struct heap_node* node,
152 heap_compare_fn less_than)) {
153 struct heap_node* smallest;
154 struct heap_node** max;
155 struct heap_node* child;
156 unsigned int path;
157 unsigned int k;
158 unsigned int n;
159
160 if (heap->nelts == 0)
161 return;
162
163 /* Calculate the path from the min (the root) to the max, the left-most node
164 * of the bottom row.
165 */
166 path = 0;
167 for (k = 0, n = heap->nelts; n >= 2; k += 1, n /= 2)
168 path = (path << 1) | (n & 1);
169
170 /* Now traverse the heap using the path we calculated in the previous step. */
171 max = &heap->min;
172 while (k > 0) {
173 if (path & 1)
174 max = &(*max)->right;
175 else
176 max = &(*max)->left;
177 path >>= 1;
178 k -= 1;
179 }
180
181 heap->nelts -= 1;
182
183 /* Unlink the max node. */
184 child = *max;
185 *max = NULL;
186
187 if (child == node) {
188 /* We're removing either the max or the last node in the tree. */
189 if (child == heap->min) {
190 heap->min = NULL;
191 }
192 return;
193 }
194
195 /* Replace the to be deleted node with the max node. */
196 child->left = node->left;
197 child->right = node->right;
198 child->parent = node->parent;
199
200 if (child->left != NULL) {
201 child->left->parent = child;
202 }
203
204 if (child->right != NULL) {
205 child->right->parent = child;
206 }
207
208 if (node->parent == NULL) {
209 heap->min = child;
210 } else if (node->parent->left == node) {
211 node->parent->left = child;
212 } else {
213 node->parent->right = child;
214 }
215
216 /* Walk down the subtree and check at each node if the heap property holds.
217 * It's a min heap so parent < child must be true. If the parent is bigger,
218 * swap it with the smallest child.
219 */
220 for (;;) {
221 smallest = child;
222 if (child->left != NULL && less_than(child->left, smallest))
223 smallest = child->left;
224 if (child->right != NULL && less_than(child->right, smallest))
225 smallest = child->right;
226 if (smallest == child)
227 break;
228 heap_node_swap(heap, child, smallest);
229 }
230
231 /* Walk up the subtree and check that each parent is less than the node
232 * this is required, because `max` node is not guaranteed to be the
233 * actual maximum in tree
234 */
235 while (child->parent != NULL && less_than(child, child->parent))
236 heap_node_swap(heap, child->parent, child);
237 }
238
HEAP_EXPORT(void heap_dequeue (struct heap * heap,heap_compare_fn less_than))239 HEAP_EXPORT(void heap_dequeue(struct heap* heap, heap_compare_fn less_than)) {
240 heap_remove(heap, heap->min, less_than);
241 }
242
243 #undef HEAP_EXPORT
244
245 #endif /* UV_SRC_HEAP_H_ */
246
