0
|
1
|
|
2 /*
|
|
3 * Copyright (C) Igor Sysoev
|
644
|
4 * Copyright (C) Nginx, Inc.
|
0
|
5 */
|
|
6
|
|
7
|
|
8 #include <ngx_config.h>
|
|
9 #include <ngx_core.h>
|
|
10
|
|
11
|
|
12 /*
|
108
|
13 * The red-black tree code is based on the algorithm described in
|
|
14 * the "Introduction to Algorithms" by Cormen, Leiserson and Rivest.
|
0
|
15 */
|
|
16
|
|
17
|
108
|
18 static ngx_inline void ngx_rbtree_left_rotate(ngx_rbtree_node_t **root,
|
|
19 ngx_rbtree_node_t *sentinel, ngx_rbtree_node_t *node);
|
|
20 static ngx_inline void ngx_rbtree_right_rotate(ngx_rbtree_node_t **root,
|
|
21 ngx_rbtree_node_t *sentinel, ngx_rbtree_node_t *node);
|
0
|
22
|
|
23
|
42
|
24 void
|
108
|
25 ngx_rbtree_insert(ngx_thread_volatile ngx_rbtree_t *tree,
|
|
26 ngx_rbtree_node_t *node)
|
0
|
27 {
|
108
|
28 ngx_rbtree_node_t **root, *temp, *sentinel;
|
0
|
29
|
|
30 /* a binary tree insert */
|
|
31
|
108
|
32 root = (ngx_rbtree_node_t **) &tree->root;
|
|
33 sentinel = tree->sentinel;
|
|
34
|
0
|
35 if (*root == sentinel) {
|
|
36 node->parent = NULL;
|
|
37 node->left = sentinel;
|
|
38 node->right = sentinel;
|
|
39 ngx_rbt_black(node);
|
|
40 *root = node;
|
|
41
|
|
42 return;
|
|
43 }
|
|
44
|
258
|
45 tree->insert(*root, node, sentinel);
|
0
|
46
|
|
47 /* re-balance tree */
|
|
48
|
|
49 while (node != *root && ngx_rbt_is_red(node->parent)) {
|
|
50
|
|
51 if (node->parent == node->parent->parent->left) {
|
|
52 temp = node->parent->parent->right;
|
|
53
|
|
54 if (ngx_rbt_is_red(temp)) {
|
|
55 ngx_rbt_black(node->parent);
|
|
56 ngx_rbt_black(temp);
|
|
57 ngx_rbt_red(node->parent->parent);
|
|
58 node = node->parent->parent;
|
|
59
|
|
60 } else {
|
|
61 if (node == node->parent->right) {
|
|
62 node = node->parent;
|
|
63 ngx_rbtree_left_rotate(root, sentinel, node);
|
|
64 }
|
|
65
|
|
66 ngx_rbt_black(node->parent);
|
|
67 ngx_rbt_red(node->parent->parent);
|
|
68 ngx_rbtree_right_rotate(root, sentinel, node->parent->parent);
|
|
69 }
|
|
70
|
|
71 } else {
|
|
72 temp = node->parent->parent->left;
|
|
73
|
|
74 if (ngx_rbt_is_red(temp)) {
|
|
75 ngx_rbt_black(node->parent);
|
|
76 ngx_rbt_black(temp);
|
|
77 ngx_rbt_red(node->parent->parent);
|
|
78 node = node->parent->parent;
|
|
79
|
|
80 } else {
|
|
81 if (node == node->parent->left) {
|
|
82 node = node->parent;
|
|
83 ngx_rbtree_right_rotate(root, sentinel, node);
|
|
84 }
|
|
85
|
|
86 ngx_rbt_black(node->parent);
|
|
87 ngx_rbt_red(node->parent->parent);
|
|
88 ngx_rbtree_left_rotate(root, sentinel, node->parent->parent);
|
|
89 }
|
|
90 }
|
|
91 }
|
|
92
|
|
93 ngx_rbt_black(*root);
|
|
94 }
|
|
95
|
|
96
|
42
|
97 void
|
258
|
98 ngx_rbtree_insert_value(ngx_rbtree_node_t *temp, ngx_rbtree_node_t *node,
|
|
99 ngx_rbtree_node_t *sentinel)
|
|
100 {
|
356
|
101 ngx_rbtree_node_t **p;
|
|
102
|
258
|
103 for ( ;; ) {
|
|
104
|
356
|
105 p = (node->key < temp->key) ? &temp->left : &temp->right;
|
258
|
106
|
356
|
107 if (*p == sentinel) {
|
|
108 break;
|
|
109 }
|
258
|
110
|
356
|
111 temp = *p;
|
258
|
112 }
|
|
113
|
356
|
114 *p = node;
|
258
|
115 node->parent = temp;
|
|
116 node->left = sentinel;
|
|
117 node->right = sentinel;
|
|
118 ngx_rbt_red(node);
|
|
119 }
|
|
120
|
|
121
|
|
122 void
|
|
123 ngx_rbtree_insert_timer_value(ngx_rbtree_node_t *temp, ngx_rbtree_node_t *node,
|
|
124 ngx_rbtree_node_t *sentinel)
|
|
125 {
|
356
|
126 ngx_rbtree_node_t **p;
|
|
127
|
258
|
128 for ( ;; ) {
|
|
129
|
|
130 /*
|
|
131 * Timer values
|
|
132 * 1) are spread in small range, usually several minutes,
|
|
133 * 2) and overflow each 49 days, if milliseconds are stored in 32 bits.
|
|
134 * The comparison takes into account that overflow.
|
|
135 */
|
|
136
|
356
|
137 /* node->key < temp->key */
|
258
|
138
|
356
|
139 p = ((ngx_rbtree_key_int_t) node->key - (ngx_rbtree_key_int_t) temp->key
|
|
140 < 0)
|
|
141 ? &temp->left : &temp->right;
|
258
|
142
|
356
|
143 if (*p == sentinel) {
|
|
144 break;
|
|
145 }
|
258
|
146
|
356
|
147 temp = *p;
|
258
|
148 }
|
|
149
|
356
|
150 *p = node;
|
258
|
151 node->parent = temp;
|
|
152 node->left = sentinel;
|
|
153 node->right = sentinel;
|
|
154 ngx_rbt_red(node);
|
|
155 }
|
|
156
|
|
157
|
|
158 void
|
108
|
159 ngx_rbtree_delete(ngx_thread_volatile ngx_rbtree_t *tree,
|
|
160 ngx_rbtree_node_t *node)
|
0
|
161 {
|
258
|
162 ngx_uint_t red;
|
108
|
163 ngx_rbtree_node_t **root, *sentinel, *subst, *temp, *w;
|
0
|
164
|
|
165 /* a binary tree delete */
|
|
166
|
108
|
167 root = (ngx_rbtree_node_t **) &tree->root;
|
|
168 sentinel = tree->sentinel;
|
|
169
|
0
|
170 if (node->left == sentinel) {
|
|
171 temp = node->right;
|
|
172 subst = node;
|
|
173
|
|
174 } else if (node->right == sentinel) {
|
|
175 temp = node->left;
|
|
176 subst = node;
|
|
177
|
|
178 } else {
|
|
179 subst = ngx_rbtree_min(node->right, sentinel);
|
|
180
|
|
181 if (subst->left != sentinel) {
|
|
182 temp = subst->left;
|
|
183 } else {
|
|
184 temp = subst->right;
|
|
185 }
|
|
186 }
|
|
187
|
|
188 if (subst == *root) {
|
|
189 *root = temp;
|
|
190 ngx_rbt_black(temp);
|
|
191
|
|
192 /* DEBUG stuff */
|
|
193 node->left = NULL;
|
|
194 node->right = NULL;
|
|
195 node->parent = NULL;
|
|
196 node->key = 0;
|
|
197
|
|
198 return;
|
|
199 }
|
|
200
|
258
|
201 red = ngx_rbt_is_red(subst);
|
0
|
202
|
|
203 if (subst == subst->parent->left) {
|
|
204 subst->parent->left = temp;
|
|
205
|
|
206 } else {
|
|
207 subst->parent->right = temp;
|
|
208 }
|
|
209
|
|
210 if (subst == node) {
|
|
211
|
|
212 temp->parent = subst->parent;
|
|
213
|
|
214 } else {
|
|
215
|
|
216 if (subst->parent == node) {
|
|
217 temp->parent = subst;
|
|
218
|
|
219 } else {
|
|
220 temp->parent = subst->parent;
|
|
221 }
|
|
222
|
|
223 subst->left = node->left;
|
|
224 subst->right = node->right;
|
|
225 subst->parent = node->parent;
|
|
226 ngx_rbt_copy_color(subst, node);
|
|
227
|
|
228 if (node == *root) {
|
|
229 *root = subst;
|
|
230
|
|
231 } else {
|
|
232 if (node == node->parent->left) {
|
|
233 node->parent->left = subst;
|
|
234 } else {
|
|
235 node->parent->right = subst;
|
|
236 }
|
|
237 }
|
|
238
|
|
239 if (subst->left != sentinel) {
|
|
240 subst->left->parent = subst;
|
|
241 }
|
|
242
|
|
243 if (subst->right != sentinel) {
|
|
244 subst->right->parent = subst;
|
|
245 }
|
358
|
246 }
|
0
|
247
|
358
|
248 /* DEBUG stuff */
|
|
249 node->left = NULL;
|
|
250 node->right = NULL;
|
|
251 node->parent = NULL;
|
|
252 node->key = 0;
|
0
|
253
|
258
|
254 if (red) {
|
0
|
255 return;
|
|
256 }
|
|
257
|
|
258 /* a delete fixup */
|
|
259
|
|
260 while (temp != *root && ngx_rbt_is_black(temp)) {
|
|
261
|
|
262 if (temp == temp->parent->left) {
|
|
263 w = temp->parent->right;
|
|
264
|
|
265 if (ngx_rbt_is_red(w)) {
|
|
266 ngx_rbt_black(w);
|
|
267 ngx_rbt_red(temp->parent);
|
|
268 ngx_rbtree_left_rotate(root, sentinel, temp->parent);
|
|
269 w = temp->parent->right;
|
|
270 }
|
|
271
|
|
272 if (ngx_rbt_is_black(w->left) && ngx_rbt_is_black(w->right)) {
|
|
273 ngx_rbt_red(w);
|
|
274 temp = temp->parent;
|
|
275
|
|
276 } else {
|
|
277 if (ngx_rbt_is_black(w->right)) {
|
|
278 ngx_rbt_black(w->left);
|
|
279 ngx_rbt_red(w);
|
|
280 ngx_rbtree_right_rotate(root, sentinel, w);
|
|
281 w = temp->parent->right;
|
|
282 }
|
|
283
|
|
284 ngx_rbt_copy_color(w, temp->parent);
|
|
285 ngx_rbt_black(temp->parent);
|
|
286 ngx_rbt_black(w->right);
|
|
287 ngx_rbtree_left_rotate(root, sentinel, temp->parent);
|
|
288 temp = *root;
|
|
289 }
|
|
290
|
|
291 } else {
|
|
292 w = temp->parent->left;
|
|
293
|
|
294 if (ngx_rbt_is_red(w)) {
|
|
295 ngx_rbt_black(w);
|
|
296 ngx_rbt_red(temp->parent);
|
|
297 ngx_rbtree_right_rotate(root, sentinel, temp->parent);
|
|
298 w = temp->parent->left;
|
|
299 }
|
|
300
|
|
301 if (ngx_rbt_is_black(w->left) && ngx_rbt_is_black(w->right)) {
|
|
302 ngx_rbt_red(w);
|
|
303 temp = temp->parent;
|
|
304
|
|
305 } else {
|
|
306 if (ngx_rbt_is_black(w->left)) {
|
|
307 ngx_rbt_black(w->right);
|
|
308 ngx_rbt_red(w);
|
|
309 ngx_rbtree_left_rotate(root, sentinel, w);
|
|
310 w = temp->parent->left;
|
|
311 }
|
|
312
|
|
313 ngx_rbt_copy_color(w, temp->parent);
|
|
314 ngx_rbt_black(temp->parent);
|
|
315 ngx_rbt_black(w->left);
|
|
316 ngx_rbtree_right_rotate(root, sentinel, temp->parent);
|
|
317 temp = *root;
|
|
318 }
|
|
319 }
|
|
320 }
|
|
321
|
|
322 ngx_rbt_black(temp);
|
|
323 }
|
|
324
|
|
325
|
42
|
326 static ngx_inline void
|
108
|
327 ngx_rbtree_left_rotate(ngx_rbtree_node_t **root, ngx_rbtree_node_t *sentinel,
|
|
328 ngx_rbtree_node_t *node)
|
0
|
329 {
|
108
|
330 ngx_rbtree_node_t *temp;
|
0
|
331
|
|
332 temp = node->right;
|
|
333 node->right = temp->left;
|
|
334
|
|
335 if (temp->left != sentinel) {
|
|
336 temp->left->parent = node;
|
|
337 }
|
|
338
|
|
339 temp->parent = node->parent;
|
|
340
|
|
341 if (node == *root) {
|
|
342 *root = temp;
|
|
343
|
|
344 } else if (node == node->parent->left) {
|
|
345 node->parent->left = temp;
|
|
346
|
|
347 } else {
|
|
348 node->parent->right = temp;
|
|
349 }
|
|
350
|
|
351 temp->left = node;
|
|
352 node->parent = temp;
|
|
353 }
|
|
354
|
|
355
|
42
|
356 static ngx_inline void
|
108
|
357 ngx_rbtree_right_rotate(ngx_rbtree_node_t **root, ngx_rbtree_node_t *sentinel,
|
|
358 ngx_rbtree_node_t *node)
|
0
|
359 {
|
108
|
360 ngx_rbtree_node_t *temp;
|
0
|
361
|
|
362 temp = node->left;
|
|
363 node->left = temp->right;
|
|
364
|
|
365 if (temp->right != sentinel) {
|
|
366 temp->right->parent = node;
|
|
367 }
|
|
368
|
|
369 temp->parent = node->parent;
|
|
370
|
|
371 if (node == *root) {
|
|
372 *root = temp;
|
|
373
|
|
374 } else if (node == node->parent->right) {
|
|
375 node->parent->right = temp;
|
|
376
|
|
377 } else {
|
|
378 node->parent->left = temp;
|
|
379 }
|
|
380
|
|
381 temp->right = node;
|
|
382 node->parent = temp;
|
|
383 }
|