|
0
|
1
|
|
|
2 /*
|
|
|
3 * Copyright (C) Igor Sysoev
|
|
|
4 */
|
|
|
5
|
|
|
6
|
|
|
7 #include <ngx_config.h>
|
|
|
8 #include <ngx_core.h>
|
|
|
9
|
|
|
10
|
|
|
11 /*
|
|
|
12 * The code is based on the algorithm described in the "Introduction
|
|
|
13 * to Algorithms" by Cormen, Leiserson and Rivest.
|
|
|
14 */
|
|
|
15
|
|
|
16 #define ngx_rbt_red(node) ((node)->color = 1)
|
|
|
17 #define ngx_rbt_black(node) ((node)->color = 0)
|
|
|
18 #define ngx_rbt_is_red(node) ((node)->color)
|
|
|
19 #define ngx_rbt_is_black(node) (!ngx_rbt_is_red(node))
|
|
|
20 #define ngx_rbt_copy_color(n1, n2) (n1->color = n2->color)
|
|
|
21
|
|
|
22
|
|
16
|
23 static ngx_inline void ngx_rbtree_left_rotate(ngx_rbtree_t **root,
|
|
|
24 ngx_rbtree_t *sentinel,
|
|
|
25 ngx_rbtree_t *node);
|
|
|
26 static ngx_inline void ngx_rbtree_right_rotate(ngx_rbtree_t **root,
|
|
|
27 ngx_rbtree_t *sentinel,
|
|
|
28 ngx_rbtree_t *node);
|
|
0
|
29
|
|
|
30
|
|
|
31 void ngx_rbtree_insert(ngx_rbtree_t **root, ngx_rbtree_t *sentinel,
|
|
|
32 ngx_rbtree_t *node)
|
|
|
33 {
|
|
|
34 ngx_rbtree_t *temp;
|
|
|
35
|
|
|
36 /* a binary tree insert */
|
|
|
37
|
|
|
38 if (*root == sentinel) {
|
|
|
39 node->parent = NULL;
|
|
|
40 node->left = sentinel;
|
|
|
41 node->right = sentinel;
|
|
|
42 ngx_rbt_black(node);
|
|
|
43 *root = node;
|
|
|
44
|
|
|
45 return;
|
|
|
46 }
|
|
|
47
|
|
|
48 temp = *root;
|
|
|
49
|
|
|
50 for ( ;; ) {
|
|
|
51 if (node->key < temp->key) {
|
|
|
52 if (temp->left == sentinel) {
|
|
|
53 temp->left = node;
|
|
|
54 break;
|
|
|
55 }
|
|
|
56
|
|
|
57 temp = temp->left;
|
|
|
58 continue;
|
|
|
59 }
|
|
|
60
|
|
|
61 if (temp->right == sentinel) {
|
|
|
62 temp->right = node;
|
|
|
63 break;
|
|
|
64 }
|
|
|
65
|
|
|
66 temp = temp->right;
|
|
|
67 continue;
|
|
|
68 }
|
|
|
69
|
|
|
70 node->parent = temp;
|
|
|
71 node->left = sentinel;
|
|
|
72 node->right = sentinel;
|
|
|
73
|
|
|
74
|
|
|
75 /* re-balance tree */
|
|
|
76
|
|
|
77 ngx_rbt_red(node);
|
|
|
78
|
|
|
79 while (node != *root && ngx_rbt_is_red(node->parent)) {
|
|
|
80
|
|
|
81 if (node->parent == node->parent->parent->left) {
|
|
|
82 temp = node->parent->parent->right;
|
|
|
83
|
|
|
84 if (ngx_rbt_is_red(temp)) {
|
|
|
85 ngx_rbt_black(node->parent);
|
|
|
86 ngx_rbt_black(temp);
|
|
|
87 ngx_rbt_red(node->parent->parent);
|
|
|
88 node = node->parent->parent;
|
|
|
89
|
|
|
90 } else {
|
|
|
91 if (node == node->parent->right) {
|
|
|
92 node = node->parent;
|
|
|
93 ngx_rbtree_left_rotate(root, sentinel, node);
|
|
|
94 }
|
|
|
95
|
|
|
96 ngx_rbt_black(node->parent);
|
|
|
97 ngx_rbt_red(node->parent->parent);
|
|
|
98 ngx_rbtree_right_rotate(root, sentinel, node->parent->parent);
|
|
|
99 }
|
|
|
100
|
|
|
101 } else {
|
|
|
102 temp = node->parent->parent->left;
|
|
|
103
|
|
|
104 if (ngx_rbt_is_red(temp)) {
|
|
|
105 ngx_rbt_black(node->parent);
|
|
|
106 ngx_rbt_black(temp);
|
|
|
107 ngx_rbt_red(node->parent->parent);
|
|
|
108 node = node->parent->parent;
|
|
|
109
|
|
|
110 } else {
|
|
|
111 if (node == node->parent->left) {
|
|
|
112 node = node->parent;
|
|
|
113 ngx_rbtree_right_rotate(root, sentinel, node);
|
|
|
114 }
|
|
|
115
|
|
|
116 ngx_rbt_black(node->parent);
|
|
|
117 ngx_rbt_red(node->parent->parent);
|
|
|
118 ngx_rbtree_left_rotate(root, sentinel, node->parent->parent);
|
|
|
119 }
|
|
|
120 }
|
|
|
121
|
|
|
122 }
|
|
|
123
|
|
|
124 ngx_rbt_black(*root);
|
|
|
125 }
|
|
|
126
|
|
|
127
|
|
|
128 void ngx_rbtree_delete(ngx_rbtree_t **root, ngx_rbtree_t *sentinel,
|
|
|
129 ngx_rbtree_t *node)
|
|
|
130 {
|
|
|
131 ngx_int_t is_red;
|
|
|
132 ngx_rbtree_t *subst, *temp, *w;
|
|
|
133
|
|
|
134 /* a binary tree delete */
|
|
|
135
|
|
|
136 if (node->left == sentinel) {
|
|
|
137 temp = node->right;
|
|
|
138 subst = node;
|
|
|
139
|
|
|
140 } else if (node->right == sentinel) {
|
|
|
141 temp = node->left;
|
|
|
142 subst = node;
|
|
|
143
|
|
|
144 } else {
|
|
|
145 subst = ngx_rbtree_min(node->right, sentinel);
|
|
|
146
|
|
|
147 if (subst->left != sentinel) {
|
|
|
148 temp = subst->left;
|
|
|
149 } else {
|
|
|
150 temp = subst->right;
|
|
|
151 }
|
|
|
152 }
|
|
|
153
|
|
|
154 if (subst == *root) {
|
|
|
155 *root = temp;
|
|
|
156 ngx_rbt_black(temp);
|
|
|
157
|
|
|
158 /* DEBUG stuff */
|
|
|
159 node->left = NULL;
|
|
|
160 node->right = NULL;
|
|
|
161 node->parent = NULL;
|
|
|
162 node->key = 0;
|
|
|
163
|
|
|
164 return;
|
|
|
165 }
|
|
|
166
|
|
|
167 is_red = ngx_rbt_is_red(subst);
|
|
|
168
|
|
|
169 if (subst == subst->parent->left) {
|
|
|
170 subst->parent->left = temp;
|
|
|
171
|
|
|
172 } else {
|
|
|
173 subst->parent->right = temp;
|
|
|
174 }
|
|
|
175
|
|
|
176 if (subst == node) {
|
|
|
177
|
|
|
178 temp->parent = subst->parent;
|
|
|
179
|
|
|
180 } else {
|
|
|
181
|
|
|
182 if (subst->parent == node) {
|
|
|
183 temp->parent = subst;
|
|
|
184
|
|
|
185 } else {
|
|
|
186 temp->parent = subst->parent;
|
|
|
187 }
|
|
|
188
|
|
|
189 subst->left = node->left;
|
|
|
190 subst->right = node->right;
|
|
|
191 subst->parent = node->parent;
|
|
|
192 ngx_rbt_copy_color(subst, node);
|
|
|
193
|
|
|
194 if (node == *root) {
|
|
|
195 *root = subst;
|
|
|
196
|
|
|
197 } else {
|
|
|
198 if (node == node->parent->left) {
|
|
|
199 node->parent->left = subst;
|
|
|
200 } else {
|
|
|
201 node->parent->right = subst;
|
|
|
202 }
|
|
|
203 }
|
|
|
204
|
|
|
205 if (subst->left != sentinel) {
|
|
|
206 subst->left->parent = subst;
|
|
|
207 }
|
|
|
208
|
|
|
209 if (subst->right != sentinel) {
|
|
|
210 subst->right->parent = subst;
|
|
|
211 }
|
|
|
212
|
|
|
213 /* DEBUG stuff */
|
|
|
214 node->left = NULL;
|
|
|
215 node->right = NULL;
|
|
|
216 node->parent = NULL;
|
|
|
217 node->key = 0;
|
|
|
218 }
|
|
|
219
|
|
|
220 if (is_red) {
|
|
|
221 return;
|
|
|
222 }
|
|
|
223
|
|
|
224 /* a delete fixup */
|
|
|
225
|
|
|
226 while (temp != *root && ngx_rbt_is_black(temp)) {
|
|
|
227
|
|
|
228 if (temp == temp->parent->left) {
|
|
|
229 w = temp->parent->right;
|
|
|
230
|
|
|
231 if (ngx_rbt_is_red(w)) {
|
|
|
232 ngx_rbt_black(w);
|
|
|
233 ngx_rbt_red(temp->parent);
|
|
|
234 ngx_rbtree_left_rotate(root, sentinel, temp->parent);
|
|
|
235 w = temp->parent->right;
|
|
|
236 }
|
|
|
237
|
|
|
238 if (ngx_rbt_is_black(w->left) && ngx_rbt_is_black(w->right)) {
|
|
|
239 ngx_rbt_red(w);
|
|
|
240 temp = temp->parent;
|
|
|
241
|
|
|
242 } else {
|
|
|
243 if (ngx_rbt_is_black(w->right)) {
|
|
|
244 ngx_rbt_black(w->left);
|
|
|
245 ngx_rbt_red(w);
|
|
|
246 ngx_rbtree_right_rotate(root, sentinel, w);
|
|
|
247 w = temp->parent->right;
|
|
|
248 }
|
|
|
249
|
|
|
250 ngx_rbt_copy_color(w, temp->parent);
|
|
|
251 ngx_rbt_black(temp->parent);
|
|
|
252 ngx_rbt_black(w->right);
|
|
|
253 ngx_rbtree_left_rotate(root, sentinel, temp->parent);
|
|
|
254 temp = *root;
|
|
|
255 }
|
|
|
256
|
|
|
257 } else {
|
|
|
258 w = temp->parent->left;
|
|
|
259
|
|
|
260 if (ngx_rbt_is_red(w)) {
|
|
|
261 ngx_rbt_black(w);
|
|
|
262 ngx_rbt_red(temp->parent);
|
|
|
263 ngx_rbtree_right_rotate(root, sentinel, temp->parent);
|
|
|
264 w = temp->parent->left;
|
|
|
265 }
|
|
|
266
|
|
|
267 if (ngx_rbt_is_black(w->left) && ngx_rbt_is_black(w->right)) {
|
|
|
268 ngx_rbt_red(w);
|
|
|
269 temp = temp->parent;
|
|
|
270
|
|
|
271 } else {
|
|
|
272 if (ngx_rbt_is_black(w->left)) {
|
|
|
273 ngx_rbt_black(w->right);
|
|
|
274 ngx_rbt_red(w);
|
|
|
275 ngx_rbtree_left_rotate(root, sentinel, w);
|
|
|
276 w = temp->parent->left;
|
|
|
277 }
|
|
|
278
|
|
|
279 ngx_rbt_copy_color(w, temp->parent);
|
|
|
280 ngx_rbt_black(temp->parent);
|
|
|
281 ngx_rbt_black(w->left);
|
|
|
282 ngx_rbtree_right_rotate(root, sentinel, temp->parent);
|
|
|
283 temp = *root;
|
|
|
284 }
|
|
|
285 }
|
|
|
286 }
|
|
|
287
|
|
|
288 ngx_rbt_black(temp);
|
|
|
289 }
|
|
|
290
|
|
|
291
|
|
16
|
292 static ngx_inline void ngx_rbtree_left_rotate(ngx_rbtree_t **root,
|
|
|
293 ngx_rbtree_t *sentinel,
|
|
|
294 ngx_rbtree_t *node)
|
|
0
|
295 {
|
|
|
296 ngx_rbtree_t *temp;
|
|
|
297
|
|
|
298 temp = node->right;
|
|
|
299 node->right = temp->left;
|
|
|
300
|
|
|
301 if (temp->left != sentinel) {
|
|
|
302 temp->left->parent = node;
|
|
|
303 }
|
|
|
304
|
|
|
305 temp->parent = node->parent;
|
|
|
306
|
|
|
307 if (node == *root) {
|
|
|
308 *root = temp;
|
|
|
309
|
|
|
310 } else if (node == node->parent->left) {
|
|
|
311 node->parent->left = temp;
|
|
|
312
|
|
|
313 } else {
|
|
|
314 node->parent->right = temp;
|
|
|
315 }
|
|
|
316
|
|
|
317 temp->left = node;
|
|
|
318 node->parent = temp;
|
|
|
319 }
|
|
|
320
|
|
|
321
|
|
16
|
322 static ngx_inline void ngx_rbtree_right_rotate(ngx_rbtree_t **root,
|
|
|
323 ngx_rbtree_t *sentinel,
|
|
|
324 ngx_rbtree_t *node)
|
|
0
|
325 {
|
|
|
326 ngx_rbtree_t *temp;
|
|
|
327
|
|
|
328 temp = node->left;
|
|
|
329 node->left = temp->right;
|
|
|
330
|
|
|
331 if (temp->right != sentinel) {
|
|
|
332 temp->right->parent = node;
|
|
|
333 }
|
|
|
334
|
|
|
335 temp->parent = node->parent;
|
|
|
336
|
|
|
337 if (node == *root) {
|
|
|
338 *root = temp;
|
|
|
339
|
|
|
340 } else if (node == node->parent->right) {
|
|
|
341 node->parent->right = temp;
|
|
|
342
|
|
|
343 } else {
|
|
|
344 node->parent->left = temp;
|
|
|
345 }
|
|
|
346
|
|
|
347 temp->right = node;
|
|
|
348 node->parent = temp;
|
|
|
349 }
|
