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Commit | Line | Data |
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1da177e4 LT |
1 | /* |
2 | Red Black Trees | |
3 | (C) 1999 Andrea Arcangeli <andrea@suse.de> | |
4 | (C) 2002 David Woodhouse <dwmw2@infradead.org> | |
5 | ||
6 | This program is free software; you can redistribute it and/or modify | |
7 | it under the terms of the GNU General Public License as published by | |
8 | the Free Software Foundation; either version 2 of the License, or | |
9 | (at your option) any later version. | |
10 | ||
11 | This program is distributed in the hope that it will be useful, | |
12 | but WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
14 | GNU General Public License for more details. | |
15 | ||
16 | You should have received a copy of the GNU General Public License | |
17 | along with this program; if not, write to the Free Software | |
18 | Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA | |
19 | ||
20 | linux/lib/rbtree.c | |
21 | */ | |
22 | ||
23 | #include <linux/rbtree.h> | |
8bc3bcc9 | 24 | #include <linux/export.h> |
1da177e4 | 25 | |
5bc9188a ML |
26 | /* |
27 | * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree | |
28 | * | |
29 | * 1) A node is either red or black | |
30 | * 2) The root is black | |
31 | * 3) All leaves (NULL) are black | |
32 | * 4) Both children of every red node are black | |
33 | * 5) Every simple path from root to leaves contains the same number | |
34 | * of black nodes. | |
35 | * | |
36 | * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two | |
37 | * consecutive red nodes in a path and every red node is therefore followed by | |
38 | * a black. So if B is the number of black nodes on every simple path (as per | |
39 | * 5), then the longest possible path due to 4 is 2B. | |
40 | * | |
41 | * We shall indicate color with case, where black nodes are uppercase and red | |
42 | * nodes will be lowercase. | |
43 | */ | |
44 | ||
bf7ad8ee ML |
45 | #define RB_RED 0 |
46 | #define RB_BLACK 1 | |
47 | ||
48 | #define rb_color(r) ((r)->__rb_parent_color & 1) | |
49 | #define rb_is_red(r) (!rb_color(r)) | |
50 | #define rb_is_black(r) rb_color(r) | |
51 | #define rb_set_red(r) do { (r)->__rb_parent_color &= ~1; } while (0) | |
52 | #define rb_set_black(r) do { (r)->__rb_parent_color |= 1; } while (0) | |
53 | ||
54 | static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p) | |
55 | { | |
56 | rb->__rb_parent_color = rb_color(rb) | (unsigned long)p; | |
57 | } | |
58 | static inline void rb_set_color(struct rb_node *rb, int color) | |
59 | { | |
60 | rb->__rb_parent_color = (rb->__rb_parent_color & ~1) | color; | |
61 | } | |
62 | ||
5bc9188a ML |
63 | static inline void rb_set_parent_color(struct rb_node *rb, |
64 | struct rb_node *p, int color) | |
65 | { | |
66 | rb->__rb_parent_color = (unsigned long)p | color; | |
67 | } | |
68 | ||
69 | static inline struct rb_node *rb_red_parent(struct rb_node *red) | |
70 | { | |
71 | return (struct rb_node *)red->__rb_parent_color; | |
72 | } | |
73 | ||
1da177e4 LT |
74 | static void __rb_rotate_left(struct rb_node *node, struct rb_root *root) |
75 | { | |
76 | struct rb_node *right = node->rb_right; | |
55a98102 | 77 | struct rb_node *parent = rb_parent(node); |
1da177e4 LT |
78 | |
79 | if ((node->rb_right = right->rb_left)) | |
55a98102 | 80 | rb_set_parent(right->rb_left, node); |
1da177e4 LT |
81 | right->rb_left = node; |
82 | ||
55a98102 DW |
83 | rb_set_parent(right, parent); |
84 | ||
85 | if (parent) | |
1da177e4 | 86 | { |
55a98102 DW |
87 | if (node == parent->rb_left) |
88 | parent->rb_left = right; | |
1da177e4 | 89 | else |
55a98102 | 90 | parent->rb_right = right; |
1da177e4 LT |
91 | } |
92 | else | |
93 | root->rb_node = right; | |
55a98102 | 94 | rb_set_parent(node, right); |
1da177e4 LT |
95 | } |
96 | ||
97 | static void __rb_rotate_right(struct rb_node *node, struct rb_root *root) | |
98 | { | |
99 | struct rb_node *left = node->rb_left; | |
55a98102 | 100 | struct rb_node *parent = rb_parent(node); |
1da177e4 LT |
101 | |
102 | if ((node->rb_left = left->rb_right)) | |
55a98102 | 103 | rb_set_parent(left->rb_right, node); |
1da177e4 LT |
104 | left->rb_right = node; |
105 | ||
55a98102 DW |
106 | rb_set_parent(left, parent); |
107 | ||
108 | if (parent) | |
1da177e4 | 109 | { |
55a98102 DW |
110 | if (node == parent->rb_right) |
111 | parent->rb_right = left; | |
1da177e4 | 112 | else |
55a98102 | 113 | parent->rb_left = left; |
1da177e4 LT |
114 | } |
115 | else | |
116 | root->rb_node = left; | |
55a98102 | 117 | rb_set_parent(node, left); |
1da177e4 LT |
118 | } |
119 | ||
5bc9188a ML |
120 | /* |
121 | * Helper function for rotations: | |
122 | * - old's parent and color get assigned to new | |
123 | * - old gets assigned new as a parent and 'color' as a color. | |
124 | */ | |
125 | static inline void | |
126 | __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new, | |
127 | struct rb_root *root, int color) | |
128 | { | |
129 | struct rb_node *parent = rb_parent(old); | |
130 | new->__rb_parent_color = old->__rb_parent_color; | |
131 | rb_set_parent_color(old, new, color); | |
132 | if (parent) { | |
133 | if (parent->rb_left == old) | |
134 | parent->rb_left = new; | |
135 | else | |
136 | parent->rb_right = new; | |
137 | } else | |
138 | root->rb_node = new; | |
139 | } | |
140 | ||
1da177e4 LT |
141 | void rb_insert_color(struct rb_node *node, struct rb_root *root) |
142 | { | |
5bc9188a | 143 | struct rb_node *parent = rb_red_parent(node), *gparent, *tmp; |
1da177e4 | 144 | |
6d58452d ML |
145 | while (true) { |
146 | /* | |
147 | * Loop invariant: node is red | |
148 | * | |
149 | * If there is a black parent, we are done. | |
150 | * Otherwise, take some corrective action as we don't | |
151 | * want a red root or two consecutive red nodes. | |
152 | */ | |
6d58452d | 153 | if (!parent) { |
5bc9188a | 154 | rb_set_parent_color(node, NULL, RB_BLACK); |
6d58452d ML |
155 | break; |
156 | } else if (rb_is_black(parent)) | |
157 | break; | |
158 | ||
5bc9188a ML |
159 | gparent = rb_red_parent(parent); |
160 | ||
161 | if (parent == gparent->rb_left) { | |
162 | tmp = gparent->rb_right; | |
163 | if (tmp && rb_is_red(tmp)) { | |
164 | /* | |
165 | * Case 1 - color flips | |
166 | * | |
167 | * G g | |
168 | * / \ / \ | |
169 | * p u --> P U | |
170 | * / / | |
171 | * n N | |
172 | * | |
173 | * However, since g's parent might be red, and | |
174 | * 4) does not allow this, we need to recurse | |
175 | * at g. | |
176 | */ | |
177 | rb_set_parent_color(tmp, gparent, RB_BLACK); | |
178 | rb_set_parent_color(parent, gparent, RB_BLACK); | |
179 | node = gparent; | |
180 | parent = rb_parent(node); | |
181 | rb_set_parent_color(node, parent, RB_RED); | |
182 | continue; | |
1da177e4 LT |
183 | } |
184 | ||
1f052865 | 185 | if (parent->rb_right == node) { |
5bc9188a ML |
186 | /* |
187 | * Case 2 - left rotate at parent | |
188 | * | |
189 | * G G | |
190 | * / \ / \ | |
191 | * p U --> n U | |
192 | * \ / | |
193 | * n p | |
194 | * | |
195 | * This still leaves us in violation of 4), the | |
196 | * continuation into Case 3 will fix that. | |
197 | */ | |
198 | parent->rb_right = tmp = node->rb_left; | |
199 | node->rb_left = parent; | |
200 | if (tmp) | |
201 | rb_set_parent_color(tmp, parent, | |
202 | RB_BLACK); | |
203 | rb_set_parent_color(parent, node, RB_RED); | |
1da177e4 | 204 | parent = node; |
1da177e4 LT |
205 | } |
206 | ||
5bc9188a ML |
207 | /* |
208 | * Case 3 - right rotate at gparent | |
209 | * | |
210 | * G P | |
211 | * / \ / \ | |
212 | * p U --> n g | |
213 | * / \ | |
214 | * n U | |
215 | */ | |
216 | gparent->rb_left = tmp = parent->rb_right; | |
217 | parent->rb_right = gparent; | |
218 | if (tmp) | |
219 | rb_set_parent_color(tmp, gparent, RB_BLACK); | |
220 | __rb_rotate_set_parents(gparent, parent, root, RB_RED); | |
1f052865 | 221 | break; |
1da177e4 | 222 | } else { |
5bc9188a ML |
223 | tmp = gparent->rb_left; |
224 | if (tmp && rb_is_red(tmp)) { | |
225 | /* Case 1 - color flips */ | |
226 | rb_set_parent_color(tmp, gparent, RB_BLACK); | |
227 | rb_set_parent_color(parent, gparent, RB_BLACK); | |
228 | node = gparent; | |
229 | parent = rb_parent(node); | |
230 | rb_set_parent_color(node, parent, RB_RED); | |
231 | continue; | |
1da177e4 LT |
232 | } |
233 | ||
1f052865 | 234 | if (parent->rb_left == node) { |
5bc9188a ML |
235 | /* Case 2 - right rotate at parent */ |
236 | parent->rb_left = tmp = node->rb_right; | |
237 | node->rb_right = parent; | |
238 | if (tmp) | |
239 | rb_set_parent_color(tmp, parent, | |
240 | RB_BLACK); | |
241 | rb_set_parent_color(parent, node, RB_RED); | |
1da177e4 | 242 | parent = node; |
1da177e4 LT |
243 | } |
244 | ||
5bc9188a ML |
245 | /* Case 3 - left rotate at gparent */ |
246 | gparent->rb_right = tmp = parent->rb_left; | |
247 | parent->rb_left = gparent; | |
248 | if (tmp) | |
249 | rb_set_parent_color(tmp, gparent, RB_BLACK); | |
250 | __rb_rotate_set_parents(gparent, parent, root, RB_RED); | |
1f052865 | 251 | break; |
1da177e4 LT |
252 | } |
253 | } | |
1da177e4 LT |
254 | } |
255 | EXPORT_SYMBOL(rb_insert_color); | |
256 | ||
257 | static void __rb_erase_color(struct rb_node *node, struct rb_node *parent, | |
258 | struct rb_root *root) | |
259 | { | |
260 | struct rb_node *other; | |
261 | ||
d6ff1273 ML |
262 | while (true) { |
263 | /* | |
264 | * Loop invariant: all leaf paths going through node have a | |
265 | * black node count that is 1 lower than other leaf paths. | |
266 | * | |
267 | * If node is red, we can flip it to black to adjust. | |
268 | * If node is the root, all leaf paths go through it. | |
269 | * Otherwise, we need to adjust the tree through color flips | |
270 | * and tree rotations as per one of the 4 cases below. | |
271 | */ | |
272 | if (node && rb_is_red(node)) { | |
273 | rb_set_black(node); | |
274 | break; | |
275 | } else if (!parent) { | |
276 | break; | |
277 | } else if (parent->rb_left == node) { | |
1da177e4 | 278 | other = parent->rb_right; |
55a98102 | 279 | if (rb_is_red(other)) |
1da177e4 | 280 | { |
55a98102 DW |
281 | rb_set_black(other); |
282 | rb_set_red(parent); | |
1da177e4 LT |
283 | __rb_rotate_left(parent, root); |
284 | other = parent->rb_right; | |
285 | } | |
e125d147 ML |
286 | if (!other->rb_right || rb_is_black(other->rb_right)) { |
287 | if (!other->rb_left || | |
288 | rb_is_black(other->rb_left)) { | |
55a98102 | 289 | rb_set_red(other); |
e125d147 ML |
290 | node = parent; |
291 | parent = rb_parent(node); | |
292 | continue; | |
1da177e4 | 293 | } |
e125d147 ML |
294 | rb_set_black(other->rb_left); |
295 | rb_set_red(other); | |
296 | __rb_rotate_right(other, root); | |
297 | other = parent->rb_right; | |
1da177e4 | 298 | } |
e125d147 ML |
299 | rb_set_color(other, rb_color(parent)); |
300 | rb_set_black(parent); | |
301 | rb_set_black(other->rb_right); | |
302 | __rb_rotate_left(parent, root); | |
303 | break; | |
d6ff1273 | 304 | } else { |
1da177e4 | 305 | other = parent->rb_left; |
55a98102 | 306 | if (rb_is_red(other)) |
1da177e4 | 307 | { |
55a98102 DW |
308 | rb_set_black(other); |
309 | rb_set_red(parent); | |
1da177e4 LT |
310 | __rb_rotate_right(parent, root); |
311 | other = parent->rb_left; | |
312 | } | |
e125d147 ML |
313 | if (!other->rb_left || rb_is_black(other->rb_left)) { |
314 | if (!other->rb_right || | |
315 | rb_is_black(other->rb_right)) { | |
55a98102 | 316 | rb_set_red(other); |
e125d147 ML |
317 | node = parent; |
318 | parent = rb_parent(node); | |
319 | continue; | |
1da177e4 | 320 | } |
e125d147 ML |
321 | rb_set_black(other->rb_right); |
322 | rb_set_red(other); | |
323 | __rb_rotate_left(other, root); | |
324 | other = parent->rb_left; | |
1da177e4 | 325 | } |
e125d147 ML |
326 | rb_set_color(other, rb_color(parent)); |
327 | rb_set_black(parent); | |
328 | rb_set_black(other->rb_left); | |
329 | __rb_rotate_right(parent, root); | |
330 | break; | |
1da177e4 LT |
331 | } |
332 | } | |
1da177e4 LT |
333 | } |
334 | ||
335 | void rb_erase(struct rb_node *node, struct rb_root *root) | |
336 | { | |
337 | struct rb_node *child, *parent; | |
338 | int color; | |
339 | ||
340 | if (!node->rb_left) | |
341 | child = node->rb_right; | |
342 | else if (!node->rb_right) | |
343 | child = node->rb_left; | |
344 | else | |
345 | { | |
346 | struct rb_node *old = node, *left; | |
347 | ||
348 | node = node->rb_right; | |
349 | while ((left = node->rb_left) != NULL) | |
350 | node = left; | |
16c047ad WS |
351 | |
352 | if (rb_parent(old)) { | |
353 | if (rb_parent(old)->rb_left == old) | |
354 | rb_parent(old)->rb_left = node; | |
355 | else | |
356 | rb_parent(old)->rb_right = node; | |
357 | } else | |
358 | root->rb_node = node; | |
359 | ||
1da177e4 | 360 | child = node->rb_right; |
55a98102 | 361 | parent = rb_parent(node); |
2f3243ae | 362 | color = rb_color(node); |
1da177e4 | 363 | |
55a98102 | 364 | if (parent == old) { |
1da177e4 | 365 | parent = node; |
4c601178 WS |
366 | } else { |
367 | if (child) | |
368 | rb_set_parent(child, parent); | |
1975e593 | 369 | parent->rb_left = child; |
4b324126 WS |
370 | |
371 | node->rb_right = old->rb_right; | |
372 | rb_set_parent(old->rb_right, node); | |
4c601178 | 373 | } |
1975e593 | 374 | |
bf7ad8ee | 375 | node->__rb_parent_color = old->__rb_parent_color; |
1da177e4 | 376 | node->rb_left = old->rb_left; |
55a98102 | 377 | rb_set_parent(old->rb_left, node); |
4b324126 | 378 | |
1da177e4 LT |
379 | goto color; |
380 | } | |
381 | ||
55a98102 | 382 | parent = rb_parent(node); |
2f3243ae | 383 | color = rb_color(node); |
1da177e4 LT |
384 | |
385 | if (child) | |
55a98102 | 386 | rb_set_parent(child, parent); |
b945d6b2 PZ |
387 | if (parent) |
388 | { | |
1da177e4 LT |
389 | if (parent->rb_left == node) |
390 | parent->rb_left = child; | |
391 | else | |
392 | parent->rb_right = child; | |
17d9ddc7 | 393 | } |
b945d6b2 PZ |
394 | else |
395 | root->rb_node = child; | |
1da177e4 LT |
396 | |
397 | color: | |
398 | if (color == RB_BLACK) | |
399 | __rb_erase_color(child, parent, root); | |
400 | } | |
401 | EXPORT_SYMBOL(rb_erase); | |
402 | ||
b945d6b2 PZ |
403 | static void rb_augment_path(struct rb_node *node, rb_augment_f func, void *data) |
404 | { | |
405 | struct rb_node *parent; | |
406 | ||
407 | up: | |
408 | func(node, data); | |
409 | parent = rb_parent(node); | |
410 | if (!parent) | |
411 | return; | |
412 | ||
413 | if (node == parent->rb_left && parent->rb_right) | |
414 | func(parent->rb_right, data); | |
415 | else if (parent->rb_left) | |
416 | func(parent->rb_left, data); | |
417 | ||
418 | node = parent; | |
419 | goto up; | |
420 | } | |
421 | ||
422 | /* | |
423 | * after inserting @node into the tree, update the tree to account for | |
424 | * both the new entry and any damage done by rebalance | |
425 | */ | |
426 | void rb_augment_insert(struct rb_node *node, rb_augment_f func, void *data) | |
427 | { | |
428 | if (node->rb_left) | |
429 | node = node->rb_left; | |
430 | else if (node->rb_right) | |
431 | node = node->rb_right; | |
432 | ||
433 | rb_augment_path(node, func, data); | |
434 | } | |
0b6bb66d | 435 | EXPORT_SYMBOL(rb_augment_insert); |
b945d6b2 PZ |
436 | |
437 | /* | |
438 | * before removing the node, find the deepest node on the rebalance path | |
439 | * that will still be there after @node gets removed | |
440 | */ | |
441 | struct rb_node *rb_augment_erase_begin(struct rb_node *node) | |
442 | { | |
443 | struct rb_node *deepest; | |
444 | ||
445 | if (!node->rb_right && !node->rb_left) | |
446 | deepest = rb_parent(node); | |
447 | else if (!node->rb_right) | |
448 | deepest = node->rb_left; | |
449 | else if (!node->rb_left) | |
450 | deepest = node->rb_right; | |
451 | else { | |
452 | deepest = rb_next(node); | |
453 | if (deepest->rb_right) | |
454 | deepest = deepest->rb_right; | |
455 | else if (rb_parent(deepest) != node) | |
456 | deepest = rb_parent(deepest); | |
457 | } | |
458 | ||
459 | return deepest; | |
460 | } | |
0b6bb66d | 461 | EXPORT_SYMBOL(rb_augment_erase_begin); |
b945d6b2 PZ |
462 | |
463 | /* | |
464 | * after removal, update the tree to account for the removed entry | |
465 | * and any rebalance damage. | |
466 | */ | |
467 | void rb_augment_erase_end(struct rb_node *node, rb_augment_f func, void *data) | |
468 | { | |
469 | if (node) | |
470 | rb_augment_path(node, func, data); | |
471 | } | |
0b6bb66d | 472 | EXPORT_SYMBOL(rb_augment_erase_end); |
b945d6b2 | 473 | |
1da177e4 LT |
474 | /* |
475 | * This function returns the first node (in sort order) of the tree. | |
476 | */ | |
f4b477c4 | 477 | struct rb_node *rb_first(const struct rb_root *root) |
1da177e4 LT |
478 | { |
479 | struct rb_node *n; | |
480 | ||
481 | n = root->rb_node; | |
482 | if (!n) | |
483 | return NULL; | |
484 | while (n->rb_left) | |
485 | n = n->rb_left; | |
486 | return n; | |
487 | } | |
488 | EXPORT_SYMBOL(rb_first); | |
489 | ||
f4b477c4 | 490 | struct rb_node *rb_last(const struct rb_root *root) |
1da177e4 LT |
491 | { |
492 | struct rb_node *n; | |
493 | ||
494 | n = root->rb_node; | |
495 | if (!n) | |
496 | return NULL; | |
497 | while (n->rb_right) | |
498 | n = n->rb_right; | |
499 | return n; | |
500 | } | |
501 | EXPORT_SYMBOL(rb_last); | |
502 | ||
f4b477c4 | 503 | struct rb_node *rb_next(const struct rb_node *node) |
1da177e4 | 504 | { |
55a98102 DW |
505 | struct rb_node *parent; |
506 | ||
4c199a93 | 507 | if (RB_EMPTY_NODE(node)) |
10fd48f2 JA |
508 | return NULL; |
509 | ||
1da177e4 LT |
510 | /* If we have a right-hand child, go down and then left as far |
511 | as we can. */ | |
512 | if (node->rb_right) { | |
513 | node = node->rb_right; | |
514 | while (node->rb_left) | |
515 | node=node->rb_left; | |
f4b477c4 | 516 | return (struct rb_node *)node; |
1da177e4 LT |
517 | } |
518 | ||
519 | /* No right-hand children. Everything down and left is | |
520 | smaller than us, so any 'next' node must be in the general | |
521 | direction of our parent. Go up the tree; any time the | |
522 | ancestor is a right-hand child of its parent, keep going | |
523 | up. First time it's a left-hand child of its parent, said | |
524 | parent is our 'next' node. */ | |
55a98102 DW |
525 | while ((parent = rb_parent(node)) && node == parent->rb_right) |
526 | node = parent; | |
1da177e4 | 527 | |
55a98102 | 528 | return parent; |
1da177e4 LT |
529 | } |
530 | EXPORT_SYMBOL(rb_next); | |
531 | ||
f4b477c4 | 532 | struct rb_node *rb_prev(const struct rb_node *node) |
1da177e4 | 533 | { |
55a98102 DW |
534 | struct rb_node *parent; |
535 | ||
4c199a93 | 536 | if (RB_EMPTY_NODE(node)) |
10fd48f2 JA |
537 | return NULL; |
538 | ||
1da177e4 LT |
539 | /* If we have a left-hand child, go down and then right as far |
540 | as we can. */ | |
541 | if (node->rb_left) { | |
542 | node = node->rb_left; | |
543 | while (node->rb_right) | |
544 | node=node->rb_right; | |
f4b477c4 | 545 | return (struct rb_node *)node; |
1da177e4 LT |
546 | } |
547 | ||
548 | /* No left-hand children. Go up till we find an ancestor which | |
549 | is a right-hand child of its parent */ | |
55a98102 DW |
550 | while ((parent = rb_parent(node)) && node == parent->rb_left) |
551 | node = parent; | |
1da177e4 | 552 | |
55a98102 | 553 | return parent; |
1da177e4 LT |
554 | } |
555 | EXPORT_SYMBOL(rb_prev); | |
556 | ||
557 | void rb_replace_node(struct rb_node *victim, struct rb_node *new, | |
558 | struct rb_root *root) | |
559 | { | |
55a98102 | 560 | struct rb_node *parent = rb_parent(victim); |
1da177e4 LT |
561 | |
562 | /* Set the surrounding nodes to point to the replacement */ | |
563 | if (parent) { | |
564 | if (victim == parent->rb_left) | |
565 | parent->rb_left = new; | |
566 | else | |
567 | parent->rb_right = new; | |
568 | } else { | |
569 | root->rb_node = new; | |
570 | } | |
571 | if (victim->rb_left) | |
55a98102 | 572 | rb_set_parent(victim->rb_left, new); |
1da177e4 | 573 | if (victim->rb_right) |
55a98102 | 574 | rb_set_parent(victim->rb_right, new); |
1da177e4 LT |
575 | |
576 | /* Copy the pointers/colour from the victim to the replacement */ | |
577 | *new = *victim; | |
578 | } | |
579 | EXPORT_SYMBOL(rb_replace_node); |