-
-
Notifications
You must be signed in to change notification settings - Fork 103
/
rbtree.c
553 lines (482 loc) · 13.5 KB
/
rbtree.c
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
/*
* rbtree.c -- generic red black tree
*
* Copyright (c) 2001-2006, NLnet Labs. All rights reserved.
*
* See LICENSE for the license.
*
*/
#include "config.h"
#include <assert.h>
#include <stdlib.h>
#include "rbtree.h"
#define BLACK 0
#define RED 1
rbnode_type rbtree_null_node = {
RBTREE_NULL, /* Parent. */
RBTREE_NULL, /* Left. */
RBTREE_NULL, /* Right. */
NULL, /* Key. */
BLACK /* Color. */
};
static void rbtree_rotate_left(rbtree_type *rbtree, rbnode_type *node);
static void rbtree_rotate_right(rbtree_type *rbtree, rbnode_type *node);
static void rbtree_insert_fixup(rbtree_type *rbtree, rbnode_type *node);
static void rbtree_delete_fixup(rbtree_type* rbtree, rbnode_type* child, rbnode_type* child_parent);
/*
* Creates a new red black tree, initializes and returns a pointer to it.
*
* Return NULL on failure.
*
*/
rbtree_type *
rbtree_create (region_type *region, int (*cmpf)(const void *, const void *))
{
rbtree_type *rbtree;
/* Allocate memory for it */
rbtree = (rbtree_type *) region_alloc(region, sizeof(rbtree_type));
if (!rbtree) {
return NULL;
}
/* Initialize it */
rbtree->root = RBTREE_NULL;
rbtree->count = 0;
rbtree->region = region;
rbtree->cmp = cmpf;
return rbtree;
}
/*
* Rotates the node to the left.
*
*/
static void
rbtree_rotate_left(rbtree_type *rbtree, rbnode_type *node)
{
rbnode_type *right = node->right;
node->right = right->left;
if (right->left != RBTREE_NULL)
right->left->parent = node;
right->parent = node->parent;
if (node->parent != RBTREE_NULL) {
if (node == node->parent->left) {
node->parent->left = right;
} else {
node->parent->right = right;
}
} else {
rbtree->root = right;
}
right->left = node;
node->parent = right;
}
/*
* Rotates the node to the right.
*
*/
static void
rbtree_rotate_right(rbtree_type *rbtree, rbnode_type *node)
{
rbnode_type *left = node->left;
node->left = left->right;
if (left->right != RBTREE_NULL)
left->right->parent = node;
left->parent = node->parent;
if (node->parent != RBTREE_NULL) {
if (node == node->parent->right) {
node->parent->right = left;
} else {
node->parent->left = left;
}
} else {
rbtree->root = left;
}
left->right = node;
node->parent = left;
}
static void
rbtree_insert_fixup(rbtree_type *rbtree, rbnode_type *node)
{
rbnode_type *uncle;
/* While not at the root and need fixing... */
while (node != rbtree->root && node->parent->color == RED) {
/* If our parent is left child of our grandparent... */
if (node->parent == node->parent->parent->left) {
uncle = node->parent->parent->right;
/* If our uncle is red... */
if (uncle->color == RED) {
/* Paint the parent and the uncle black... */
node->parent->color = BLACK;
uncle->color = BLACK;
/* And the grandparent red... */
node->parent->parent->color = RED;
/* And continue fixing the grandparent */
node = node->parent->parent;
} else { /* Our uncle is black... */
/* Are we the right child? */
if (node == node->parent->right) {
node = node->parent;
rbtree_rotate_left(rbtree, node);
}
/* Now we're the left child, repaint and rotate... */
node->parent->color = BLACK;
node->parent->parent->color = RED;
rbtree_rotate_right(rbtree, node->parent->parent);
}
} else {
uncle = node->parent->parent->left;
/* If our uncle is red... */
if (uncle->color == RED) {
/* Paint the parent and the uncle black... */
node->parent->color = BLACK;
uncle->color = BLACK;
/* And the grandparent red... */
node->parent->parent->color = RED;
/* And continue fixing the grandparent */
node = node->parent->parent;
} else { /* Our uncle is black... */
/* Are we the right child? */
if (node == node->parent->left) {
node = node->parent;
rbtree_rotate_right(rbtree, node);
}
/* Now we're the right child, repaint and rotate... */
node->parent->color = BLACK;
node->parent->parent->color = RED;
rbtree_rotate_left(rbtree, node->parent->parent);
}
}
}
rbtree->root->color = BLACK;
}
/*
* Inserts a node into a red black tree.
*
* Returns NULL on failure or the pointer to the newly added node
* otherwise.
*/
rbnode_type *
rbtree_insert (rbtree_type *rbtree, rbnode_type *data)
{
/* XXX Not necessary, but keeps compiler quiet... */
int r = 0;
/* We start at the root of the tree */
rbnode_type *node = rbtree->root;
rbnode_type *parent = RBTREE_NULL;
/* Lets find the new parent... */
while (node != RBTREE_NULL) {
/* Compare two keys, do we have a duplicate? */
if ((r = rbtree->cmp(data->key, node->key)) == 0) {
return NULL;
}
parent = node;
if (r < 0) {
node = node->left;
} else {
node = node->right;
}
}
/* Initialize the new node */
data->parent = parent;
data->left = data->right = RBTREE_NULL;
data->color = RED;
rbtree->count++;
/* Insert it into the tree... */
if (parent != RBTREE_NULL) {
if (r < 0) {
parent->left = data;
} else {
parent->right = data;
}
} else {
rbtree->root = data;
}
/* Fix up the red-black properties... */
rbtree_insert_fixup(rbtree, data);
return data;
}
/*
* Searches the red black tree, returns the data if key is found or NULL otherwise.
*
*/
rbnode_type *
rbtree_search (rbtree_type *rbtree, const void *key)
{
rbnode_type *node;
if (rbtree_find_less_equal(rbtree, key, &node)) {
return node;
} else {
return NULL;
}
}
/* helpers for delete */
static void swap_int8(uint8_t* x, uint8_t* y)
{
uint8_t t = *x; *x = *y; *y = t;
}
static void swap_np(rbnode_type** x, rbnode_type** y)
{
rbnode_type* t = *x; *x = *y; *y = t;
}
static void change_parent_ptr(rbtree_type* rbtree, rbnode_type* parent, rbnode_type* old, rbnode_type* new)
{
if(parent == RBTREE_NULL)
{
assert(rbtree->root == old);
if(rbtree->root == old) rbtree->root = new;
return;
}
assert(parent->left == old || parent->right == old
|| parent->left == new || parent->right == new);
if(parent->left == old) parent->left = new;
if(parent->right == old) parent->right = new;
}
static void change_child_ptr(rbnode_type* child, rbnode_type* old, rbnode_type* new)
{
if(child == RBTREE_NULL) return;
assert(child->parent == old || child->parent == new);
if(child->parent == old) child->parent = new;
}
rbnode_type*
rbtree_delete(rbtree_type *rbtree, const void *key)
{
rbnode_type *to_delete;
rbnode_type *child;
if((to_delete = rbtree_search(rbtree, key)) == 0) return 0;
rbtree->count--;
/* make sure we have at most one non-leaf child */
if(to_delete->left != RBTREE_NULL && to_delete->right != RBTREE_NULL)
{
/* swap with smallest from right subtree (or largest from left) */
rbnode_type *smright = to_delete->right;
while(smright->left != RBTREE_NULL)
smright = smright->left;
/* swap the smright and to_delete elements in the tree,
* but the rbnode_type is first part of user data struct
* so cannot just swap the keys and data pointers. Instead
* readjust the pointers left,right,parent */
/* swap colors - colors are tied to the position in the tree */
swap_int8(&to_delete->color, &smright->color);
/* swap child pointers in parents of smright/to_delete */
change_parent_ptr(rbtree, to_delete->parent, to_delete, smright);
if(to_delete->right != smright)
change_parent_ptr(rbtree, smright->parent, smright, to_delete);
/* swap parent pointers in children of smright/to_delete */
change_child_ptr(smright->left, smright, to_delete);
change_child_ptr(smright->left, smright, to_delete);
change_child_ptr(smright->right, smright, to_delete);
change_child_ptr(smright->right, smright, to_delete);
change_child_ptr(to_delete->left, to_delete, smright);
if(to_delete->right != smright)
change_child_ptr(to_delete->right, to_delete, smright);
if(to_delete->right == smright)
{
/* set up so after swap they work */
to_delete->right = to_delete;
smright->parent = smright;
}
/* swap pointers in to_delete/smright nodes */
swap_np(&to_delete->parent, &smright->parent);
swap_np(&to_delete->left, &smright->left);
swap_np(&to_delete->right, &smright->right);
/* now delete to_delete (which is at the location where the smright previously was) */
}
assert(to_delete->left == RBTREE_NULL || to_delete->right == RBTREE_NULL);
if(to_delete->left != RBTREE_NULL) child = to_delete->left;
else child = to_delete->right;
/* unlink to_delete from the tree, replace to_delete with child */
change_parent_ptr(rbtree, to_delete->parent, to_delete, child);
change_child_ptr(child, to_delete, to_delete->parent);
if(to_delete->color == RED)
{
/* if node is red then the child (black) can be swapped in */
}
else if(child->color == RED)
{
/* change child to BLACK, removing a RED node is no problem */
if(child!=RBTREE_NULL) child->color = BLACK;
}
else rbtree_delete_fixup(rbtree, child, to_delete->parent);
/* unlink completely */
to_delete->parent = RBTREE_NULL;
to_delete->left = RBTREE_NULL;
to_delete->right = RBTREE_NULL;
to_delete->color = BLACK;
return to_delete;
}
static void rbtree_delete_fixup(rbtree_type* rbtree, rbnode_type* child, rbnode_type* child_parent)
{
rbnode_type* sibling;
int go_up = 1;
/* determine sibling to the node that is one-black short */
if(child_parent->right == child) sibling = child_parent->left;
else sibling = child_parent->right;
while(go_up)
{
if(child_parent == RBTREE_NULL)
{
/* removed parent==black from root, every path, so ok */
return;
}
if(sibling->color == RED)
{ /* rotate to get a black sibling */
child_parent->color = RED;
sibling->color = BLACK;
if(child_parent->right == child)
rbtree_rotate_right(rbtree, child_parent);
else rbtree_rotate_left(rbtree, child_parent);
/* new sibling after rotation */
if(child_parent->right == child) sibling = child_parent->left;
else sibling = child_parent->right;
}
if(child_parent->color == BLACK
&& sibling->color == BLACK
&& sibling->left->color == BLACK
&& sibling->right->color == BLACK)
{ /* fixup local with recolor of sibling */
if(sibling != RBTREE_NULL)
sibling->color = RED;
child = child_parent;
child_parent = child_parent->parent;
/* prepare to go up, new sibling */
if(child_parent->right == child) sibling = child_parent->left;
else sibling = child_parent->right;
}
else go_up = 0;
}
if(child_parent->color == RED
&& sibling->color == BLACK
&& sibling->left->color == BLACK
&& sibling->right->color == BLACK)
{
/* move red to sibling to rebalance */
if(sibling != RBTREE_NULL)
sibling->color = RED;
child_parent->color = BLACK;
return;
}
assert(sibling != RBTREE_NULL);
/* get a new sibling, by rotating at sibling. See which child
of sibling is red */
if(child_parent->right == child
&& sibling->color == BLACK
&& sibling->right->color == RED
&& sibling->left->color == BLACK)
{
sibling->color = RED;
sibling->right->color = BLACK;
rbtree_rotate_left(rbtree, sibling);
/* new sibling after rotation */
if(child_parent->right == child) sibling = child_parent->left;
else sibling = child_parent->right;
}
else if(child_parent->left == child
&& sibling->color == BLACK
&& sibling->left->color == RED
&& sibling->right->color == BLACK)
{
sibling->color = RED;
sibling->left->color = BLACK;
rbtree_rotate_right(rbtree, sibling);
/* new sibling after rotation */
if(child_parent->right == child) sibling = child_parent->left;
else sibling = child_parent->right;
}
/* now we have a black sibling with a red child. rotate and exchange colors. */
sibling->color = child_parent->color;
child_parent->color = BLACK;
if(child_parent->right == child)
{
assert(sibling->left->color == RED);
sibling->left->color = BLACK;
rbtree_rotate_right(rbtree, child_parent);
}
else
{
assert(sibling->right->color == RED);
sibling->right->color = BLACK;
rbtree_rotate_left(rbtree, child_parent);
}
}
int
rbtree_find_less_equal(rbtree_type *rbtree, const void *key, rbnode_type **result)
{
int r;
rbnode_type *node;
assert(result);
/* We start at root... */
node = rbtree->root;
*result = NULL;
/* While there are children... */
while (node != RBTREE_NULL) {
r = rbtree->cmp(key, node->key);
if (r == 0) {
/* Exact match */
*result = node;
return 1;
}
if (r < 0) {
node = node->left;
} else {
/* Temporary match */
*result = node;
node = node->right;
}
}
return 0;
}
/*
* Finds the first element in the red black tree
*
*/
rbnode_type *
rbtree_first (rbtree_type *rbtree)
{
rbnode_type *node;
for (node = rbtree->root; node->left != RBTREE_NULL; node = node->left);
return node;
}
rbnode_type *
rbtree_last (rbtree_type *rbtree)
{
rbnode_type *node;
for (node = rbtree->root; node->right != RBTREE_NULL; node = node->right);
return node;
}
/*
* Returns the next node...
*
*/
rbnode_type *
rbtree_next (rbnode_type *node)
{
rbnode_type *parent;
if (node->right != RBTREE_NULL) {
/* One right, then keep on going left... */
for (node = node->right; node->left != RBTREE_NULL; node = node->left);
} else {
parent = node->parent;
while (parent != RBTREE_NULL && node == parent->right) {
node = parent;
parent = parent->parent;
}
node = parent;
}
return node;
}
rbnode_type *
rbtree_previous(rbnode_type *node)
{
rbnode_type *parent;
if (node->left != RBTREE_NULL) {
/* One left, then keep on going right... */
for (node = node->left; node->right != RBTREE_NULL; node = node->right);
} else {
parent = node->parent;
while (parent != RBTREE_NULL && node == parent->left) {
node = parent;
parent = parent->parent;
}
node = parent;
}
return node;
}