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1 | /* |
1 | /* |
2 | * Copyright (c) 2007 Vojtech Mencl |
2 | * Copyright (c) 2007 Vojtech Mencl |
3 | * All rights reserved. |
3 | * All rights reserved. |
4 | * |
4 | * |
5 | * Redistribution and use in source and binary forms, with or without |
5 | * Redistribution and use in source and binary forms, with or without |
6 | * modification, are permitted provided that the following conditions |
6 | * modification, are permitted provided that the following conditions |
7 | * are met: |
7 | * are met: |
8 | * |
8 | * |
9 | * - Redistributions of source code must retain the above copyright |
9 | * - Redistributions of source code must retain the above copyright |
10 | * notice, this list of conditions and the following disclaimer. |
10 | * notice, this list of conditions and the following disclaimer. |
11 | * - Redistributions in binary form must reproduce the above copyright |
11 | * - Redistributions in binary form must reproduce the above copyright |
12 | * notice, this list of conditions and the following disclaimer in the |
12 | * notice, this list of conditions and the following disclaimer in the |
13 | * documentation and/or other materials provided with the distribution. |
13 | * documentation and/or other materials provided with the distribution. |
14 | * - The name of the author may not be used to endorse or promote products |
14 | * - The name of the author may not be used to endorse or promote products |
15 | * derived from this software without specific prior written permission. |
15 | * derived from this software without specific prior written permission. |
16 | * |
16 | * |
17 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR |
17 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR |
18 | * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES |
18 | * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES |
19 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. |
19 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. |
20 | * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, |
20 | * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, |
21 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
21 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
22 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
22 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
23 | * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
23 | * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
24 | * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
24 | * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
25 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF |
25 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF |
26 | * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
26 | * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
27 | */ |
27 | */ |
28 | 28 | ||
29 | /** @addtogroup genericadt |
29 | /** @addtogroup genericadt |
30 | * @{ |
30 | * @{ |
31 | */ |
31 | */ |
32 | 32 | ||
33 | /** |
33 | /** |
34 | * @file |
34 | * @file |
35 | * @brief AVL tree implementation. |
35 | * @brief AVL tree implementation. |
36 | * |
36 | * |
37 | * This file implements AVL tree type and operations. |
37 | * This file implements AVL tree type and operations. |
38 | * |
38 | * |
39 | * Implemented AVL tree has the following properties: |
39 | * Implemented AVL tree has the following properties: |
40 | * @li It is a binary search tree with non-unique keys. |
40 | * @li It is a binary search tree with non-unique keys. |
41 | * @li Difference of heights of the left and the right subtree of every node is |
41 | * @li Difference of heights of the left and the right subtree of every node is |
42 | * one at maximum. |
42 | * one at maximum. |
43 | * |
43 | * |
44 | * Every node has a pointer to its parent which allows insertion of multiple |
44 | * Every node has a pointer to its parent which allows insertion of multiple |
45 | * identical keys into the tree. |
45 | * identical keys into the tree. |
46 | * |
46 | * |
47 | * Be careful when using this tree because of the base atribute which is added |
47 | * Be careful when using this tree because of the base atribute which is added |
48 | * to every inserted node key. There is no rule in which order nodes with the |
48 | * to every inserted node key. There is no rule in which order nodes with the |
49 | * same key are visited. |
49 | * same key are visited. |
50 | */ |
50 | */ |
51 | 51 | ||
52 | #include <adt/avl.h> |
52 | #include <adt/avl.h> |
53 | #include <debug.h> |
53 | #include <debug.h> |
54 | 54 | ||
55 | #define LEFT 0 |
55 | #define LEFT 0 |
56 | #define RIGHT 1 |
56 | #define RIGHT 1 |
57 | 57 | ||
58 | /** Search for the first occurence of the given key in an AVL tree. |
58 | /** Search for the first occurence of the given key in an AVL tree. |
59 | * |
59 | * |
60 | * @param t AVL tree. |
60 | * @param t AVL tree. |
61 | * @param key Key to be searched. |
61 | * @param key Key to be searched. |
62 | * |
62 | * |
63 | * @return Pointer to a node or NULL if there is no such key. |
63 | * @return Pointer to a node or NULL if there is no such key. |
64 | */ |
64 | */ |
65 | avltree_node_t *avltree_search(avltree_t *t, avltree_key_t key) |
65 | avltree_node_t *avltree_search(avltree_t *t, avltree_key_t key) |
66 | { |
66 | { |
67 | avltree_node_t *p; |
67 | avltree_node_t *p; |
68 | 68 | ||
69 | /* |
69 | /* |
70 | * Iteratively descend to the leaf that can contain the searched key. |
70 | * Iteratively descend to the leaf that can contain the searched key. |
71 | */ |
71 | */ |
72 | p = t->root; |
72 | p = t->root; |
73 | while (p != NULL) { |
73 | while (p != NULL) { |
74 | if (p->key > key) |
74 | if (p->key > key) |
75 | p = p->lft; |
75 | p = p->lft; |
76 | else if (p->key < key) |
76 | else if (p->key < key) |
77 | p = p->rgt; |
77 | p = p->rgt; |
78 | else |
78 | else |
79 | return p; |
79 | return p; |
80 | } |
80 | } |
81 | return NULL; |
81 | return NULL; |
82 | } |
82 | } |
83 | 83 | ||
84 | 84 | ||
85 | /** Find the node with the smallest key in an AVL tree. |
85 | /** Find the node with the smallest key in an AVL tree. |
86 | * |
86 | * |
87 | * @param t AVL tree. |
87 | * @param t AVL tree. |
88 | * |
88 | * |
89 | * @return Pointer to a node or NULL if there is no node in the tree. |
89 | * @return Pointer to a node or NULL if there is no node in the tree. |
90 | */ |
90 | */ |
91 | avltree_node_t *avltree_find_min(avltree_t *t) |
91 | avltree_node_t *avltree_find_min(avltree_t *t) |
92 | { |
92 | { |
93 | avltree_node_t *p = t->root; |
93 | avltree_node_t *p = t->root; |
94 | 94 | ||
95 | /* |
95 | /* |
96 | * Check whether the tree is empty. |
96 | * Check whether the tree is empty. |
97 | */ |
97 | */ |
98 | if (!p) |
98 | if (!p) |
99 | return NULL; |
99 | return NULL; |
100 | 100 | ||
101 | /* |
101 | /* |
102 | * Iteratively descend to the leftmost leaf in the tree. |
102 | * Iteratively descend to the leftmost leaf in the tree. |
103 | */ |
103 | */ |
104 | while (p->lft != NULL) |
104 | while (p->lft != NULL) |
105 | p = p->lft; |
105 | p = p->lft; |
106 | 106 | ||
107 | return p; |
107 | return p; |
108 | } |
108 | } |
109 | 109 | ||
- | 110 | #define REBALANCE_INSERT_XX(DIR1, DIR2) \ |
|
- | 111 | top->DIR1 = par->DIR2; \ |
|
- | 112 | if (top->DIR1 != NULL) \ |
|
- | 113 | top->DIR1->par = top; \ |
|
- | 114 | par->par = top->par; \ |
|
- | 115 | top->par = par; \ |
|
- | 116 | par->DIR2 = top; \ |
|
- | 117 | par->balance = 0; \ |
|
- | 118 | top->balance = 0; \ |
|
- | 119 | *dpc = par; |
|
- | 120 | ||
- | 121 | #define REBALANCE_INSERT_LL() REBALANCE_INSERT_XX(lft, rgt) |
|
- | 122 | #define REBALANCE_INSERT_RR() REBALANCE_INSERT_XX(rgt, lft) |
|
- | 123 | ||
- | 124 | #define REBALANCE_INSERT_XY(DIR1, DIR2, SGN) \ |
|
- | 125 | gpa = par->DIR2; \ |
|
- | 126 | par->DIR2 = gpa->DIR1; \ |
|
- | 127 | if (gpa->DIR1 != NULL) \ |
|
- | 128 | gpa->DIR1->par = par; \ |
|
- | 129 | gpa->DIR1 = par; \ |
|
- | 130 | par->par = gpa; \ |
|
- | 131 | top->DIR1 = gpa->DIR2; \ |
|
- | 132 | if (gpa->DIR2 != NULL) \ |
|
- | 133 | gpa->DIR2->par = top; \ |
|
- | 134 | gpa->DIR2 = top; \ |
|
- | 135 | gpa->par = top->par; \ |
|
- | 136 | top->par = gpa; \ |
|
- | 137 | \ |
|
- | 138 | if (gpa->balance == -1 * SGN) { \ |
|
- | 139 | par->balance = 0; \ |
|
- | 140 | top->balance = 1 * SGN; \ |
|
- | 141 | } else if (gpa->balance == 0) { \ |
|
- | 142 | par->balance = 0; \ |
|
- | 143 | top->balance = 0; \ |
|
- | 144 | } else { \ |
|
- | 145 | par->balance = -1 * SGN; \ |
|
- | 146 | top->balance = 0; \ |
|
- | 147 | } \ |
|
- | 148 | gpa->balance = 0; \ |
|
- | 149 | *dpc = gpa; |
|
- | 150 | ||
- | 151 | #define REBALANCE_INSERT_LR() REBALANCE_INSERT_XY(lft, rgt, 1) |
|
- | 152 | #define REBALANCE_INSERT_RL() REBALANCE_INSERT_XY(rgt, lft, -1) |
|
- | 153 | ||
110 | /** Insert new node into AVL tree. |
154 | /** Insert new node into AVL tree. |
111 | * |
155 | * |
112 | * @param t AVL tree. |
156 | * @param t AVL tree. |
113 | * @param newnode New node to be inserted. |
157 | * @param newnode New node to be inserted. |
114 | */ |
158 | */ |
115 | void avltree_insert(avltree_t *t, avltree_node_t *newnode) |
159 | void avltree_insert(avltree_t *t, avltree_node_t *newnode) |
116 | { |
160 | { |
117 | avltree_node_t *par; |
161 | avltree_node_t *par; |
118 | avltree_node_t *gpa; |
162 | avltree_node_t *gpa; |
119 | avltree_node_t *top; |
163 | avltree_node_t *top; |
120 | avltree_node_t **dpc; |
164 | avltree_node_t **dpc; |
121 | avltree_key_t key; |
165 | avltree_key_t key; |
122 | 166 | ||
123 | ASSERT(t); |
167 | ASSERT(t); |
124 | ASSERT(newnode); |
168 | ASSERT(newnode); |
125 | 169 | ||
126 | /* |
170 | /* |
127 | * Creating absolute key. |
171 | * Creating absolute key. |
128 | */ |
172 | */ |
129 | key = newnode->key + t->base; |
173 | key = newnode->key + t->base; |
130 | 174 | ||
131 | /* |
175 | /* |
132 | * Iteratively descend to the leaf that can contain the new node. |
176 | * Iteratively descend to the leaf that can contain the new node. |
133 | * Last node with non-zero balance in the way to leaf is stored as top - |
177 | * Last node with non-zero balance in the way to leaf is stored as top - |
134 | * it is a place of possible inbalance. |
178 | * it is a place of possible inbalance. |
135 | */ |
179 | */ |
136 | dpc = &t->root; |
180 | dpc = &t->root; |
137 | gpa = NULL; |
181 | gpa = NULL; |
138 | top = t->root; |
182 | top = t->root; |
139 | while ((par = (*dpc)) != NULL) { |
183 | while ((par = (*dpc)) != NULL) { |
140 | if (par->balance != 0) { |
184 | if (par->balance != 0) { |
141 | top = par; |
185 | top = par; |
142 | } |
186 | } |
143 | gpa = par; |
187 | gpa = par; |
144 | dpc = par->key > key ? &par->lft: &par->rgt; |
188 | dpc = par->key > key ? &par->lft: &par->rgt; |
145 | } |
189 | } |
146 | 190 | ||
147 | /* |
191 | /* |
148 | * Initialize new node. |
192 | * Initialize the new node. |
149 | */ |
193 | */ |
150 | newnode->key = key; |
194 | newnode->key = key; |
151 | newnode->lft = NULL; |
195 | newnode->lft = NULL; |
152 | newnode->rgt = NULL; |
196 | newnode->rgt = NULL; |
153 | newnode->par = gpa; |
197 | newnode->par = gpa; |
154 | newnode->balance = 0; |
198 | newnode->balance = 0; |
155 | 199 | ||
156 | /* |
200 | /* |
157 | * Insert first node into the empty tree. |
201 | * Insert first node into the empty tree. |
158 | */ |
202 | */ |
159 | if (t->root == NULL) { |
203 | if (t->root == NULL) { |
160 | *dpc = newnode; |
204 | *dpc = newnode; |
161 | return; |
205 | return; |
162 | } |
206 | } |
163 | 207 | ||
164 | /* |
208 | /* |
165 | * Insert new node into previously found leaf place. |
209 | * Insert the new node into the previously found leaf position. |
166 | */ |
210 | */ |
167 | *dpc = newnode; |
211 | *dpc = newnode; |
168 | 212 | ||
169 | /* |
213 | /* |
170 | * If the tree contains one node - end. |
214 | * If the tree contains one node - end. |
171 | */ |
215 | */ |
172 | if (top == NULL) |
216 | if (top == NULL) |
173 | return; |
217 | return; |
174 | 218 | ||
175 | /* |
219 | /* |
176 | * Store pointer of top's father which points to the node with |
220 | * Store pointer of top's father which points to the node with |
177 | * potentially broken balance (top). |
221 | * potentially broken balance (top). |
178 | */ |
222 | */ |
179 | if (top->par == NULL) { |
223 | if (top->par == NULL) { |
180 | dpc = &t->root; |
224 | dpc = &t->root; |
181 | } else { |
225 | } else { |
182 | if (top->par->lft == top) |
226 | if (top->par->lft == top) |
183 | dpc = &top->par->lft; |
227 | dpc = &top->par->lft; |
184 | else |
228 | else |
185 | dpc = &top->par->rgt; |
229 | dpc = &top->par->rgt; |
186 | } |
230 | } |
187 | 231 | ||
188 | /* |
232 | /* |
189 | * Repair all balances on the way from top node to the newly inserted |
233 | * Repair all balances on the way from top node to the newly inserted |
190 | * node. |
234 | * node. |
191 | */ |
235 | */ |
192 | par = top; |
236 | par = top; |
193 | while (par != newnode) { |
237 | while (par != newnode) { |
194 | if (par->key > key) { |
238 | if (par->key > key) { |
195 | par->balance--; |
239 | par->balance--; |
196 | par = par->lft; |
240 | par = par->lft; |
197 | } else { |
241 | } else { |
198 | par->balance++; |
242 | par->balance++; |
199 | par = par->rgt; |
243 | par = par->rgt; |
200 | } |
244 | } |
201 | } |
245 | } |
202 | 246 | ||
203 | /* |
247 | /* |
204 | * To balance the tree, we must check and balance top node. |
248 | * To balance the tree, we must check and balance top node. |
205 | */ |
249 | */ |
206 | if (top->balance == -2) { |
250 | if (top->balance == -2) { |
207 | par = top->lft; |
251 | par = top->lft; |
208 | if (par->balance == -1) { |
252 | if (par->balance == -1) { |
209 | /* |
253 | /* |
210 | * LL rotation. |
254 | * LL rotation. |
211 | */ |
255 | */ |
212 | top->lft = par->rgt; |
- | |
213 | if (top->lft != NULL) |
256 | REBALANCE_INSERT_LL(); |
214 | top->lft->par = top; |
- | |
215 | par->par = top->par; |
- | |
216 | top->par = par; |
- | |
217 | par->rgt = top; |
- | |
218 | par->balance = 0; |
- | |
219 | top->balance = 0; |
- | |
220 | *dpc = par; |
- | |
221 | } else { |
257 | } else { |
222 | /* |
258 | /* |
223 | * LR rotation. |
259 | * LR rotation. |
224 | */ |
260 | */ |
225 | ASSERT(par->balance == 1); |
261 | ASSERT(par->balance == 1); |
226 | 262 | ||
227 | gpa = par->rgt; |
- | |
228 | par->rgt = gpa->lft; |
- | |
229 | if (gpa->lft != NULL) |
- | |
230 | gpa->lft->par = par; |
263 | REBALANCE_INSERT_LR(); |
231 | gpa->lft = par; |
- | |
232 | par->par = gpa; |
- | |
233 | top->lft = gpa->rgt; |
- | |
234 | if (gpa->rgt != NULL) |
- | |
235 | gpa->rgt->par = top; |
- | |
236 | gpa->rgt = top; |
- | |
237 | gpa->par = top->par; |
- | |
238 | top->par = gpa; |
- | |
239 | - | ||
240 | if (gpa->balance == -1) { |
- | |
241 | par->balance = 0; |
- | |
242 | top->balance = 1; |
- | |
243 | } else if (gpa->balance == 0) { |
- | |
244 | par->balance = 0; |
- | |
245 | top->balance = 0; |
- | |
246 | } else { |
- | |
247 | par->balance = -1; |
- | |
248 | top->balance = 0; |
- | |
249 | } |
- | |
250 | gpa->balance = 0; |
- | |
251 | *dpc = gpa; |
- | |
252 | } |
264 | } |
253 | } else if (top->balance == 2) { |
265 | } else if (top->balance == 2) { |
254 | par = top->rgt; |
266 | par = top->rgt; |
255 | if (par->balance == 1) { |
267 | if (par->balance == 1) { |
256 | /* |
268 | /* |
257 | * RR rotation. |
269 | * RR rotation. |
258 | */ |
270 | */ |
259 | top->rgt = par->lft; |
- | |
260 | if (top->rgt != NULL) |
- | |
261 | top->rgt->par = top; |
271 | REBALANCE_INSERT_RR(); |
262 | par->par = top->par; |
- | |
263 | top->par = par; |
- | |
264 | par->lft = top; |
- | |
265 | par->balance = 0; |
- | |
266 | top->balance = 0; |
- | |
267 | *dpc = par; |
- | |
268 | } else { |
272 | } else { |
269 | /* |
273 | /* |
270 | * RL rotation. |
274 | * RL rotation. |
271 | */ |
275 | */ |
272 | ASSERT(par->balance == -1); |
276 | ASSERT(par->balance == -1); |
273 | 277 | ||
274 | gpa = par->lft; |
- | |
275 | par->lft = gpa->rgt; |
- | |
276 | if (gpa->rgt != NULL) |
- | |
277 | gpa->rgt->par = par; |
- | |
278 | gpa->rgt = par; |
- | |
279 | par->par = gpa; |
- | |
280 | top->rgt = gpa->lft; |
- | |
281 | if (gpa->lft != NULL) |
278 | REBALANCE_INSERT_RL(); |
282 | gpa->lft->par = top; |
- | |
283 | gpa->lft = top; |
- | |
284 | gpa->par = top->par; |
- | |
285 | top->par = gpa; |
- | |
286 | - | ||
287 | if (gpa->balance == 1) { |
- | |
288 | par->balance = 0; |
- | |
289 | top->balance = -1; |
- | |
290 | } else if (gpa->balance == 0) { |
- | |
291 | par->balance = 0; |
- | |
292 | top->balance = 0; |
- | |
293 | } else { |
- | |
294 | par->balance = 1; |
- | |
295 | top->balance = 0; |
- | |
296 | } |
- | |
297 | gpa->balance = 0; |
- | |
298 | *dpc = gpa; |
- | |
299 | } |
279 | } |
300 | } else { |
280 | } else { |
301 | /* |
281 | /* |
302 | * Balance is not broken, insertion is finised. |
282 | * Balance is not broken, insertion is finised. |
303 | */ |
283 | */ |
304 | return; |
284 | return; |
305 | } |
285 | } |
306 | 286 | ||
307 | } |
287 | } |
308 | 288 | ||
309 | /** Repair the tree after reparenting node u. |
289 | /** Repair the tree after reparenting node u. |
310 | * |
290 | * |
311 | * If node u has no parent, mark it as the root of the whole tree. Otherwise |
291 | * If node u has no parent, mark it as the root of the whole tree. Otherwise |
312 | * node v represents stale address of one of the children of node u's parent. |
292 | * node v represents stale address of one of the children of node u's parent. |
313 | * Replace v with w as node u parent's child (for most uses, u and w will be the |
293 | * Replace v with w as node u parent's child (for most uses, u and w will be the |
314 | * same). |
294 | * same). |
315 | * |
295 | * |
316 | * @param t AVL tree. |
296 | * @param t AVL tree. |
317 | * @param u Node whose new parent has a stale child pointer. |
297 | * @param u Node whose new parent has a stale child pointer. |
318 | * @param v Stale child of node u's new parent. |
298 | * @param v Stale child of node u's new parent. |
319 | * @param w New child of node u's new parent. |
299 | * @param w New child of node u's new parent. |
320 | * @param dir If not NULL, address of the variable where to store information |
300 | * @param dir If not NULL, address of the variable where to store information |
321 | * about whether w replaced v in the left or the right subtree of |
301 | * about whether w replaced v in the left or the right subtree of |
322 | * u's new parent. |
302 | * u's new parent. |
323 | * @param ro Read only operation; do not modify any tree pointers. This is |
303 | * @param ro Read only operation; do not modify any tree pointers. This is |
324 | * useful for tracking direction via the dir pointer. |
304 | * useful for tracking direction via the dir pointer. |
325 | * |
305 | * |
326 | * @return Zero if w became the new root of the tree, otherwise return |
306 | * @return Zero if w became the new root of the tree, otherwise return |
327 | * non-zero. |
307 | * non-zero. |
328 | */ |
308 | */ |
329 | static int |
309 | static int |
330 | repair(avltree_t *t, avltree_node_t *u, avltree_node_t *v, avltree_node_t *w, |
310 | repair(avltree_t *t, avltree_node_t *u, avltree_node_t *v, avltree_node_t *w, |
331 | int *dir, int ro) |
311 | int *dir, int ro) |
332 | { |
312 | { |
333 | if (u->par == NULL) { |
313 | if (u->par == NULL) { |
334 | if (!ro) |
314 | if (!ro) |
335 | t->root = w; |
315 | t->root = w; |
336 | return 0; |
316 | return 0; |
337 | } else { |
317 | } else { |
338 | if (u->par->lft == v) { |
318 | if (u->par->lft == v) { |
339 | if (!ro) |
319 | if (!ro) |
340 | u->par->lft = w; |
320 | u->par->lft = w; |
341 | if (dir) |
321 | if (dir) |
342 | *dir = LEFT; |
322 | *dir = LEFT; |
343 | } else { |
323 | } else { |
344 | ASSERT(u->par->rgt == v); |
324 | ASSERT(u->par->rgt == v); |
345 | if (!ro) |
325 | if (!ro) |
346 | u->par->rgt = w; |
326 | u->par->rgt = w; |
347 | if (dir) |
327 | if (dir) |
348 | *dir = RIGHT; |
328 | *dir = RIGHT; |
349 | } |
329 | } |
350 | } |
330 | } |
351 | return 1; |
331 | return 1; |
352 | } |
332 | } |
353 | 333 | ||
354 | #define REBALANCE(DIR1, DIR2, SIGN) \ |
334 | #define REBALANCE_DELETE(DIR1, DIR2, SIGN) \ |
355 | if (cur->balance == -1 * SIGN) { \ |
335 | if (cur->balance == -1 * SIGN) { \ |
356 | par->balance = 0; \ |
336 | par->balance = 0; \ |
357 | gpa->balance = 1 * SIGN; \ |
337 | gpa->balance = 1 * SIGN; \ |
358 | if (gpa->DIR1) \ |
338 | if (gpa->DIR1) \ |
359 | gpa->DIR1->par = gpa; \ |
339 | gpa->DIR1->par = gpa; \ |
360 | par->DIR2->par = par; \ |
340 | par->DIR2->par = par; \ |
361 | } else if (cur->balance == 0) { \ |
341 | } else if (cur->balance == 0) { \ |
362 | par->balance = 0; \ |
342 | par->balance = 0; \ |
363 | gpa->balance = 0; \ |
343 | gpa->balance = 0; \ |
364 | if (gpa->DIR1) \ |
344 | if (gpa->DIR1) \ |
365 | gpa->DIR1->par = gpa; \ |
345 | gpa->DIR1->par = gpa; \ |
366 | if (par->DIR2) \ |
346 | if (par->DIR2) \ |
367 | par->DIR2->par = par; \ |
347 | par->DIR2->par = par; \ |
368 | } else { \ |
348 | } else { \ |
369 | par->balance = -1 * SIGN; \ |
349 | par->balance = -1 * SIGN; \ |
370 | gpa->balance = 0; \ |
350 | gpa->balance = 0; \ |
371 | if (par->DIR2) \ |
351 | if (par->DIR2) \ |
372 | par->DIR2->par = par; \ |
352 | par->DIR2->par = par; \ |
373 | gpa->DIR1->par = gpa; \ |
353 | gpa->DIR1->par = gpa; \ |
374 | } \ |
354 | } \ |
375 | cur->balance = 0; |
355 | cur->balance = 0; |
376 | 356 | ||
377 | #define REBALANCE_LR() REBALANCE(lft, rgt, 1) |
357 | #define REBALANCE_DELETE_LR() REBALANCE_DELETE(lft, rgt, 1) |
378 | #define REBALANCE_RL() REBALANCE(rgt, lft, -1) |
358 | #define REBALANCE_DELETE_RL() REBALANCE_DELETE(rgt, lft, -1) |
379 | 359 | ||
380 | /** Delete a node from the AVL tree. |
360 | /** Delete a node from the AVL tree. |
381 | * |
361 | * |
382 | * Because multiple identical keys are allowed, the parent pointers are |
362 | * Because multiple identical keys are allowed, the parent pointers are |
383 | * essential during deletion. |
363 | * essential during deletion. |
384 | * |
364 | * |
385 | * @param t AVL tree structure. |
365 | * @param t AVL tree structure. |
386 | * @param node Address of the node which will be deleted. |
366 | * @param node Address of the node which will be deleted. |
387 | */ |
367 | */ |
388 | void avltree_delete(avltree_t *t, avltree_node_t *node) |
368 | void avltree_delete(avltree_t *t, avltree_node_t *node) |
389 | { |
369 | { |
390 | avltree_node_t *cur; |
370 | avltree_node_t *cur; |
391 | avltree_node_t *par; |
371 | avltree_node_t *par; |
392 | avltree_node_t *gpa; |
372 | avltree_node_t *gpa; |
393 | int dir; |
373 | int dir; |
394 | 374 | ||
395 | ASSERT(t); |
375 | ASSERT(t); |
396 | ASSERT(node); |
376 | ASSERT(node); |
397 | 377 | ||
398 | if (node->lft == NULL) { |
378 | if (node->lft == NULL) { |
399 | if (node->rgt) { |
379 | if (node->rgt) { |
400 | /* |
380 | /* |
401 | * Replace the node with its only right son. |
381 | * Replace the node with its only right son. |
402 | * |
382 | * |
403 | * Balance of the right son will be repaired in the |
383 | * Balance of the right son will be repaired in the |
404 | * balancing cycle. |
384 | * balancing cycle. |
405 | */ |
385 | */ |
406 | cur = node->rgt; |
386 | cur = node->rgt; |
407 | cur->par = node->par; |
387 | cur->par = node->par; |
408 | gpa = cur; |
388 | gpa = cur; |
409 | dir = RIGHT; |
389 | dir = RIGHT; |
410 | cur->balance = node->balance; |
390 | cur->balance = node->balance; |
411 | } else { |
391 | } else { |
412 | if (node->par == NULL) { |
392 | if (node->par == NULL) { |
413 | /* |
393 | /* |
414 | * The tree has only one node - it will become |
394 | * The tree has only one node - it will become |
415 | * an empty tree and the balancing can end. |
395 | * an empty tree and the balancing can end. |
416 | */ |
396 | */ |
417 | t->root = NULL; |
397 | t->root = NULL; |
418 | return; |
398 | return; |
419 | } |
399 | } |
420 | /* |
400 | /* |
421 | * The node has no child, it will be deleted with no |
401 | * The node has no child, it will be deleted with no |
422 | * substitution. |
402 | * substitution. |
423 | */ |
403 | */ |
424 | gpa = node->par; |
404 | gpa = node->par; |
425 | cur = NULL; |
405 | cur = NULL; |
426 | dir = (gpa->lft == node) ? LEFT: RIGHT; |
406 | dir = (gpa->lft == node) ? LEFT: RIGHT; |
427 | } |
407 | } |
428 | } else { |
408 | } else { |
429 | /* |
409 | /* |
430 | * The node has the left son. Find a node with the smallest key |
410 | * The node has the left son. Find a node with the smallest key |
431 | * in the left subtree and replace the deleted node with that |
411 | * in the left subtree and replace the deleted node with that |
432 | * node. |
412 | * node. |
433 | */ |
413 | */ |
434 | for (cur = node->lft; cur->rgt != NULL; cur = cur->rgt) |
414 | for (cur = node->lft; cur->rgt != NULL; cur = cur->rgt) |
435 | ; |
415 | ; |
436 | 416 | ||
437 | if (cur != node->lft) { |
417 | if (cur != node->lft) { |
438 | /* |
418 | /* |
439 | * The rightmost node of the deleted node's left subtree |
419 | * The rightmost node of the deleted node's left subtree |
440 | * was found. Replace the deleted node with this node. |
420 | * was found. Replace the deleted node with this node. |
441 | * Cutting off of the found node has two cases that |
421 | * Cutting off of the found node has two cases that |
442 | * depend on its left son. |
422 | * depend on its left son. |
443 | */ |
423 | */ |
444 | if (cur->lft) { |
424 | if (cur->lft) { |
445 | /* |
425 | /* |
446 | * The found node has a left son. |
426 | * The found node has a left son. |
447 | */ |
427 | */ |
448 | gpa = cur->lft; |
428 | gpa = cur->lft; |
449 | gpa->par = cur->par; |
429 | gpa->par = cur->par; |
450 | dir = LEFT; |
430 | dir = LEFT; |
451 | gpa->balance = cur->balance; |
431 | gpa->balance = cur->balance; |
452 | } else { |
432 | } else { |
453 | dir = RIGHT; |
433 | dir = RIGHT; |
454 | gpa = cur->par; |
434 | gpa = cur->par; |
455 | } |
435 | } |
456 | cur->par->rgt = cur->lft; |
436 | cur->par->rgt = cur->lft; |
457 | cur->lft = node->lft; |
437 | cur->lft = node->lft; |
458 | cur->lft->par = cur; |
438 | cur->lft->par = cur; |
459 | } else { |
439 | } else { |
460 | /* |
440 | /* |
461 | * The left son of the node hasn't got a right son. The |
441 | * The left son of the node hasn't got a right son. The |
462 | * left son will take the deleted node's place. |
442 | * left son will take the deleted node's place. |
463 | */ |
443 | */ |
464 | dir = LEFT; |
444 | dir = LEFT; |
465 | gpa = cur; |
445 | gpa = cur; |
466 | } |
446 | } |
467 | if (node->rgt) |
447 | if (node->rgt) |
468 | node->rgt->par = cur; |
448 | node->rgt->par = cur; |
469 | cur->rgt = node->rgt; |
449 | cur->rgt = node->rgt; |
470 | cur->balance = node->balance; |
450 | cur->balance = node->balance; |
471 | cur->par = node->par; |
451 | cur->par = node->par; |
472 | } |
452 | } |
473 | 453 | ||
474 | /* |
454 | /* |
475 | * Repair the parent node's pointer which pointed previously to the |
455 | * Repair the parent node's pointer which pointed previously to the |
476 | * deleted node. |
456 | * deleted node. |
477 | */ |
457 | */ |
478 | (void) repair(t, node, node, cur, NULL, false); |
458 | (void) repair(t, node, node, cur, NULL, false); |
479 | 459 | ||
480 | /* |
460 | /* |
481 | * Repair cycle which repairs balances of nodes on the way from from the |
461 | * Repair cycle which repairs balances of nodes on the way from from the |
482 | * cut-off node up to the root. |
462 | * cut-off node up to the root. |
483 | */ |
463 | */ |
484 | for (;;) { |
464 | for (;;) { |
485 | if (dir == LEFT) { |
465 | if (dir == LEFT) { |
486 | /* |
466 | /* |
487 | * Deletion was made in the left subtree. |
467 | * Deletion was made in the left subtree. |
488 | */ |
468 | */ |
489 | gpa->balance++; |
469 | gpa->balance++; |
490 | if (gpa->balance == 1) { |
470 | if (gpa->balance == 1) { |
491 | /* |
471 | /* |
492 | * Stop balancing, the tree is balanced. |
472 | * Stop balancing, the tree is balanced. |
493 | */ |
473 | */ |
494 | break; |
474 | break; |
495 | } else if (gpa->balance == 2) { |
475 | } else if (gpa->balance == 2) { |
496 | /* |
476 | /* |
497 | * Bad balance, heights of left and right |
477 | * Bad balance, heights of left and right |
498 | * subtrees differ more than by one. |
478 | * subtrees differ more than by one. |
499 | */ |
479 | */ |
500 | par = gpa->rgt; |
480 | par = gpa->rgt; |
501 | 481 | ||
502 | if (par->balance == -1) { |
482 | if (par->balance == -1) { |
503 | /* |
483 | /* |
504 | * RL rotation. |
484 | * RL rotation. |
505 | */ |
485 | */ |
506 | 486 | ||
507 | cur = par->lft; |
487 | cur = par->lft; |
508 | par->lft = cur->rgt; |
488 | par->lft = cur->rgt; |
509 | cur->rgt = par; |
489 | cur->rgt = par; |
510 | gpa->rgt = cur->lft; |
490 | gpa->rgt = cur->lft; |
511 | cur->lft = gpa; |
491 | cur->lft = gpa; |
512 | 492 | ||
513 | /* |
493 | /* |
514 | * Repair balances and paternity of |
494 | * Repair balances and paternity of |
515 | * children, depending on the balance |
495 | * children, depending on the balance |
516 | * factor of the grand child (cur). |
496 | * factor of the grand child (cur). |
517 | */ |
497 | */ |
518 | REBALANCE_RL(); |
498 | REBALANCE_DELETE_RL(); |
519 | 499 | ||
520 | /* |
500 | /* |
521 | * Repair paternity. |
501 | * Repair paternity. |
522 | */ |
502 | */ |
523 | cur->par = gpa->par; |
503 | cur->par = gpa->par; |
524 | gpa->par = cur; |
504 | gpa->par = cur; |
525 | par->par = cur; |
505 | par->par = cur; |
526 | 506 | ||
527 | if (!repair(t, cur, gpa, cur, &dir, |
507 | if (!repair(t, cur, gpa, cur, &dir, |
528 | false)) |
508 | false)) |
529 | break; |
509 | break; |
530 | gpa = cur->par; |
510 | gpa = cur->par; |
531 | } else { |
511 | } else { |
532 | /* |
512 | /* |
533 | * RR rotation. |
513 | * RR rotation. |
534 | */ |
514 | */ |
535 | 515 | ||
536 | gpa->rgt = par->lft; |
516 | gpa->rgt = par->lft; |
537 | if (par->lft) |
517 | if (par->lft) |
538 | par->lft->par = gpa; |
518 | par->lft->par = gpa; |
539 | par->lft = gpa; |
519 | par->lft = gpa; |
540 | 520 | ||
541 | /* |
521 | /* |
542 | * Repair paternity. |
522 | * Repair paternity. |
543 | */ |
523 | */ |
544 | par->par = gpa->par; |
524 | par->par = gpa->par; |
545 | gpa->par = par; |
525 | gpa->par = par; |
546 | 526 | ||
547 | if (par->balance == 0) { |
527 | if (par->balance == 0) { |
548 | /* |
528 | /* |
549 | * The right child of the |
529 | * The right child of the |
550 | * balanced node is balanced, |
530 | * balanced node is balanced, |
551 | * after RR rotation is done, |
531 | * after RR rotation is done, |
552 | * the whole tree will be |
532 | * the whole tree will be |
553 | * balanced. |
533 | * balanced. |
554 | */ |
534 | */ |
555 | par->balance = -1; |
535 | par->balance = -1; |
556 | gpa->balance = 1; |
536 | gpa->balance = 1; |
557 | 537 | ||
558 | (void) repair(t, par, gpa, par, |
538 | (void) repair(t, par, gpa, par, |
559 | NULL, false); |
539 | NULL, false); |
560 | break; |
540 | break; |
561 | } else { |
541 | } else { |
562 | par->balance = 0; |
542 | par->balance = 0; |
563 | gpa->balance = 0; |
543 | gpa->balance = 0; |
564 | if (!repair(t, par, gpa, par, |
544 | if (!repair(t, par, gpa, par, |
565 | &dir, false)) |
545 | &dir, false)) |
566 | break; |
546 | break; |
567 | } |
547 | } |
568 | gpa = par->par; |
548 | gpa = par->par; |
569 | } |
549 | } |
570 | } else { |
550 | } else { |
571 | /* |
551 | /* |
572 | * Repair the pointer which pointed to the |
552 | * Repair the pointer which pointed to the |
573 | * balanced node. If it was root then balancing |
553 | * balanced node. If it was root then balancing |
574 | * is finished else continue with the next |
554 | * is finished else continue with the next |
575 | * iteration (parent node). |
555 | * iteration (parent node). |
576 | */ |
556 | */ |
577 | if (!repair(t, gpa, gpa, NULL, &dir, true)) |
557 | if (!repair(t, gpa, gpa, NULL, &dir, true)) |
578 | break; |
558 | break; |
579 | gpa = gpa->par; |
559 | gpa = gpa->par; |
580 | } |
560 | } |
581 | } else { |
561 | } else { |
582 | /* |
562 | /* |
583 | * Deletion was made in the right subtree. |
563 | * Deletion was made in the right subtree. |
584 | */ |
564 | */ |
585 | gpa->balance--; |
565 | gpa->balance--; |
586 | if (gpa->balance == -1) { |
566 | if (gpa->balance == -1) { |
587 | /* |
567 | /* |
588 | * Stop balancing, the tree is balanced. |
568 | * Stop balancing, the tree is balanced. |
589 | */ |
569 | */ |
590 | break; |
570 | break; |
591 | } else if (gpa->balance == -2) { |
571 | } else if (gpa->balance == -2) { |
592 | /* |
572 | /* |
593 | * Bad balance, heights of left and right |
573 | * Bad balance, heights of left and right |
594 | * subtrees differ more than by one. |
574 | * subtrees differ more than by one. |
595 | */ |
575 | */ |
596 | par = gpa->lft; |
576 | par = gpa->lft; |
597 | 577 | ||
598 | if (par->balance == 1) { |
578 | if (par->balance == 1) { |
599 | /* |
579 | /* |
600 | * LR rotation. |
580 | * LR rotation. |
601 | */ |
581 | */ |
602 | 582 | ||
603 | cur = par->rgt; |
583 | cur = par->rgt; |
604 | par->rgt = cur->lft; |
584 | par->rgt = cur->lft; |
605 | cur->lft = par; |
585 | cur->lft = par; |
606 | gpa->lft = cur->rgt; |
586 | gpa->lft = cur->rgt; |
607 | cur->rgt = gpa; |
587 | cur->rgt = gpa; |
608 | 588 | ||
609 | /* |
589 | /* |
610 | * Repair balances and paternity of |
590 | * Repair balances and paternity of |
611 | * children, depending on the balance |
591 | * children, depending on the balance |
612 | * factor of the grand child (cur). |
592 | * factor of the grand child (cur). |
613 | */ |
593 | */ |
614 | REBALANCE_LR(); |
594 | REBALANCE_DELETE_LR(); |
615 | 595 | ||
616 | /* |
596 | /* |
617 | * Repair paternity. |
597 | * Repair paternity. |
618 | */ |
598 | */ |
619 | cur->par = gpa->par; |
599 | cur->par = gpa->par; |
620 | gpa->par = cur; |
600 | gpa->par = cur; |
621 | par->par = cur; |
601 | par->par = cur; |
622 | 602 | ||
623 | if (!repair(t, cur, gpa, cur, &dir, |
603 | if (!repair(t, cur, gpa, cur, &dir, |
624 | false)) |
604 | false)) |
625 | break; |
605 | break; |
626 | gpa = cur->par; |
606 | gpa = cur->par; |
627 | } else { |
607 | } else { |
628 | /* |
608 | /* |
629 | * LL rotation. |
609 | * LL rotation. |
630 | */ |
610 | */ |
631 | 611 | ||
632 | gpa->lft = par->rgt; |
612 | gpa->lft = par->rgt; |
633 | if (par->rgt) |
613 | if (par->rgt) |
634 | par->rgt->par = gpa; |
614 | par->rgt->par = gpa; |
635 | par->rgt = gpa; |
615 | par->rgt = gpa; |
636 | /* |
616 | /* |
637 | * Repair paternity. |
617 | * Repair paternity. |
638 | */ |
618 | */ |
639 | par->par = gpa->par; |
619 | par->par = gpa->par; |
640 | gpa->par = par; |
620 | gpa->par = par; |
641 | 621 | ||
642 | if (par->balance == 0) { |
622 | if (par->balance == 0) { |
643 | /* |
623 | /* |
644 | * The left child of the |
624 | * The left child of the |
645 | * balanced node is balanced, |
625 | * balanced node is balanced, |
646 | * after LL rotation is done, |
626 | * after LL rotation is done, |
647 | * the whole tree will be |
627 | * the whole tree will be |
648 | * balanced. |
628 | * balanced. |
649 | */ |
629 | */ |
650 | par->balance = 1; |
630 | par->balance = 1; |
651 | gpa->balance = -1; |
631 | gpa->balance = -1; |
652 | 632 | ||
653 | (void) repair(t, par, gpa, par, |
633 | (void) repair(t, par, gpa, par, |
654 | NULL, false); |
634 | NULL, false); |
655 | break; |
635 | break; |
656 | } else { |
636 | } else { |
657 | par->balance = 0; |
637 | par->balance = 0; |
658 | gpa->balance = 0; |
638 | gpa->balance = 0; |
659 | 639 | ||
660 | if (!repair(t, par, gpa, par, |
640 | if (!repair(t, par, gpa, par, |
661 | &dir, false)) |
641 | &dir, false)) |
662 | break; |
642 | break; |
663 | } |
643 | } |
664 | gpa = par->par; |
644 | gpa = par->par; |
665 | } |
645 | } |
666 | } else { |
646 | } else { |
667 | /* |
647 | /* |
668 | * Repair the pointer which pointed to the |
648 | * Repair the pointer which pointed to the |
669 | * balanced node. If it was root then balancing |
649 | * balanced node. If it was root then balancing |
670 | * is finished. Otherwise continue with the next |
650 | * is finished. Otherwise continue with the next |
671 | * iteration (parent node). |
651 | * iteration (parent node). |
672 | */ |
652 | */ |
673 | if (!repair(t, gpa, gpa, NULL, &dir, true)) |
653 | if (!repair(t, gpa, gpa, NULL, &dir, true)) |
674 | break; |
654 | break; |
675 | gpa = gpa->par; |
655 | gpa = gpa->par; |
676 | } |
656 | } |
677 | } |
657 | } |
678 | } |
658 | } |
679 | } |
659 | } |
680 | 660 | ||
681 | 661 | ||
682 | /** Delete a node with the smallest key from the AVL tree. |
662 | /** Delete a node with the smallest key from the AVL tree. |
683 | * |
663 | * |
684 | * @param t AVL tree structure. |
664 | * @param t AVL tree structure. |
685 | */ |
665 | */ |
686 | bool avltree_delete_min(avltree_t *t) |
666 | bool avltree_delete_min(avltree_t *t) |
687 | { |
667 | { |
688 | avltree_node_t *node; |
668 | avltree_node_t *node; |
689 | 669 | ||
690 | /* |
670 | /* |
691 | * Start searching for the smallest key in the tree starting in the root |
671 | * Start searching for the smallest key in the tree starting in the root |
692 | * node and continue in cycle to the leftmost node in the tree (which |
672 | * node and continue in cycle to the leftmost node in the tree (which |
693 | * must have the smallest key). |
673 | * must have the smallest key). |
694 | */ |
674 | */ |
695 | 675 | ||
696 | node = t->root; |
676 | node = t->root; |
697 | if (!node) |
677 | if (!node) |
698 | return false; |
678 | return false; |
699 | 679 | ||
700 | while (node->lft != NULL) |
680 | while (node->lft != NULL) |
701 | node = node->lft; |
681 | node = node->lft; |
702 | 682 | ||
703 | avltree_delete(t, node); |
683 | avltree_delete(t, node); |
704 | 684 | ||
705 | return true; |
685 | return true; |
706 | } |
686 | } |
707 | 687 | ||
708 | static void _avltree_walk(avltree_node_t *node, avltree_walker_t walker) |
688 | static void _avltree_walk(avltree_node_t *node, avltree_walker_t walker) |
709 | { |
689 | { |
710 | if (node->lft) |
690 | if (node->lft) |
711 | _avltree_walk(node->lft, walker); |
691 | _avltree_walk(node->lft, walker); |
712 | walker(node); |
692 | walker(node); |
713 | if (node->rgt) |
693 | if (node->rgt) |
714 | _avltree_walk(node->rgt, walker); |
694 | _avltree_walk(node->rgt, walker); |
715 | } |
695 | } |
716 | 696 | ||
717 | /** Walk the AVL tree and apply the walker function on each visited node. |
697 | /** Walk the AVL tree and apply the walker function on each visited node. |
718 | * |
698 | * |
719 | * @param t AVL tree to be walked. |
699 | * @param t AVL tree to be walked. |
720 | * @param walker Walker function that will be called on each visited |
700 | * @param walker Walker function that will be called on each visited |
721 | * node. |
701 | * node. |
722 | */ |
702 | */ |
723 | void avltree_walk(avltree_t *t, avltree_walker_t walker) |
703 | void avltree_walk(avltree_t *t, avltree_walker_t walker) |
724 | { |
704 | { |
725 | _avltree_walk(t->root, walker); |
705 | _avltree_walk(t->root, walker); |
726 | } |
706 | } |
727 | 707 | ||
728 | /** @} |
708 | /** @} |
729 | */ |
709 | */ |
730 | 710 | ||
731 | 711 |