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1 | /* |
1 | /* |
2 | * Copyright (C) 2006 Jakub Jermar |
2 | * Copyright (C) 2006 Jakub Jermar |
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 | /* |
29 | /* |
30 | * This B-tree has the following properties: |
30 | * This B-tree has the following properties: |
31 | * - it is a ballanced 2-3-4-5 tree (i.e. BTREE_M = 5) |
31 | * - it is a ballanced 2-3-4-5 tree (i.e. BTREE_M = 5) |
32 | * - values (i.e. pointers to values) are stored only in leaves |
32 | * - values (i.e. pointers to values) are stored only in leaves |
33 | * - leaves are linked in a list |
33 | * - leaves are linked in a list |
34 | * - technically, it is a B+-tree (because of the previous properties) |
34 | * - technically, it is a B+-tree (because of the previous properties) |
35 | * |
35 | * |
36 | * Be carefull when using these trees. They need to allocate |
36 | * Be carefull when using these trees. They need to allocate |
37 | * and deallocate memory for their index nodes and as such |
37 | * and deallocate memory for their index nodes and as such |
38 | * can sleep. |
38 | * can sleep. |
39 | */ |
39 | */ |
40 | 40 | ||
41 | #include <adt/btree.h> |
41 | #include <adt/btree.h> |
42 | #include <adt/list.h> |
42 | #include <adt/list.h> |
43 | #include <mm/slab.h> |
43 | #include <mm/slab.h> |
44 | #include <debug.h> |
44 | #include <debug.h> |
45 | #include <panic.h> |
45 | #include <panic.h> |
46 | #include <typedefs.h> |
46 | #include <typedefs.h> |
47 | #include <print.h> |
47 | #include <print.h> |
48 | 48 | ||
49 | static void _btree_insert(btree_t *t, __native key, void *value, btree_node_t *rsubtree, btree_node_t *node); |
49 | static void _btree_insert(btree_t *t, __native key, void *value, btree_node_t *rsubtree, btree_node_t *node); |
50 | static void _btree_remove(btree_t *t, __native key, btree_node_t *node); |
50 | static void _btree_remove(btree_t *t, __native key, btree_node_t *node); |
51 | static void node_initialize(btree_node_t *node); |
51 | static void node_initialize(btree_node_t *node); |
52 | static void node_insert_key_and_lsubtree(btree_node_t *node, __native key, void *value, btree_node_t *lsubtree); |
52 | static void node_insert_key_and_lsubtree(btree_node_t *node, __native key, void *value, btree_node_t *lsubtree); |
53 | static void node_insert_key_and_rsubtree(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree); |
53 | static void node_insert_key_and_rsubtree(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree); |
54 | static void node_remove_key_and_lsubtree(btree_node_t *node, __native key); |
54 | static void node_remove_key_and_lsubtree(btree_node_t *node, __native key); |
55 | static void node_remove_key_and_rsubtree(btree_node_t *node, __native key); |
55 | static void node_remove_key_and_rsubtree(btree_node_t *node, __native key); |
56 | static btree_node_t *node_split(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree, __native *median); |
56 | static btree_node_t *node_split(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree, __native *median); |
57 | static btree_node_t *node_combine(btree_node_t *node); |
57 | static btree_node_t *node_combine(btree_node_t *node); |
58 | static index_t find_key_by_subtree(btree_node_t *node, btree_node_t *subtree, bool right); |
58 | static index_t find_key_by_subtree(btree_node_t *node, btree_node_t *subtree, bool right); |
59 | static void rotate_from_right(btree_node_t *lnode, btree_node_t *rnode, index_t idx); |
59 | static void rotate_from_right(btree_node_t *lnode, btree_node_t *rnode, index_t idx); |
60 | static void rotate_from_left(btree_node_t *lnode, btree_node_t *rnode, index_t idx); |
60 | static void rotate_from_left(btree_node_t *lnode, btree_node_t *rnode, index_t idx); |
61 | static bool try_insert_by_rotation_to_left(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree); |
61 | static bool try_insert_by_rotation_to_left(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree); |
62 | static bool try_insert_by_rotation_to_right(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree); |
62 | static bool try_insert_by_rotation_to_right(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree); |
63 | static bool try_rotation_from_left(btree_node_t *rnode); |
63 | static bool try_rotation_from_left(btree_node_t *rnode); |
64 | static bool try_rotation_from_right(btree_node_t *lnode); |
64 | static bool try_rotation_from_right(btree_node_t *lnode); |
65 | 65 | ||
66 | #define ROOT_NODE(n) (!(n)->parent) |
66 | #define ROOT_NODE(n) (!(n)->parent) |
67 | #define INDEX_NODE(n) ((n)->subtree[0] != NULL) |
67 | #define INDEX_NODE(n) ((n)->subtree[0] != NULL) |
68 | #define LEAF_NODE(n) ((n)->subtree[0] == NULL) |
68 | #define LEAF_NODE(n) ((n)->subtree[0] == NULL) |
69 | 69 | ||
70 | #define FILL_FACTOR ((BTREE_M-1)/2) |
70 | #define FILL_FACTOR ((BTREE_M-1)/2) |
71 | 71 | ||
72 | #define MEDIAN_LOW_INDEX(n) (((n)->keys-1)/2) |
72 | #define MEDIAN_LOW_INDEX(n) (((n)->keys-1)/2) |
73 | #define MEDIAN_HIGH_INDEX(n) ((n)->keys/2) |
73 | #define MEDIAN_HIGH_INDEX(n) ((n)->keys/2) |
74 | #define MEDIAN_LOW(n) ((n)->key[MEDIAN_LOW_INDEX((n))]); |
74 | #define MEDIAN_LOW(n) ((n)->key[MEDIAN_LOW_INDEX((n))]); |
75 | #define MEDIAN_HIGH(n) ((n)->key[MEDIAN_HIGH_INDEX((n))]); |
75 | #define MEDIAN_HIGH(n) ((n)->key[MEDIAN_HIGH_INDEX((n))]); |
76 | 76 | ||
77 | /** Create empty B-tree. |
77 | /** Create empty B-tree. |
78 | * |
78 | * |
79 | * @param t B-tree. |
79 | * @param t B-tree. |
80 | */ |
80 | */ |
81 | void btree_create(btree_t *t) |
81 | void btree_create(btree_t *t) |
82 | { |
82 | { |
83 | list_initialize(&t->leaf_head); |
83 | list_initialize(&t->leaf_head); |
84 | t->root = (btree_node_t *) malloc(sizeof(btree_node_t), 0); |
84 | t->root = (btree_node_t *) malloc(sizeof(btree_node_t), 0); |
85 | node_initialize(t->root); |
85 | node_initialize(t->root); |
86 | list_append(&t->root->leaf_link, &t->leaf_head); |
86 | list_append(&t->root->leaf_link, &t->leaf_head); |
87 | } |
87 | } |
88 | 88 | ||
89 | /** Destroy empty B-tree. */ |
89 | /** Destroy empty B-tree. */ |
90 | void btree_destroy(btree_t *t) |
90 | void btree_destroy(btree_t *t) |
91 | { |
91 | { |
92 | ASSERT(!t->root->keys); |
92 | ASSERT(!t->root->keys); |
93 | free(t->root); |
93 | free(t->root); |
94 | } |
94 | } |
95 | 95 | ||
96 | /** Insert key-value pair into B-tree. |
96 | /** Insert key-value pair into B-tree. |
97 | * |
97 | * |
98 | * @param t B-tree. |
98 | * @param t B-tree. |
99 | * @param key Key to be inserted. |
99 | * @param key Key to be inserted. |
100 | * @param value Value to be inserted. |
100 | * @param value Value to be inserted. |
101 | * @param leaf_node Leaf node where the insertion should begin. |
101 | * @param leaf_node Leaf node where the insertion should begin. |
102 | */ |
102 | */ |
103 | void btree_insert(btree_t *t, __native key, void *value, btree_node_t *leaf_node) |
103 | void btree_insert(btree_t *t, __native key, void *value, btree_node_t *leaf_node) |
104 | { |
104 | { |
105 | btree_node_t *lnode; |
105 | btree_node_t *lnode; |
106 | 106 | ||
107 | ASSERT(value); |
107 | ASSERT(value); |
108 | 108 | ||
109 | lnode = leaf_node; |
109 | lnode = leaf_node; |
110 | if (!lnode) { |
110 | if (!lnode) { |
111 | if (btree_search(t, key, &lnode)) { |
111 | if (btree_search(t, key, &lnode)) { |
112 | panic("B-tree %P already contains key %d\n", t, key); |
112 | panic("B-tree %P already contains key %d\n", t, key); |
113 | } |
113 | } |
114 | } |
114 | } |
115 | 115 | ||
116 | _btree_insert(t, key, value, NULL, lnode); |
116 | _btree_insert(t, key, value, NULL, lnode); |
117 | } |
117 | } |
118 | 118 | ||
119 | /** Recursively insert into B-tree. |
119 | /** Recursively insert into B-tree. |
120 | * |
120 | * |
121 | * @param t B-tree. |
121 | * @param t B-tree. |
122 | * @param key Key to be inserted. |
122 | * @param key Key to be inserted. |
123 | * @param value Value to be inserted. |
123 | * @param value Value to be inserted. |
124 | * @param rsubtree Right subtree of the inserted key. |
124 | * @param rsubtree Right subtree of the inserted key. |
125 | * @param node Start inserting into this node. |
125 | * @param node Start inserting into this node. |
126 | */ |
126 | */ |
127 | void _btree_insert(btree_t *t, __native key, void *value, btree_node_t *rsubtree, btree_node_t *node) |
127 | void _btree_insert(btree_t *t, __native key, void *value, btree_node_t *rsubtree, btree_node_t *node) |
128 | { |
128 | { |
129 | if (node->keys < BTREE_MAX_KEYS) { |
129 | if (node->keys < BTREE_MAX_KEYS) { |
130 | /* |
130 | /* |
131 | * Node conatins enough space, the key can be stored immediately. |
131 | * Node conatins enough space, the key can be stored immediately. |
132 | */ |
132 | */ |
133 | node_insert_key_and_rsubtree(node, key, value, rsubtree); |
133 | node_insert_key_and_rsubtree(node, key, value, rsubtree); |
134 | } else if (try_insert_by_rotation_to_left(node, key, value, rsubtree)) { |
134 | } else if (try_insert_by_rotation_to_left(node, key, value, rsubtree)) { |
135 | /* |
135 | /* |
136 | * The key-value-rsubtree triplet has been inserted because |
136 | * The key-value-rsubtree triplet has been inserted because |
137 | * some keys could have been moved to the left sibling. |
137 | * some keys could have been moved to the left sibling. |
138 | */ |
138 | */ |
139 | } else if (try_insert_by_rotation_to_right(node, key, value, rsubtree)) { |
139 | } else if (try_insert_by_rotation_to_right(node, key, value, rsubtree)) { |
140 | /* |
140 | /* |
141 | * The key-value-rsubtree triplet has been inserted because |
141 | * The key-value-rsubtree triplet has been inserted because |
142 | * some keys could have been moved to the right sibling. |
142 | * some keys could have been moved to the right sibling. |
143 | */ |
143 | */ |
144 | } else { |
144 | } else { |
145 | btree_node_t *rnode; |
145 | btree_node_t *rnode; |
146 | __native median; |
146 | __native median; |
147 | 147 | ||
148 | /* |
148 | /* |
149 | * Node is full and both siblings (if both exist) are full too. |
149 | * Node is full and both siblings (if both exist) are full too. |
150 | * Split the node and insert the smallest key from the node containing |
150 | * Split the node and insert the smallest key from the node containing |
151 | * bigger keys (i.e. the new node) into its parent. |
151 | * bigger keys (i.e. the new node) into its parent. |
152 | */ |
152 | */ |
153 | 153 | ||
154 | rnode = node_split(node, key, value, rsubtree, &median); |
154 | rnode = node_split(node, key, value, rsubtree, &median); |
155 | 155 | ||
156 | if (LEAF_NODE(node)) { |
156 | if (LEAF_NODE(node)) { |
157 | list_prepend(&rnode->leaf_link, &node->leaf_link); |
157 | list_prepend(&rnode->leaf_link, &node->leaf_link); |
158 | } |
158 | } |
159 | 159 | ||
160 | if (ROOT_NODE(node)) { |
160 | if (ROOT_NODE(node)) { |
161 | /* |
161 | /* |
162 | * We split the root node. Create new root. |
162 | * We split the root node. Create new root. |
163 | */ |
163 | */ |
164 | t->root = (btree_node_t *) malloc(sizeof(btree_node_t), 0); |
164 | t->root = (btree_node_t *) malloc(sizeof(btree_node_t), 0); |
165 | node->parent = t->root; |
165 | node->parent = t->root; |
166 | rnode->parent = t->root; |
166 | rnode->parent = t->root; |
167 | node_initialize(t->root); |
167 | node_initialize(t->root); |
168 | 168 | ||
169 | /* |
169 | /* |
170 | * Left-hand side subtree will be the old root (i.e. node). |
170 | * Left-hand side subtree will be the old root (i.e. node). |
171 | * Right-hand side subtree will be rnode. |
171 | * Right-hand side subtree will be rnode. |
172 | */ |
172 | */ |
173 | t->root->subtree[0] = node; |
173 | t->root->subtree[0] = node; |
174 | 174 | ||
175 | t->root->depth = node->depth + 1; |
175 | t->root->depth = node->depth + 1; |
176 | } |
176 | } |
177 | _btree_insert(t, median, NULL, rnode, node->parent); |
177 | _btree_insert(t, median, NULL, rnode, node->parent); |
178 | } |
178 | } |
179 | 179 | ||
180 | } |
180 | } |
181 | 181 | ||
182 | /** Remove B-tree node. |
182 | /** Remove B-tree node. |
183 | * |
183 | * |
184 | * @param B-tree. |
184 | * @param B-tree. |
185 | * @param key Key to be removed from the B-tree along with its associated value. |
185 | * @param key Key to be removed from the B-tree along with its associated value. |
186 | * @param leaf_node If not NULL, pointer to the leaf node where the key is found. |
186 | * @param leaf_node If not NULL, pointer to the leaf node where the key is found. |
187 | */ |
187 | */ |
188 | void btree_remove(btree_t *t, __native key, btree_node_t *leaf_node) |
188 | void btree_remove(btree_t *t, __native key, btree_node_t *leaf_node) |
189 | { |
189 | { |
190 | btree_node_t *lnode; |
190 | btree_node_t *lnode; |
191 | 191 | ||
192 | lnode = leaf_node; |
192 | lnode = leaf_node; |
193 | if (!lnode) { |
193 | if (!lnode) { |
194 | if (!btree_search(t, key, &lnode)) { |
194 | if (!btree_search(t, key, &lnode)) { |
195 | panic("B-tree %P does not contain key %d\n", t, key); |
195 | panic("B-tree %P does not contain key %d\n", t, key); |
196 | } |
196 | } |
197 | } |
197 | } |
198 | 198 | ||
199 | _btree_remove(t, key, lnode); |
199 | _btree_remove(t, key, lnode); |
200 | } |
200 | } |
201 | 201 | ||
202 | /** Recursively remove B-tree node. |
202 | /** Recursively remove B-tree node. |
203 | * |
203 | * |
204 | * @param B-tree. |
204 | * @param B-tree. |
205 | * @param key Key to be removed from the B-tree along with its associated value. |
205 | * @param key Key to be removed from the B-tree along with its associated value. |
206 | * @param node Node where the key being removed resides. |
206 | * @param node Node where the key being removed resides. |
207 | */ |
207 | */ |
208 | void _btree_remove(btree_t *t, __native key, btree_node_t *node) |
208 | void _btree_remove(btree_t *t, __native key, btree_node_t *node) |
209 | { |
209 | { |
210 | if (ROOT_NODE(node)) { |
210 | if (ROOT_NODE(node)) { |
211 | if (node->keys == 1 && node->subtree[0]) { |
211 | if (node->keys == 1 && node->subtree[0]) { |
212 | /* |
212 | /* |
213 | * Free the current root and set new root. |
213 | * Free the current root and set new root. |
214 | */ |
214 | */ |
215 | t->root = node->subtree[0]; |
215 | t->root = node->subtree[0]; |
216 | t->root->parent = NULL; |
216 | t->root->parent = NULL; |
217 | free(node); |
217 | free(node); |
218 | } else { |
218 | } else { |
219 | /* |
219 | /* |
220 | * Remove the key from the root node. |
220 | * Remove the key from the root node. |
221 | * Note that the right subtree is removed because when |
221 | * Note that the right subtree is removed because when |
222 | * combining two nodes, the left-side sibling is preserved |
222 | * combining two nodes, the left-side sibling is preserved |
223 | * and the right-side sibling is freed. |
223 | * and the right-side sibling is freed. |
224 | */ |
224 | */ |
225 | node_remove_key_and_rsubtree(node, key); |
225 | node_remove_key_and_rsubtree(node, key); |
226 | } |
226 | } |
227 | return; |
227 | return; |
228 | } |
228 | } |
229 | 229 | ||
230 | if (node->keys <= FILL_FACTOR) { |
230 | if (node->keys <= FILL_FACTOR) { |
231 | /* |
231 | /* |
232 | * If the node is below the fill factor, |
232 | * If the node is below the fill factor, |
233 | * try to borrow keys from left or right sibling. |
233 | * try to borrow keys from left or right sibling. |
234 | */ |
234 | */ |
235 | if (!try_rotation_from_left(node)) |
235 | if (!try_rotation_from_left(node)) |
236 | try_rotation_from_right(node); |
236 | try_rotation_from_right(node); |
237 | } |
237 | } |
238 | 238 | ||
239 | if (node->keys > FILL_FACTOR) { |
239 | if (node->keys > FILL_FACTOR) { |
240 | int i; |
240 | int i; |
241 | 241 | ||
242 | /* |
242 | /* |
243 | * The key can be immediatelly removed. |
243 | * The key can be immediatelly removed. |
244 | * |
244 | * |
245 | * Note that the right subtree is removed because when |
245 | * Note that the right subtree is removed because when |
246 | * combining two nodes, the left-side sibling is preserved |
246 | * combining two nodes, the left-side sibling is preserved |
247 | * and the right-side sibling is freed. |
247 | * and the right-side sibling is freed. |
248 | */ |
248 | */ |
249 | node_remove_key_and_rsubtree(node, key); |
249 | node_remove_key_and_rsubtree(node, key); |
250 | for (i = 0; i < node->parent->keys; i++) { |
250 | for (i = 0; i < node->parent->keys; i++) { |
251 | if (node->parent->key[i] == key) |
251 | if (node->parent->key[i] == key) |
252 | node->parent->key[i] = node->key[0]; |
252 | node->parent->key[i] = node->key[0]; |
253 | } |
253 | } |
254 | 254 | ||
255 | } else { |
255 | } else { |
256 | index_t idx; |
256 | index_t idx; |
257 | btree_node_t *rnode, *parent; |
257 | btree_node_t *rnode, *parent; |
258 | 258 | ||
259 | /* |
259 | /* |
260 | * The node is below the fill factor as well as its left and right sibling. |
260 | * The node is below the fill factor as well as its left and right sibling. |
261 | * Resort to combining the node with one of its siblings. |
261 | * Resort to combining the node with one of its siblings. |
262 | * The node which is on the left is preserved and the node on the right is |
262 | * The node which is on the left is preserved and the node on the right is |
263 | * freed. |
263 | * freed. |
264 | */ |
264 | */ |
265 | parent = node->parent; |
265 | parent = node->parent; |
266 | node_remove_key_and_rsubtree(node, key); |
266 | node_remove_key_and_rsubtree(node, key); |
267 | rnode = node_combine(node); |
267 | rnode = node_combine(node); |
268 | if (LEAF_NODE(rnode)) |
268 | if (LEAF_NODE(rnode)) |
269 | list_remove(&rnode->leaf_link); |
269 | list_remove(&rnode->leaf_link); |
270 | idx = find_key_by_subtree(parent, rnode, true); |
270 | idx = find_key_by_subtree(parent, rnode, true); |
271 | ASSERT((int) idx != -1); |
271 | ASSERT((int) idx != -1); |
272 | free(rnode); |
272 | free(rnode); |
273 | _btree_remove(t, parent->key[idx], parent); |
273 | _btree_remove(t, parent->key[idx], parent); |
274 | } |
274 | } |
275 | } |
275 | } |
276 | 276 | ||
277 | /** Search key in a B-tree. |
277 | /** Search key in a B-tree. |
278 | * |
278 | * |
279 | * @param t B-tree. |
279 | * @param t B-tree. |
280 | * @param key Key to be searched. |
280 | * @param key Key to be searched. |
281 | * @param leaf_node Address where to put pointer to visited leaf node. |
281 | * @param leaf_node Address where to put pointer to visited leaf node. |
282 | * |
282 | * |
283 | * @return Pointer to value or NULL if there is no such key. |
283 | * @return Pointer to value or NULL if there is no such key. |
284 | */ |
284 | */ |
285 | void *btree_search(btree_t *t, __native key, btree_node_t **leaf_node) |
285 | void *btree_search(btree_t *t, __native key, btree_node_t **leaf_node) |
286 | { |
286 | { |
287 | btree_node_t *cur, *next; |
287 | btree_node_t *cur, *next; |
288 | 288 | ||
289 | /* |
289 | /* |
290 | * Iteratively descend to the leaf that can contain the searched key. |
290 | * Iteratively descend to the leaf that can contain the searched key. |
291 | */ |
291 | */ |
292 | for (cur = t->root; cur; cur = next) { |
292 | for (cur = t->root; cur; cur = next) { |
293 | 293 | ||
294 | /* Last iteration will set this with proper leaf node address. */ |
294 | /* Last iteration will set this with proper leaf node address. */ |
295 | *leaf_node = cur; |
295 | *leaf_node = cur; |
296 | 296 | ||
297 | /* |
297 | /* |
298 | * The key can be in the leftmost subtree. |
298 | * The key can be in the leftmost subtree. |
299 | * Test it separately. |
299 | * Test it separately. |
300 | */ |
300 | */ |
301 | if (key < cur->key[0]) { |
301 | if (key < cur->key[0]) { |
302 | next = cur->subtree[0]; |
302 | next = cur->subtree[0]; |
303 | continue; |
303 | continue; |
304 | } else { |
304 | } else { |
305 | void *val; |
305 | void *val; |
306 | int i; |
306 | int i; |
307 | 307 | ||
308 | /* |
308 | /* |
309 | * Now if the key is smaller than cur->key[i] |
309 | * Now if the key is smaller than cur->key[i] |
310 | * it can only mean that the value is in cur->subtree[i] |
310 | * it can only mean that the value is in cur->subtree[i] |
311 | * or it is not in the tree at all. |
311 | * or it is not in the tree at all. |
312 | */ |
312 | */ |
313 | for (i = 1; i < cur->keys; i++) { |
313 | for (i = 1; i < cur->keys; i++) { |
314 | if (key < cur->key[i]) { |
314 | if (key < cur->key[i]) { |
315 | next = cur->subtree[i]; |
315 | next = cur->subtree[i]; |
316 | val = cur->value[i - 1]; |
316 | val = cur->value[i - 1]; |
317 | 317 | ||
318 | if (LEAF_NODE(cur)) |
318 | if (LEAF_NODE(cur)) |
319 | return key == cur->key[i - 1] ? val : NULL; |
319 | return key == cur->key[i - 1] ? val : NULL; |
320 | 320 | ||
321 | goto descend; |
321 | goto descend; |
322 | } |
322 | } |
323 | } |
323 | } |
324 | 324 | ||
325 | /* |
325 | /* |
326 | * Last possibility is that the key is in the rightmost subtree. |
326 | * Last possibility is that the key is in the rightmost subtree. |
327 | */ |
327 | */ |
328 | next = cur->subtree[i]; |
328 | next = cur->subtree[i]; |
329 | val = cur->value[i - 1]; |
329 | val = cur->value[i - 1]; |
330 | if (LEAF_NODE(cur)) |
330 | if (LEAF_NODE(cur)) |
331 | return key == cur->key[i - 1] ? val : NULL; |
331 | return key == cur->key[i - 1] ? val : NULL; |
332 | } |
332 | } |
333 | descend: |
333 | descend: |
334 | ; |
334 | ; |
335 | } |
335 | } |
336 | 336 | ||
337 | /* |
337 | /* |
338 | * The key was not found in the *leaf_node and is smaller than any of its keys. |
338 | * The key was not found in the *leaf_node and is smaller than any of its keys. |
339 | */ |
339 | */ |
340 | return NULL; |
340 | return NULL; |
341 | } |
341 | } |
342 | 342 | ||
- | 343 | /** Return pointer to B-tree node's left sibling. |
|
- | 344 | * |
|
- | 345 | * @param t B-tree. |
|
- | 346 | * @param node Node whose left sibling will be returned. |
|
- | 347 | * |
|
- | 348 | * @return Left sibling of the node or NULL if the node does not have the left sibling. |
|
- | 349 | */ |
|
- | 350 | btree_node_t *btree_node_left_sibling(btree_t *t, btree_node_t *node) |
|
- | 351 | { |
|
- | 352 | ASSERT(LEAF_NODE(node)); |
|
- | 353 | if (node->leaf_link.prev != &t->leaf_head) |
|
- | 354 | return list_get_instance(node->leaf_link.prev, btree_node_t, leaf_link); |
|
- | 355 | else |
|
- | 356 | return NULL; |
|
- | 357 | } |
|
- | 358 | ||
- | 359 | /** Return pointer to B-tree node's right sibling. |
|
- | 360 | * |
|
- | 361 | * @param t B-tree. |
|
- | 362 | * @param node Node whose right sibling will be returned. |
|
- | 363 | * |
|
- | 364 | * @return Right sibling of the node or NULL if the node does not have the right sibling. |
|
- | 365 | */ |
|
- | 366 | btree_node_t *btree_node_right_sibling(btree_t *t, btree_node_t *node) |
|
- | 367 | { |
|
- | 368 | ASSERT(LEAF_NODE(node)); |
|
- | 369 | if (node->leaf_link.next != &t->leaf_head) |
|
- | 370 | return list_get_instance(node->leaf_link.next, btree_node_t, leaf_link); |
|
- | 371 | else |
|
- | 372 | return NULL; |
|
- | 373 | } |
|
- | 374 | ||
343 | /** Initialize B-tree node. |
375 | /** Initialize B-tree node. |
344 | * |
376 | * |
345 | * @param node B-tree node. |
377 | * @param node B-tree node. |
346 | */ |
378 | */ |
347 | void node_initialize(btree_node_t *node) |
379 | void node_initialize(btree_node_t *node) |
348 | { |
380 | { |
349 | int i; |
381 | int i; |
350 | 382 | ||
351 | node->keys = 0; |
383 | node->keys = 0; |
352 | 384 | ||
353 | /* Clean also space for the extra key. */ |
385 | /* Clean also space for the extra key. */ |
354 | for (i = 0; i < BTREE_MAX_KEYS + 1; i++) { |
386 | for (i = 0; i < BTREE_MAX_KEYS + 1; i++) { |
355 | node->key[i] = 0; |
387 | node->key[i] = 0; |
356 | node->value[i] = NULL; |
388 | node->value[i] = NULL; |
357 | node->subtree[i] = NULL; |
389 | node->subtree[i] = NULL; |
358 | } |
390 | } |
359 | node->subtree[i] = NULL; |
391 | node->subtree[i] = NULL; |
360 | 392 | ||
361 | node->parent = NULL; |
393 | node->parent = NULL; |
362 | 394 | ||
363 | link_initialize(&node->leaf_link); |
395 | link_initialize(&node->leaf_link); |
364 | 396 | ||
365 | link_initialize(&node->bfs_link); |
397 | link_initialize(&node->bfs_link); |
366 | node->depth = 0; |
398 | node->depth = 0; |
367 | } |
399 | } |
368 | 400 | ||
369 | /** Insert key-value-lsubtree triplet into B-tree node. |
401 | /** Insert key-value-lsubtree triplet into B-tree node. |
370 | * |
402 | * |
371 | * It is actually possible to have more keys than BTREE_MAX_KEYS. |
403 | * It is actually possible to have more keys than BTREE_MAX_KEYS. |
372 | * This feature is used during insert by right rotation. |
404 | * This feature is used during insert by right rotation. |
373 | * |
405 | * |
374 | * @param node B-tree node into wich the new key is to be inserted. |
406 | * @param node B-tree node into wich the new key is to be inserted. |
375 | * @param key The key to be inserted. |
407 | * @param key The key to be inserted. |
376 | * @param value Pointer to value to be inserted. |
408 | * @param value Pointer to value to be inserted. |
377 | * @param lsubtree Pointer to the left subtree. |
409 | * @param lsubtree Pointer to the left subtree. |
378 | */ |
410 | */ |
379 | void node_insert_key_and_lsubtree(btree_node_t *node, __native key, void *value, btree_node_t *lsubtree) |
411 | void node_insert_key_and_lsubtree(btree_node_t *node, __native key, void *value, btree_node_t *lsubtree) |
380 | { |
412 | { |
381 | int i; |
413 | int i; |
382 | 414 | ||
383 | for (i = 0; i < node->keys; i++) { |
415 | for (i = 0; i < node->keys; i++) { |
384 | if (key < node->key[i]) { |
416 | if (key < node->key[i]) { |
385 | int j; |
417 | int j; |
386 | 418 | ||
387 | for (j = node->keys; j > i; j--) { |
419 | for (j = node->keys; j > i; j--) { |
388 | node->key[j] = node->key[j - 1]; |
420 | node->key[j] = node->key[j - 1]; |
389 | node->value[j] = node->value[j - 1]; |
421 | node->value[j] = node->value[j - 1]; |
390 | node->subtree[j + 1] = node->subtree[j]; |
422 | node->subtree[j + 1] = node->subtree[j]; |
391 | } |
423 | } |
392 | node->subtree[j + 1] = node->subtree[j]; |
424 | node->subtree[j + 1] = node->subtree[j]; |
393 | break; |
425 | break; |
394 | } |
426 | } |
395 | } |
427 | } |
396 | node->key[i] = key; |
428 | node->key[i] = key; |
397 | node->value[i] = value; |
429 | node->value[i] = value; |
398 | node->subtree[i] = lsubtree; |
430 | node->subtree[i] = lsubtree; |
399 | 431 | ||
400 | node->keys++; |
432 | node->keys++; |
401 | } |
433 | } |
402 | 434 | ||
403 | /** Insert key-value-rsubtree triplet into B-tree node. |
435 | /** Insert key-value-rsubtree triplet into B-tree node. |
404 | * |
436 | * |
405 | * It is actually possible to have more keys than BTREE_MAX_KEYS. |
437 | * It is actually possible to have more keys than BTREE_MAX_KEYS. |
406 | * This feature is used during splitting the node when the |
438 | * This feature is used during splitting the node when the |
407 | * number of keys is BTREE_MAX_KEYS + 1. Insert by left rotation |
439 | * number of keys is BTREE_MAX_KEYS + 1. Insert by left rotation |
408 | * also makes use of this feature. |
440 | * also makes use of this feature. |
409 | * |
441 | * |
410 | * @param node B-tree node into wich the new key is to be inserted. |
442 | * @param node B-tree node into wich the new key is to be inserted. |
411 | * @param key The key to be inserted. |
443 | * @param key The key to be inserted. |
412 | * @param value Pointer to value to be inserted. |
444 | * @param value Pointer to value to be inserted. |
413 | * @param rsubtree Pointer to the right subtree. |
445 | * @param rsubtree Pointer to the right subtree. |
414 | */ |
446 | */ |
415 | void node_insert_key_and_rsubtree(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree) |
447 | void node_insert_key_and_rsubtree(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree) |
416 | { |
448 | { |
417 | int i; |
449 | int i; |
418 | 450 | ||
419 | for (i = 0; i < node->keys; i++) { |
451 | for (i = 0; i < node->keys; i++) { |
420 | if (key < node->key[i]) { |
452 | if (key < node->key[i]) { |
421 | int j; |
453 | int j; |
422 | 454 | ||
423 | for (j = node->keys; j > i; j--) { |
455 | for (j = node->keys; j > i; j--) { |
424 | node->key[j] = node->key[j - 1]; |
456 | node->key[j] = node->key[j - 1]; |
425 | node->value[j] = node->value[j - 1]; |
457 | node->value[j] = node->value[j - 1]; |
426 | node->subtree[j + 1] = node->subtree[j]; |
458 | node->subtree[j + 1] = node->subtree[j]; |
427 | } |
459 | } |
428 | break; |
460 | break; |
429 | } |
461 | } |
430 | } |
462 | } |
431 | node->key[i] = key; |
463 | node->key[i] = key; |
432 | node->value[i] = value; |
464 | node->value[i] = value; |
433 | node->subtree[i + 1] = rsubtree; |
465 | node->subtree[i + 1] = rsubtree; |
434 | 466 | ||
435 | node->keys++; |
467 | node->keys++; |
436 | } |
468 | } |
437 | 469 | ||
438 | /** Remove key and its left subtree pointer from B-tree node. |
470 | /** Remove key and its left subtree pointer from B-tree node. |
439 | * |
471 | * |
440 | * Remove the key and eliminate gaps in node->key array. |
472 | * Remove the key and eliminate gaps in node->key array. |
441 | * Note that the value pointer and the left subtree pointer |
473 | * Note that the value pointer and the left subtree pointer |
442 | * is removed from the node as well. |
474 | * is removed from the node as well. |
443 | * |
475 | * |
444 | * @param node B-tree node. |
476 | * @param node B-tree node. |
445 | * @param key Key to be removed. |
477 | * @param key Key to be removed. |
446 | */ |
478 | */ |
447 | void node_remove_key_and_lsubtree(btree_node_t *node, __native key) |
479 | void node_remove_key_and_lsubtree(btree_node_t *node, __native key) |
448 | { |
480 | { |
449 | int i, j; |
481 | int i, j; |
450 | 482 | ||
451 | for (i = 0; i < node->keys; i++) { |
483 | for (i = 0; i < node->keys; i++) { |
452 | if (key == node->key[i]) { |
484 | if (key == node->key[i]) { |
453 | for (j = i + 1; j < node->keys; j++) { |
485 | for (j = i + 1; j < node->keys; j++) { |
454 | node->key[j - 1] = node->key[j]; |
486 | node->key[j - 1] = node->key[j]; |
455 | node->value[j - 1] = node->value[j]; |
487 | node->value[j - 1] = node->value[j]; |
456 | node->subtree[j - 1] = node->subtree[j]; |
488 | node->subtree[j - 1] = node->subtree[j]; |
457 | } |
489 | } |
458 | node->subtree[j - 1] = node->subtree[j]; |
490 | node->subtree[j - 1] = node->subtree[j]; |
459 | node->keys--; |
491 | node->keys--; |
460 | return; |
492 | return; |
461 | } |
493 | } |
462 | } |
494 | } |
463 | panic("node %P does not contain key %d\n", node, key); |
495 | panic("node %P does not contain key %d\n", node, key); |
464 | } |
496 | } |
465 | 497 | ||
466 | /** Remove key and its right subtree pointer from B-tree node. |
498 | /** Remove key and its right subtree pointer from B-tree node. |
467 | * |
499 | * |
468 | * Remove the key and eliminate gaps in node->key array. |
500 | * Remove the key and eliminate gaps in node->key array. |
469 | * Note that the value pointer and the right subtree pointer |
501 | * Note that the value pointer and the right subtree pointer |
470 | * is removed from the node as well. |
502 | * is removed from the node as well. |
471 | * |
503 | * |
472 | * @param node B-tree node. |
504 | * @param node B-tree node. |
473 | * @param key Key to be removed. |
505 | * @param key Key to be removed. |
474 | */ |
506 | */ |
475 | void node_remove_key_and_rsubtree(btree_node_t *node, __native key) |
507 | void node_remove_key_and_rsubtree(btree_node_t *node, __native key) |
476 | { |
508 | { |
477 | int i, j; |
509 | int i, j; |
478 | 510 | ||
479 | for (i = 0; i < node->keys; i++) { |
511 | for (i = 0; i < node->keys; i++) { |
480 | if (key == node->key[i]) { |
512 | if (key == node->key[i]) { |
481 | for (j = i + 1; j < node->keys; j++) { |
513 | for (j = i + 1; j < node->keys; j++) { |
482 | node->key[j - 1] = node->key[j]; |
514 | node->key[j - 1] = node->key[j]; |
483 | node->value[j - 1] = node->value[j]; |
515 | node->value[j - 1] = node->value[j]; |
484 | node->subtree[j] = node->subtree[j + 1]; |
516 | node->subtree[j] = node->subtree[j + 1]; |
485 | } |
517 | } |
486 | node->keys--; |
518 | node->keys--; |
487 | return; |
519 | return; |
488 | } |
520 | } |
489 | } |
521 | } |
490 | panic("node %P does not contain key %d\n", node, key); |
522 | panic("node %P does not contain key %d\n", node, key); |
491 | } |
523 | } |
492 | 524 | ||
493 | /** Split full B-tree node and insert new key-value-right-subtree triplet. |
525 | /** Split full B-tree node and insert new key-value-right-subtree triplet. |
494 | * |
526 | * |
495 | * This function will split a node and return pointer to a newly created |
527 | * This function will split a node and return pointer to a newly created |
496 | * node containing keys greater than or equal to the greater of medians |
528 | * node containing keys greater than or equal to the greater of medians |
497 | * (or median) of the old keys and the newly added key. It will also write |
529 | * (or median) of the old keys and the newly added key. It will also write |
498 | * the median key to a memory address supplied by the caller. |
530 | * the median key to a memory address supplied by the caller. |
499 | * |
531 | * |
500 | * If the node being split is an index node, the median will not be |
532 | * If the node being split is an index node, the median will not be |
501 | * included in the new node. If the node is a leaf node, |
533 | * included in the new node. If the node is a leaf node, |
502 | * the median will be copied there. |
534 | * the median will be copied there. |
503 | * |
535 | * |
504 | * @param node B-tree node wich is going to be split. |
536 | * @param node B-tree node wich is going to be split. |
505 | * @param key The key to be inserted. |
537 | * @param key The key to be inserted. |
506 | * @param value Pointer to the value to be inserted. |
538 | * @param value Pointer to the value to be inserted. |
507 | * @param rsubtree Pointer to the right subtree of the key being added. |
539 | * @param rsubtree Pointer to the right subtree of the key being added. |
508 | * @param median Address in memory, where the median key will be stored. |
540 | * @param median Address in memory, where the median key will be stored. |
509 | * |
541 | * |
510 | * @return Newly created right sibling of node. |
542 | * @return Newly created right sibling of node. |
511 | */ |
543 | */ |
512 | btree_node_t *node_split(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree, __native *median) |
544 | btree_node_t *node_split(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree, __native *median) |
513 | { |
545 | { |
514 | btree_node_t *rnode; |
546 | btree_node_t *rnode; |
515 | int i, j; |
547 | int i, j; |
516 | 548 | ||
517 | ASSERT(median); |
549 | ASSERT(median); |
518 | ASSERT(node->keys == BTREE_MAX_KEYS); |
550 | ASSERT(node->keys == BTREE_MAX_KEYS); |
519 | 551 | ||
520 | /* |
552 | /* |
521 | * Use the extra space to store the extra node. |
553 | * Use the extra space to store the extra node. |
522 | */ |
554 | */ |
523 | node_insert_key_and_rsubtree(node, key, value, rsubtree); |
555 | node_insert_key_and_rsubtree(node, key, value, rsubtree); |
524 | 556 | ||
525 | /* |
557 | /* |
526 | * Compute median of keys. |
558 | * Compute median of keys. |
527 | */ |
559 | */ |
528 | *median = MEDIAN_HIGH(node); |
560 | *median = MEDIAN_HIGH(node); |
529 | 561 | ||
530 | /* |
562 | /* |
531 | * Allocate and initialize new right sibling. |
563 | * Allocate and initialize new right sibling. |
532 | */ |
564 | */ |
533 | rnode = (btree_node_t *) malloc(sizeof(btree_node_t), 0); |
565 | rnode = (btree_node_t *) malloc(sizeof(btree_node_t), 0); |
534 | node_initialize(rnode); |
566 | node_initialize(rnode); |
535 | rnode->parent = node->parent; |
567 | rnode->parent = node->parent; |
536 | rnode->depth = node->depth; |
568 | rnode->depth = node->depth; |
537 | 569 | ||
538 | /* |
570 | /* |
539 | * Copy big keys, values and subtree pointers to the new right sibling. |
571 | * Copy big keys, values and subtree pointers to the new right sibling. |
540 | * If this is an index node, do not copy the median. |
572 | * If this is an index node, do not copy the median. |
541 | */ |
573 | */ |
542 | i = (int) INDEX_NODE(node); |
574 | i = (int) INDEX_NODE(node); |
543 | for (i += MEDIAN_HIGH_INDEX(node), j = 0; i < node->keys; i++, j++) { |
575 | for (i += MEDIAN_HIGH_INDEX(node), j = 0; i < node->keys; i++, j++) { |
544 | rnode->key[j] = node->key[i]; |
576 | rnode->key[j] = node->key[i]; |
545 | rnode->value[j] = node->value[i]; |
577 | rnode->value[j] = node->value[i]; |
546 | rnode->subtree[j] = node->subtree[i]; |
578 | rnode->subtree[j] = node->subtree[i]; |
547 | 579 | ||
548 | /* |
580 | /* |
549 | * Fix parent links in subtrees. |
581 | * Fix parent links in subtrees. |
550 | */ |
582 | */ |
551 | if (rnode->subtree[j]) |
583 | if (rnode->subtree[j]) |
552 | rnode->subtree[j]->parent = rnode; |
584 | rnode->subtree[j]->parent = rnode; |
553 | 585 | ||
554 | } |
586 | } |
555 | rnode->subtree[j] = node->subtree[i]; |
587 | rnode->subtree[j] = node->subtree[i]; |
556 | if (rnode->subtree[j]) |
588 | if (rnode->subtree[j]) |
557 | rnode->subtree[j]->parent = rnode; |
589 | rnode->subtree[j]->parent = rnode; |
558 | 590 | ||
559 | rnode->keys = j; /* Set number of keys of the new node. */ |
591 | rnode->keys = j; /* Set number of keys of the new node. */ |
560 | node->keys /= 2; /* Shrink the old node. */ |
592 | node->keys /= 2; /* Shrink the old node. */ |
561 | 593 | ||
562 | return rnode; |
594 | return rnode; |
563 | } |
595 | } |
564 | 596 | ||
565 | /** Combine node with any of its siblings. |
597 | /** Combine node with any of its siblings. |
566 | * |
598 | * |
567 | * The siblings are required to be below the fill factor. |
599 | * The siblings are required to be below the fill factor. |
568 | * |
600 | * |
569 | * @param node Node to combine with one of its siblings. |
601 | * @param node Node to combine with one of its siblings. |
570 | * |
602 | * |
571 | * @return Pointer to the rightmost of the two nodes. |
603 | * @return Pointer to the rightmost of the two nodes. |
572 | */ |
604 | */ |
573 | btree_node_t *node_combine(btree_node_t *node) |
605 | btree_node_t *node_combine(btree_node_t *node) |
574 | { |
606 | { |
575 | index_t idx; |
607 | index_t idx; |
576 | btree_node_t *rnode; |
608 | btree_node_t *rnode; |
577 | int i; |
609 | int i; |
578 | 610 | ||
579 | ASSERT(!ROOT_NODE(node)); |
611 | ASSERT(!ROOT_NODE(node)); |
580 | 612 | ||
581 | idx = find_key_by_subtree(node->parent, node, false); |
613 | idx = find_key_by_subtree(node->parent, node, false); |
582 | if (idx == node->parent->keys) { |
614 | if (idx == node->parent->keys) { |
583 | /* |
615 | /* |
584 | * Rightmost subtree of its parent, combine with the left sibling. |
616 | * Rightmost subtree of its parent, combine with the left sibling. |
585 | */ |
617 | */ |
586 | idx--; |
618 | idx--; |
587 | rnode = node; |
619 | rnode = node; |
588 | node = node->parent->subtree[idx]; |
620 | node = node->parent->subtree[idx]; |
589 | } else { |
621 | } else { |
590 | rnode = node->parent->subtree[idx + 1]; |
622 | rnode = node->parent->subtree[idx + 1]; |
591 | } |
623 | } |
592 | 624 | ||
593 | /* Index nodes need to insert parent node key in between left and right node. */ |
625 | /* Index nodes need to insert parent node key in between left and right node. */ |
594 | if (INDEX_NODE(node)) |
626 | if (INDEX_NODE(node)) |
595 | node->key[node->keys++] = node->parent->key[idx]; |
627 | node->key[node->keys++] = node->parent->key[idx]; |
596 | 628 | ||
597 | /* Copy the key-value-subtree triplets from the right node. */ |
629 | /* Copy the key-value-subtree triplets from the right node. */ |
598 | for (i = 0; i < rnode->keys; i++) { |
630 | for (i = 0; i < rnode->keys; i++) { |
599 | node->key[node->keys + i] = rnode->key[i]; |
631 | node->key[node->keys + i] = rnode->key[i]; |
600 | node->value[node->keys + i] = rnode->value[i]; |
632 | node->value[node->keys + i] = rnode->value[i]; |
601 | if (INDEX_NODE(node)) { |
633 | if (INDEX_NODE(node)) { |
602 | node->subtree[node->keys + i] = rnode->subtree[i]; |
634 | node->subtree[node->keys + i] = rnode->subtree[i]; |
603 | rnode->subtree[i]->parent = node; |
635 | rnode->subtree[i]->parent = node; |
604 | } |
636 | } |
605 | } |
637 | } |
606 | if (INDEX_NODE(node)) { |
638 | if (INDEX_NODE(node)) { |
607 | node->subtree[node->keys + i] = rnode->subtree[i]; |
639 | node->subtree[node->keys + i] = rnode->subtree[i]; |
608 | rnode->subtree[i]->parent = node; |
640 | rnode->subtree[i]->parent = node; |
609 | } |
641 | } |
610 | 642 | ||
611 | node->keys += rnode->keys; |
643 | node->keys += rnode->keys; |
612 | 644 | ||
613 | return rnode; |
645 | return rnode; |
614 | } |
646 | } |
615 | 647 | ||
616 | /** Find key by its left or right subtree. |
648 | /** Find key by its left or right subtree. |
617 | * |
649 | * |
618 | * @param node B-tree node. |
650 | * @param node B-tree node. |
619 | * @param subtree Left or right subtree of a key found in node. |
651 | * @param subtree Left or right subtree of a key found in node. |
620 | * @param right If true, subtree is a right subtree. If false, subtree is a left subtree. |
652 | * @param right If true, subtree is a right subtree. If false, subtree is a left subtree. |
621 | * |
653 | * |
622 | * @return Index of the key associated with the subtree. |
654 | * @return Index of the key associated with the subtree. |
623 | */ |
655 | */ |
624 | index_t find_key_by_subtree(btree_node_t *node, btree_node_t *subtree, bool right) |
656 | index_t find_key_by_subtree(btree_node_t *node, btree_node_t *subtree, bool right) |
625 | { |
657 | { |
626 | int i; |
658 | int i; |
627 | 659 | ||
628 | for (i = 0; i < node->keys + 1; i++) { |
660 | for (i = 0; i < node->keys + 1; i++) { |
629 | if (subtree == node->subtree[i]) |
661 | if (subtree == node->subtree[i]) |
630 | return i - (int) (right != false); |
662 | return i - (int) (right != false); |
631 | } |
663 | } |
632 | panic("node %P does not contain subtree %P\n", node, subtree); |
664 | panic("node %P does not contain subtree %P\n", node, subtree); |
633 | } |
665 | } |
634 | 666 | ||
635 | /** Rotate one key-value-rsubtree triplet from the left sibling to the right sibling. |
667 | /** Rotate one key-value-rsubtree triplet from the left sibling to the right sibling. |
636 | * |
668 | * |
637 | * The biggest key and its value and right subtree is rotated from the left node |
669 | * The biggest key and its value and right subtree is rotated from the left node |
638 | * to the right. If the node is an index node, than the parent node key belonging to |
670 | * to the right. If the node is an index node, than the parent node key belonging to |
639 | * the left node takes part in the rotation. |
671 | * the left node takes part in the rotation. |
640 | * |
672 | * |
641 | * @param lnode Left sibling. |
673 | * @param lnode Left sibling. |
642 | * @param rnode Right sibling. |
674 | * @param rnode Right sibling. |
643 | * @param idx Index of the parent node key that is taking part in the rotation. |
675 | * @param idx Index of the parent node key that is taking part in the rotation. |
644 | */ |
676 | */ |
645 | void rotate_from_left(btree_node_t *lnode, btree_node_t *rnode, index_t idx) |
677 | void rotate_from_left(btree_node_t *lnode, btree_node_t *rnode, index_t idx) |
646 | { |
678 | { |
647 | __native key; |
679 | __native key; |
648 | 680 | ||
649 | key = lnode->key[lnode->keys - 1]; |
681 | key = lnode->key[lnode->keys - 1]; |
650 | 682 | ||
651 | if (LEAF_NODE(lnode)) { |
683 | if (LEAF_NODE(lnode)) { |
652 | void *value; |
684 | void *value; |
653 | 685 | ||
654 | value = lnode->value[lnode->keys - 1]; |
686 | value = lnode->value[lnode->keys - 1]; |
655 | node_remove_key_and_rsubtree(lnode, key); |
687 | node_remove_key_and_rsubtree(lnode, key); |
656 | node_insert_key_and_lsubtree(rnode, key, value, NULL); |
688 | node_insert_key_and_lsubtree(rnode, key, value, NULL); |
657 | lnode->parent->key[idx] = key; |
689 | lnode->parent->key[idx] = key; |
658 | } else { |
690 | } else { |
659 | btree_node_t *rsubtree; |
691 | btree_node_t *rsubtree; |
660 | 692 | ||
661 | rsubtree = lnode->subtree[lnode->keys]; |
693 | rsubtree = lnode->subtree[lnode->keys]; |
662 | node_remove_key_and_rsubtree(lnode, key); |
694 | node_remove_key_and_rsubtree(lnode, key); |
663 | node_insert_key_and_lsubtree(rnode, lnode->parent->key[idx], NULL, rsubtree); |
695 | node_insert_key_and_lsubtree(rnode, lnode->parent->key[idx], NULL, rsubtree); |
664 | lnode->parent->key[idx] = key; |
696 | lnode->parent->key[idx] = key; |
665 | 697 | ||
666 | /* Fix parent link of the reconnected right subtree. */ |
698 | /* Fix parent link of the reconnected right subtree. */ |
667 | rsubtree->parent = rnode; |
699 | rsubtree->parent = rnode; |
668 | } |
700 | } |
669 | 701 | ||
670 | } |
702 | } |
671 | 703 | ||
672 | /** Rotate one key-value-lsubtree triplet from the right sibling to the left sibling. |
704 | /** Rotate one key-value-lsubtree triplet from the right sibling to the left sibling. |
673 | * |
705 | * |
674 | * The smallest key and its value and left subtree is rotated from the right node |
706 | * The smallest key and its value and left subtree is rotated from the right node |
675 | * to the left. If the node is an index node, than the parent node key belonging to |
707 | * to the left. If the node is an index node, than the parent node key belonging to |
676 | * the right node takes part in the rotation. |
708 | * the right node takes part in the rotation. |
677 | * |
709 | * |
678 | * @param lnode Left sibling. |
710 | * @param lnode Left sibling. |
679 | * @param rnode Right sibling. |
711 | * @param rnode Right sibling. |
680 | * @param idx Index of the parent node key that is taking part in the rotation. |
712 | * @param idx Index of the parent node key that is taking part in the rotation. |
681 | */ |
713 | */ |
682 | void rotate_from_right(btree_node_t *lnode, btree_node_t *rnode, index_t idx) |
714 | void rotate_from_right(btree_node_t *lnode, btree_node_t *rnode, index_t idx) |
683 | { |
715 | { |
684 | __native key; |
716 | __native key; |
685 | 717 | ||
686 | key = rnode->key[0]; |
718 | key = rnode->key[0]; |
687 | 719 | ||
688 | if (LEAF_NODE(rnode)) { |
720 | if (LEAF_NODE(rnode)) { |
689 | void *value; |
721 | void *value; |
690 | 722 | ||
691 | value = rnode->value[0]; |
723 | value = rnode->value[0]; |
692 | node_remove_key_and_lsubtree(rnode, key); |
724 | node_remove_key_and_lsubtree(rnode, key); |
693 | node_insert_key_and_rsubtree(lnode, key, value, NULL); |
725 | node_insert_key_and_rsubtree(lnode, key, value, NULL); |
694 | rnode->parent->key[idx] = rnode->key[0]; |
726 | rnode->parent->key[idx] = rnode->key[0]; |
695 | } else { |
727 | } else { |
696 | btree_node_t *lsubtree; |
728 | btree_node_t *lsubtree; |
697 | 729 | ||
698 | lsubtree = rnode->subtree[0]; |
730 | lsubtree = rnode->subtree[0]; |
699 | node_remove_key_and_lsubtree(rnode, key); |
731 | node_remove_key_and_lsubtree(rnode, key); |
700 | node_insert_key_and_rsubtree(lnode, rnode->parent->key[idx], NULL, lsubtree); |
732 | node_insert_key_and_rsubtree(lnode, rnode->parent->key[idx], NULL, lsubtree); |
701 | rnode->parent->key[idx] = key; |
733 | rnode->parent->key[idx] = key; |
702 | 734 | ||
703 | /* Fix parent link of the reconnected left subtree. */ |
735 | /* Fix parent link of the reconnected left subtree. */ |
704 | lsubtree->parent = lnode; |
736 | lsubtree->parent = lnode; |
705 | } |
737 | } |
706 | 738 | ||
707 | } |
739 | } |
708 | 740 | ||
709 | /** Insert key-value-rsubtree triplet and rotate the node to the left, if this operation can be done. |
741 | /** Insert key-value-rsubtree triplet and rotate the node to the left, if this operation can be done. |
710 | * |
742 | * |
711 | * Left sibling of the node (if it exists) is checked for free space. |
743 | * Left sibling of the node (if it exists) is checked for free space. |
712 | * If there is free space, the key is inserted and the smallest key of |
744 | * If there is free space, the key is inserted and the smallest key of |
713 | * the node is moved there. The index node which is the parent of both |
745 | * the node is moved there. The index node which is the parent of both |
714 | * nodes is fixed. |
746 | * nodes is fixed. |
715 | * |
747 | * |
716 | * @param node B-tree node. |
748 | * @param node B-tree node. |
717 | * @param inskey Key to be inserted. |
749 | * @param inskey Key to be inserted. |
718 | * @param insvalue Value to be inserted. |
750 | * @param insvalue Value to be inserted. |
719 | * @param rsubtree Right subtree of inskey. |
751 | * @param rsubtree Right subtree of inskey. |
720 | * |
752 | * |
721 | * @return True if the rotation was performed, false otherwise. |
753 | * @return True if the rotation was performed, false otherwise. |
722 | */ |
754 | */ |
723 | bool try_insert_by_rotation_to_left(btree_node_t *node, __native inskey, void *insvalue, btree_node_t *rsubtree) |
755 | bool try_insert_by_rotation_to_left(btree_node_t *node, __native inskey, void *insvalue, btree_node_t *rsubtree) |
724 | { |
756 | { |
725 | index_t idx; |
757 | index_t idx; |
726 | btree_node_t *lnode; |
758 | btree_node_t *lnode; |
727 | 759 | ||
728 | /* |
760 | /* |
729 | * If this is root node, the rotation can not be done. |
761 | * If this is root node, the rotation can not be done. |
730 | */ |
762 | */ |
731 | if (ROOT_NODE(node)) |
763 | if (ROOT_NODE(node)) |
732 | return false; |
764 | return false; |
733 | 765 | ||
734 | idx = find_key_by_subtree(node->parent, node, true); |
766 | idx = find_key_by_subtree(node->parent, node, true); |
735 | if ((int) idx == -1) { |
767 | if ((int) idx == -1) { |
736 | /* |
768 | /* |
737 | * If this node is the leftmost subtree of its parent, |
769 | * If this node is the leftmost subtree of its parent, |
738 | * the rotation can not be done. |
770 | * the rotation can not be done. |
739 | */ |
771 | */ |
740 | return false; |
772 | return false; |
741 | } |
773 | } |
742 | 774 | ||
743 | lnode = node->parent->subtree[idx]; |
775 | lnode = node->parent->subtree[idx]; |
744 | if (lnode->keys < BTREE_MAX_KEYS) { |
776 | if (lnode->keys < BTREE_MAX_KEYS) { |
745 | /* |
777 | /* |
746 | * The rotaion can be done. The left sibling has free space. |
778 | * The rotaion can be done. The left sibling has free space. |
747 | */ |
779 | */ |
748 | node_insert_key_and_rsubtree(node, inskey, insvalue, rsubtree); |
780 | node_insert_key_and_rsubtree(node, inskey, insvalue, rsubtree); |
749 | rotate_from_right(lnode, node, idx); |
781 | rotate_from_right(lnode, node, idx); |
750 | return true; |
782 | return true; |
751 | } |
783 | } |
752 | 784 | ||
753 | return false; |
785 | return false; |
754 | } |
786 | } |
755 | 787 | ||
756 | /** Insert key-value-rsubtree triplet and rotate the node to the right, if this operation can be done. |
788 | /** Insert key-value-rsubtree triplet and rotate the node to the right, if this operation can be done. |
757 | * |
789 | * |
758 | * Right sibling of the node (if it exists) is checked for free space. |
790 | * Right sibling of the node (if it exists) is checked for free space. |
759 | * If there is free space, the key is inserted and the biggest key of |
791 | * If there is free space, the key is inserted and the biggest key of |
760 | * the node is moved there. The index node which is the parent of both |
792 | * the node is moved there. The index node which is the parent of both |
761 | * nodes is fixed. |
793 | * nodes is fixed. |
762 | * |
794 | * |
763 | * @param node B-tree node. |
795 | * @param node B-tree node. |
764 | * @param inskey Key to be inserted. |
796 | * @param inskey Key to be inserted. |
765 | * @param insvalue Value to be inserted. |
797 | * @param insvalue Value to be inserted. |
766 | * @param rsubtree Right subtree of inskey. |
798 | * @param rsubtree Right subtree of inskey. |
767 | * |
799 | * |
768 | * @return True if the rotation was performed, false otherwise. |
800 | * @return True if the rotation was performed, false otherwise. |
769 | */ |
801 | */ |
770 | bool try_insert_by_rotation_to_right(btree_node_t *node, __native inskey, void *insvalue, btree_node_t *rsubtree) |
802 | bool try_insert_by_rotation_to_right(btree_node_t *node, __native inskey, void *insvalue, btree_node_t *rsubtree) |
771 | { |
803 | { |
772 | index_t idx; |
804 | index_t idx; |
773 | btree_node_t *rnode; |
805 | btree_node_t *rnode; |
774 | 806 | ||
775 | /* |
807 | /* |
776 | * If this is root node, the rotation can not be done. |
808 | * If this is root node, the rotation can not be done. |
777 | */ |
809 | */ |
778 | if (ROOT_NODE(node)) |
810 | if (ROOT_NODE(node)) |
779 | return false; |
811 | return false; |
780 | 812 | ||
781 | idx = find_key_by_subtree(node->parent, node, false); |
813 | idx = find_key_by_subtree(node->parent, node, false); |
782 | if (idx == node->parent->keys) { |
814 | if (idx == node->parent->keys) { |
783 | /* |
815 | /* |
784 | * If this node is the rightmost subtree of its parent, |
816 | * If this node is the rightmost subtree of its parent, |
785 | * the rotation can not be done. |
817 | * the rotation can not be done. |
786 | */ |
818 | */ |
787 | return false; |
819 | return false; |
788 | } |
820 | } |
789 | 821 | ||
790 | rnode = node->parent->subtree[idx + 1]; |
822 | rnode = node->parent->subtree[idx + 1]; |
791 | if (rnode->keys < BTREE_MAX_KEYS) { |
823 | if (rnode->keys < BTREE_MAX_KEYS) { |
792 | /* |
824 | /* |
793 | * The rotaion can be done. The right sibling has free space. |
825 | * The rotaion can be done. The right sibling has free space. |
794 | */ |
826 | */ |
795 | node_insert_key_and_rsubtree(node, inskey, insvalue, rsubtree); |
827 | node_insert_key_and_rsubtree(node, inskey, insvalue, rsubtree); |
796 | rotate_from_left(node, rnode, idx); |
828 | rotate_from_left(node, rnode, idx); |
797 | return true; |
829 | return true; |
798 | } |
830 | } |
799 | 831 | ||
800 | return false; |
832 | return false; |
801 | } |
833 | } |
802 | 834 | ||
803 | /** Rotate in a key from the left sibling or from the index node, if this operation can be done. |
835 | /** Rotate in a key from the left sibling or from the index node, if this operation can be done. |
804 | * |
836 | * |
805 | * @param rnode Node into which to add key from its left sibling or from the index node. |
837 | * @param rnode Node into which to add key from its left sibling or from the index node. |
806 | * |
838 | * |
807 | * @return True if the rotation was performed, false otherwise. |
839 | * @return True if the rotation was performed, false otherwise. |
808 | */ |
840 | */ |
809 | bool try_rotation_from_left(btree_node_t *rnode) |
841 | bool try_rotation_from_left(btree_node_t *rnode) |
810 | { |
842 | { |
811 | index_t idx; |
843 | index_t idx; |
812 | btree_node_t *lnode; |
844 | btree_node_t *lnode; |
813 | 845 | ||
814 | /* |
846 | /* |
815 | * If this is root node, the rotation can not be done. |
847 | * If this is root node, the rotation can not be done. |
816 | */ |
848 | */ |
817 | if (ROOT_NODE(rnode)) |
849 | if (ROOT_NODE(rnode)) |
818 | return false; |
850 | return false; |
819 | 851 | ||
820 | idx = find_key_by_subtree(rnode->parent, rnode, true); |
852 | idx = find_key_by_subtree(rnode->parent, rnode, true); |
821 | if ((int) idx == -1) { |
853 | if ((int) idx == -1) { |
822 | /* |
854 | /* |
823 | * If this node is the leftmost subtree of its parent, |
855 | * If this node is the leftmost subtree of its parent, |
824 | * the rotation can not be done. |
856 | * the rotation can not be done. |
825 | */ |
857 | */ |
826 | return false; |
858 | return false; |
827 | } |
859 | } |
828 | 860 | ||
829 | lnode = rnode->parent->subtree[idx]; |
861 | lnode = rnode->parent->subtree[idx]; |
830 | if (lnode->keys > FILL_FACTOR) { |
862 | if (lnode->keys > FILL_FACTOR) { |
831 | rotate_from_left(lnode, rnode, idx); |
863 | rotate_from_left(lnode, rnode, idx); |
832 | return true; |
864 | return true; |
833 | } |
865 | } |
834 | 866 | ||
835 | return false; |
867 | return false; |
836 | } |
868 | } |
837 | 869 | ||
838 | /** Rotate in a key from the right sibling or from the index node, if this operation can be done. |
870 | /** Rotate in a key from the right sibling or from the index node, if this operation can be done. |
839 | * |
871 | * |
840 | * @param rnode Node into which to add key from its right sibling or from the index node. |
872 | * @param rnode Node into which to add key from its right sibling or from the index node. |
841 | * |
873 | * |
842 | * @return True if the rotation was performed, false otherwise. |
874 | * @return True if the rotation was performed, false otherwise. |
843 | */ |
875 | */ |
844 | bool try_rotation_from_right(btree_node_t *lnode) |
876 | bool try_rotation_from_right(btree_node_t *lnode) |
845 | { |
877 | { |
846 | index_t idx; |
878 | index_t idx; |
847 | btree_node_t *rnode; |
879 | btree_node_t *rnode; |
848 | 880 | ||
849 | /* |
881 | /* |
850 | * If this is root node, the rotation can not be done. |
882 | * If this is root node, the rotation can not be done. |
851 | */ |
883 | */ |
852 | if (ROOT_NODE(lnode)) |
884 | if (ROOT_NODE(lnode)) |
853 | return false; |
885 | return false; |
854 | 886 | ||
855 | idx = find_key_by_subtree(lnode->parent, lnode, false); |
887 | idx = find_key_by_subtree(lnode->parent, lnode, false); |
856 | if (idx == lnode->parent->keys) { |
888 | if (idx == lnode->parent->keys) { |
857 | /* |
889 | /* |
858 | * If this node is the rightmost subtree of its parent, |
890 | * If this node is the rightmost subtree of its parent, |
859 | * the rotation can not be done. |
891 | * the rotation can not be done. |
860 | */ |
892 | */ |
861 | return false; |
893 | return false; |
862 | } |
894 | } |
863 | 895 | ||
864 | rnode = lnode->parent->subtree[idx + 1]; |
896 | rnode = lnode->parent->subtree[idx + 1]; |
865 | if (rnode->keys > FILL_FACTOR) { |
897 | if (rnode->keys > FILL_FACTOR) { |
866 | rotate_from_right(lnode, rnode, idx); |
898 | rotate_from_right(lnode, rnode, idx); |
867 | return true; |
899 | return true; |
868 | } |
900 | } |
869 | 901 | ||
870 | return false; |
902 | return false; |
871 | } |
903 | } |
872 | 904 | ||
873 | /** Print B-tree. |
905 | /** Print B-tree. |
874 | * |
906 | * |
875 | * @param t Print out B-tree. |
907 | * @param t Print out B-tree. |
876 | */ |
908 | */ |
877 | void btree_print(btree_t *t) |
909 | void btree_print(btree_t *t) |
878 | { |
910 | { |
879 | int i, depth = t->root->depth; |
911 | int i, depth = t->root->depth; |
880 | link_t head, *cur; |
912 | link_t head, *cur; |
881 | 913 | ||
882 | printf("Printing B-tree:\n"); |
914 | printf("Printing B-tree:\n"); |
883 | list_initialize(&head); |
915 | list_initialize(&head); |
884 | list_append(&t->root->bfs_link, &head); |
916 | list_append(&t->root->bfs_link, &head); |
885 | 917 | ||
886 | /* |
918 | /* |
887 | * Use BFS search to print out the tree. |
919 | * Use BFS search to print out the tree. |
888 | * Levels are distinguished from one another by node->depth. |
920 | * Levels are distinguished from one another by node->depth. |
889 | */ |
921 | */ |
890 | while (!list_empty(&head)) { |
922 | while (!list_empty(&head)) { |
891 | link_t *hlp; |
923 | link_t *hlp; |
892 | btree_node_t *node; |
924 | btree_node_t *node; |
893 | 925 | ||
894 | hlp = head.next; |
926 | hlp = head.next; |
895 | ASSERT(hlp != &head); |
927 | ASSERT(hlp != &head); |
896 | node = list_get_instance(hlp, btree_node_t, bfs_link); |
928 | node = list_get_instance(hlp, btree_node_t, bfs_link); |
897 | list_remove(hlp); |
929 | list_remove(hlp); |
898 | 930 | ||
899 | ASSERT(node); |
931 | ASSERT(node); |
900 | 932 | ||
901 | if (node->depth != depth) { |
933 | if (node->depth != depth) { |
902 | printf("\n"); |
934 | printf("\n"); |
903 | depth = node->depth; |
935 | depth = node->depth; |
904 | } |
936 | } |
905 | 937 | ||
906 | printf("("); |
938 | printf("("); |
907 | for (i = 0; i < node->keys; i++) { |
939 | for (i = 0; i < node->keys; i++) { |
908 | printf("%d%s", node->key[i], i < node->keys - 1 ? "," : ""); |
940 | printf("%d%s", node->key[i], i < node->keys - 1 ? "," : ""); |
909 | if (node->depth && node->subtree[i]) { |
941 | if (node->depth && node->subtree[i]) { |
910 | list_append(&node->subtree[i]->bfs_link, &head); |
942 | list_append(&node->subtree[i]->bfs_link, &head); |
911 | } |
943 | } |
912 | } |
944 | } |
913 | if (node->depth && node->subtree[i]) { |
945 | if (node->depth && node->subtree[i]) { |
914 | list_append(&node->subtree[i]->bfs_link, &head); |
946 | list_append(&node->subtree[i]->bfs_link, &head); |
915 | } |
947 | } |
916 | printf(")"); |
948 | printf(")"); |
917 | } |
949 | } |
918 | printf("\n"); |
950 | printf("\n"); |
919 | 951 | ||
920 | printf("Printing list of leaves:\n"); |
952 | printf("Printing list of leaves:\n"); |
921 | for (cur = t->leaf_head.next; cur != &t->leaf_head; cur = cur->next) { |
953 | for (cur = t->leaf_head.next; cur != &t->leaf_head; cur = cur->next) { |
922 | btree_node_t *node; |
954 | btree_node_t *node; |
923 | 955 | ||
924 | node = list_get_instance(cur, btree_node_t, leaf_link); |
956 | node = list_get_instance(cur, btree_node_t, leaf_link); |
925 | 957 | ||
926 | ASSERT(node); |
958 | ASSERT(node); |
927 | 959 | ||
928 | printf("("); |
960 | printf("("); |
929 | for (i = 0; i < node->keys; i++) |
961 | for (i = 0; i < node->keys; i++) |
930 | printf("%d%s", node->key[i], i < node->keys - 1 ? "," : ""); |
962 | printf("%d%s", node->key[i], i < node->keys - 1 ? "," : ""); |
931 | printf(")"); |
963 | printf(")"); |
932 | } |
964 | } |
933 | printf("\n"); |
965 | printf("\n"); |
934 | } |
966 | } |
935 | 967 |