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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 | * @file btree.c |
|
- | 31 | * @brief B+tree implementation. |
|
- | 32 | * |
|
- | 33 | * This file implements B+tree type and operations. |
|
- | 34 | * |
|
30 | * This B-tree has the following properties: |
35 | * The B+tree has the following properties: |
31 | * - it is a ballanced 3-4-5 tree (i.e. BTREE_M = 5) |
36 | * @li it is a ballanced 3-4-5 tree (i.e. BTREE_M = 5) |
32 | * - values (i.e. pointers to values) are stored only in leaves |
37 | * @li values (i.e. pointers to values) are stored only in leaves |
33 | * - leaves are linked in a list |
38 | * @li leaves are linked in a list |
34 | * - technically, it is a B+tree (because of the previous properties) |
- | |
35 | * |
39 | * |
36 | * Be carefull when using these trees. They need to allocate |
40 | * Be carefull when using these trees. They need to allocate |
37 | * and deallocate memory for their index nodes and as such |
41 | * and deallocate memory for their index nodes and as such |
38 | * can sleep. |
42 | * can sleep. |
39 | */ |
43 | */ |
40 | 44 | ||
41 | #include <adt/btree.h> |
45 | #include <adt/btree.h> |
42 | #include <adt/list.h> |
46 | #include <adt/list.h> |
43 | #include <mm/slab.h> |
47 | #include <mm/slab.h> |
44 | #include <debug.h> |
48 | #include <debug.h> |
45 | #include <panic.h> |
49 | #include <panic.h> |
46 | #include <typedefs.h> |
50 | #include <typedefs.h> |
47 | #include <print.h> |
51 | #include <print.h> |
48 | 52 | ||
49 | static void _btree_insert(btree_t *t, btree_key_t key, void *value, btree_node_t *rsubtree, btree_node_t *node); |
53 | static void _btree_insert(btree_t *t, btree_key_t key, void *value, btree_node_t *rsubtree, btree_node_t *node); |
50 | static void _btree_remove(btree_t *t, btree_key_t key, btree_node_t *node); |
54 | static void _btree_remove(btree_t *t, btree_key_t key, btree_node_t *node); |
51 | static void node_initialize(btree_node_t *node); |
55 | static void node_initialize(btree_node_t *node); |
52 | static void node_insert_key_and_lsubtree(btree_node_t *node, btree_key_t key, void *value, btree_node_t *lsubtree); |
56 | static void node_insert_key_and_lsubtree(btree_node_t *node, btree_key_t key, void *value, btree_node_t *lsubtree); |
53 | static void node_insert_key_and_rsubtree(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree); |
57 | static void node_insert_key_and_rsubtree(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree); |
54 | static void node_remove_key_and_lsubtree(btree_node_t *node, btree_key_t key); |
58 | static void node_remove_key_and_lsubtree(btree_node_t *node, btree_key_t key); |
55 | static void node_remove_key_and_rsubtree(btree_node_t *node, btree_key_t key); |
59 | static void node_remove_key_and_rsubtree(btree_node_t *node, btree_key_t key); |
56 | static btree_node_t *node_split(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree, btree_key_t *median); |
60 | static btree_node_t *node_split(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree, btree_key_t *median); |
57 | static btree_node_t *node_combine(btree_node_t *node); |
61 | 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); |
62 | 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); |
63 | 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); |
64 | 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, btree_key_t key, void *value, btree_node_t *rsubtree); |
65 | static bool try_insert_by_rotation_to_left(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree); |
62 | static bool try_insert_by_rotation_to_right(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree); |
66 | static bool try_insert_by_rotation_to_right(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree); |
63 | static bool try_rotation_from_left(btree_node_t *rnode); |
67 | static bool try_rotation_from_left(btree_node_t *rnode); |
64 | static bool try_rotation_from_right(btree_node_t *lnode); |
68 | static bool try_rotation_from_right(btree_node_t *lnode); |
65 | 69 | ||
66 | #define ROOT_NODE(n) (!(n)->parent) |
70 | #define ROOT_NODE(n) (!(n)->parent) |
67 | #define INDEX_NODE(n) ((n)->subtree[0] != NULL) |
71 | #define INDEX_NODE(n) ((n)->subtree[0] != NULL) |
68 | #define LEAF_NODE(n) ((n)->subtree[0] == NULL) |
72 | #define LEAF_NODE(n) ((n)->subtree[0] == NULL) |
69 | 73 | ||
70 | #define FILL_FACTOR ((BTREE_M-1)/2) |
74 | #define FILL_FACTOR ((BTREE_M-1)/2) |
71 | 75 | ||
72 | #define MEDIAN_LOW_INDEX(n) (((n)->keys-1)/2) |
76 | #define MEDIAN_LOW_INDEX(n) (((n)->keys-1)/2) |
73 | #define MEDIAN_HIGH_INDEX(n) ((n)->keys/2) |
77 | #define MEDIAN_HIGH_INDEX(n) ((n)->keys/2) |
74 | #define MEDIAN_LOW(n) ((n)->key[MEDIAN_LOW_INDEX((n))]); |
78 | #define MEDIAN_LOW(n) ((n)->key[MEDIAN_LOW_INDEX((n))]); |
75 | #define MEDIAN_HIGH(n) ((n)->key[MEDIAN_HIGH_INDEX((n))]); |
79 | #define MEDIAN_HIGH(n) ((n)->key[MEDIAN_HIGH_INDEX((n))]); |
76 | 80 | ||
77 | static slab_cache_t *btree_node_slab; |
81 | static slab_cache_t *btree_node_slab; |
78 | 82 | ||
79 | /** Initialize B-trees. */ |
83 | /** Initialize B-trees. */ |
80 | void btree_init(void) |
84 | void btree_init(void) |
81 | { |
85 | { |
82 | btree_node_slab = slab_cache_create("btree_node_slab", sizeof(btree_node_t), 0, NULL, NULL, SLAB_CACHE_MAGDEFERRED); |
86 | btree_node_slab = slab_cache_create("btree_node_slab", sizeof(btree_node_t), 0, NULL, NULL, SLAB_CACHE_MAGDEFERRED); |
83 | } |
87 | } |
84 | 88 | ||
85 | /** Create empty B-tree. |
89 | /** Create empty B-tree. |
86 | * |
90 | * |
87 | * @param t B-tree. |
91 | * @param t B-tree. |
88 | */ |
92 | */ |
89 | void btree_create(btree_t *t) |
93 | void btree_create(btree_t *t) |
90 | { |
94 | { |
91 | list_initialize(&t->leaf_head); |
95 | list_initialize(&t->leaf_head); |
92 | t->root = (btree_node_t *) slab_alloc(btree_node_slab, 0); |
96 | t->root = (btree_node_t *) slab_alloc(btree_node_slab, 0); |
93 | node_initialize(t->root); |
97 | node_initialize(t->root); |
94 | list_append(&t->root->leaf_link, &t->leaf_head); |
98 | list_append(&t->root->leaf_link, &t->leaf_head); |
95 | } |
99 | } |
96 | 100 | ||
97 | /** Destroy empty B-tree. */ |
101 | /** Destroy empty B-tree. */ |
98 | void btree_destroy(btree_t *t) |
102 | void btree_destroy(btree_t *t) |
99 | { |
103 | { |
100 | ASSERT(!t->root->keys); |
104 | ASSERT(!t->root->keys); |
101 | slab_free(btree_node_slab, t->root); |
105 | slab_free(btree_node_slab, t->root); |
102 | } |
106 | } |
103 | 107 | ||
104 | /** Insert key-value pair into B-tree. |
108 | /** Insert key-value pair into B-tree. |
105 | * |
109 | * |
106 | * @param t B-tree. |
110 | * @param t B-tree. |
107 | * @param key Key to be inserted. |
111 | * @param key Key to be inserted. |
108 | * @param value Value to be inserted. |
112 | * @param value Value to be inserted. |
109 | * @param leaf_node Leaf node where the insertion should begin. |
113 | * @param leaf_node Leaf node where the insertion should begin. |
110 | */ |
114 | */ |
111 | void btree_insert(btree_t *t, btree_key_t key, void *value, btree_node_t *leaf_node) |
115 | void btree_insert(btree_t *t, btree_key_t key, void *value, btree_node_t *leaf_node) |
112 | { |
116 | { |
113 | btree_node_t *lnode; |
117 | btree_node_t *lnode; |
114 | 118 | ||
115 | ASSERT(value); |
119 | ASSERT(value); |
116 | 120 | ||
117 | lnode = leaf_node; |
121 | lnode = leaf_node; |
118 | if (!lnode) { |
122 | if (!lnode) { |
119 | if (btree_search(t, key, &lnode)) { |
123 | if (btree_search(t, key, &lnode)) { |
120 | panic("B-tree %p already contains key %d\n", t, key); |
124 | panic("B-tree %p already contains key %d\n", t, key); |
121 | } |
125 | } |
122 | } |
126 | } |
123 | 127 | ||
124 | _btree_insert(t, key, value, NULL, lnode); |
128 | _btree_insert(t, key, value, NULL, lnode); |
125 | } |
129 | } |
126 | 130 | ||
127 | /** Recursively insert into B-tree. |
131 | /** Recursively insert into B-tree. |
128 | * |
132 | * |
129 | * @param t B-tree. |
133 | * @param t B-tree. |
130 | * @param key Key to be inserted. |
134 | * @param key Key to be inserted. |
131 | * @param value Value to be inserted. |
135 | * @param value Value to be inserted. |
132 | * @param rsubtree Right subtree of the inserted key. |
136 | * @param rsubtree Right subtree of the inserted key. |
133 | * @param node Start inserting into this node. |
137 | * @param node Start inserting into this node. |
134 | */ |
138 | */ |
135 | void _btree_insert(btree_t *t, btree_key_t key, void *value, btree_node_t *rsubtree, btree_node_t *node) |
139 | void _btree_insert(btree_t *t, btree_key_t key, void *value, btree_node_t *rsubtree, btree_node_t *node) |
136 | { |
140 | { |
137 | if (node->keys < BTREE_MAX_KEYS) { |
141 | if (node->keys < BTREE_MAX_KEYS) { |
138 | /* |
142 | /* |
139 | * Node conatins enough space, the key can be stored immediately. |
143 | * Node conatins enough space, the key can be stored immediately. |
140 | */ |
144 | */ |
141 | node_insert_key_and_rsubtree(node, key, value, rsubtree); |
145 | node_insert_key_and_rsubtree(node, key, value, rsubtree); |
142 | } else if (try_insert_by_rotation_to_left(node, key, value, rsubtree)) { |
146 | } else if (try_insert_by_rotation_to_left(node, key, value, rsubtree)) { |
143 | /* |
147 | /* |
144 | * The key-value-rsubtree triplet has been inserted because |
148 | * The key-value-rsubtree triplet has been inserted because |
145 | * some keys could have been moved to the left sibling. |
149 | * some keys could have been moved to the left sibling. |
146 | */ |
150 | */ |
147 | } else if (try_insert_by_rotation_to_right(node, key, value, rsubtree)) { |
151 | } else if (try_insert_by_rotation_to_right(node, key, value, rsubtree)) { |
148 | /* |
152 | /* |
149 | * The key-value-rsubtree triplet has been inserted because |
153 | * The key-value-rsubtree triplet has been inserted because |
150 | * some keys could have been moved to the right sibling. |
154 | * some keys could have been moved to the right sibling. |
151 | */ |
155 | */ |
152 | } else { |
156 | } else { |
153 | btree_node_t *rnode; |
157 | btree_node_t *rnode; |
154 | btree_key_t median; |
158 | btree_key_t median; |
155 | 159 | ||
156 | /* |
160 | /* |
157 | * Node is full and both siblings (if both exist) are full too. |
161 | * Node is full and both siblings (if both exist) are full too. |
158 | * Split the node and insert the smallest key from the node containing |
162 | * Split the node and insert the smallest key from the node containing |
159 | * bigger keys (i.e. the new node) into its parent. |
163 | * bigger keys (i.e. the new node) into its parent. |
160 | */ |
164 | */ |
161 | 165 | ||
162 | rnode = node_split(node, key, value, rsubtree, &median); |
166 | rnode = node_split(node, key, value, rsubtree, &median); |
163 | 167 | ||
164 | if (LEAF_NODE(node)) { |
168 | if (LEAF_NODE(node)) { |
165 | list_prepend(&rnode->leaf_link, &node->leaf_link); |
169 | list_prepend(&rnode->leaf_link, &node->leaf_link); |
166 | } |
170 | } |
167 | 171 | ||
168 | if (ROOT_NODE(node)) { |
172 | if (ROOT_NODE(node)) { |
169 | /* |
173 | /* |
170 | * We split the root node. Create new root. |
174 | * We split the root node. Create new root. |
171 | */ |
175 | */ |
172 | t->root = (btree_node_t *) slab_alloc(btree_node_slab, 0); |
176 | t->root = (btree_node_t *) slab_alloc(btree_node_slab, 0); |
173 | node->parent = t->root; |
177 | node->parent = t->root; |
174 | rnode->parent = t->root; |
178 | rnode->parent = t->root; |
175 | node_initialize(t->root); |
179 | node_initialize(t->root); |
176 | 180 | ||
177 | /* |
181 | /* |
178 | * Left-hand side subtree will be the old root (i.e. node). |
182 | * Left-hand side subtree will be the old root (i.e. node). |
179 | * Right-hand side subtree will be rnode. |
183 | * Right-hand side subtree will be rnode. |
180 | */ |
184 | */ |
181 | t->root->subtree[0] = node; |
185 | t->root->subtree[0] = node; |
182 | 186 | ||
183 | t->root->depth = node->depth + 1; |
187 | t->root->depth = node->depth + 1; |
184 | } |
188 | } |
185 | _btree_insert(t, median, NULL, rnode, node->parent); |
189 | _btree_insert(t, median, NULL, rnode, node->parent); |
186 | } |
190 | } |
187 | 191 | ||
188 | } |
192 | } |
189 | 193 | ||
190 | /** Remove B-tree node. |
194 | /** Remove B-tree node. |
191 | * |
195 | * |
192 | * @param B-tree. |
196 | * @param B-tree. |
193 | * @param key Key to be removed from the B-tree along with its associated value. |
197 | * @param key Key to be removed from the B-tree along with its associated value. |
194 | * @param leaf_node If not NULL, pointer to the leaf node where the key is found. |
198 | * @param leaf_node If not NULL, pointer to the leaf node where the key is found. |
195 | */ |
199 | */ |
196 | void btree_remove(btree_t *t, btree_key_t key, btree_node_t *leaf_node) |
200 | void btree_remove(btree_t *t, btree_key_t key, btree_node_t *leaf_node) |
197 | { |
201 | { |
198 | btree_node_t *lnode; |
202 | btree_node_t *lnode; |
199 | 203 | ||
200 | lnode = leaf_node; |
204 | lnode = leaf_node; |
201 | if (!lnode) { |
205 | if (!lnode) { |
202 | if (!btree_search(t, key, &lnode)) { |
206 | if (!btree_search(t, key, &lnode)) { |
203 | panic("B-tree %p does not contain key %d\n", t, key); |
207 | panic("B-tree %p does not contain key %d\n", t, key); |
204 | } |
208 | } |
205 | } |
209 | } |
206 | 210 | ||
207 | _btree_remove(t, key, lnode); |
211 | _btree_remove(t, key, lnode); |
208 | } |
212 | } |
209 | 213 | ||
210 | /** Recursively remove B-tree node. |
214 | /** Recursively remove B-tree node. |
211 | * |
215 | * |
212 | * @param B-tree. |
216 | * @param B-tree. |
213 | * @param key Key to be removed from the B-tree along with its associated value. |
217 | * @param key Key to be removed from the B-tree along with its associated value. |
214 | * @param node Node where the key being removed resides. |
218 | * @param node Node where the key being removed resides. |
215 | */ |
219 | */ |
216 | void _btree_remove(btree_t *t, btree_key_t key, btree_node_t *node) |
220 | void _btree_remove(btree_t *t, btree_key_t key, btree_node_t *node) |
217 | { |
221 | { |
218 | if (ROOT_NODE(node)) { |
222 | if (ROOT_NODE(node)) { |
219 | if (node->keys == 1 && node->subtree[0]) { |
223 | if (node->keys == 1 && node->subtree[0]) { |
220 | /* |
224 | /* |
221 | * Free the current root and set new root. |
225 | * Free the current root and set new root. |
222 | */ |
226 | */ |
223 | t->root = node->subtree[0]; |
227 | t->root = node->subtree[0]; |
224 | t->root->parent = NULL; |
228 | t->root->parent = NULL; |
225 | slab_free(btree_node_slab, node); |
229 | slab_free(btree_node_slab, node); |
226 | } else { |
230 | } else { |
227 | /* |
231 | /* |
228 | * Remove the key from the root node. |
232 | * Remove the key from the root node. |
229 | * Note that the right subtree is removed because when |
233 | * Note that the right subtree is removed because when |
230 | * combining two nodes, the left-side sibling is preserved |
234 | * combining two nodes, the left-side sibling is preserved |
231 | * and the right-side sibling is freed. |
235 | * and the right-side sibling is freed. |
232 | */ |
236 | */ |
233 | node_remove_key_and_rsubtree(node, key); |
237 | node_remove_key_and_rsubtree(node, key); |
234 | } |
238 | } |
235 | return; |
239 | return; |
236 | } |
240 | } |
237 | 241 | ||
238 | if (node->keys <= FILL_FACTOR) { |
242 | if (node->keys <= FILL_FACTOR) { |
239 | /* |
243 | /* |
240 | * If the node is below the fill factor, |
244 | * If the node is below the fill factor, |
241 | * try to borrow keys from left or right sibling. |
245 | * try to borrow keys from left or right sibling. |
242 | */ |
246 | */ |
243 | if (!try_rotation_from_left(node)) |
247 | if (!try_rotation_from_left(node)) |
244 | try_rotation_from_right(node); |
248 | try_rotation_from_right(node); |
245 | } |
249 | } |
246 | 250 | ||
247 | if (node->keys > FILL_FACTOR) { |
251 | if (node->keys > FILL_FACTOR) { |
248 | int i; |
252 | int i; |
249 | 253 | ||
250 | /* |
254 | /* |
251 | * The key can be immediatelly removed. |
255 | * The key can be immediatelly removed. |
252 | * |
256 | * |
253 | * Note that the right subtree is removed because when |
257 | * Note that the right subtree is removed because when |
254 | * combining two nodes, the left-side sibling is preserved |
258 | * combining two nodes, the left-side sibling is preserved |
255 | * and the right-side sibling is freed. |
259 | * and the right-side sibling is freed. |
256 | */ |
260 | */ |
257 | node_remove_key_and_rsubtree(node, key); |
261 | node_remove_key_and_rsubtree(node, key); |
258 | for (i = 0; i < node->parent->keys; i++) { |
262 | for (i = 0; i < node->parent->keys; i++) { |
259 | if (node->parent->key[i] == key) |
263 | if (node->parent->key[i] == key) |
260 | node->parent->key[i] = node->key[0]; |
264 | node->parent->key[i] = node->key[0]; |
261 | } |
265 | } |
262 | 266 | ||
263 | } else { |
267 | } else { |
264 | index_t idx; |
268 | index_t idx; |
265 | btree_node_t *rnode, *parent; |
269 | btree_node_t *rnode, *parent; |
266 | 270 | ||
267 | /* |
271 | /* |
268 | * The node is below the fill factor as well as its left and right sibling. |
272 | * The node is below the fill factor as well as its left and right sibling. |
269 | * Resort to combining the node with one of its siblings. |
273 | * Resort to combining the node with one of its siblings. |
270 | * The node which is on the left is preserved and the node on the right is |
274 | * The node which is on the left is preserved and the node on the right is |
271 | * freed. |
275 | * freed. |
272 | */ |
276 | */ |
273 | parent = node->parent; |
277 | parent = node->parent; |
274 | node_remove_key_and_rsubtree(node, key); |
278 | node_remove_key_and_rsubtree(node, key); |
275 | rnode = node_combine(node); |
279 | rnode = node_combine(node); |
276 | if (LEAF_NODE(rnode)) |
280 | if (LEAF_NODE(rnode)) |
277 | list_remove(&rnode->leaf_link); |
281 | list_remove(&rnode->leaf_link); |
278 | idx = find_key_by_subtree(parent, rnode, true); |
282 | idx = find_key_by_subtree(parent, rnode, true); |
279 | ASSERT((int) idx != -1); |
283 | ASSERT((int) idx != -1); |
280 | slab_free(btree_node_slab, rnode); |
284 | slab_free(btree_node_slab, rnode); |
281 | _btree_remove(t, parent->key[idx], parent); |
285 | _btree_remove(t, parent->key[idx], parent); |
282 | } |
286 | } |
283 | } |
287 | } |
284 | 288 | ||
285 | /** Search key in a B-tree. |
289 | /** Search key in a B-tree. |
286 | * |
290 | * |
287 | * @param t B-tree. |
291 | * @param t B-tree. |
288 | * @param key Key to be searched. |
292 | * @param key Key to be searched. |
289 | * @param leaf_node Address where to put pointer to visited leaf node. |
293 | * @param leaf_node Address where to put pointer to visited leaf node. |
290 | * |
294 | * |
291 | * @return Pointer to value or NULL if there is no such key. |
295 | * @return Pointer to value or NULL if there is no such key. |
292 | */ |
296 | */ |
293 | void *btree_search(btree_t *t, btree_key_t key, btree_node_t **leaf_node) |
297 | void *btree_search(btree_t *t, btree_key_t key, btree_node_t **leaf_node) |
294 | { |
298 | { |
295 | btree_node_t *cur, *next; |
299 | btree_node_t *cur, *next; |
296 | 300 | ||
297 | /* |
301 | /* |
298 | * Iteratively descend to the leaf that can contain the searched key. |
302 | * Iteratively descend to the leaf that can contain the searched key. |
299 | */ |
303 | */ |
300 | for (cur = t->root; cur; cur = next) { |
304 | for (cur = t->root; cur; cur = next) { |
301 | 305 | ||
302 | /* Last iteration will set this with proper leaf node address. */ |
306 | /* Last iteration will set this with proper leaf node address. */ |
303 | *leaf_node = cur; |
307 | *leaf_node = cur; |
304 | 308 | ||
305 | /* |
309 | /* |
306 | * The key can be in the leftmost subtree. |
310 | * The key can be in the leftmost subtree. |
307 | * Test it separately. |
311 | * Test it separately. |
308 | */ |
312 | */ |
309 | if (key < cur->key[0]) { |
313 | if (key < cur->key[0]) { |
310 | next = cur->subtree[0]; |
314 | next = cur->subtree[0]; |
311 | continue; |
315 | continue; |
312 | } else { |
316 | } else { |
313 | void *val; |
317 | void *val; |
314 | int i; |
318 | int i; |
315 | 319 | ||
316 | /* |
320 | /* |
317 | * Now if the key is smaller than cur->key[i] |
321 | * Now if the key is smaller than cur->key[i] |
318 | * it can only mean that the value is in cur->subtree[i] |
322 | * it can only mean that the value is in cur->subtree[i] |
319 | * or it is not in the tree at all. |
323 | * or it is not in the tree at all. |
320 | */ |
324 | */ |
321 | for (i = 1; i < cur->keys; i++) { |
325 | for (i = 1; i < cur->keys; i++) { |
322 | if (key < cur->key[i]) { |
326 | if (key < cur->key[i]) { |
323 | next = cur->subtree[i]; |
327 | next = cur->subtree[i]; |
324 | val = cur->value[i - 1]; |
328 | val = cur->value[i - 1]; |
325 | 329 | ||
326 | if (LEAF_NODE(cur)) |
330 | if (LEAF_NODE(cur)) |
327 | return key == cur->key[i - 1] ? val : NULL; |
331 | return key == cur->key[i - 1] ? val : NULL; |
328 | 332 | ||
329 | goto descend; |
333 | goto descend; |
330 | } |
334 | } |
331 | } |
335 | } |
332 | 336 | ||
333 | /* |
337 | /* |
334 | * Last possibility is that the key is in the rightmost subtree. |
338 | * Last possibility is that the key is in the rightmost subtree. |
335 | */ |
339 | */ |
336 | next = cur->subtree[i]; |
340 | next = cur->subtree[i]; |
337 | val = cur->value[i - 1]; |
341 | val = cur->value[i - 1]; |
338 | if (LEAF_NODE(cur)) |
342 | if (LEAF_NODE(cur)) |
339 | return key == cur->key[i - 1] ? val : NULL; |
343 | return key == cur->key[i - 1] ? val : NULL; |
340 | } |
344 | } |
341 | descend: |
345 | descend: |
342 | ; |
346 | ; |
343 | } |
347 | } |
344 | 348 | ||
345 | /* |
349 | /* |
346 | * The key was not found in the *leaf_node and is smaller than any of its keys. |
350 | * The key was not found in the *leaf_node and is smaller than any of its keys. |
347 | */ |
351 | */ |
348 | return NULL; |
352 | return NULL; |
349 | } |
353 | } |
350 | 354 | ||
351 | /** Return pointer to B-tree leaf node's left neighbour. |
355 | /** Return pointer to B-tree leaf node's left neighbour. |
352 | * |
356 | * |
353 | * @param t B-tree. |
357 | * @param t B-tree. |
354 | * @param node Node whose left neighbour will be returned. |
358 | * @param node Node whose left neighbour will be returned. |
355 | * |
359 | * |
356 | * @return Left neighbour of the node or NULL if the node does not have the left neighbour. |
360 | * @return Left neighbour of the node or NULL if the node does not have the left neighbour. |
357 | */ |
361 | */ |
358 | btree_node_t *btree_leaf_node_left_neighbour(btree_t *t, btree_node_t *node) |
362 | btree_node_t *btree_leaf_node_left_neighbour(btree_t *t, btree_node_t *node) |
359 | { |
363 | { |
360 | ASSERT(LEAF_NODE(node)); |
364 | ASSERT(LEAF_NODE(node)); |
361 | if (node->leaf_link.prev != &t->leaf_head) |
365 | if (node->leaf_link.prev != &t->leaf_head) |
362 | return list_get_instance(node->leaf_link.prev, btree_node_t, leaf_link); |
366 | return list_get_instance(node->leaf_link.prev, btree_node_t, leaf_link); |
363 | else |
367 | else |
364 | return NULL; |
368 | return NULL; |
365 | } |
369 | } |
366 | 370 | ||
367 | /** Return pointer to B-tree leaf node's right neighbour. |
371 | /** Return pointer to B-tree leaf node's right neighbour. |
368 | * |
372 | * |
369 | * @param t B-tree. |
373 | * @param t B-tree. |
370 | * @param node Node whose right neighbour will be returned. |
374 | * @param node Node whose right neighbour will be returned. |
371 | * |
375 | * |
372 | * @return Right neighbour of the node or NULL if the node does not have the right neighbour. |
376 | * @return Right neighbour of the node or NULL if the node does not have the right neighbour. |
373 | */ |
377 | */ |
374 | btree_node_t *btree_leaf_node_right_neighbour(btree_t *t, btree_node_t *node) |
378 | btree_node_t *btree_leaf_node_right_neighbour(btree_t *t, btree_node_t *node) |
375 | { |
379 | { |
376 | ASSERT(LEAF_NODE(node)); |
380 | ASSERT(LEAF_NODE(node)); |
377 | if (node->leaf_link.next != &t->leaf_head) |
381 | if (node->leaf_link.next != &t->leaf_head) |
378 | return list_get_instance(node->leaf_link.next, btree_node_t, leaf_link); |
382 | return list_get_instance(node->leaf_link.next, btree_node_t, leaf_link); |
379 | else |
383 | else |
380 | return NULL; |
384 | return NULL; |
381 | } |
385 | } |
382 | 386 | ||
383 | /** Initialize B-tree node. |
387 | /** Initialize B-tree node. |
384 | * |
388 | * |
385 | * @param node B-tree node. |
389 | * @param node B-tree node. |
386 | */ |
390 | */ |
387 | void node_initialize(btree_node_t *node) |
391 | void node_initialize(btree_node_t *node) |
388 | { |
392 | { |
389 | int i; |
393 | int i; |
390 | 394 | ||
391 | node->keys = 0; |
395 | node->keys = 0; |
392 | 396 | ||
393 | /* Clean also space for the extra key. */ |
397 | /* Clean also space for the extra key. */ |
394 | for (i = 0; i < BTREE_MAX_KEYS + 1; i++) { |
398 | for (i = 0; i < BTREE_MAX_KEYS + 1; i++) { |
395 | node->key[i] = 0; |
399 | node->key[i] = 0; |
396 | node->value[i] = NULL; |
400 | node->value[i] = NULL; |
397 | node->subtree[i] = NULL; |
401 | node->subtree[i] = NULL; |
398 | } |
402 | } |
399 | node->subtree[i] = NULL; |
403 | node->subtree[i] = NULL; |
400 | 404 | ||
401 | node->parent = NULL; |
405 | node->parent = NULL; |
402 | 406 | ||
403 | link_initialize(&node->leaf_link); |
407 | link_initialize(&node->leaf_link); |
404 | 408 | ||
405 | link_initialize(&node->bfs_link); |
409 | link_initialize(&node->bfs_link); |
406 | node->depth = 0; |
410 | node->depth = 0; |
407 | } |
411 | } |
408 | 412 | ||
409 | /** Insert key-value-lsubtree triplet into B-tree node. |
413 | /** Insert key-value-lsubtree triplet into B-tree node. |
410 | * |
414 | * |
411 | * It is actually possible to have more keys than BTREE_MAX_KEYS. |
415 | * It is actually possible to have more keys than BTREE_MAX_KEYS. |
412 | * This feature is used during insert by right rotation. |
416 | * This feature is used during insert by right rotation. |
413 | * |
417 | * |
414 | * @param node B-tree node into wich the new key is to be inserted. |
418 | * @param node B-tree node into wich the new key is to be inserted. |
415 | * @param key The key to be inserted. |
419 | * @param key The key to be inserted. |
416 | * @param value Pointer to value to be inserted. |
420 | * @param value Pointer to value to be inserted. |
417 | * @param lsubtree Pointer to the left subtree. |
421 | * @param lsubtree Pointer to the left subtree. |
418 | */ |
422 | */ |
419 | void node_insert_key_and_lsubtree(btree_node_t *node, btree_key_t key, void *value, btree_node_t *lsubtree) |
423 | void node_insert_key_and_lsubtree(btree_node_t *node, btree_key_t key, void *value, btree_node_t *lsubtree) |
420 | { |
424 | { |
421 | int i; |
425 | int i; |
422 | 426 | ||
423 | for (i = 0; i < node->keys; i++) { |
427 | for (i = 0; i < node->keys; i++) { |
424 | if (key < node->key[i]) { |
428 | if (key < node->key[i]) { |
425 | int j; |
429 | int j; |
426 | 430 | ||
427 | for (j = node->keys; j > i; j--) { |
431 | for (j = node->keys; j > i; j--) { |
428 | node->key[j] = node->key[j - 1]; |
432 | node->key[j] = node->key[j - 1]; |
429 | node->value[j] = node->value[j - 1]; |
433 | node->value[j] = node->value[j - 1]; |
430 | node->subtree[j + 1] = node->subtree[j]; |
434 | node->subtree[j + 1] = node->subtree[j]; |
431 | } |
435 | } |
432 | node->subtree[j + 1] = node->subtree[j]; |
436 | node->subtree[j + 1] = node->subtree[j]; |
433 | break; |
437 | break; |
434 | } |
438 | } |
435 | } |
439 | } |
436 | node->key[i] = key; |
440 | node->key[i] = key; |
437 | node->value[i] = value; |
441 | node->value[i] = value; |
438 | node->subtree[i] = lsubtree; |
442 | node->subtree[i] = lsubtree; |
439 | 443 | ||
440 | node->keys++; |
444 | node->keys++; |
441 | } |
445 | } |
442 | 446 | ||
443 | /** Insert key-value-rsubtree triplet into B-tree node. |
447 | /** Insert key-value-rsubtree triplet into B-tree node. |
444 | * |
448 | * |
445 | * It is actually possible to have more keys than BTREE_MAX_KEYS. |
449 | * It is actually possible to have more keys than BTREE_MAX_KEYS. |
446 | * This feature is used during splitting the node when the |
450 | * This feature is used during splitting the node when the |
447 | * number of keys is BTREE_MAX_KEYS + 1. Insert by left rotation |
451 | * number of keys is BTREE_MAX_KEYS + 1. Insert by left rotation |
448 | * also makes use of this feature. |
452 | * also makes use of this feature. |
449 | * |
453 | * |
450 | * @param node B-tree node into wich the new key is to be inserted. |
454 | * @param node B-tree node into wich the new key is to be inserted. |
451 | * @param key The key to be inserted. |
455 | * @param key The key to be inserted. |
452 | * @param value Pointer to value to be inserted. |
456 | * @param value Pointer to value to be inserted. |
453 | * @param rsubtree Pointer to the right subtree. |
457 | * @param rsubtree Pointer to the right subtree. |
454 | */ |
458 | */ |
455 | void node_insert_key_and_rsubtree(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree) |
459 | void node_insert_key_and_rsubtree(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree) |
456 | { |
460 | { |
457 | int i; |
461 | int i; |
458 | 462 | ||
459 | for (i = 0; i < node->keys; i++) { |
463 | for (i = 0; i < node->keys; i++) { |
460 | if (key < node->key[i]) { |
464 | if (key < node->key[i]) { |
461 | int j; |
465 | int j; |
462 | 466 | ||
463 | for (j = node->keys; j > i; j--) { |
467 | for (j = node->keys; j > i; j--) { |
464 | node->key[j] = node->key[j - 1]; |
468 | node->key[j] = node->key[j - 1]; |
465 | node->value[j] = node->value[j - 1]; |
469 | node->value[j] = node->value[j - 1]; |
466 | node->subtree[j + 1] = node->subtree[j]; |
470 | node->subtree[j + 1] = node->subtree[j]; |
467 | } |
471 | } |
468 | break; |
472 | break; |
469 | } |
473 | } |
470 | } |
474 | } |
471 | node->key[i] = key; |
475 | node->key[i] = key; |
472 | node->value[i] = value; |
476 | node->value[i] = value; |
473 | node->subtree[i + 1] = rsubtree; |
477 | node->subtree[i + 1] = rsubtree; |
474 | 478 | ||
475 | node->keys++; |
479 | node->keys++; |
476 | } |
480 | } |
477 | 481 | ||
478 | /** Remove key and its left subtree pointer from B-tree node. |
482 | /** Remove key and its left subtree pointer from B-tree node. |
479 | * |
483 | * |
480 | * Remove the key and eliminate gaps in node->key array. |
484 | * Remove the key and eliminate gaps in node->key array. |
481 | * Note that the value pointer and the left subtree pointer |
485 | * Note that the value pointer and the left subtree pointer |
482 | * is removed from the node as well. |
486 | * is removed from the node as well. |
483 | * |
487 | * |
484 | * @param node B-tree node. |
488 | * @param node B-tree node. |
485 | * @param key Key to be removed. |
489 | * @param key Key to be removed. |
486 | */ |
490 | */ |
487 | void node_remove_key_and_lsubtree(btree_node_t *node, btree_key_t key) |
491 | void node_remove_key_and_lsubtree(btree_node_t *node, btree_key_t key) |
488 | { |
492 | { |
489 | int i, j; |
493 | int i, j; |
490 | 494 | ||
491 | for (i = 0; i < node->keys; i++) { |
495 | for (i = 0; i < node->keys; i++) { |
492 | if (key == node->key[i]) { |
496 | if (key == node->key[i]) { |
493 | for (j = i + 1; j < node->keys; j++) { |
497 | for (j = i + 1; j < node->keys; j++) { |
494 | node->key[j - 1] = node->key[j]; |
498 | node->key[j - 1] = node->key[j]; |
495 | node->value[j - 1] = node->value[j]; |
499 | node->value[j - 1] = node->value[j]; |
496 | node->subtree[j - 1] = node->subtree[j]; |
500 | node->subtree[j - 1] = node->subtree[j]; |
497 | } |
501 | } |
498 | node->subtree[j - 1] = node->subtree[j]; |
502 | node->subtree[j - 1] = node->subtree[j]; |
499 | node->keys--; |
503 | node->keys--; |
500 | return; |
504 | return; |
501 | } |
505 | } |
502 | } |
506 | } |
503 | panic("node %p does not contain key %d\n", node, key); |
507 | panic("node %p does not contain key %d\n", node, key); |
504 | } |
508 | } |
505 | 509 | ||
506 | /** Remove key and its right subtree pointer from B-tree node. |
510 | /** Remove key and its right subtree pointer from B-tree node. |
507 | * |
511 | * |
508 | * Remove the key and eliminate gaps in node->key array. |
512 | * Remove the key and eliminate gaps in node->key array. |
509 | * Note that the value pointer and the right subtree pointer |
513 | * Note that the value pointer and the right subtree pointer |
510 | * is removed from the node as well. |
514 | * is removed from the node as well. |
511 | * |
515 | * |
512 | * @param node B-tree node. |
516 | * @param node B-tree node. |
513 | * @param key Key to be removed. |
517 | * @param key Key to be removed. |
514 | */ |
518 | */ |
515 | void node_remove_key_and_rsubtree(btree_node_t *node, btree_key_t key) |
519 | void node_remove_key_and_rsubtree(btree_node_t *node, btree_key_t key) |
516 | { |
520 | { |
517 | int i, j; |
521 | int i, j; |
518 | 522 | ||
519 | for (i = 0; i < node->keys; i++) { |
523 | for (i = 0; i < node->keys; i++) { |
520 | if (key == node->key[i]) { |
524 | if (key == node->key[i]) { |
521 | for (j = i + 1; j < node->keys; j++) { |
525 | for (j = i + 1; j < node->keys; j++) { |
522 | node->key[j - 1] = node->key[j]; |
526 | node->key[j - 1] = node->key[j]; |
523 | node->value[j - 1] = node->value[j]; |
527 | node->value[j - 1] = node->value[j]; |
524 | node->subtree[j] = node->subtree[j + 1]; |
528 | node->subtree[j] = node->subtree[j + 1]; |
525 | } |
529 | } |
526 | node->keys--; |
530 | node->keys--; |
527 | return; |
531 | return; |
528 | } |
532 | } |
529 | } |
533 | } |
530 | panic("node %p does not contain key %d\n", node, key); |
534 | panic("node %p does not contain key %d\n", node, key); |
531 | } |
535 | } |
532 | 536 | ||
533 | /** Split full B-tree node and insert new key-value-right-subtree triplet. |
537 | /** Split full B-tree node and insert new key-value-right-subtree triplet. |
534 | * |
538 | * |
535 | * This function will split a node and return pointer to a newly created |
539 | * This function will split a node and return pointer to a newly created |
536 | * node containing keys greater than or equal to the greater of medians |
540 | * node containing keys greater than or equal to the greater of medians |
537 | * (or median) of the old keys and the newly added key. It will also write |
541 | * (or median) of the old keys and the newly added key. It will also write |
538 | * the median key to a memory address supplied by the caller. |
542 | * the median key to a memory address supplied by the caller. |
539 | * |
543 | * |
540 | * If the node being split is an index node, the median will not be |
544 | * If the node being split is an index node, the median will not be |
541 | * included in the new node. If the node is a leaf node, |
545 | * included in the new node. If the node is a leaf node, |
542 | * the median will be copied there. |
546 | * the median will be copied there. |
543 | * |
547 | * |
544 | * @param node B-tree node wich is going to be split. |
548 | * @param node B-tree node wich is going to be split. |
545 | * @param key The key to be inserted. |
549 | * @param key The key to be inserted. |
546 | * @param value Pointer to the value to be inserted. |
550 | * @param value Pointer to the value to be inserted. |
547 | * @param rsubtree Pointer to the right subtree of the key being added. |
551 | * @param rsubtree Pointer to the right subtree of the key being added. |
548 | * @param median Address in memory, where the median key will be stored. |
552 | * @param median Address in memory, where the median key will be stored. |
549 | * |
553 | * |
550 | * @return Newly created right sibling of node. |
554 | * @return Newly created right sibling of node. |
551 | */ |
555 | */ |
552 | btree_node_t *node_split(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree, btree_key_t *median) |
556 | btree_node_t *node_split(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree, btree_key_t *median) |
553 | { |
557 | { |
554 | btree_node_t *rnode; |
558 | btree_node_t *rnode; |
555 | int i, j; |
559 | int i, j; |
556 | 560 | ||
557 | ASSERT(median); |
561 | ASSERT(median); |
558 | ASSERT(node->keys == BTREE_MAX_KEYS); |
562 | ASSERT(node->keys == BTREE_MAX_KEYS); |
559 | 563 | ||
560 | /* |
564 | /* |
561 | * Use the extra space to store the extra node. |
565 | * Use the extra space to store the extra node. |
562 | */ |
566 | */ |
563 | node_insert_key_and_rsubtree(node, key, value, rsubtree); |
567 | node_insert_key_and_rsubtree(node, key, value, rsubtree); |
564 | 568 | ||
565 | /* |
569 | /* |
566 | * Compute median of keys. |
570 | * Compute median of keys. |
567 | */ |
571 | */ |
568 | *median = MEDIAN_HIGH(node); |
572 | *median = MEDIAN_HIGH(node); |
569 | 573 | ||
570 | /* |
574 | /* |
571 | * Allocate and initialize new right sibling. |
575 | * Allocate and initialize new right sibling. |
572 | */ |
576 | */ |
573 | rnode = (btree_node_t *) slab_alloc(btree_node_slab, 0); |
577 | rnode = (btree_node_t *) slab_alloc(btree_node_slab, 0); |
574 | node_initialize(rnode); |
578 | node_initialize(rnode); |
575 | rnode->parent = node->parent; |
579 | rnode->parent = node->parent; |
576 | rnode->depth = node->depth; |
580 | rnode->depth = node->depth; |
577 | 581 | ||
578 | /* |
582 | /* |
579 | * Copy big keys, values and subtree pointers to the new right sibling. |
583 | * Copy big keys, values and subtree pointers to the new right sibling. |
580 | * If this is an index node, do not copy the median. |
584 | * If this is an index node, do not copy the median. |
581 | */ |
585 | */ |
582 | i = (int) INDEX_NODE(node); |
586 | i = (int) INDEX_NODE(node); |
583 | for (i += MEDIAN_HIGH_INDEX(node), j = 0; i < node->keys; i++, j++) { |
587 | for (i += MEDIAN_HIGH_INDEX(node), j = 0; i < node->keys; i++, j++) { |
584 | rnode->key[j] = node->key[i]; |
588 | rnode->key[j] = node->key[i]; |
585 | rnode->value[j] = node->value[i]; |
589 | rnode->value[j] = node->value[i]; |
586 | rnode->subtree[j] = node->subtree[i]; |
590 | rnode->subtree[j] = node->subtree[i]; |
587 | 591 | ||
588 | /* |
592 | /* |
589 | * Fix parent links in subtrees. |
593 | * Fix parent links in subtrees. |
590 | */ |
594 | */ |
591 | if (rnode->subtree[j]) |
595 | if (rnode->subtree[j]) |
592 | rnode->subtree[j]->parent = rnode; |
596 | rnode->subtree[j]->parent = rnode; |
593 | 597 | ||
594 | } |
598 | } |
595 | rnode->subtree[j] = node->subtree[i]; |
599 | rnode->subtree[j] = node->subtree[i]; |
596 | if (rnode->subtree[j]) |
600 | if (rnode->subtree[j]) |
597 | rnode->subtree[j]->parent = rnode; |
601 | rnode->subtree[j]->parent = rnode; |
598 | 602 | ||
599 | rnode->keys = j; /* Set number of keys of the new node. */ |
603 | rnode->keys = j; /* Set number of keys of the new node. */ |
600 | node->keys /= 2; /* Shrink the old node. */ |
604 | node->keys /= 2; /* Shrink the old node. */ |
601 | 605 | ||
602 | return rnode; |
606 | return rnode; |
603 | } |
607 | } |
604 | 608 | ||
605 | /** Combine node with any of its siblings. |
609 | /** Combine node with any of its siblings. |
606 | * |
610 | * |
607 | * The siblings are required to be below the fill factor. |
611 | * The siblings are required to be below the fill factor. |
608 | * |
612 | * |
609 | * @param node Node to combine with one of its siblings. |
613 | * @param node Node to combine with one of its siblings. |
610 | * |
614 | * |
611 | * @return Pointer to the rightmost of the two nodes. |
615 | * @return Pointer to the rightmost of the two nodes. |
612 | */ |
616 | */ |
613 | btree_node_t *node_combine(btree_node_t *node) |
617 | btree_node_t *node_combine(btree_node_t *node) |
614 | { |
618 | { |
615 | index_t idx; |
619 | index_t idx; |
616 | btree_node_t *rnode; |
620 | btree_node_t *rnode; |
617 | int i; |
621 | int i; |
618 | 622 | ||
619 | ASSERT(!ROOT_NODE(node)); |
623 | ASSERT(!ROOT_NODE(node)); |
620 | 624 | ||
621 | idx = find_key_by_subtree(node->parent, node, false); |
625 | idx = find_key_by_subtree(node->parent, node, false); |
622 | if (idx == node->parent->keys) { |
626 | if (idx == node->parent->keys) { |
623 | /* |
627 | /* |
624 | * Rightmost subtree of its parent, combine with the left sibling. |
628 | * Rightmost subtree of its parent, combine with the left sibling. |
625 | */ |
629 | */ |
626 | idx--; |
630 | idx--; |
627 | rnode = node; |
631 | rnode = node; |
628 | node = node->parent->subtree[idx]; |
632 | node = node->parent->subtree[idx]; |
629 | } else { |
633 | } else { |
630 | rnode = node->parent->subtree[idx + 1]; |
634 | rnode = node->parent->subtree[idx + 1]; |
631 | } |
635 | } |
632 | 636 | ||
633 | /* Index nodes need to insert parent node key in between left and right node. */ |
637 | /* Index nodes need to insert parent node key in between left and right node. */ |
634 | if (INDEX_NODE(node)) |
638 | if (INDEX_NODE(node)) |
635 | node->key[node->keys++] = node->parent->key[idx]; |
639 | node->key[node->keys++] = node->parent->key[idx]; |
636 | 640 | ||
637 | /* Copy the key-value-subtree triplets from the right node. */ |
641 | /* Copy the key-value-subtree triplets from the right node. */ |
638 | for (i = 0; i < rnode->keys; i++) { |
642 | for (i = 0; i < rnode->keys; i++) { |
639 | node->key[node->keys + i] = rnode->key[i]; |
643 | node->key[node->keys + i] = rnode->key[i]; |
640 | node->value[node->keys + i] = rnode->value[i]; |
644 | node->value[node->keys + i] = rnode->value[i]; |
641 | if (INDEX_NODE(node)) { |
645 | if (INDEX_NODE(node)) { |
642 | node->subtree[node->keys + i] = rnode->subtree[i]; |
646 | node->subtree[node->keys + i] = rnode->subtree[i]; |
643 | rnode->subtree[i]->parent = node; |
647 | rnode->subtree[i]->parent = node; |
644 | } |
648 | } |
645 | } |
649 | } |
646 | if (INDEX_NODE(node)) { |
650 | if (INDEX_NODE(node)) { |
647 | node->subtree[node->keys + i] = rnode->subtree[i]; |
651 | node->subtree[node->keys + i] = rnode->subtree[i]; |
648 | rnode->subtree[i]->parent = node; |
652 | rnode->subtree[i]->parent = node; |
649 | } |
653 | } |
650 | 654 | ||
651 | node->keys += rnode->keys; |
655 | node->keys += rnode->keys; |
652 | 656 | ||
653 | return rnode; |
657 | return rnode; |
654 | } |
658 | } |
655 | 659 | ||
656 | /** Find key by its left or right subtree. |
660 | /** Find key by its left or right subtree. |
657 | * |
661 | * |
658 | * @param node B-tree node. |
662 | * @param node B-tree node. |
659 | * @param subtree Left or right subtree of a key found in node. |
663 | * @param subtree Left or right subtree of a key found in node. |
660 | * @param right If true, subtree is a right subtree. If false, subtree is a left subtree. |
664 | * @param right If true, subtree is a right subtree. If false, subtree is a left subtree. |
661 | * |
665 | * |
662 | * @return Index of the key associated with the subtree. |
666 | * @return Index of the key associated with the subtree. |
663 | */ |
667 | */ |
664 | index_t find_key_by_subtree(btree_node_t *node, btree_node_t *subtree, bool right) |
668 | index_t find_key_by_subtree(btree_node_t *node, btree_node_t *subtree, bool right) |
665 | { |
669 | { |
666 | int i; |
670 | int i; |
667 | 671 | ||
668 | for (i = 0; i < node->keys + 1; i++) { |
672 | for (i = 0; i < node->keys + 1; i++) { |
669 | if (subtree == node->subtree[i]) |
673 | if (subtree == node->subtree[i]) |
670 | return i - (int) (right != false); |
674 | return i - (int) (right != false); |
671 | } |
675 | } |
672 | panic("node %p does not contain subtree %p\n", node, subtree); |
676 | panic("node %p does not contain subtree %p\n", node, subtree); |
673 | } |
677 | } |
674 | 678 | ||
675 | /** Rotate one key-value-rsubtree triplet from the left sibling to the right sibling. |
679 | /** Rotate one key-value-rsubtree triplet from the left sibling to the right sibling. |
676 | * |
680 | * |
677 | * The biggest key and its value and right subtree is rotated from the left node |
681 | * The biggest key and its value and right subtree is rotated from the left node |
678 | * to the right. If the node is an index node, than the parent node key belonging to |
682 | * to the right. If the node is an index node, than the parent node key belonging to |
679 | * the left node takes part in the rotation. |
683 | * the left node takes part in the rotation. |
680 | * |
684 | * |
681 | * @param lnode Left sibling. |
685 | * @param lnode Left sibling. |
682 | * @param rnode Right sibling. |
686 | * @param rnode Right sibling. |
683 | * @param idx Index of the parent node key that is taking part in the rotation. |
687 | * @param idx Index of the parent node key that is taking part in the rotation. |
684 | */ |
688 | */ |
685 | void rotate_from_left(btree_node_t *lnode, btree_node_t *rnode, index_t idx) |
689 | void rotate_from_left(btree_node_t *lnode, btree_node_t *rnode, index_t idx) |
686 | { |
690 | { |
687 | btree_key_t key; |
691 | btree_key_t key; |
688 | 692 | ||
689 | key = lnode->key[lnode->keys - 1]; |
693 | key = lnode->key[lnode->keys - 1]; |
690 | 694 | ||
691 | if (LEAF_NODE(lnode)) { |
695 | if (LEAF_NODE(lnode)) { |
692 | void *value; |
696 | void *value; |
693 | 697 | ||
694 | value = lnode->value[lnode->keys - 1]; |
698 | value = lnode->value[lnode->keys - 1]; |
695 | node_remove_key_and_rsubtree(lnode, key); |
699 | node_remove_key_and_rsubtree(lnode, key); |
696 | node_insert_key_and_lsubtree(rnode, key, value, NULL); |
700 | node_insert_key_and_lsubtree(rnode, key, value, NULL); |
697 | lnode->parent->key[idx] = key; |
701 | lnode->parent->key[idx] = key; |
698 | } else { |
702 | } else { |
699 | btree_node_t *rsubtree; |
703 | btree_node_t *rsubtree; |
700 | 704 | ||
701 | rsubtree = lnode->subtree[lnode->keys]; |
705 | rsubtree = lnode->subtree[lnode->keys]; |
702 | node_remove_key_and_rsubtree(lnode, key); |
706 | node_remove_key_and_rsubtree(lnode, key); |
703 | node_insert_key_and_lsubtree(rnode, lnode->parent->key[idx], NULL, rsubtree); |
707 | node_insert_key_and_lsubtree(rnode, lnode->parent->key[idx], NULL, rsubtree); |
704 | lnode->parent->key[idx] = key; |
708 | lnode->parent->key[idx] = key; |
705 | 709 | ||
706 | /* Fix parent link of the reconnected right subtree. */ |
710 | /* Fix parent link of the reconnected right subtree. */ |
707 | rsubtree->parent = rnode; |
711 | rsubtree->parent = rnode; |
708 | } |
712 | } |
709 | 713 | ||
710 | } |
714 | } |
711 | 715 | ||
712 | /** Rotate one key-value-lsubtree triplet from the right sibling to the left sibling. |
716 | /** Rotate one key-value-lsubtree triplet from the right sibling to the left sibling. |
713 | * |
717 | * |
714 | * The smallest key and its value and left subtree is rotated from the right node |
718 | * The smallest key and its value and left subtree is rotated from the right node |
715 | * to the left. If the node is an index node, than the parent node key belonging to |
719 | * to the left. If the node is an index node, than the parent node key belonging to |
716 | * the right node takes part in the rotation. |
720 | * the right node takes part in the rotation. |
717 | * |
721 | * |
718 | * @param lnode Left sibling. |
722 | * @param lnode Left sibling. |
719 | * @param rnode Right sibling. |
723 | * @param rnode Right sibling. |
720 | * @param idx Index of the parent node key that is taking part in the rotation. |
724 | * @param idx Index of the parent node key that is taking part in the rotation. |
721 | */ |
725 | */ |
722 | void rotate_from_right(btree_node_t *lnode, btree_node_t *rnode, index_t idx) |
726 | void rotate_from_right(btree_node_t *lnode, btree_node_t *rnode, index_t idx) |
723 | { |
727 | { |
724 | btree_key_t key; |
728 | btree_key_t key; |
725 | 729 | ||
726 | key = rnode->key[0]; |
730 | key = rnode->key[0]; |
727 | 731 | ||
728 | if (LEAF_NODE(rnode)) { |
732 | if (LEAF_NODE(rnode)) { |
729 | void *value; |
733 | void *value; |
730 | 734 | ||
731 | value = rnode->value[0]; |
735 | value = rnode->value[0]; |
732 | node_remove_key_and_lsubtree(rnode, key); |
736 | node_remove_key_and_lsubtree(rnode, key); |
733 | node_insert_key_and_rsubtree(lnode, key, value, NULL); |
737 | node_insert_key_and_rsubtree(lnode, key, value, NULL); |
734 | rnode->parent->key[idx] = rnode->key[0]; |
738 | rnode->parent->key[idx] = rnode->key[0]; |
735 | } else { |
739 | } else { |
736 | btree_node_t *lsubtree; |
740 | btree_node_t *lsubtree; |
737 | 741 | ||
738 | lsubtree = rnode->subtree[0]; |
742 | lsubtree = rnode->subtree[0]; |
739 | node_remove_key_and_lsubtree(rnode, key); |
743 | node_remove_key_and_lsubtree(rnode, key); |
740 | node_insert_key_and_rsubtree(lnode, rnode->parent->key[idx], NULL, lsubtree); |
744 | node_insert_key_and_rsubtree(lnode, rnode->parent->key[idx], NULL, lsubtree); |
741 | rnode->parent->key[idx] = key; |
745 | rnode->parent->key[idx] = key; |
742 | 746 | ||
743 | /* Fix parent link of the reconnected left subtree. */ |
747 | /* Fix parent link of the reconnected left subtree. */ |
744 | lsubtree->parent = lnode; |
748 | lsubtree->parent = lnode; |
745 | } |
749 | } |
746 | 750 | ||
747 | } |
751 | } |
748 | 752 | ||
749 | /** Insert key-value-rsubtree triplet and rotate the node to the left, if this operation can be done. |
753 | /** Insert key-value-rsubtree triplet and rotate the node to the left, if this operation can be done. |
750 | * |
754 | * |
751 | * Left sibling of the node (if it exists) is checked for free space. |
755 | * Left sibling of the node (if it exists) is checked for free space. |
752 | * If there is free space, the key is inserted and the smallest key of |
756 | * If there is free space, the key is inserted and the smallest key of |
753 | * the node is moved there. The index node which is the parent of both |
757 | * the node is moved there. The index node which is the parent of both |
754 | * nodes is fixed. |
758 | * nodes is fixed. |
755 | * |
759 | * |
756 | * @param node B-tree node. |
760 | * @param node B-tree node. |
757 | * @param inskey Key to be inserted. |
761 | * @param inskey Key to be inserted. |
758 | * @param insvalue Value to be inserted. |
762 | * @param insvalue Value to be inserted. |
759 | * @param rsubtree Right subtree of inskey. |
763 | * @param rsubtree Right subtree of inskey. |
760 | * |
764 | * |
761 | * @return True if the rotation was performed, false otherwise. |
765 | * @return True if the rotation was performed, false otherwise. |
762 | */ |
766 | */ |
763 | bool try_insert_by_rotation_to_left(btree_node_t *node, btree_key_t inskey, void *insvalue, btree_node_t *rsubtree) |
767 | bool try_insert_by_rotation_to_left(btree_node_t *node, btree_key_t inskey, void *insvalue, btree_node_t *rsubtree) |
764 | { |
768 | { |
765 | index_t idx; |
769 | index_t idx; |
766 | btree_node_t *lnode; |
770 | btree_node_t *lnode; |
767 | 771 | ||
768 | /* |
772 | /* |
769 | * If this is root node, the rotation can not be done. |
773 | * If this is root node, the rotation can not be done. |
770 | */ |
774 | */ |
771 | if (ROOT_NODE(node)) |
775 | if (ROOT_NODE(node)) |
772 | return false; |
776 | return false; |
773 | 777 | ||
774 | idx = find_key_by_subtree(node->parent, node, true); |
778 | idx = find_key_by_subtree(node->parent, node, true); |
775 | if ((int) idx == -1) { |
779 | if ((int) idx == -1) { |
776 | /* |
780 | /* |
777 | * If this node is the leftmost subtree of its parent, |
781 | * If this node is the leftmost subtree of its parent, |
778 | * the rotation can not be done. |
782 | * the rotation can not be done. |
779 | */ |
783 | */ |
780 | return false; |
784 | return false; |
781 | } |
785 | } |
782 | 786 | ||
783 | lnode = node->parent->subtree[idx]; |
787 | lnode = node->parent->subtree[idx]; |
784 | if (lnode->keys < BTREE_MAX_KEYS) { |
788 | if (lnode->keys < BTREE_MAX_KEYS) { |
785 | /* |
789 | /* |
786 | * The rotaion can be done. The left sibling has free space. |
790 | * The rotaion can be done. The left sibling has free space. |
787 | */ |
791 | */ |
788 | node_insert_key_and_rsubtree(node, inskey, insvalue, rsubtree); |
792 | node_insert_key_and_rsubtree(node, inskey, insvalue, rsubtree); |
789 | rotate_from_right(lnode, node, idx); |
793 | rotate_from_right(lnode, node, idx); |
790 | return true; |
794 | return true; |
791 | } |
795 | } |
792 | 796 | ||
793 | return false; |
797 | return false; |
794 | } |
798 | } |
795 | 799 | ||
796 | /** Insert key-value-rsubtree triplet and rotate the node to the right, if this operation can be done. |
800 | /** Insert key-value-rsubtree triplet and rotate the node to the right, if this operation can be done. |
797 | * |
801 | * |
798 | * Right sibling of the node (if it exists) is checked for free space. |
802 | * Right sibling of the node (if it exists) is checked for free space. |
799 | * If there is free space, the key is inserted and the biggest key of |
803 | * If there is free space, the key is inserted and the biggest key of |
800 | * the node is moved there. The index node which is the parent of both |
804 | * the node is moved there. The index node which is the parent of both |
801 | * nodes is fixed. |
805 | * nodes is fixed. |
802 | * |
806 | * |
803 | * @param node B-tree node. |
807 | * @param node B-tree node. |
804 | * @param inskey Key to be inserted. |
808 | * @param inskey Key to be inserted. |
805 | * @param insvalue Value to be inserted. |
809 | * @param insvalue Value to be inserted. |
806 | * @param rsubtree Right subtree of inskey. |
810 | * @param rsubtree Right subtree of inskey. |
807 | * |
811 | * |
808 | * @return True if the rotation was performed, false otherwise. |
812 | * @return True if the rotation was performed, false otherwise. |
809 | */ |
813 | */ |
810 | bool try_insert_by_rotation_to_right(btree_node_t *node, btree_key_t inskey, void *insvalue, btree_node_t *rsubtree) |
814 | bool try_insert_by_rotation_to_right(btree_node_t *node, btree_key_t inskey, void *insvalue, btree_node_t *rsubtree) |
811 | { |
815 | { |
812 | index_t idx; |
816 | index_t idx; |
813 | btree_node_t *rnode; |
817 | btree_node_t *rnode; |
814 | 818 | ||
815 | /* |
819 | /* |
816 | * If this is root node, the rotation can not be done. |
820 | * If this is root node, the rotation can not be done. |
817 | */ |
821 | */ |
818 | if (ROOT_NODE(node)) |
822 | if (ROOT_NODE(node)) |
819 | return false; |
823 | return false; |
820 | 824 | ||
821 | idx = find_key_by_subtree(node->parent, node, false); |
825 | idx = find_key_by_subtree(node->parent, node, false); |
822 | if (idx == node->parent->keys) { |
826 | if (idx == node->parent->keys) { |
823 | /* |
827 | /* |
824 | * If this node is the rightmost subtree of its parent, |
828 | * If this node is the rightmost subtree of its parent, |
825 | * the rotation can not be done. |
829 | * the rotation can not be done. |
826 | */ |
830 | */ |
827 | return false; |
831 | return false; |
828 | } |
832 | } |
829 | 833 | ||
830 | rnode = node->parent->subtree[idx + 1]; |
834 | rnode = node->parent->subtree[idx + 1]; |
831 | if (rnode->keys < BTREE_MAX_KEYS) { |
835 | if (rnode->keys < BTREE_MAX_KEYS) { |
832 | /* |
836 | /* |
833 | * The rotaion can be done. The right sibling has free space. |
837 | * The rotaion can be done. The right sibling has free space. |
834 | */ |
838 | */ |
835 | node_insert_key_and_rsubtree(node, inskey, insvalue, rsubtree); |
839 | node_insert_key_and_rsubtree(node, inskey, insvalue, rsubtree); |
836 | rotate_from_left(node, rnode, idx); |
840 | rotate_from_left(node, rnode, idx); |
837 | return true; |
841 | return true; |
838 | } |
842 | } |
839 | 843 | ||
840 | return false; |
844 | return false; |
841 | } |
845 | } |
842 | 846 | ||
843 | /** Rotate in a key from the left sibling or from the index node, if this operation can be done. |
847 | /** Rotate in a key from the left sibling or from the index node, if this operation can be done. |
844 | * |
848 | * |
845 | * @param rnode Node into which to add key from its left sibling or from the index node. |
849 | * @param rnode Node into which to add key from its left sibling or from the index node. |
846 | * |
850 | * |
847 | * @return True if the rotation was performed, false otherwise. |
851 | * @return True if the rotation was performed, false otherwise. |
848 | */ |
852 | */ |
849 | bool try_rotation_from_left(btree_node_t *rnode) |
853 | bool try_rotation_from_left(btree_node_t *rnode) |
850 | { |
854 | { |
851 | index_t idx; |
855 | index_t idx; |
852 | btree_node_t *lnode; |
856 | btree_node_t *lnode; |
853 | 857 | ||
854 | /* |
858 | /* |
855 | * If this is root node, the rotation can not be done. |
859 | * If this is root node, the rotation can not be done. |
856 | */ |
860 | */ |
857 | if (ROOT_NODE(rnode)) |
861 | if (ROOT_NODE(rnode)) |
858 | return false; |
862 | return false; |
859 | 863 | ||
860 | idx = find_key_by_subtree(rnode->parent, rnode, true); |
864 | idx = find_key_by_subtree(rnode->parent, rnode, true); |
861 | if ((int) idx == -1) { |
865 | if ((int) idx == -1) { |
862 | /* |
866 | /* |
863 | * If this node is the leftmost subtree of its parent, |
867 | * If this node is the leftmost subtree of its parent, |
864 | * the rotation can not be done. |
868 | * the rotation can not be done. |
865 | */ |
869 | */ |
866 | return false; |
870 | return false; |
867 | } |
871 | } |
868 | 872 | ||
869 | lnode = rnode->parent->subtree[idx]; |
873 | lnode = rnode->parent->subtree[idx]; |
870 | if (lnode->keys > FILL_FACTOR) { |
874 | if (lnode->keys > FILL_FACTOR) { |
871 | rotate_from_left(lnode, rnode, idx); |
875 | rotate_from_left(lnode, rnode, idx); |
872 | return true; |
876 | return true; |
873 | } |
877 | } |
874 | 878 | ||
875 | return false; |
879 | return false; |
876 | } |
880 | } |
877 | 881 | ||
878 | /** Rotate in a key from the right sibling or from the index node, if this operation can be done. |
882 | /** Rotate in a key from the right sibling or from the index node, if this operation can be done. |
879 | * |
883 | * |
880 | * @param rnode Node into which to add key from its right sibling or from the index node. |
884 | * @param rnode Node into which to add key from its right sibling or from the index node. |
881 | * |
885 | * |
882 | * @return True if the rotation was performed, false otherwise. |
886 | * @return True if the rotation was performed, false otherwise. |
883 | */ |
887 | */ |
884 | bool try_rotation_from_right(btree_node_t *lnode) |
888 | bool try_rotation_from_right(btree_node_t *lnode) |
885 | { |
889 | { |
886 | index_t idx; |
890 | index_t idx; |
887 | btree_node_t *rnode; |
891 | btree_node_t *rnode; |
888 | 892 | ||
889 | /* |
893 | /* |
890 | * If this is root node, the rotation can not be done. |
894 | * If this is root node, the rotation can not be done. |
891 | */ |
895 | */ |
892 | if (ROOT_NODE(lnode)) |
896 | if (ROOT_NODE(lnode)) |
893 | return false; |
897 | return false; |
894 | 898 | ||
895 | idx = find_key_by_subtree(lnode->parent, lnode, false); |
899 | idx = find_key_by_subtree(lnode->parent, lnode, false); |
896 | if (idx == lnode->parent->keys) { |
900 | if (idx == lnode->parent->keys) { |
897 | /* |
901 | /* |
898 | * If this node is the rightmost subtree of its parent, |
902 | * If this node is the rightmost subtree of its parent, |
899 | * the rotation can not be done. |
903 | * the rotation can not be done. |
900 | */ |
904 | */ |
901 | return false; |
905 | return false; |
902 | } |
906 | } |
903 | 907 | ||
904 | rnode = lnode->parent->subtree[idx + 1]; |
908 | rnode = lnode->parent->subtree[idx + 1]; |
905 | if (rnode->keys > FILL_FACTOR) { |
909 | if (rnode->keys > FILL_FACTOR) { |
906 | rotate_from_right(lnode, rnode, idx); |
910 | rotate_from_right(lnode, rnode, idx); |
907 | return true; |
911 | return true; |
908 | } |
912 | } |
909 | 913 | ||
910 | return false; |
914 | return false; |
911 | } |
915 | } |
912 | 916 | ||
913 | /** Print B-tree. |
917 | /** Print B-tree. |
914 | * |
918 | * |
915 | * @param t Print out B-tree. |
919 | * @param t Print out B-tree. |
916 | */ |
920 | */ |
917 | void btree_print(btree_t *t) |
921 | void btree_print(btree_t *t) |
918 | { |
922 | { |
919 | int i, depth = t->root->depth; |
923 | int i, depth = t->root->depth; |
920 | link_t head, *cur; |
924 | link_t head, *cur; |
921 | 925 | ||
922 | printf("Printing B-tree:\n"); |
926 | printf("Printing B-tree:\n"); |
923 | list_initialize(&head); |
927 | list_initialize(&head); |
924 | list_append(&t->root->bfs_link, &head); |
928 | list_append(&t->root->bfs_link, &head); |
925 | 929 | ||
926 | /* |
930 | /* |
927 | * Use BFS search to print out the tree. |
931 | * Use BFS search to print out the tree. |
928 | * Levels are distinguished from one another by node->depth. |
932 | * Levels are distinguished from one another by node->depth. |
929 | */ |
933 | */ |
930 | while (!list_empty(&head)) { |
934 | while (!list_empty(&head)) { |
931 | link_t *hlp; |
935 | link_t *hlp; |
932 | btree_node_t *node; |
936 | btree_node_t *node; |
933 | 937 | ||
934 | hlp = head.next; |
938 | hlp = head.next; |
935 | ASSERT(hlp != &head); |
939 | ASSERT(hlp != &head); |
936 | node = list_get_instance(hlp, btree_node_t, bfs_link); |
940 | node = list_get_instance(hlp, btree_node_t, bfs_link); |
937 | list_remove(hlp); |
941 | list_remove(hlp); |
938 | 942 | ||
939 | ASSERT(node); |
943 | ASSERT(node); |
940 | 944 | ||
941 | if (node->depth != depth) { |
945 | if (node->depth != depth) { |
942 | printf("\n"); |
946 | printf("\n"); |
943 | depth = node->depth; |
947 | depth = node->depth; |
944 | } |
948 | } |
945 | 949 | ||
946 | printf("("); |
950 | printf("("); |
947 | for (i = 0; i < node->keys; i++) { |
951 | for (i = 0; i < node->keys; i++) { |
948 | printf("%lld%s", node->key[i], i < node->keys - 1 ? "," : ""); |
952 | printf("%lld%s", node->key[i], i < node->keys - 1 ? "," : ""); |
949 | if (node->depth && node->subtree[i]) { |
953 | if (node->depth && node->subtree[i]) { |
950 | list_append(&node->subtree[i]->bfs_link, &head); |
954 | list_append(&node->subtree[i]->bfs_link, &head); |
951 | } |
955 | } |
952 | } |
956 | } |
953 | if (node->depth && node->subtree[i]) { |
957 | if (node->depth && node->subtree[i]) { |
954 | list_append(&node->subtree[i]->bfs_link, &head); |
958 | list_append(&node->subtree[i]->bfs_link, &head); |
955 | } |
959 | } |
956 | printf(")"); |
960 | printf(")"); |
957 | } |
961 | } |
958 | printf("\n"); |
962 | printf("\n"); |
959 | 963 | ||
960 | printf("Printing list of leaves:\n"); |
964 | printf("Printing list of leaves:\n"); |
961 | for (cur = t->leaf_head.next; cur != &t->leaf_head; cur = cur->next) { |
965 | for (cur = t->leaf_head.next; cur != &t->leaf_head; cur = cur->next) { |
962 | btree_node_t *node; |
966 | btree_node_t *node; |
963 | 967 | ||
964 | node = list_get_instance(cur, btree_node_t, leaf_link); |
968 | node = list_get_instance(cur, btree_node_t, leaf_link); |
965 | 969 | ||
966 | ASSERT(node); |
970 | ASSERT(node); |
967 | 971 | ||
968 | printf("("); |
972 | printf("("); |
969 | for (i = 0; i < node->keys; i++) |
973 | for (i = 0; i < node->keys; i++) |
970 | printf("%lld%s", node->key[i], i < node->keys - 1 ? "," : ""); |
974 | printf("%lld%s", node->key[i], i < node->keys - 1 ? "," : ""); |
971 | printf(")"); |
975 | printf(")"); |
972 | } |
976 | } |
973 | printf("\n"); |
977 | printf("\n"); |
974 | } |
978 | } |
975 | 979 |