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1101 | jermar | 1 | /* |
2 | * Copyright (C) 2006 Jakub Jermar |
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3 | * All rights reserved. |
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4 | * |
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5 | * Redistribution and use in source and binary forms, with or without |
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6 | * modification, are permitted provided that the following conditions |
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7 | * are met: |
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8 | * |
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9 | * - Redistributions of source code must retain the above copyright |
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10 | * notice, this list of conditions and the following disclaimer. |
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11 | * - Redistributions in binary form must reproduce the above copyright |
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12 | * notice, this list of conditions and the following disclaimer in the |
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13 | * documentation and/or other materials provided with the distribution. |
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14 | * - The name of the author may not be used to endorse or promote products |
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15 | * derived from this software without specific prior written permission. |
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16 | * |
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17 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR |
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18 | * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES |
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19 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. |
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20 | * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, |
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21 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
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22 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
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23 | * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
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24 | * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
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25 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF |
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26 | * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
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27 | */ |
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28 | |||
29 | /* |
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30 | * This B-tree has the following properties: |
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1140 | jermar | 31 | * - it is a ballanced 2-3-4-5 tree (i.e. BTREE_M = 5) |
1101 | jermar | 32 | * - values (i.e. pointers to values) are stored only in leaves |
33 | * - leaves are linked in a list |
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1148 | jermar | 34 | * - technically, it is a B+tree (because of the previous properties) |
1101 | jermar | 35 | * |
1134 | jermar | 36 | * Be carefull when using these trees. They need to allocate |
37 | * and deallocate memory for their index nodes and as such |
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38 | * can sleep. |
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1101 | jermar | 39 | */ |
40 | |||
41 | #include <adt/btree.h> |
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42 | #include <adt/list.h> |
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43 | #include <mm/slab.h> |
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44 | #include <debug.h> |
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45 | #include <panic.h> |
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46 | #include <typedefs.h> |
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47 | #include <print.h> |
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48 | |||
49 | static void _btree_insert(btree_t *t, __native key, void *value, btree_node_t *rsubtree, btree_node_t *node); |
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1142 | jermar | 50 | static void _btree_remove(btree_t *t, __native key, btree_node_t *node); |
1101 | jermar | 51 | static void node_initialize(btree_node_t *node); |
1144 | jermar | 52 | static void node_insert_key_and_lsubtree(btree_node_t *node, __native key, void *value, btree_node_t *lsubtree); |
1142 | jermar | 53 | static void node_insert_key_and_rsubtree(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree); |
1144 | jermar | 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); |
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1101 | jermar | 56 | static btree_node_t *node_split(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree, __native *median); |
1142 | jermar | 57 | static btree_node_t *node_combine(btree_node_t *node); |
1136 | jermar | 58 | static index_t find_key_by_subtree(btree_node_t *node, btree_node_t *subtree, bool right); |
1142 | jermar | 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); |
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61 | static bool try_insert_by_rotation_to_left(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree); |
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62 | static bool try_insert_by_rotation_to_right(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree); |
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63 | static bool try_rotation_from_left(btree_node_t *rnode); |
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64 | static bool try_rotation_from_right(btree_node_t *lnode); |
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1101 | jermar | 65 | |
66 | #define ROOT_NODE(n) (!(n)->parent) |
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67 | #define INDEX_NODE(n) ((n)->subtree[0] != NULL) |
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68 | #define LEAF_NODE(n) ((n)->subtree[0] == NULL) |
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69 | |||
1140 | jermar | 70 | #define FILL_FACTOR ((BTREE_M-1)/2) |
71 | |||
1101 | jermar | 72 | #define MEDIAN_LOW_INDEX(n) (((n)->keys-1)/2) |
73 | #define MEDIAN_HIGH_INDEX(n) ((n)->keys/2) |
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74 | #define MEDIAN_LOW(n) ((n)->key[MEDIAN_LOW_INDEX((n))]); |
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75 | #define MEDIAN_HIGH(n) ((n)->key[MEDIAN_HIGH_INDEX((n))]); |
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76 | |||
77 | /** Create empty B-tree. |
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78 | * |
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79 | * @param t B-tree. |
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80 | */ |
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81 | void btree_create(btree_t *t) |
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82 | { |
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83 | list_initialize(&t->leaf_head); |
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84 | t->root = (btree_node_t *) malloc(sizeof(btree_node_t), 0); |
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85 | node_initialize(t->root); |
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86 | list_append(&t->root->leaf_link, &t->leaf_head); |
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87 | } |
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88 | |||
89 | /** Destroy empty B-tree. */ |
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90 | void btree_destroy(btree_t *t) |
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91 | { |
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92 | ASSERT(!t->root->keys); |
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93 | free(t->root); |
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94 | } |
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95 | |||
96 | /** Insert key-value pair into B-tree. |
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97 | * |
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98 | * @param t B-tree. |
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99 | * @param key Key to be inserted. |
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100 | * @param value Value to be inserted. |
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101 | * @param leaf_node Leaf node where the insertion should begin. |
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102 | */ |
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103 | void btree_insert(btree_t *t, __native key, void *value, btree_node_t *leaf_node) |
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104 | { |
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105 | btree_node_t *lnode; |
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106 | |||
107 | ASSERT(value); |
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108 | |||
109 | lnode = leaf_node; |
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110 | if (!lnode) { |
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111 | if (btree_search(t, key, &lnode)) { |
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112 | panic("B-tree %P already contains key %d\n", t, key); |
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113 | } |
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114 | } |
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115 | |||
116 | _btree_insert(t, key, value, NULL, lnode); |
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117 | } |
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118 | |||
119 | /** Recursively insert into B-tree. |
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120 | * |
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121 | * @param t B-tree. |
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122 | * @param key Key to be inserted. |
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123 | * @param value Value to be inserted. |
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124 | * @param rsubtree Right subtree of the inserted key. |
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125 | * @param node Start inserting into this node. |
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126 | */ |
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127 | void _btree_insert(btree_t *t, __native key, void *value, btree_node_t *rsubtree, btree_node_t *node) |
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128 | { |
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129 | if (node->keys < BTREE_MAX_KEYS) { |
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130 | /* |
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131 | * Node conatins enough space, the key can be stored immediately. |
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132 | */ |
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1142 | jermar | 133 | node_insert_key_and_rsubtree(node, key, value, rsubtree); |
134 | } else if (try_insert_by_rotation_to_left(node, key, value, rsubtree)) { |
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1136 | jermar | 135 | /* |
136 | * The key-value-rsubtree triplet has been inserted because |
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137 | * some keys could have been moved to the left sibling. |
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138 | */ |
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1142 | jermar | 139 | } else if (try_insert_by_rotation_to_right(node, key, value, rsubtree)) { |
1136 | jermar | 140 | /* |
141 | * The key-value-rsubtree triplet has been inserted because |
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142 | * some keys could have been moved to the right sibling. |
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143 | */ |
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1101 | jermar | 144 | } else { |
145 | btree_node_t *rnode; |
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146 | __native median; |
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147 | |||
148 | /* |
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1136 | jermar | 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 |
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151 | * bigger keys (i.e. the new node) into its parent. |
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1101 | jermar | 152 | */ |
153 | |||
154 | rnode = node_split(node, key, value, rsubtree, &median); |
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155 | |||
156 | if (LEAF_NODE(node)) { |
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1144 | jermar | 157 | list_prepend(&rnode->leaf_link, &node->leaf_link); |
1101 | jermar | 158 | } |
159 | |||
160 | if (ROOT_NODE(node)) { |
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161 | /* |
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162 | * We split the root node. Create new root. |
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163 | */ |
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164 | t->root = (btree_node_t *) malloc(sizeof(btree_node_t), 0); |
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165 | node->parent = t->root; |
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166 | rnode->parent = t->root; |
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167 | node_initialize(t->root); |
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168 | |||
169 | /* |
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170 | * Left-hand side subtree will be the old root (i.e. node). |
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171 | * Right-hand side subtree will be rnode. |
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172 | */ |
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173 | t->root->subtree[0] = node; |
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174 | |||
175 | t->root->depth = node->depth + 1; |
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176 | } |
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177 | _btree_insert(t, median, NULL, rnode, node->parent); |
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178 | } |
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179 | |||
180 | } |
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181 | |||
1140 | jermar | 182 | /** Remove B-tree node. |
183 | * |
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184 | * @param B-tree. |
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185 | * @param key Key to be removed from the B-tree along with its associated value. |
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186 | * @param leaf_node If not NULL, pointer to the leaf node where the key is found. |
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187 | */ |
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188 | void btree_remove(btree_t *t, __native key, btree_node_t *leaf_node) |
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1101 | jermar | 189 | { |
1140 | jermar | 190 | btree_node_t *lnode; |
191 | |||
192 | lnode = leaf_node; |
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193 | if (!lnode) { |
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194 | if (!btree_search(t, key, &lnode)) { |
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195 | panic("B-tree %P does not contain key %d\n", t, key); |
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196 | } |
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197 | } |
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198 | |||
1142 | jermar | 199 | _btree_remove(t, key, lnode); |
200 | } |
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1140 | jermar | 201 | |
1142 | jermar | 202 | /** Recursively remove B-tree node. |
203 | * |
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204 | * @param B-tree. |
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205 | * @param key Key to be removed from the B-tree along with its associated value. |
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206 | * @param node Node where the key being removed resides. |
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207 | */ |
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208 | void _btree_remove(btree_t *t, __native key, btree_node_t *node) |
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209 | { |
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210 | if (ROOT_NODE(node)) { |
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211 | if (node->keys == 1 && node->subtree[0]) { |
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212 | /* |
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213 | * Free the current root and set new root. |
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214 | */ |
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215 | t->root = node->subtree[0]; |
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216 | t->root->parent = NULL; |
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217 | free(node); |
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218 | } else { |
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219 | /* |
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220 | * Remove the key from the root node. |
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221 | * Note that the right subtree is removed because when |
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222 | * combining two nodes, the left-side sibling is preserved |
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223 | * and the right-side sibling is freed. |
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224 | */ |
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225 | node_remove_key_and_rsubtree(node, key); |
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226 | } |
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227 | return; |
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228 | } |
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229 | |||
230 | if (node->keys <= FILL_FACTOR) { |
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231 | /* |
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232 | * If the node is below the fill factor, |
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233 | * try to borrow keys from left or right sibling. |
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234 | */ |
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235 | if (!try_rotation_from_left(node)) |
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236 | try_rotation_from_right(node); |
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237 | } |
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238 | |||
239 | if (node->keys > FILL_FACTOR) { |
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240 | int i; |
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241 | |||
242 | /* |
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243 | * The key can be immediatelly removed. |
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244 | * |
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245 | * Note that the right subtree is removed because when |
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246 | * combining two nodes, the left-side sibling is preserved |
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247 | * and the right-side sibling is freed. |
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248 | */ |
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249 | node_remove_key_and_rsubtree(node, key); |
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250 | for (i = 0; i < node->parent->keys; i++) { |
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251 | if (node->parent->key[i] == key) |
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252 | node->parent->key[i] = node->key[0]; |
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253 | } |
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254 | |||
255 | } else { |
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256 | index_t idx; |
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257 | btree_node_t *rnode, *parent; |
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258 | |||
259 | /* |
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260 | * The node is below the fill factor as well as its left and right sibling. |
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261 | * Resort to combining the node with one of its siblings. |
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262 | * The node which is on the left is preserved and the node on the right is |
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263 | * freed. |
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264 | */ |
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265 | parent = node->parent; |
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266 | node_remove_key_and_rsubtree(node, key); |
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267 | rnode = node_combine(node); |
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268 | if (LEAF_NODE(rnode)) |
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269 | list_remove(&rnode->leaf_link); |
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270 | idx = find_key_by_subtree(parent, rnode, true); |
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271 | ASSERT((int) idx != -1); |
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272 | free(rnode); |
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273 | _btree_remove(t, parent->key[idx], parent); |
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274 | } |
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1101 | jermar | 275 | } |
276 | |||
277 | /** Search key in a B-tree. |
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278 | * |
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279 | * @param t B-tree. |
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280 | * @param key Key to be searched. |
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281 | * @param leaf_node Address where to put pointer to visited leaf node. |
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282 | * |
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283 | * @return Pointer to value or NULL if there is no such key. |
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284 | */ |
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285 | void *btree_search(btree_t *t, __native key, btree_node_t **leaf_node) |
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286 | { |
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287 | btree_node_t *cur, *next; |
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288 | |||
289 | /* |
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1134 | jermar | 290 | * Iteratively descend to the leaf that can contain the searched key. |
1101 | jermar | 291 | */ |
292 | for (cur = t->root; cur; cur = next) { |
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1134 | jermar | 293 | |
1101 | jermar | 294 | /* Last iteration will set this with proper leaf node address. */ |
295 | *leaf_node = cur; |
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1134 | jermar | 296 | |
297 | /* |
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298 | * The key can be in the leftmost subtree. |
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299 | * Test it separately. |
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300 | */ |
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301 | if (key < cur->key[0]) { |
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302 | next = cur->subtree[0]; |
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303 | continue; |
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304 | } else { |
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305 | void *val; |
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306 | int i; |
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307 | |||
308 | /* |
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309 | * Now if the key is smaller than cur->key[i] |
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310 | * it can only mean that the value is in cur->subtree[i] |
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311 | * or it is not in the tree at all. |
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312 | */ |
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313 | for (i = 1; i < cur->keys; i++) { |
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314 | if (key < cur->key[i]) { |
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315 | next = cur->subtree[i]; |
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316 | val = cur->value[i - 1]; |
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317 | |||
318 | if (LEAF_NODE(cur)) |
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319 | return key == cur->key[i - 1] ? val : NULL; |
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320 | |||
321 | goto descend; |
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322 | } |
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1101 | jermar | 323 | } |
1134 | jermar | 324 | |
325 | /* |
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326 | * Last possibility is that the key is in the rightmost subtree. |
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327 | */ |
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328 | next = cur->subtree[i]; |
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329 | val = cur->value[i - 1]; |
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330 | if (LEAF_NODE(cur)) |
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331 | return key == cur->key[i - 1] ? val : NULL; |
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1101 | jermar | 332 | } |
1134 | jermar | 333 | descend: |
334 | ; |
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1101 | jermar | 335 | } |
336 | |||
337 | /* |
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1134 | jermar | 338 | * The key was not found in the *leaf_node and is smaller than any of its keys. |
1101 | jermar | 339 | */ |
340 | return NULL; |
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341 | } |
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342 | |||
1150 | jermar | 343 | /** Return pointer to B-tree leaf node's left neighbour. |
1147 | jermar | 344 | * |
345 | * @param t B-tree. |
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1150 | jermar | 346 | * @param node Node whose left neighbour will be returned. |
1147 | jermar | 347 | * |
1150 | jermar | 348 | * @return Left neighbour of the node or NULL if the node does not have the left neighbour. |
1147 | jermar | 349 | */ |
1150 | jermar | 350 | btree_node_t *btree_leaf_node_left_neighbour(btree_t *t, btree_node_t *node) |
1147 | jermar | 351 | { |
352 | ASSERT(LEAF_NODE(node)); |
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353 | if (node->leaf_link.prev != &t->leaf_head) |
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354 | return list_get_instance(node->leaf_link.prev, btree_node_t, leaf_link); |
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355 | else |
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356 | return NULL; |
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357 | } |
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358 | |||
1150 | jermar | 359 | /** Return pointer to B-tree leaf node's right neighbour. |
1147 | jermar | 360 | * |
361 | * @param t B-tree. |
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1150 | jermar | 362 | * @param node Node whose right neighbour will be returned. |
1147 | jermar | 363 | * |
1150 | jermar | 364 | * @return Right neighbour of the node or NULL if the node does not have the right neighbour. |
1147 | jermar | 365 | */ |
1150 | jermar | 366 | btree_node_t *btree_leaf_node_right_neighbour(btree_t *t, btree_node_t *node) |
1147 | jermar | 367 | { |
368 | ASSERT(LEAF_NODE(node)); |
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369 | if (node->leaf_link.next != &t->leaf_head) |
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370 | return list_get_instance(node->leaf_link.next, btree_node_t, leaf_link); |
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371 | else |
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372 | return NULL; |
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373 | } |
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374 | |||
1101 | jermar | 375 | /** Initialize B-tree node. |
376 | * |
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377 | * @param node B-tree node. |
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378 | */ |
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379 | void node_initialize(btree_node_t *node) |
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380 | { |
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381 | int i; |
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382 | |||
383 | node->keys = 0; |
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384 | |||
385 | /* Clean also space for the extra key. */ |
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386 | for (i = 0; i < BTREE_MAX_KEYS + 1; i++) { |
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387 | node->key[i] = 0; |
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388 | node->value[i] = NULL; |
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389 | node->subtree[i] = NULL; |
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390 | } |
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391 | node->subtree[i] = NULL; |
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392 | |||
393 | node->parent = NULL; |
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394 | |||
395 | link_initialize(&node->leaf_link); |
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396 | |||
397 | link_initialize(&node->bfs_link); |
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398 | node->depth = 0; |
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399 | } |
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400 | |||
1136 | jermar | 401 | /** Insert key-value-lsubtree triplet into B-tree node. |
1101 | jermar | 402 | * |
403 | * It is actually possible to have more keys than BTREE_MAX_KEYS. |
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1136 | jermar | 404 | * This feature is used during insert by right rotation. |
405 | * |
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406 | * @param node B-tree node into wich the new key is to be inserted. |
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407 | * @param key The key to be inserted. |
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408 | * @param value Pointer to value to be inserted. |
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409 | * @param lsubtree Pointer to the left subtree. |
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410 | */ |
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1142 | jermar | 411 | void node_insert_key_and_lsubtree(btree_node_t *node, __native key, void *value, btree_node_t *lsubtree) |
1136 | jermar | 412 | { |
413 | int i; |
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414 | |||
415 | for (i = 0; i < node->keys; i++) { |
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416 | if (key < node->key[i]) { |
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417 | int j; |
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418 | |||
419 | for (j = node->keys; j > i; j--) { |
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420 | node->key[j] = node->key[j - 1]; |
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421 | node->value[j] = node->value[j - 1]; |
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422 | node->subtree[j + 1] = node->subtree[j]; |
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423 | } |
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424 | node->subtree[j + 1] = node->subtree[j]; |
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425 | break; |
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426 | } |
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427 | } |
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428 | node->key[i] = key; |
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429 | node->value[i] = value; |
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430 | node->subtree[i] = lsubtree; |
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431 | |||
432 | node->keys++; |
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433 | } |
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434 | |||
435 | /** Insert key-value-rsubtree triplet into B-tree node. |
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436 | * |
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437 | * It is actually possible to have more keys than BTREE_MAX_KEYS. |
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1101 | jermar | 438 | * This feature is used during splitting the node when the |
1136 | jermar | 439 | * number of keys is BTREE_MAX_KEYS + 1. Insert by left rotation |
440 | * also makes use of this feature. |
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1101 | jermar | 441 | * |
442 | * @param node B-tree node into wich the new key is to be inserted. |
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443 | * @param key The key to be inserted. |
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444 | * @param value Pointer to value to be inserted. |
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445 | * @param rsubtree Pointer to the right subtree. |
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446 | */ |
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1142 | jermar | 447 | void node_insert_key_and_rsubtree(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree) |
1101 | jermar | 448 | { |
449 | int i; |
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450 | |||
451 | for (i = 0; i < node->keys; i++) { |
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452 | if (key < node->key[i]) { |
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453 | int j; |
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454 | |||
455 | for (j = node->keys; j > i; j--) { |
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456 | node->key[j] = node->key[j - 1]; |
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457 | node->value[j] = node->value[j - 1]; |
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458 | node->subtree[j + 1] = node->subtree[j]; |
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459 | } |
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460 | break; |
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461 | } |
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462 | } |
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463 | node->key[i] = key; |
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464 | node->value[i] = value; |
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465 | node->subtree[i + 1] = rsubtree; |
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466 | |||
467 | node->keys++; |
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468 | } |
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469 | |||
1144 | jermar | 470 | /** Remove key and its left subtree pointer from B-tree node. |
471 | * |
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472 | * Remove the key and eliminate gaps in node->key array. |
||
473 | * Note that the value pointer and the left subtree pointer |
||
474 | * is removed from the node as well. |
||
475 | * |
||
476 | * @param node B-tree node. |
||
477 | * @param key Key to be removed. |
||
478 | */ |
||
479 | void node_remove_key_and_lsubtree(btree_node_t *node, __native key) |
||
480 | { |
||
481 | int i, j; |
||
482 | |||
483 | for (i = 0; i < node->keys; i++) { |
||
484 | if (key == node->key[i]) { |
||
485 | for (j = i + 1; j < node->keys; j++) { |
||
486 | node->key[j - 1] = node->key[j]; |
||
487 | node->value[j - 1] = node->value[j]; |
||
488 | node->subtree[j - 1] = node->subtree[j]; |
||
489 | } |
||
490 | node->subtree[j - 1] = node->subtree[j]; |
||
491 | node->keys--; |
||
492 | return; |
||
493 | } |
||
494 | } |
||
495 | panic("node %P does not contain key %d\n", node, key); |
||
496 | } |
||
497 | |||
498 | /** Remove key and its right subtree pointer from B-tree node. |
||
499 | * |
||
500 | * Remove the key and eliminate gaps in node->key array. |
||
501 | * Note that the value pointer and the right subtree pointer |
||
502 | * is removed from the node as well. |
||
503 | * |
||
504 | * @param node B-tree node. |
||
505 | * @param key Key to be removed. |
||
506 | */ |
||
507 | void node_remove_key_and_rsubtree(btree_node_t *node, __native key) |
||
508 | { |
||
509 | int i, j; |
||
510 | |||
511 | for (i = 0; i < node->keys; i++) { |
||
512 | if (key == node->key[i]) { |
||
513 | for (j = i + 1; j < node->keys; j++) { |
||
514 | node->key[j - 1] = node->key[j]; |
||
515 | node->value[j - 1] = node->value[j]; |
||
516 | node->subtree[j] = node->subtree[j + 1]; |
||
517 | } |
||
518 | node->keys--; |
||
519 | return; |
||
520 | } |
||
521 | } |
||
522 | panic("node %P does not contain key %d\n", node, key); |
||
523 | } |
||
524 | |||
1134 | jermar | 525 | /** Split full B-tree node and insert new key-value-right-subtree triplet. |
1101 | jermar | 526 | * |
527 | * This function will split a node and return pointer to a newly created |
||
1134 | jermar | 528 | * node containing keys greater than or equal to the greater of medians |
529 | * (or median) of the old keys and the newly added key. It will also write |
||
530 | * the median key to a memory address supplied by the caller. |
||
1101 | jermar | 531 | * |
1134 | jermar | 532 | * If the node being split is an index node, the median will not be |
533 | * included in the new node. If the node is a leaf node, |
||
534 | * the median will be copied there. |
||
1101 | jermar | 535 | * |
536 | * @param node B-tree node wich is going to be split. |
||
537 | * @param key The key to be inserted. |
||
538 | * @param value Pointer to the value to be inserted. |
||
539 | * @param rsubtree Pointer to the right subtree of the key being added. |
||
540 | * @param median Address in memory, where the median key will be stored. |
||
541 | * |
||
542 | * @return Newly created right sibling of node. |
||
543 | */ |
||
544 | btree_node_t *node_split(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree, __native *median) |
||
545 | { |
||
546 | btree_node_t *rnode; |
||
547 | int i, j; |
||
548 | |||
549 | ASSERT(median); |
||
550 | ASSERT(node->keys == BTREE_MAX_KEYS); |
||
1136 | jermar | 551 | |
1101 | jermar | 552 | /* |
553 | * Use the extra space to store the extra node. |
||
554 | */ |
||
1142 | jermar | 555 | node_insert_key_and_rsubtree(node, key, value, rsubtree); |
1101 | jermar | 556 | |
557 | /* |
||
558 | * Compute median of keys. |
||
559 | */ |
||
1134 | jermar | 560 | *median = MEDIAN_HIGH(node); |
1101 | jermar | 561 | |
1134 | jermar | 562 | /* |
563 | * Allocate and initialize new right sibling. |
||
564 | */ |
||
1101 | jermar | 565 | rnode = (btree_node_t *) malloc(sizeof(btree_node_t), 0); |
566 | node_initialize(rnode); |
||
567 | rnode->parent = node->parent; |
||
568 | rnode->depth = node->depth; |
||
569 | |||
570 | /* |
||
571 | * Copy big keys, values and subtree pointers to the new right sibling. |
||
1134 | jermar | 572 | * If this is an index node, do not copy the median. |
1101 | jermar | 573 | */ |
1134 | jermar | 574 | i = (int) INDEX_NODE(node); |
575 | for (i += MEDIAN_HIGH_INDEX(node), j = 0; i < node->keys; i++, j++) { |
||
1101 | jermar | 576 | rnode->key[j] = node->key[i]; |
577 | rnode->value[j] = node->value[i]; |
||
578 | rnode->subtree[j] = node->subtree[i]; |
||
579 | |||
580 | /* |
||
581 | * Fix parent links in subtrees. |
||
582 | */ |
||
583 | if (rnode->subtree[j]) |
||
584 | rnode->subtree[j]->parent = rnode; |
||
585 | |||
586 | } |
||
587 | rnode->subtree[j] = node->subtree[i]; |
||
588 | if (rnode->subtree[j]) |
||
589 | rnode->subtree[j]->parent = rnode; |
||
1134 | jermar | 590 | |
591 | rnode->keys = j; /* Set number of keys of the new node. */ |
||
592 | node->keys /= 2; /* Shrink the old node. */ |
||
1101 | jermar | 593 | |
594 | return rnode; |
||
595 | } |
||
596 | |||
1142 | jermar | 597 | /** Combine node with any of its siblings. |
598 | * |
||
599 | * The siblings are required to be below the fill factor. |
||
600 | * |
||
601 | * @param node Node to combine with one of its siblings. |
||
602 | * |
||
603 | * @return Pointer to the rightmost of the two nodes. |
||
604 | */ |
||
605 | btree_node_t *node_combine(btree_node_t *node) |
||
606 | { |
||
607 | index_t idx; |
||
608 | btree_node_t *rnode; |
||
609 | int i; |
||
610 | |||
611 | ASSERT(!ROOT_NODE(node)); |
||
612 | |||
613 | idx = find_key_by_subtree(node->parent, node, false); |
||
614 | if (idx == node->parent->keys) { |
||
615 | /* |
||
616 | * Rightmost subtree of its parent, combine with the left sibling. |
||
617 | */ |
||
618 | idx--; |
||
619 | rnode = node; |
||
620 | node = node->parent->subtree[idx]; |
||
621 | } else { |
||
622 | rnode = node->parent->subtree[idx + 1]; |
||
623 | } |
||
624 | |||
625 | /* Index nodes need to insert parent node key in between left and right node. */ |
||
626 | if (INDEX_NODE(node)) |
||
627 | node->key[node->keys++] = node->parent->key[idx]; |
||
628 | |||
629 | /* Copy the key-value-subtree triplets from the right node. */ |
||
630 | for (i = 0; i < rnode->keys; i++) { |
||
631 | node->key[node->keys + i] = rnode->key[i]; |
||
632 | node->value[node->keys + i] = rnode->value[i]; |
||
633 | if (INDEX_NODE(node)) { |
||
634 | node->subtree[node->keys + i] = rnode->subtree[i]; |
||
635 | rnode->subtree[i]->parent = node; |
||
636 | } |
||
637 | } |
||
638 | if (INDEX_NODE(node)) { |
||
639 | node->subtree[node->keys + i] = rnode->subtree[i]; |
||
640 | rnode->subtree[i]->parent = node; |
||
641 | } |
||
642 | |||
643 | node->keys += rnode->keys; |
||
644 | |||
645 | return rnode; |
||
646 | } |
||
647 | |||
1136 | jermar | 648 | /** Find key by its left or right subtree. |
649 | * |
||
650 | * @param node B-tree node. |
||
651 | * @param subtree Left or right subtree of a key found in node. |
||
652 | * @param right If true, subtree is a right subtree. If false, subtree is a left subtree. |
||
653 | * |
||
654 | * @return Index of the key associated with the subtree. |
||
655 | */ |
||
656 | index_t find_key_by_subtree(btree_node_t *node, btree_node_t *subtree, bool right) |
||
657 | { |
||
658 | int i; |
||
659 | |||
660 | for (i = 0; i < node->keys + 1; i++) { |
||
661 | if (subtree == node->subtree[i]) |
||
662 | return i - (int) (right != false); |
||
663 | } |
||
664 | panic("node %P does not contain subtree %P\n", node, subtree); |
||
665 | } |
||
666 | |||
1142 | jermar | 667 | /** Rotate one key-value-rsubtree triplet from the left sibling to the right sibling. |
668 | * |
||
669 | * The biggest key and its value and right subtree is rotated from the left node |
||
670 | * to the right. If the node is an index node, than the parent node key belonging to |
||
671 | * the left node takes part in the rotation. |
||
672 | * |
||
673 | * @param lnode Left sibling. |
||
674 | * @param rnode Right sibling. |
||
675 | * @param idx Index of the parent node key that is taking part in the rotation. |
||
676 | */ |
||
677 | void rotate_from_left(btree_node_t *lnode, btree_node_t *rnode, index_t idx) |
||
678 | { |
||
679 | __native key; |
||
680 | |||
681 | key = lnode->key[lnode->keys - 1]; |
||
682 | |||
683 | if (LEAF_NODE(lnode)) { |
||
684 | void *value; |
||
685 | |||
686 | value = lnode->value[lnode->keys - 1]; |
||
687 | node_remove_key_and_rsubtree(lnode, key); |
||
688 | node_insert_key_and_lsubtree(rnode, key, value, NULL); |
||
689 | lnode->parent->key[idx] = key; |
||
690 | } else { |
||
691 | btree_node_t *rsubtree; |
||
692 | |||
693 | rsubtree = lnode->subtree[lnode->keys]; |
||
694 | node_remove_key_and_rsubtree(lnode, key); |
||
695 | node_insert_key_and_lsubtree(rnode, lnode->parent->key[idx], NULL, rsubtree); |
||
696 | lnode->parent->key[idx] = key; |
||
697 | |||
698 | /* Fix parent link of the reconnected right subtree. */ |
||
699 | rsubtree->parent = rnode; |
||
700 | } |
||
701 | |||
702 | } |
||
703 | |||
704 | /** Rotate one key-value-lsubtree triplet from the right sibling to the left sibling. |
||
705 | * |
||
706 | * The smallest key and its value and left subtree is rotated from the right node |
||
707 | * to the left. If the node is an index node, than the parent node key belonging to |
||
708 | * the right node takes part in the rotation. |
||
709 | * |
||
710 | * @param lnode Left sibling. |
||
711 | * @param rnode Right sibling. |
||
712 | * @param idx Index of the parent node key that is taking part in the rotation. |
||
713 | */ |
||
714 | void rotate_from_right(btree_node_t *lnode, btree_node_t *rnode, index_t idx) |
||
715 | { |
||
716 | __native key; |
||
717 | |||
718 | key = rnode->key[0]; |
||
719 | |||
720 | if (LEAF_NODE(rnode)) { |
||
721 | void *value; |
||
722 | |||
723 | value = rnode->value[0]; |
||
724 | node_remove_key_and_lsubtree(rnode, key); |
||
725 | node_insert_key_and_rsubtree(lnode, key, value, NULL); |
||
726 | rnode->parent->key[idx] = rnode->key[0]; |
||
727 | } else { |
||
728 | btree_node_t *lsubtree; |
||
729 | |||
730 | lsubtree = rnode->subtree[0]; |
||
731 | node_remove_key_and_lsubtree(rnode, key); |
||
732 | node_insert_key_and_rsubtree(lnode, rnode->parent->key[idx], NULL, lsubtree); |
||
733 | rnode->parent->key[idx] = key; |
||
734 | |||
735 | /* Fix parent link of the reconnected left subtree. */ |
||
736 | lsubtree->parent = lnode; |
||
737 | } |
||
738 | |||
739 | } |
||
740 | |||
1136 | jermar | 741 | /** Insert key-value-rsubtree triplet and rotate the node to the left, if this operation can be done. |
742 | * |
||
743 | * Left sibling of the node (if it exists) is checked for free space. |
||
744 | * If there is free space, the key is inserted and the smallest key of |
||
745 | * the node is moved there. The index node which is the parent of both |
||
746 | * nodes is fixed. |
||
747 | * |
||
748 | * @param node B-tree node. |
||
749 | * @param inskey Key to be inserted. |
||
750 | * @param insvalue Value to be inserted. |
||
751 | * @param rsubtree Right subtree of inskey. |
||
752 | * |
||
753 | * @return True if the rotation was performed, false otherwise. |
||
754 | */ |
||
1142 | jermar | 755 | bool try_insert_by_rotation_to_left(btree_node_t *node, __native inskey, void *insvalue, btree_node_t *rsubtree) |
1136 | jermar | 756 | { |
757 | index_t idx; |
||
758 | btree_node_t *lnode; |
||
759 | |||
760 | /* |
||
761 | * If this is root node, the rotation can not be done. |
||
762 | */ |
||
763 | if (ROOT_NODE(node)) |
||
764 | return false; |
||
765 | |||
766 | idx = find_key_by_subtree(node->parent, node, true); |
||
767 | if ((int) idx == -1) { |
||
768 | /* |
||
769 | * If this node is the leftmost subtree of its parent, |
||
770 | * the rotation can not be done. |
||
771 | */ |
||
772 | return false; |
||
773 | } |
||
774 | |||
775 | lnode = node->parent->subtree[idx]; |
||
776 | if (lnode->keys < BTREE_MAX_KEYS) { |
||
777 | /* |
||
778 | * The rotaion can be done. The left sibling has free space. |
||
779 | */ |
||
1142 | jermar | 780 | node_insert_key_and_rsubtree(node, inskey, insvalue, rsubtree); |
781 | rotate_from_right(lnode, node, idx); |
||
1136 | jermar | 782 | return true; |
783 | } |
||
784 | |||
785 | return false; |
||
786 | } |
||
787 | |||
788 | /** Insert key-value-rsubtree triplet and rotate the node to the right, if this operation can be done. |
||
789 | * |
||
790 | * Right sibling of the node (if it exists) is checked for free space. |
||
791 | * If there is free space, the key is inserted and the biggest key of |
||
792 | * the node is moved there. The index node which is the parent of both |
||
793 | * nodes is fixed. |
||
794 | * |
||
795 | * @param node B-tree node. |
||
796 | * @param inskey Key to be inserted. |
||
797 | * @param insvalue Value to be inserted. |
||
798 | * @param rsubtree Right subtree of inskey. |
||
799 | * |
||
800 | * @return True if the rotation was performed, false otherwise. |
||
801 | */ |
||
1142 | jermar | 802 | bool try_insert_by_rotation_to_right(btree_node_t *node, __native inskey, void *insvalue, btree_node_t *rsubtree) |
1136 | jermar | 803 | { |
804 | index_t idx; |
||
805 | btree_node_t *rnode; |
||
806 | |||
807 | /* |
||
808 | * If this is root node, the rotation can not be done. |
||
809 | */ |
||
810 | if (ROOT_NODE(node)) |
||
811 | return false; |
||
812 | |||
813 | idx = find_key_by_subtree(node->parent, node, false); |
||
814 | if (idx == node->parent->keys) { |
||
815 | /* |
||
816 | * If this node is the rightmost subtree of its parent, |
||
817 | * the rotation can not be done. |
||
818 | */ |
||
819 | return false; |
||
820 | } |
||
821 | |||
822 | rnode = node->parent->subtree[idx + 1]; |
||
823 | if (rnode->keys < BTREE_MAX_KEYS) { |
||
824 | /* |
||
825 | * The rotaion can be done. The right sibling has free space. |
||
826 | */ |
||
1142 | jermar | 827 | node_insert_key_and_rsubtree(node, inskey, insvalue, rsubtree); |
828 | rotate_from_left(node, rnode, idx); |
||
829 | return true; |
||
830 | } |
||
1136 | jermar | 831 | |
1142 | jermar | 832 | return false; |
833 | } |
||
1136 | jermar | 834 | |
1142 | jermar | 835 | /** Rotate in a key from the left sibling or from the index node, if this operation can be done. |
836 | * |
||
837 | * @param rnode Node into which to add key from its left sibling or from the index node. |
||
838 | * |
||
839 | * @return True if the rotation was performed, false otherwise. |
||
840 | */ |
||
841 | bool try_rotation_from_left(btree_node_t *rnode) |
||
842 | { |
||
843 | index_t idx; |
||
844 | btree_node_t *lnode; |
||
1136 | jermar | 845 | |
1142 | jermar | 846 | /* |
847 | * If this is root node, the rotation can not be done. |
||
848 | */ |
||
849 | if (ROOT_NODE(rnode)) |
||
850 | return false; |
||
851 | |||
852 | idx = find_key_by_subtree(rnode->parent, rnode, true); |
||
853 | if ((int) idx == -1) { |
||
854 | /* |
||
855 | * If this node is the leftmost subtree of its parent, |
||
856 | * the rotation can not be done. |
||
857 | */ |
||
858 | return false; |
||
859 | } |
||
860 | |||
861 | lnode = rnode->parent->subtree[idx]; |
||
862 | if (lnode->keys > FILL_FACTOR) { |
||
863 | rotate_from_left(lnode, rnode, idx); |
||
1136 | jermar | 864 | return true; |
865 | } |
||
1142 | jermar | 866 | |
867 | return false; |
||
868 | } |
||
1136 | jermar | 869 | |
1142 | jermar | 870 | /** Rotate in a key from the right sibling or from the index node, if this operation can be done. |
871 | * |
||
872 | * @param rnode Node into which to add key from its right sibling or from the index node. |
||
873 | * |
||
874 | * @return True if the rotation was performed, false otherwise. |
||
875 | */ |
||
876 | bool try_rotation_from_right(btree_node_t *lnode) |
||
877 | { |
||
878 | index_t idx; |
||
879 | btree_node_t *rnode; |
||
880 | |||
881 | /* |
||
882 | * If this is root node, the rotation can not be done. |
||
883 | */ |
||
884 | if (ROOT_NODE(lnode)) |
||
885 | return false; |
||
886 | |||
887 | idx = find_key_by_subtree(lnode->parent, lnode, false); |
||
888 | if (idx == lnode->parent->keys) { |
||
889 | /* |
||
890 | * If this node is the rightmost subtree of its parent, |
||
891 | * the rotation can not be done. |
||
892 | */ |
||
893 | return false; |
||
894 | } |
||
895 | |||
896 | rnode = lnode->parent->subtree[idx + 1]; |
||
897 | if (rnode->keys > FILL_FACTOR) { |
||
898 | rotate_from_right(lnode, rnode, idx); |
||
899 | return true; |
||
900 | } |
||
901 | |||
1136 | jermar | 902 | return false; |
903 | } |
||
904 | |||
1101 | jermar | 905 | /** Print B-tree. |
906 | * |
||
907 | * @param t Print out B-tree. |
||
908 | */ |
||
909 | void btree_print(btree_t *t) |
||
910 | { |
||
911 | int i, depth = t->root->depth; |
||
1144 | jermar | 912 | link_t head, *cur; |
913 | |||
914 | printf("Printing B-tree:\n"); |
||
1101 | jermar | 915 | list_initialize(&head); |
916 | list_append(&t->root->bfs_link, &head); |
||
917 | |||
918 | /* |
||
919 | * Use BFS search to print out the tree. |
||
920 | * Levels are distinguished from one another by node->depth. |
||
921 | */ |
||
922 | while (!list_empty(&head)) { |
||
923 | link_t *hlp; |
||
924 | btree_node_t *node; |
||
925 | |||
926 | hlp = head.next; |
||
927 | ASSERT(hlp != &head); |
||
928 | node = list_get_instance(hlp, btree_node_t, bfs_link); |
||
929 | list_remove(hlp); |
||
930 | |||
931 | ASSERT(node); |
||
932 | |||
933 | if (node->depth != depth) { |
||
934 | printf("\n"); |
||
935 | depth = node->depth; |
||
936 | } |
||
937 | |||
938 | printf("("); |
||
939 | for (i = 0; i < node->keys; i++) { |
||
1144 | jermar | 940 | printf("%d%s", node->key[i], i < node->keys - 1 ? "," : ""); |
1101 | jermar | 941 | if (node->depth && node->subtree[i]) { |
942 | list_append(&node->subtree[i]->bfs_link, &head); |
||
943 | } |
||
944 | } |
||
945 | if (node->depth && node->subtree[i]) { |
||
946 | list_append(&node->subtree[i]->bfs_link, &head); |
||
947 | } |
||
948 | printf(")"); |
||
949 | } |
||
950 | printf("\n"); |
||
1144 | jermar | 951 | |
952 | printf("Printing list of leaves:\n"); |
||
953 | for (cur = t->leaf_head.next; cur != &t->leaf_head; cur = cur->next) { |
||
954 | btree_node_t *node; |
||
955 | |||
956 | node = list_get_instance(cur, btree_node_t, leaf_link); |
||
957 | |||
958 | ASSERT(node); |
||
959 | |||
960 | printf("("); |
||
961 | for (i = 0; i < node->keys; i++) |
||
962 | printf("%d%s", node->key[i], i < node->keys - 1 ? "," : ""); |
||
963 | printf(")"); |
||
964 | } |
||
965 | printf("\n"); |
||
1101 | jermar | 966 | } |