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| Rev | Author | Line No. | Line |
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| 2416 | mencl | 1 | /* |
| 2421 | mencl | 2 | * Copyright (c) 2007 Vojtech Mencl |
| 2416 | mencl | 3 | * All rights reserved. |
| 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 | /** @addtogroup genericadt |
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| 30 | * @{ |
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| 31 | */ |
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| 32 | |||
| 33 | /** |
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| 34 | * @file |
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| 35 | * @brief AVL tree implementation. |
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| 36 | * |
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| 37 | * This file implements AVL tree type and operations. |
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| 38 | * |
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| 39 | * Implemented AVL tree has the following properties: |
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| 2496 | jermar | 40 | * @li It is a binary search tree with non-unique keys. |
| 41 | * @li Difference of heights of the left and the right subtree of every node is |
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| 42 | * one at maximum. |
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| 2416 | mencl | 43 | * |
| 2496 | jermar | 44 | * Every node has a pointer to its parent which allows insertion of multiple |
| 45 | * identical keys into the tree. |
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| 2416 | mencl | 46 | * |
| 2496 | jermar | 47 | * Be careful when using this tree because of the base atribute which is added |
| 48 | * to every inserted node key. There is no rule in which order nodes with the |
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| 49 | * same key are visited. |
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| 2416 | mencl | 50 | */ |
| 51 | |||
| 52 | #include <adt/avl.h> |
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| 53 | #include <debug.h> |
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| 54 | |||
| 55 | |||
| 2496 | jermar | 56 | #define LEFT 0 |
| 57 | #define RIGHT 1 |
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| 2416 | mencl | 58 | |
| 59 | |||
| 2496 | jermar | 60 | /** Search for the first occurence of the given key in an AVL tree. |
| 2416 | mencl | 61 | * |
| 62 | * @param t AVL tree. |
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| 63 | * @param key Key to be searched. |
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| 64 | * |
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| 2496 | jermar | 65 | * @return Pointer to a node or NULL if there is no such key. |
| 2416 | mencl | 66 | */ |
| 67 | avltree_node_t *avltree_search(avltree_t *t, uint64_t key) |
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| 68 | { |
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| 69 | avltree_node_t *p; |
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| 70 | |||
| 71 | /* |
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| 72 | * Iteratively descend to the leaf that can contain the searched key. |
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| 73 | */ |
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| 74 | p = t->root; |
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| 75 | while (p != NULL) { |
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| 76 | if (p->key > key) |
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| 77 | p = p->lft; |
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| 78 | else if (p->key < key) |
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| 79 | p = p->rgt; |
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| 2496 | jermar | 80 | else |
| 2416 | mencl | 81 | return p; |
| 82 | } |
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| 83 | return NULL; |
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| 84 | } |
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| 85 | |||
| 86 | |||
| 2496 | jermar | 87 | /** Find the node with the smallest key in an AVL tree. |
| 2421 | mencl | 88 | * |
| 89 | * @param t AVL tree. |
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| 90 | * |
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| 2496 | jermar | 91 | * @return Pointer to a node or NULL if there is no node in the tree. |
| 2421 | mencl | 92 | */ |
| 93 | avltree_node_t *avltree_find_min(avltree_t *t) |
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| 94 | { |
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| 95 | avltree_node_t *p = t->root; |
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| 96 | |||
| 97 | /* |
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| 2496 | jermar | 98 | * Check whether the tree is empty. |
| 2421 | mencl | 99 | */ |
| 2496 | jermar | 100 | if (!p) |
| 101 | return NULL; |
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| 2421 | mencl | 102 | |
| 103 | /* |
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| 104 | * Iteratively descend to the leftmost leaf in the tree. |
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| 105 | */ |
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| 106 | while (p->lft != NULL) |
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| 107 | p = p->lft; |
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| 108 | |||
| 109 | return p; |
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| 110 | } |
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| 111 | |||
| 2416 | mencl | 112 | /** Insert new node into AVL tree. |
| 113 | * |
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| 114 | * @param t AVL tree. |
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| 115 | * @param newnode New node to be inserted. |
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| 116 | */ |
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| 117 | void avltree_insert(avltree_t *t, avltree_node_t *newnode) |
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| 118 | { |
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| 119 | avltree_node_t *par; |
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| 120 | avltree_node_t *gpa; |
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| 121 | avltree_node_t *top; |
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| 122 | avltree_node_t **dpc; |
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| 123 | uint64_t key; |
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| 124 | |||
| 125 | ASSERT(t); |
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| 126 | ASSERT(newnode); |
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| 127 | |||
| 128 | /* |
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| 129 | * Creating absolute key. |
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| 130 | */ |
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| 131 | key = newnode->key + t->base; |
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| 132 | |||
| 133 | /* |
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| 2496 | jermar | 134 | * Iteratively descend to the leaf that can contain the new node. |
| 2416 | mencl | 135 | * Last node with non-zero balance in the way to leaf is stored as top - |
| 2496 | jermar | 136 | * it is a place of possible inbalance. |
| 2416 | mencl | 137 | */ |
| 138 | dpc = &t->root; |
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| 139 | gpa = NULL; |
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| 140 | top = t->root; |
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| 2421 | mencl | 141 | while ((par = (*dpc)) != NULL) { |
| 2416 | mencl | 142 | if (par->balance != 0) { |
| 143 | top = par; |
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| 144 | } |
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| 145 | gpa = par; |
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| 2496 | jermar | 146 | dpc = par->key > key ? &par->lft: &par->rgt; |
| 2416 | mencl | 147 | } |
| 148 | |||
| 149 | /* |
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| 150 | * Initialize new node. |
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| 151 | */ |
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| 152 | newnode->key = key; |
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| 153 | newnode->lft = NULL; |
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| 154 | newnode->rgt = NULL; |
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| 155 | newnode->par = gpa; |
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| 156 | newnode->balance = 0; |
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| 157 | |||
| 158 | /* |
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| 2496 | jermar | 159 | * Insert first node into the empty tree. |
| 2416 | mencl | 160 | */ |
| 161 | if (t->root == NULL) { |
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| 162 | *dpc = newnode; |
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| 163 | return; |
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| 164 | } |
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| 165 | |||
| 166 | /* |
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| 167 | * Insert new node into previously found leaf place. |
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| 168 | */ |
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| 169 | *dpc = newnode; |
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| 170 | |||
| 171 | /* |
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| 2496 | jermar | 172 | * If the tree contains one node - end. |
| 2416 | mencl | 173 | */ |
| 2496 | jermar | 174 | if (top == NULL) |
| 175 | return; |
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| 2416 | mencl | 176 | |
| 177 | /* |
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| 2496 | jermar | 178 | * Store pointer of top's father which points to the node with |
| 179 | * potentially broken balance (top). |
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| 2416 | mencl | 180 | */ |
| 2496 | jermar | 181 | if (top->par == NULL) { |
| 2416 | mencl | 182 | dpc = &t->root; |
| 2496 | jermar | 183 | } else { |
| 2416 | mencl | 184 | if (top->par->lft == top) |
| 2496 | jermar | 185 | dpc = &top->par->lft; |
| 2416 | mencl | 186 | else |
| 2496 | jermar | 187 | dpc = &top->par->rgt; |
| 188 | } |
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| 2416 | mencl | 189 | |
| 190 | /* |
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| 2496 | jermar | 191 | * Repair all balances on the way from top node to the newly inserted |
| 192 | * node. |
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| 2416 | mencl | 193 | */ |
| 194 | par = top; |
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| 195 | while (par != newnode) { |
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| 196 | if (par->key > key) { |
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| 197 | par->balance--; |
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| 198 | par = par->lft; |
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| 199 | } else { |
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| 200 | par->balance++; |
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| 201 | par = par->rgt; |
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| 202 | } |
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| 203 | } |
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| 204 | |||
| 205 | /* |
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| 2496 | jermar | 206 | * To balance the tree, we must check and balance top node. |
| 2416 | mencl | 207 | */ |
| 208 | if (top->balance == -2) { |
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| 209 | par = top->lft; |
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| 210 | if (par->balance == -1) { |
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| 211 | /* |
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| 212 | * LL rotation. |
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| 213 | */ |
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| 214 | top->lft = par->rgt; |
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| 2496 | jermar | 215 | if (top->lft != NULL) |
| 216 | top->lft->par = top; |
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| 2416 | mencl | 217 | par->par = top->par; |
| 218 | top->par = par; |
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| 219 | par->rgt = top; |
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| 220 | par->balance = top->balance = 0; |
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| 221 | *dpc = par; |
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| 222 | } else { |
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| 223 | /* |
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| 224 | * LR rotation. |
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| 225 | */ |
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| 226 | ASSERT(par->balance == 1); |
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| 227 | |||
| 228 | gpa = par->rgt; |
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| 229 | par->rgt = gpa->lft; |
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| 2496 | jermar | 230 | if (gpa->lft != NULL) |
| 231 | gpa->lft->par = par; |
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| 2416 | mencl | 232 | gpa->lft = par; |
| 233 | par->par = gpa; |
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| 234 | top->lft = gpa->rgt; |
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| 2496 | jermar | 235 | if (gpa->rgt != NULL) |
| 236 | gpa->rgt->par = top; |
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| 2416 | mencl | 237 | gpa->rgt = top; |
| 238 | gpa->par = top->par; |
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| 239 | top->par = gpa; |
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| 240 | |||
| 241 | if (gpa->balance == -1) { |
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| 242 | par->balance = 0; |
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| 243 | top->balance = 1; |
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| 244 | } else if (gpa->balance == 0) { |
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| 245 | par->balance = top->balance = 0; |
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| 246 | } else { |
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| 247 | par->balance = -1; |
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| 248 | top->balance = 0; |
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| 249 | } |
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| 250 | gpa->balance = 0; |
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| 251 | *dpc = gpa; |
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| 252 | } |
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| 253 | } else if (top->balance == 2) { |
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| 254 | par = top->rgt; |
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| 255 | if (par->balance == 1) { |
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| 256 | /* |
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| 257 | * RR rotation. |
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| 258 | */ |
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| 259 | top->rgt = par->lft; |
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| 2496 | jermar | 260 | if (top->rgt != NULL) |
| 261 | top->rgt->par = top; |
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| 2416 | mencl | 262 | par->par = top->par; |
| 263 | top->par = par; |
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| 264 | par->lft = top; |
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| 265 | par->balance = top->balance = 0; |
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| 266 | *dpc = par; |
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| 267 | } else { |
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| 268 | /* |
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| 269 | * RL rotation. |
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| 270 | */ |
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| 271 | ASSERT(par->balance == -1); |
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| 272 | |||
| 273 | gpa = par->lft; |
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| 274 | par->lft = gpa->rgt; |
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| 2496 | jermar | 275 | if (gpa->rgt != NULL) |
| 276 | gpa->rgt->par = par; |
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| 2416 | mencl | 277 | gpa->rgt = par; |
| 278 | par->par = gpa; |
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| 279 | top->rgt = gpa->lft; |
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| 2496 | jermar | 280 | if (gpa->lft != NULL) |
| 281 | gpa->lft->par = top; |
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| 2416 | mencl | 282 | gpa->lft = top; |
| 283 | gpa->par = top->par; |
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| 284 | top->par = gpa; |
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| 285 | |||
| 286 | if (gpa->balance == 1) { |
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| 287 | par->balance = 0; |
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| 288 | top->balance = -1; |
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| 289 | } else if (gpa->balance == 0) { |
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| 290 | par->balance = top->balance = 0; |
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| 291 | } else { |
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| 292 | par->balance = 1; |
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| 293 | top->balance = 0; |
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| 294 | } |
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| 295 | gpa->balance = 0; |
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| 296 | *dpc = gpa; |
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| 297 | } |
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| 298 | } else { |
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| 299 | /* |
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| 300 | * Balance is not broken, insertion is finised. |
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| 301 | */ |
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| 302 | return; |
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| 303 | } |
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| 304 | |||
| 305 | } |
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| 306 | |||
| 2496 | jermar | 307 | /** Delete a node from the AVL tree. |
| 2416 | mencl | 308 | * |
| 2496 | jermar | 309 | * Because multiple identical keys are allowed, the parent pointers are |
| 310 | * essential during deletion. |
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| 2416 | mencl | 311 | * |
| 312 | * @param t AVL tree structure. |
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| 2496 | jermar | 313 | * @param node Address of the node which will be deleted. |
| 2416 | mencl | 314 | */ |
| 315 | void avltree_delete(avltree_t *t, avltree_node_t *node) |
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| 316 | { |
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| 317 | avltree_node_t *cur; |
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| 318 | avltree_node_t *par; |
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| 319 | avltree_node_t *gpa; |
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| 320 | uint8_t dir; |
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| 321 | |||
| 322 | ASSERT(t); |
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| 323 | ASSERT(node); |
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| 324 | |||
| 325 | if (node->lft == NULL) { |
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| 326 | if (node->rgt) { |
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| 327 | /* |
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| 2496 | jermar | 328 | * Replace the node with its only right son. |
| 2416 | mencl | 329 | * |
| 2496 | jermar | 330 | * Balance of the right son will be repaired in the |
| 331 | * balancing cycle. |
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| 2416 | mencl | 332 | */ |
| 333 | cur = node->rgt; |
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| 334 | cur->par = node->par; |
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| 335 | gpa = cur; |
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| 2496 | jermar | 336 | dir = RIGHT; |
| 2416 | mencl | 337 | cur->balance = node->balance; |
| 338 | } else { |
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| 339 | if (node->par == NULL) { |
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| 340 | /* |
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| 2496 | jermar | 341 | * The tree has only one node - it will become |
| 342 | * an empty tree and the balancing can end. |
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| 2416 | mencl | 343 | */ |
| 344 | t->root = NULL; |
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| 345 | return; |
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| 346 | } |
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| 347 | /* |
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| 2496 | jermar | 348 | * The node has no child, it will be deleted with no |
| 349 | * substitution. |
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| 2416 | mencl | 350 | */ |
| 351 | gpa = node->par; |
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| 352 | cur = NULL; |
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| 2496 | jermar | 353 | dir = (gpa->lft == node) ? LEFT: RIGHT; |
| 2416 | mencl | 354 | } |
| 355 | } else { |
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| 356 | /* |
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| 2496 | jermar | 357 | * The node has left and right son. Find a node with the |
| 358 | * smallest key in the left subtree and replace the deleted node |
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| 359 | * with that node. |
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| 2416 | mencl | 360 | */ |
| 361 | for (cur = node->lft; cur->rgt != NULL; cur = cur->rgt) |
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| 362 | ; |
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| 2496 | jermar | 363 | |
| 2416 | mencl | 364 | if (cur != node->lft) { |
| 365 | /* |
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| 2496 | jermar | 366 | * The rightmost node of the deleted node's left subtree |
| 367 | * was found. Replace the deleted node with this node. |
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| 368 | * Cutting off of the found node has two cases that |
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| 369 | * depend on its left son. |
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| 2416 | mencl | 370 | */ |
| 371 | if (cur->lft) { |
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| 372 | /* |
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| 2496 | jermar | 373 | * The found node has a left son. |
| 2416 | mencl | 374 | */ |
| 375 | gpa = cur->lft; |
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| 376 | gpa->par = cur->par; |
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| 2496 | jermar | 377 | dir = LEFT; |
| 2416 | mencl | 378 | gpa->balance = cur->balance; |
| 379 | } else { |
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| 2496 | jermar | 380 | dir = RIGHT; |
| 2416 | mencl | 381 | gpa = cur->par; |
| 382 | } |
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| 383 | cur->par->rgt = cur->lft; |
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| 384 | cur->lft = node->lft; |
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| 385 | cur->lft->par = cur; |
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| 386 | } else { |
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| 387 | /* |
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| 2496 | jermar | 388 | * The left son of the node hasn't got a right son. The |
| 389 | * left son will take the deleted node's place. |
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| 2416 | mencl | 390 | */ |
| 2496 | jermar | 391 | dir = LEFT; |
| 2416 | mencl | 392 | gpa = cur; |
| 393 | } |
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| 2496 | jermar | 394 | if (node->rgt) |
| 395 | node->rgt->par = cur; |
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| 2416 | mencl | 396 | cur->rgt = node->rgt; |
| 397 | cur->balance = node->balance; |
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| 398 | cur->par = node->par; |
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| 399 | } |
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| 400 | |||
| 401 | /* |
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| 2496 | jermar | 402 | * Repair the parent node's pointer which pointed previously to the |
| 403 | * deleted node. |
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| 2416 | mencl | 404 | */ |
| 405 | if (node->par == NULL) { |
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| 406 | t->root = cur; |
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| 407 | } else { |
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| 408 | if (node->par->lft == node) { |
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| 409 | node->par->lft = cur; |
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| 410 | } else { |
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| 411 | node->par->rgt = cur; |
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| 412 | } |
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| 413 | } |
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| 414 | |||
| 415 | /* |
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| 2496 | jermar | 416 | * Repair cycle which repairs balances of nodes on the way from from the |
| 417 | * cut-off node up to the root. |
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| 2416 | mencl | 418 | */ |
| 2496 | jermar | 419 | for (;;) { |
| 420 | if (dir == LEFT) { |
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| 2416 | mencl | 421 | /* |
| 2496 | jermar | 422 | * Deletion was made in the left subtree. |
| 2416 | mencl | 423 | */ |
| 424 | gpa->balance++; |
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| 2496 | jermar | 425 | if (gpa->balance == 1) { |
| 2416 | mencl | 426 | /* |
| 2496 | jermar | 427 | * Stop balancing, the tree is balanced. |
| 2416 | mencl | 428 | */ |
| 429 | break; |
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| 2496 | jermar | 430 | } else if (gpa->balance == 2) { |
| 2416 | mencl | 431 | /* |
| 2496 | jermar | 432 | * Bad balance, heights of left and right |
| 433 | * subtrees differ more than by one. |
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| 2416 | mencl | 434 | */ |
| 435 | par = gpa->rgt; |
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| 436 | |||
| 437 | if (par->balance == -1) { |
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| 438 | /* |
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| 439 | * RL rotation. |
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| 440 | */ |
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| 441 | |||
| 442 | cur = par->lft; |
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| 443 | par->lft = cur->rgt; |
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| 444 | cur->rgt = par; |
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| 445 | gpa->rgt = cur->lft; |
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| 446 | cur->lft = gpa; |
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| 447 | |||
| 448 | /* |
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| 2496 | jermar | 449 | * Repair balances and paternity of |
| 450 | * children, depending on the balance |
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| 451 | * factor of the grand child (cur). |
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| 2416 | mencl | 452 | */ |
| 2496 | jermar | 453 | if (cur->balance == 1) { |
| 2416 | mencl | 454 | par->balance = 0; |
| 455 | gpa->balance = -1; |
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| 2496 | jermar | 456 | if (gpa->rgt) |
| 457 | gpa->rgt->par = gpa; |
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| 2416 | mencl | 458 | par->lft->par = par; |
| 459 | } else if (cur->balance == 0) { |
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| 460 | par->balance = gpa->balance = 0; |
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| 2496 | jermar | 461 | if (gpa->rgt) |
| 462 | gpa->rgt->par = gpa; |
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| 463 | if (par->lft) |
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| 464 | par->lft->par = par; |
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| 2416 | mencl | 465 | } else { |
| 2496 | jermar | 466 | par->balance = 1; |
| 2416 | mencl | 467 | gpa->balance = 0; |
| 2496 | jermar | 468 | if (par->lft) |
| 469 | par->lft->par = par; |
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| 2416 | mencl | 470 | gpa->rgt->par = gpa; |
| 471 | } |
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| 472 | cur->balance = 0; |
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| 473 | |||
| 474 | /* |
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| 475 | * Repair paternity. |
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| 476 | */ |
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| 477 | cur->par = gpa->par; |
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| 478 | gpa->par = cur; |
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| 479 | par->par = cur; |
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| 480 | |||
| 481 | /* |
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| 2496 | jermar | 482 | * Repair the pointer which pointed to |
| 483 | * the balanced node. If it was root |
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| 484 | * then the balancing is finished. |
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| 485 | * Otherwise continue with the next |
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| 486 | * iteration (parent node). |
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| 2416 | mencl | 487 | */ |
| 488 | if (cur->par == NULL) { |
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| 489 | t->root = cur; |
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| 490 | break; |
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| 2496 | jermar | 491 | } else { |
| 2416 | mencl | 492 | if (cur->par->lft == gpa) { |
| 493 | cur->par->lft = cur; |
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| 2496 | jermar | 494 | dir = LEFT; |
| 2416 | mencl | 495 | } else { |
| 496 | cur->par->rgt = cur; |
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| 2496 | jermar | 497 | dir = RIGHT; |
| 2416 | mencl | 498 | } |
| 2496 | jermar | 499 | } |
| 2416 | mencl | 500 | gpa = cur->par; |
| 501 | } else { |
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| 502 | /* |
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| 503 | * RR rotation. |
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| 504 | */ |
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| 505 | |||
| 506 | gpa->rgt = par->lft; |
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| 2496 | jermar | 507 | if (par->lft) |
| 508 | par->lft->par = gpa; |
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| 2416 | mencl | 509 | par->lft = gpa; |
| 510 | |||
| 511 | /* |
||
| 512 | * Repair paternity. |
||
| 513 | */ |
||
| 514 | par->par = gpa->par; |
||
| 515 | gpa->par = par; |
||
| 516 | |||
| 517 | if (par->balance == 0) { |
||
| 518 | /* |
||
| 2496 | jermar | 519 | * The right child of the |
| 520 | * balanced node is balanced, |
||
| 521 | * after RR rotation is done, |
||
| 522 | * the whole tree will be |
||
| 523 | * balanced. |
||
| 2416 | mencl | 524 | */ |
| 525 | par->balance = -1; |
||
| 2496 | jermar | 526 | gpa->balance = 1; |
| 2416 | mencl | 527 | |
| 528 | /* |
||
| 2496 | jermar | 529 | * Repair the pointer which |
| 530 | * pointed to the balanced node |
||
| 531 | * and finish balancing. |
||
| 2416 | mencl | 532 | */ |
| 533 | if (par->par == NULL) { |
||
| 534 | t->root = par; |
||
| 2496 | jermar | 535 | } else { |
| 536 | if (par->par->lft == |
||
| 537 | gpa) { |
||
| 538 | par->par->lft = |
||
| 539 | par; |
||
| 2416 | mencl | 540 | } else { |
| 2496 | jermar | 541 | par->par->rgt = |
| 542 | par; |
||
| 2416 | mencl | 543 | } |
| 2496 | jermar | 544 | } |
| 2416 | mencl | 545 | break; |
| 546 | } else { |
||
| 547 | par->balance = gpa->balance = 0; |
||
| 548 | /* |
||
| 2496 | jermar | 549 | * Repair the pointer which |
| 550 | * pointed to the balanced node. |
||
| 551 | * If it was root then balancing |
||
| 552 | * is finished. Otherwise |
||
| 553 | * continue with the next |
||
| 554 | * iteration (parent node). |
||
| 2416 | mencl | 555 | */ |
| 556 | if (par->par == NULL) { |
||
| 557 | t->root = par; |
||
| 558 | break; |
||
| 2496 | jermar | 559 | } else { |
| 560 | if (par->par->lft == |
||
| 561 | gpa) { |
||
| 562 | par->par->lft = |
||
| 563 | par; |
||
| 564 | dir = LEFT; |
||
| 2416 | mencl | 565 | } else { |
| 2496 | jermar | 566 | par->par->rgt = |
| 567 | par; |
||
| 568 | dir = RIGHT; |
||
| 2416 | mencl | 569 | } |
| 570 | } |
||
| 571 | } |
||
| 572 | gpa = par->par; |
||
| 573 | } |
||
| 574 | } else { |
||
| 575 | /* |
||
| 2496 | jermar | 576 | * Repair the pointer which pointed to the |
| 577 | * balanced node. If it was root then balancing |
||
| 578 | * is finished else continue with the next |
||
| 579 | * iteration (parent node). |
||
| 2416 | mencl | 580 | */ |
| 2496 | jermar | 581 | if (!gpa->par) |
| 582 | break; |
||
| 2416 | mencl | 583 | |
| 584 | if (gpa->par->lft == gpa) { |
||
| 2496 | jermar | 585 | dir = LEFT; |
| 2416 | mencl | 586 | } else { |
| 2496 | jermar | 587 | dir = RIGHT; |
| 2416 | mencl | 588 | } |
| 589 | gpa = gpa->par; |
||
| 590 | } |
||
| 591 | } else { |
||
| 592 | /* |
||
| 2496 | jermar | 593 | * Deletion was made in the right subtree. |
| 2416 | mencl | 594 | */ |
| 595 | gpa->balance--; |
||
| 596 | if (gpa->balance == -1) { |
||
| 597 | /* |
||
| 2496 | jermar | 598 | * Stop balancing, the tree is balanced. |
| 2416 | mencl | 599 | */ |
| 600 | break; |
||
| 601 | } else if (gpa->balance == -2) { |
||
| 602 | /* |
||
| 2496 | jermar | 603 | * Bad balance, heights of left and right |
| 604 | * subtrees differ more than by one. |
||
| 2416 | mencl | 605 | */ |
| 606 | par = gpa->lft; |
||
| 607 | |||
| 2496 | jermar | 608 | if (par->balance == 1) { |
| 2416 | mencl | 609 | /* |
| 610 | * LR rotation. |
||
| 611 | */ |
||
| 612 | |||
| 613 | cur = par->rgt; |
||
| 614 | par->rgt = cur->lft; |
||
| 615 | cur->lft = par; |
||
| 616 | gpa->lft = cur->rgt; |
||
| 617 | cur->rgt = gpa; |
||
| 618 | |||
| 619 | /* |
||
| 2496 | jermar | 620 | * Repair balances and paternity of |
| 621 | * children, depending on the balance |
||
| 622 | * factor of the grand child (cur). |
||
| 2416 | mencl | 623 | */ |
| 624 | if (cur->balance == -1) { |
||
| 625 | par->balance = 0; |
||
| 2496 | jermar | 626 | gpa->balance = 1; |
| 627 | if (gpa->lft) |
||
| 628 | gpa->lft->par = gpa; |
||
| 2416 | mencl | 629 | par->rgt->par = par; |
| 630 | } else if (cur->balance == 0) { |
||
| 631 | par->balance = gpa->balance = 0; |
||
| 2496 | jermar | 632 | if (gpa->lft) |
| 633 | gpa->lft->par = gpa; |
||
| 634 | if (par->rgt) |
||
| 635 | par->rgt->par = par; |
||
| 2416 | mencl | 636 | } else { |
| 637 | par->balance = -1; |
||
| 638 | gpa->balance = 0; |
||
| 2496 | jermar | 639 | if (par->rgt) |
| 640 | par->rgt->par = par; |
||
| 2416 | mencl | 641 | gpa->lft->par = gpa; |
| 642 | } |
||
| 643 | cur->balance = 0; |
||
| 644 | |||
| 645 | /* |
||
| 646 | * Repair paternity. |
||
| 647 | */ |
||
| 648 | cur->par = gpa->par; |
||
| 649 | gpa->par = cur; |
||
| 650 | par->par = cur; |
||
| 651 | |||
| 652 | /* |
||
| 2496 | jermar | 653 | * Repair the pointer which pointed to |
| 654 | * the balanced node. If it was root |
||
| 655 | * then balancing is finished. Otherwise |
||
| 656 | * continue with the next iteration |
||
| 657 | * (parent node). |
||
| 2416 | mencl | 658 | */ |
| 659 | if (cur->par == NULL) { |
||
| 660 | t->root = cur; |
||
| 661 | break; |
||
| 2496 | jermar | 662 | } else { |
| 2416 | mencl | 663 | if (cur->par->lft == gpa) { |
| 664 | cur->par->lft = cur; |
||
| 2496 | jermar | 665 | dir = LEFT; |
| 2416 | mencl | 666 | } else { |
| 667 | cur->par->rgt = cur; |
||
| 2496 | jermar | 668 | dir = RIGHT; |
| 2416 | mencl | 669 | } |
| 2496 | jermar | 670 | } |
| 2416 | mencl | 671 | gpa = cur->par; |
| 672 | } else { |
||
| 673 | /* |
||
| 674 | * LL rotation. |
||
| 675 | */ |
||
| 676 | |||
| 677 | gpa->lft = par->rgt; |
||
| 2496 | jermar | 678 | if (par->rgt) |
| 679 | par->rgt->par = gpa; |
||
| 2416 | mencl | 680 | par->rgt = gpa; |
| 681 | /* |
||
| 682 | * Repair paternity. |
||
| 683 | */ |
||
| 684 | par->par = gpa->par; |
||
| 685 | gpa->par = par; |
||
| 686 | |||
| 687 | if (par->balance == 0) { |
||
| 688 | /* |
||
| 2496 | jermar | 689 | * The left child of the |
| 690 | * balanced node is balanced, |
||
| 691 | * after LL rotation is done, |
||
| 692 | * the whole tree will be |
||
| 693 | * balanced. |
||
| 2416 | mencl | 694 | */ |
| 2496 | jermar | 695 | par->balance = 1; |
| 2416 | mencl | 696 | gpa->balance = -1; |
| 697 | |||
| 698 | /* |
||
| 2496 | jermar | 699 | * Repair the pointer which |
| 700 | * pointed to the balanced node |
||
| 701 | * and finish balancing. |
||
| 2416 | mencl | 702 | */ |
| 703 | if (par->par == NULL) { |
||
| 704 | t->root = par; |
||
| 2496 | jermar | 705 | } else { |
| 706 | if (par->par->lft == |
||
| 707 | gpa) { |
||
| 708 | par->par->lft = |
||
| 709 | par; |
||
| 2416 | mencl | 710 | } else { |
| 2496 | jermar | 711 | par->par->rgt = |
| 712 | par; |
||
| 2416 | mencl | 713 | } |
| 2496 | jermar | 714 | } |
| 2416 | mencl | 715 | break; |
| 716 | } else { |
||
| 717 | par->balance = gpa->balance = 0; |
||
| 718 | |||
| 719 | /* |
||
| 2496 | jermar | 720 | * Repair the pointer which |
| 721 | * pointed to the balanced node. |
||
| 722 | * If it was root then balancing |
||
| 723 | * is finished. Otherwise |
||
| 724 | * continue with the next |
||
| 725 | * iteration (parent node). |
||
| 2416 | mencl | 726 | */ |
| 727 | if (par->par == NULL) { |
||
| 728 | t->root = par; |
||
| 729 | break; |
||
| 730 | } else { |
||
| 2496 | jermar | 731 | if (par->par->lft == |
| 732 | gpa) { |
||
| 733 | par->par->lft = |
||
| 734 | par; |
||
| 735 | dir = LEFT; |
||
| 2416 | mencl | 736 | } else { |
| 2496 | jermar | 737 | par->par->rgt = |
| 738 | par; |
||
| 739 | dir = RIGHT; |
||
| 2416 | mencl | 740 | } |
| 741 | } |
||
| 742 | } |
||
| 743 | gpa = par->par; |
||
| 744 | } |
||
| 745 | } else { |
||
| 746 | /* |
||
| 2496 | jermar | 747 | * Repair the pointer which pointed to the |
| 748 | * balanced node. If it was root then balancing |
||
| 749 | * is finished. Otherwise continue with the next |
||
| 750 | * iteration (parent node). |
||
| 2416 | mencl | 751 | */ |
| 2496 | jermar | 752 | if (!gpa->par) |
| 753 | break; |
||
| 2416 | mencl | 754 | |
| 755 | if (gpa->par->lft == gpa) { |
||
| 2496 | jermar | 756 | dir = LEFT; |
| 2416 | mencl | 757 | } else { |
| 2496 | jermar | 758 | dir = RIGHT; |
| 2416 | mencl | 759 | } |
| 760 | gpa = gpa->par; |
||
| 761 | } |
||
| 762 | } |
||
| 763 | } |
||
| 764 | } |
||
| 765 | |||
| 766 | |||
| 2496 | jermar | 767 | /** Delete a node with the smallest key from the AVL tree. |
| 2416 | mencl | 768 | * |
| 769 | * @param t AVL tree structure. |
||
| 770 | */ |
||
| 2421 | mencl | 771 | bool avltree_delete_min(avltree_t *t) |
| 2416 | mencl | 772 | { |
| 773 | avltree_node_t *node; |
||
| 774 | |||
| 775 | /* |
||
| 2496 | jermar | 776 | * Start searching for the smallest key in the tree starting in the root |
| 777 | * node and continue in cycle to the leftmost node in the tree (which |
||
| 778 | * must have the smallest key). |
||
| 2416 | mencl | 779 | */ |
| 2496 | jermar | 780 | |
| 2416 | mencl | 781 | node = t->root; |
| 2496 | jermar | 782 | if (!node) |
| 783 | return false; |
||
| 2416 | mencl | 784 | |
| 785 | while (node->lft != NULL) |
||
| 786 | node = node->lft; |
||
| 787 | |||
| 2496 | jermar | 788 | avltree_delete(t, node); |
| 2416 | mencl | 789 | |
| 790 | return true; |
||
| 791 | } |
||
| 2496 | jermar | 792 | |
| 793 | /** @} |
||
| 794 | */ |