[9] | 1 | /* glpavl.c (binary search tree) */ |
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| 2 | |
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| 3 | /*********************************************************************** |
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| 4 | * This code is part of GLPK (GNU Linear Programming Kit). |
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| 5 | * |
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| 6 | * Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, |
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| 7 | * 2009, 2010, 2011 Andrew Makhorin, Department for Applied Informatics, |
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| 8 | * Moscow Aviation Institute, Moscow, Russia. All rights reserved. |
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| 9 | * E-mail: <mao@gnu.org>. |
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| 10 | * |
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| 11 | * GLPK is free software: you can redistribute it and/or modify it |
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| 12 | * under the terms of the GNU General Public License as published by |
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| 13 | * the Free Software Foundation, either version 3 of the License, or |
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| 14 | * (at your option) any later version. |
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| 15 | * |
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| 16 | * GLPK is distributed in the hope that it will be useful, but WITHOUT |
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| 17 | * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY |
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| 18 | * or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public |
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| 19 | * License for more details. |
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| 20 | * |
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| 21 | * You should have received a copy of the GNU General Public License |
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| 22 | * along with GLPK. If not, see <http://www.gnu.org/licenses/>. |
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| 23 | ***********************************************************************/ |
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| 24 | |
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| 25 | #include "glpavl.h" |
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| 26 | |
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| 27 | AVL *avl_create_tree(int (*fcmp)(void *info, const void *key1, |
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| 28 | const void *key2), void *info) |
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| 29 | { /* create AVL tree */ |
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| 30 | AVL *tree; |
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| 31 | tree = xmalloc(sizeof(AVL)); |
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| 32 | tree->pool = dmp_create_pool(); |
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| 33 | tree->root = NULL; |
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| 34 | tree->fcmp = fcmp; |
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| 35 | tree->info = info; |
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| 36 | tree->size = 0; |
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| 37 | tree->height = 0; |
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| 38 | return tree; |
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| 39 | } |
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| 40 | |
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| 41 | int avl_strcmp(void *info, const void *key1, const void *key2) |
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| 42 | { /* compare character string keys */ |
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| 43 | xassert(info == info); |
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| 44 | return strcmp(key1, key2); |
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| 45 | } |
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| 46 | |
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| 47 | static AVLNODE *rotate_subtree(AVL *tree, AVLNODE *node); |
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| 48 | |
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| 49 | AVLNODE *avl_insert_node(AVL *tree, const void *key) |
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| 50 | { /* insert new node into AVL tree */ |
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| 51 | AVLNODE *p, *q, *r; |
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| 52 | short int flag; |
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| 53 | /* find an appropriate point for insertion */ |
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| 54 | p = NULL; q = tree->root; |
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| 55 | while (q != NULL) |
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| 56 | { p = q; |
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| 57 | if (tree->fcmp(tree->info, key, p->key) <= 0) |
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| 58 | { flag = 0; |
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| 59 | q = p->left; |
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| 60 | p->rank++; |
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| 61 | } |
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| 62 | else |
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| 63 | { flag = 1; |
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| 64 | q = p->right; |
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| 65 | } |
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| 66 | } |
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| 67 | /* create new node and insert it into the tree */ |
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| 68 | r = dmp_get_atom(tree->pool, sizeof(AVLNODE)); |
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| 69 | r->key = key; r->type = 0; r->link = NULL; |
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| 70 | r->rank = 1; r->up = p; |
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| 71 | r->flag = (short int)(p == NULL ? 0 : flag); |
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| 72 | r->bal = 0; r->left = NULL; r->right = NULL; |
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| 73 | tree->size++; |
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| 74 | if (p == NULL) |
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| 75 | tree->root = r; |
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| 76 | else |
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| 77 | if (flag == 0) p->left = r; else p->right = r; |
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| 78 | /* go upstairs to the root and correct all subtrees affected by |
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| 79 | insertion */ |
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| 80 | while (p != NULL) |
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| 81 | { if (flag == 0) |
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| 82 | { /* the height of the left subtree of [p] is increased */ |
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| 83 | if (p->bal > 0) |
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| 84 | { p->bal = 0; |
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| 85 | break; |
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| 86 | } |
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| 87 | if (p->bal < 0) |
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| 88 | { rotate_subtree(tree, p); |
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| 89 | break; |
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| 90 | } |
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| 91 | p->bal = -1; flag = p->flag; p = p->up; |
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| 92 | } |
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| 93 | else |
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| 94 | { /* the height of the right subtree of [p] is increased */ |
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| 95 | if (p->bal < 0) |
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| 96 | { p->bal = 0; |
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| 97 | break; |
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| 98 | } |
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| 99 | if (p->bal > 0) |
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| 100 | { rotate_subtree(tree, p); |
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| 101 | break; |
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| 102 | } |
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| 103 | p->bal = +1; flag = p->flag; p = p->up; |
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| 104 | } |
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| 105 | } |
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| 106 | /* if the root has been reached, the height of the entire tree is |
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| 107 | increased */ |
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| 108 | if (p == NULL) tree->height++; |
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| 109 | return r; |
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| 110 | } |
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| 111 | |
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| 112 | void avl_set_node_type(AVLNODE *node, int type) |
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| 113 | { /* assign the type field of specified node */ |
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| 114 | node->type = type; |
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| 115 | return; |
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| 116 | } |
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| 117 | |
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| 118 | void avl_set_node_link(AVLNODE *node, void *link) |
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| 119 | { /* assign the link field of specified node */ |
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| 120 | node->link = link; |
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| 121 | return; |
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| 122 | } |
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| 123 | |
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| 124 | AVLNODE *avl_find_node(AVL *tree, const void *key) |
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| 125 | { /* find node in AVL tree */ |
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| 126 | AVLNODE *p; |
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| 127 | int c; |
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| 128 | p = tree->root; |
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| 129 | while (p != NULL) |
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| 130 | { c = tree->fcmp(tree->info, key, p->key); |
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| 131 | if (c == 0) break; |
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| 132 | p = (c < 0 ? p->left : p->right); |
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| 133 | } |
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| 134 | return p; |
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| 135 | } |
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| 136 | |
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| 137 | int avl_get_node_type(AVLNODE *node) |
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| 138 | { /* retrieve the type field of specified node */ |
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| 139 | return node->type; |
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| 140 | } |
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| 141 | |
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| 142 | void *avl_get_node_link(AVLNODE *node) |
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| 143 | { /* retrieve the link field of specified node */ |
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| 144 | return node->link; |
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| 145 | } |
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| 146 | |
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| 147 | static AVLNODE *find_next_node(AVL *tree, AVLNODE *node) |
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| 148 | { /* find next node in AVL tree */ |
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| 149 | AVLNODE *p, *q; |
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| 150 | if (tree->root == NULL) return NULL; |
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| 151 | p = node; |
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| 152 | q = (p == NULL ? tree->root : p->right); |
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| 153 | if (q == NULL) |
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| 154 | { /* go upstairs from the left subtree */ |
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| 155 | for (;;) |
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| 156 | { q = p->up; |
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| 157 | if (q == NULL) break; |
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| 158 | if (p->flag == 0) break; |
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| 159 | p = q; |
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| 160 | } |
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| 161 | } |
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| 162 | else |
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| 163 | { /* go downstairs into the right subtree */ |
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| 164 | for (;;) |
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| 165 | { p = q->left; |
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| 166 | if (p == NULL) break; |
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| 167 | q = p; |
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| 168 | } |
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| 169 | } |
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| 170 | return q; |
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| 171 | } |
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| 172 | |
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| 173 | void avl_delete_node(AVL *tree, AVLNODE *node) |
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| 174 | { /* delete specified node from AVL tree */ |
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| 175 | AVLNODE *f, *p, *q, *r, *s, *x, *y; |
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| 176 | short int flag; |
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| 177 | p = node; |
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| 178 | /* if both subtrees of the specified node are non-empty, the node |
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| 179 | should be interchanged with the next one, at least one subtree |
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| 180 | of which is always empty */ |
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| 181 | if (p->left == NULL || p->right == NULL) goto skip; |
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| 182 | f = p->up; q = p->left; |
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| 183 | r = find_next_node(tree, p); s = r->right; |
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| 184 | if (p->right == r) |
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| 185 | { if (f == NULL) |
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| 186 | tree->root = r; |
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| 187 | else |
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| 188 | if (p->flag == 0) f->left = r; else f->right = r; |
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| 189 | r->rank = p->rank; r->up = f; |
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| 190 | r->flag = p->flag; r->bal = p->bal; |
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| 191 | r->left = q; r->right = p; |
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| 192 | q->up = r; |
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| 193 | p->rank = 1; p->up = r; p->flag = 1; |
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| 194 | p->bal = (short int)(s == NULL ? 0 : +1); |
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| 195 | p->left = NULL; p->right = s; |
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| 196 | if (s != NULL) s->up = p; |
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| 197 | } |
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| 198 | else |
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| 199 | { x = p->right; y = r->up; |
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| 200 | if (f == NULL) |
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| 201 | tree->root = r; |
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| 202 | else |
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| 203 | if (p->flag == 0) f->left = r; else f->right = r; |
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| 204 | r->rank = p->rank; r->up = f; |
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| 205 | r->flag = p->flag; r->bal = p->bal; |
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| 206 | r->left = q; r->right = x; |
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| 207 | q->up = r; x->up = r; y->left = p; |
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| 208 | p->rank = 1; p->up = y; p->flag = 0; |
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| 209 | p->bal = (short int)(s == NULL ? 0 : +1); |
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| 210 | p->left = NULL; p->right = s; |
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| 211 | if (s != NULL) s->up = p; |
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| 212 | } |
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| 213 | skip: /* now the specified node [p] has at least one empty subtree; |
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| 214 | go upstairs to the root and adjust the rank field of all nodes |
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| 215 | affected by deletion */ |
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| 216 | q = p; f = q->up; |
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| 217 | while (f != NULL) |
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| 218 | { if (q->flag == 0) f->rank--; |
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| 219 | q = f; f = q->up; |
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| 220 | } |
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| 221 | /* delete the specified node from the tree */ |
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| 222 | f = p->up; flag = p->flag; |
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| 223 | q = p->left != NULL ? p->left : p->right; |
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| 224 | if (f == NULL) |
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| 225 | tree->root = q; |
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| 226 | else |
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| 227 | if (flag == 0) f->left = q; else f->right = q; |
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| 228 | if (q != NULL) q->up = f, q->flag = flag; |
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| 229 | tree->size--; |
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| 230 | /* go upstairs to the root and correct all subtrees affected by |
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| 231 | deletion */ |
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| 232 | while (f != NULL) |
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| 233 | { if (flag == 0) |
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| 234 | { /* the height of the left subtree of [f] is decreased */ |
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| 235 | if (f->bal == 0) |
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| 236 | { f->bal = +1; |
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| 237 | break; |
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| 238 | } |
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| 239 | if (f->bal < 0) |
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| 240 | f->bal = 0; |
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| 241 | else |
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| 242 | { f = rotate_subtree(tree, f); |
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| 243 | if (f->bal < 0) break; |
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| 244 | } |
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| 245 | flag = f->flag; f = f->up; |
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| 246 | } |
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| 247 | else |
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| 248 | { /* the height of the right subtree of [f] is decreased */ |
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| 249 | if (f->bal == 0) |
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| 250 | { f->bal = -1; |
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| 251 | break; |
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| 252 | } |
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| 253 | if (f->bal > 0) |
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| 254 | f->bal = 0; |
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| 255 | else |
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| 256 | { f = rotate_subtree(tree, f); |
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| 257 | if (f->bal > 0) break; |
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| 258 | } |
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| 259 | flag = f->flag; f = f->up; |
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| 260 | } |
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| 261 | } |
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| 262 | /* if the root has been reached, the height of the entire tree is |
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| 263 | decreased */ |
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| 264 | if (f == NULL) tree->height--; |
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| 265 | /* returns the deleted node to the memory pool */ |
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| 266 | dmp_free_atom(tree->pool, p, sizeof(AVLNODE)); |
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| 267 | return; |
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| 268 | } |
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| 269 | |
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| 270 | static AVLNODE *rotate_subtree(AVL *tree, AVLNODE *node) |
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| 271 | { /* restore balance of AVL subtree */ |
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| 272 | AVLNODE *f, *p, *q, *r, *x, *y; |
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| 273 | xassert(node != NULL); |
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| 274 | p = node; |
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| 275 | if (p->bal < 0) |
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| 276 | { /* perform negative (left) rotation */ |
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| 277 | f = p->up; q = p->left; r = q->right; |
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| 278 | if (q->bal <= 0) |
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| 279 | { /* perform single negative rotation */ |
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| 280 | if (f == NULL) |
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| 281 | tree->root = q; |
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| 282 | else |
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| 283 | if (p->flag == 0) f->left = q; else f->right = q; |
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| 284 | p->rank -= q->rank; |
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| 285 | q->up = f; q->flag = p->flag; q->bal++; q->right = p; |
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| 286 | p->up = q; p->flag = 1; |
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| 287 | p->bal = (short int)(-q->bal); p->left = r; |
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| 288 | if (r != NULL) r->up = p, r->flag = 0; |
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| 289 | node = q; |
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| 290 | } |
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| 291 | else |
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| 292 | { /* perform double negative rotation */ |
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| 293 | x = r->left; y = r->right; |
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| 294 | if (f == NULL) |
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| 295 | tree->root = r; |
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| 296 | else |
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| 297 | if (p->flag == 0) f->left = r; else f->right = r; |
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| 298 | p->rank -= (q->rank + r->rank); |
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| 299 | r->rank += q->rank; |
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| 300 | p->bal = (short int)(r->bal >= 0 ? 0 : +1); |
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| 301 | q->bal = (short int)(r->bal <= 0 ? 0 : -1); |
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| 302 | r->up = f; r->flag = p->flag; r->bal = 0; |
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| 303 | r->left = q; r->right = p; |
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| 304 | p->up = r; p->flag = 1; p->left = y; |
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| 305 | q->up = r; q->flag = 0; q->right = x; |
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| 306 | if (x != NULL) x->up = q, x->flag = 1; |
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| 307 | if (y != NULL) y->up = p, y->flag = 0; |
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| 308 | node = r; |
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| 309 | } |
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| 310 | } |
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| 311 | else |
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| 312 | { /* perform positive (right) rotation */ |
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| 313 | f = p->up; q = p->right; r = q->left; |
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| 314 | if (q->bal >= 0) |
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| 315 | { /* perform single positive rotation */ |
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| 316 | if (f == NULL) |
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| 317 | tree->root = q; |
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| 318 | else |
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| 319 | if (p->flag == 0) f->left = q; else f->right = q; |
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| 320 | q->rank += p->rank; |
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| 321 | q->up = f; q->flag = p->flag; q->bal--; q->left = p; |
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| 322 | p->up = q; p->flag = 0; |
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| 323 | p->bal = (short int)(-q->bal); p->right = r; |
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| 324 | if (r != NULL) r->up = p, r->flag = 1; |
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| 325 | node = q; |
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| 326 | } |
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| 327 | else |
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| 328 | { /* perform double positive rotation */ |
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| 329 | x = r->left; y = r->right; |
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| 330 | if (f == NULL) |
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| 331 | tree->root = r; |
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| 332 | else |
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| 333 | if (p->flag == 0) f->left = r; else f->right = r; |
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| 334 | q->rank -= r->rank; |
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| 335 | r->rank += p->rank; |
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| 336 | p->bal = (short int)(r->bal <= 0 ? 0 : -1); |
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| 337 | q->bal = (short int)(r->bal >= 0 ? 0 : +1); |
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| 338 | r->up = f; r->flag = p->flag; r->bal = 0; |
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| 339 | r->left = p; r->right = q; |
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| 340 | p->up = r; p->flag = 0; p->right = x; |
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| 341 | q->up = r; q->flag = 1; q->left = y; |
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| 342 | if (x != NULL) x->up = p, x->flag = 1; |
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| 343 | if (y != NULL) y->up = q, y->flag = 0; |
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| 344 | node = r; |
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| 345 | } |
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| 346 | } |
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| 347 | return node; |
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| 348 | } |
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| 349 | |
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| 350 | void avl_delete_tree(AVL *tree) |
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| 351 | { /* delete AVL tree */ |
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| 352 | dmp_delete_pool(tree->pool); |
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| 353 | xfree(tree); |
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| 354 | return; |
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| 355 | } |
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| 356 | |
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| 357 | /* eof */ |
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