1 | /* $NetBSD: tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $ */ |
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2 | /* $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $ */ |
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3 | /* $FreeBSD$ */ |
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4 | |
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5 | /*- |
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6 | * Copyright 2002 Niels Provos <provos@citi.umich.edu> |
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7 | * All rights reserved. |
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8 | * |
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9 | * Redistribution and use in source and binary forms, with or without |
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10 | * modification, are permitted provided that the following conditions |
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11 | * are met: |
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12 | * 1. Redistributions of source code must retain the above copyright |
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13 | * notice, this list of conditions and the following disclaimer. |
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14 | * 2. Redistributions in binary form must reproduce the above copyright |
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15 | * notice, this list of conditions and the following disclaimer in the |
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16 | * documentation and/or other materials provided with the distribution. |
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17 | * |
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18 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR |
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19 | * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES |
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20 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. |
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21 | * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, |
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22 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
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23 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
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24 | * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
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25 | * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
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26 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF |
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27 | * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
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28 | */ |
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29 | |
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30 | #ifndef _SYS_TREE_H_ |
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31 | #define _SYS_TREE_H_ |
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32 | |
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33 | #include <sys/cdefs.h> |
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34 | |
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35 | /* |
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36 | * This file defines data structures for different types of trees: |
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37 | * splay trees and red-black trees. |
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38 | * |
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39 | * A splay tree is a self-organizing data structure. Every operation |
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40 | * on the tree causes a splay to happen. The splay moves the requested |
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41 | * node to the root of the tree and partly rebalances it. |
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42 | * |
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43 | * This has the benefit that request locality causes faster lookups as |
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44 | * the requested nodes move to the top of the tree. On the other hand, |
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45 | * every lookup causes memory writes. |
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46 | * |
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47 | * The Balance Theorem bounds the total access time for m operations |
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48 | * and n inserts on an initially empty tree as O((m + n)lg n). The |
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49 | * amortized cost for a sequence of m accesses to a splay tree is O(lg n); |
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50 | * |
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51 | * A red-black tree is a binary search tree with the node color as an |
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52 | * extra attribute. It fulfills a set of conditions: |
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53 | * - every search path from the root to a leaf consists of the |
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54 | * same number of black nodes, |
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55 | * - each red node (except for the root) has a black parent, |
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56 | * - each leaf node is black. |
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57 | * |
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58 | * Every operation on a red-black tree is bounded as O(lg n). |
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59 | * The maximum height of a red-black tree is 2lg (n+1). |
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60 | */ |
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61 | |
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62 | #define SPLAY_HEAD(name, type) \ |
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63 | struct name { \ |
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64 | struct type *sph_root; /* root of the tree */ \ |
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65 | } |
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66 | |
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67 | #define SPLAY_INITIALIZER(root) \ |
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68 | { NULL } |
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69 | |
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70 | #define SPLAY_INIT(root) do { \ |
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71 | (root)->sph_root = NULL; \ |
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72 | } while (/*CONSTCOND*/ 0) |
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73 | |
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74 | #define SPLAY_ENTRY(type) \ |
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75 | struct { \ |
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76 | struct type *spe_left; /* left element */ \ |
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77 | struct type *spe_right; /* right element */ \ |
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78 | } |
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79 | |
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80 | #define SPLAY_LEFT(elm, field) (elm)->field.spe_left |
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81 | #define SPLAY_RIGHT(elm, field) (elm)->field.spe_right |
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82 | #define SPLAY_ROOT(head) (head)->sph_root |
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83 | #define SPLAY_EMPTY(head) (SPLAY_ROOT(head) == NULL) |
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84 | |
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85 | /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */ |
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86 | #define SPLAY_ROTATE_RIGHT(head, tmp, field) do { \ |
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87 | SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field); \ |
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88 | SPLAY_RIGHT(tmp, field) = (head)->sph_root; \ |
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89 | (head)->sph_root = tmp; \ |
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90 | } while (/*CONSTCOND*/ 0) |
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91 | |
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92 | #define SPLAY_ROTATE_LEFT(head, tmp, field) do { \ |
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93 | SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field); \ |
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94 | SPLAY_LEFT(tmp, field) = (head)->sph_root; \ |
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95 | (head)->sph_root = tmp; \ |
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96 | } while (/*CONSTCOND*/ 0) |
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97 | |
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98 | #define SPLAY_LINKLEFT(head, tmp, field) do { \ |
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99 | SPLAY_LEFT(tmp, field) = (head)->sph_root; \ |
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100 | tmp = (head)->sph_root; \ |
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101 | (head)->sph_root = SPLAY_LEFT((head)->sph_root, field); \ |
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102 | } while (/*CONSTCOND*/ 0) |
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103 | |
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104 | #define SPLAY_LINKRIGHT(head, tmp, field) do { \ |
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105 | SPLAY_RIGHT(tmp, field) = (head)->sph_root; \ |
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106 | tmp = (head)->sph_root; \ |
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107 | (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field); \ |
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108 | } while (/*CONSTCOND*/ 0) |
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109 | |
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110 | #define SPLAY_ASSEMBLE(head, node, left, right, field) do { \ |
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111 | SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \ |
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112 | SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\ |
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113 | SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \ |
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114 | SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \ |
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115 | } while (/*CONSTCOND*/ 0) |
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116 | |
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117 | /* Generates prototypes and inline functions */ |
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118 | |
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119 | #define SPLAY_PROTOTYPE(name, type, field, cmp) \ |
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120 | void name##_SPLAY(struct name *, struct type *); \ |
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121 | void name##_SPLAY_MINMAX(struct name *, int); \ |
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122 | struct type *name##_SPLAY_INSERT(struct name *, struct type *); \ |
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123 | struct type *name##_SPLAY_REMOVE(struct name *, struct type *); \ |
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124 | \ |
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125 | /* Finds the node with the same key as elm */ \ |
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126 | static __inline struct type * \ |
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127 | name##_SPLAY_FIND(struct name *head, struct type *elm) \ |
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128 | { \ |
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129 | if (SPLAY_EMPTY(head)) \ |
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130 | return(NULL); \ |
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131 | name##_SPLAY(head, elm); \ |
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132 | if ((cmp)(elm, (head)->sph_root) == 0) \ |
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133 | return (head->sph_root); \ |
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134 | return (NULL); \ |
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135 | } \ |
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136 | \ |
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137 | static __inline struct type * \ |
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138 | name##_SPLAY_NEXT(struct name *head, struct type *elm) \ |
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139 | { \ |
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140 | name##_SPLAY(head, elm); \ |
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141 | if (SPLAY_RIGHT(elm, field) != NULL) { \ |
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142 | elm = SPLAY_RIGHT(elm, field); \ |
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143 | while (SPLAY_LEFT(elm, field) != NULL) { \ |
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144 | elm = SPLAY_LEFT(elm, field); \ |
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145 | } \ |
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146 | } else \ |
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147 | elm = NULL; \ |
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148 | return (elm); \ |
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149 | } \ |
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150 | \ |
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151 | static __inline struct type * \ |
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152 | name##_SPLAY_MIN_MAX(struct name *head, int val) \ |
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153 | { \ |
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154 | name##_SPLAY_MINMAX(head, val); \ |
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155 | return (SPLAY_ROOT(head)); \ |
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156 | } |
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157 | |
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158 | /* Main splay operation. |
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159 | * Moves node close to the key of elm to top |
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160 | */ |
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161 | #define SPLAY_GENERATE(name, type, field, cmp) \ |
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162 | struct type * \ |
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163 | name##_SPLAY_INSERT(struct name *head, struct type *elm) \ |
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164 | { \ |
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165 | if (SPLAY_EMPTY(head)) { \ |
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166 | SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL; \ |
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167 | } else { \ |
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168 | int __comp; \ |
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169 | name##_SPLAY(head, elm); \ |
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170 | __comp = (cmp)(elm, (head)->sph_root); \ |
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171 | if(__comp < 0) { \ |
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172 | SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\ |
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173 | SPLAY_RIGHT(elm, field) = (head)->sph_root; \ |
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174 | SPLAY_LEFT((head)->sph_root, field) = NULL; \ |
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175 | } else if (__comp > 0) { \ |
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176 | SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\ |
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177 | SPLAY_LEFT(elm, field) = (head)->sph_root; \ |
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178 | SPLAY_RIGHT((head)->sph_root, field) = NULL; \ |
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179 | } else \ |
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180 | return ((head)->sph_root); \ |
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181 | } \ |
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182 | (head)->sph_root = (elm); \ |
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183 | return (NULL); \ |
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184 | } \ |
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185 | \ |
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186 | struct type * \ |
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187 | name##_SPLAY_REMOVE(struct name *head, struct type *elm) \ |
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188 | { \ |
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189 | struct type *__tmp; \ |
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190 | if (SPLAY_EMPTY(head)) \ |
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191 | return (NULL); \ |
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192 | name##_SPLAY(head, elm); \ |
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193 | if ((cmp)(elm, (head)->sph_root) == 0) { \ |
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194 | if (SPLAY_LEFT((head)->sph_root, field) == NULL) { \ |
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195 | (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\ |
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196 | } else { \ |
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197 | __tmp = SPLAY_RIGHT((head)->sph_root, field); \ |
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198 | (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\ |
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199 | name##_SPLAY(head, elm); \ |
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200 | SPLAY_RIGHT((head)->sph_root, field) = __tmp; \ |
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201 | } \ |
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202 | return (elm); \ |
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203 | } \ |
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204 | return (NULL); \ |
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205 | } \ |
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206 | \ |
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207 | void \ |
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208 | name##_SPLAY(struct name *head, struct type *elm) \ |
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209 | { \ |
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210 | struct type __node, *__left, *__right, *__tmp; \ |
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211 | int __comp; \ |
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212 | \ |
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213 | SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\ |
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214 | __left = __right = &__node; \ |
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215 | \ |
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216 | while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) { \ |
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217 | if (__comp < 0) { \ |
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218 | __tmp = SPLAY_LEFT((head)->sph_root, field); \ |
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219 | if (__tmp == NULL) \ |
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220 | break; \ |
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221 | if ((cmp)(elm, __tmp) < 0){ \ |
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222 | SPLAY_ROTATE_RIGHT(head, __tmp, field); \ |
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223 | if (SPLAY_LEFT((head)->sph_root, field) == NULL)\ |
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224 | break; \ |
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225 | } \ |
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226 | SPLAY_LINKLEFT(head, __right, field); \ |
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227 | } else if (__comp > 0) { \ |
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228 | __tmp = SPLAY_RIGHT((head)->sph_root, field); \ |
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229 | if (__tmp == NULL) \ |
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230 | break; \ |
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231 | if ((cmp)(elm, __tmp) > 0){ \ |
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232 | SPLAY_ROTATE_LEFT(head, __tmp, field); \ |
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233 | if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\ |
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234 | break; \ |
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235 | } \ |
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236 | SPLAY_LINKRIGHT(head, __left, field); \ |
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237 | } \ |
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238 | } \ |
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239 | SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \ |
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240 | } \ |
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241 | \ |
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242 | /* Splay with either the minimum or the maximum element \ |
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243 | * Used to find minimum or maximum element in tree. \ |
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244 | */ \ |
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245 | void name##_SPLAY_MINMAX(struct name *head, int __comp) \ |
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246 | { \ |
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247 | struct type __node, *__left, *__right, *__tmp; \ |
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248 | \ |
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249 | SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\ |
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250 | __left = __right = &__node; \ |
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251 | \ |
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252 | while (1) { \ |
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253 | if (__comp < 0) { \ |
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254 | __tmp = SPLAY_LEFT((head)->sph_root, field); \ |
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255 | if (__tmp == NULL) \ |
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256 | break; \ |
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257 | if (__comp < 0){ \ |
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258 | SPLAY_ROTATE_RIGHT(head, __tmp, field); \ |
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259 | if (SPLAY_LEFT((head)->sph_root, field) == NULL)\ |
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260 | break; \ |
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261 | } \ |
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262 | SPLAY_LINKLEFT(head, __right, field); \ |
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263 | } else if (__comp > 0) { \ |
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264 | __tmp = SPLAY_RIGHT((head)->sph_root, field); \ |
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265 | if (__tmp == NULL) \ |
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266 | break; \ |
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267 | if (__comp > 0) { \ |
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268 | SPLAY_ROTATE_LEFT(head, __tmp, field); \ |
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269 | if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\ |
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270 | break; \ |
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271 | } \ |
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272 | SPLAY_LINKRIGHT(head, __left, field); \ |
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273 | } \ |
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274 | } \ |
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275 | SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \ |
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276 | } |
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277 | |
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278 | #define SPLAY_NEGINF -1 |
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279 | #define SPLAY_INF 1 |
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280 | |
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281 | #define SPLAY_INSERT(name, x, y) name##_SPLAY_INSERT(x, y) |
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282 | #define SPLAY_REMOVE(name, x, y) name##_SPLAY_REMOVE(x, y) |
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283 | #define SPLAY_FIND(name, x, y) name##_SPLAY_FIND(x, y) |
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284 | #define SPLAY_NEXT(name, x, y) name##_SPLAY_NEXT(x, y) |
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285 | #define SPLAY_MIN(name, x) (SPLAY_EMPTY(x) ? NULL \ |
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286 | : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF)) |
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287 | #define SPLAY_MAX(name, x) (SPLAY_EMPTY(x) ? NULL \ |
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288 | : name##_SPLAY_MIN_MAX(x, SPLAY_INF)) |
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289 | |
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290 | #define SPLAY_FOREACH(x, name, head) \ |
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291 | for ((x) = SPLAY_MIN(name, head); \ |
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292 | (x) != NULL; \ |
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293 | (x) = SPLAY_NEXT(name, head, x)) |
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294 | |
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295 | /* Macros that define a red-black tree */ |
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296 | #define RB_HEAD(name, type) \ |
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297 | struct name { \ |
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298 | struct type *rbh_root; /* root of the tree */ \ |
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299 | } |
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300 | |
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301 | #define RB_INITIALIZER(root) \ |
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302 | { NULL } |
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303 | |
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304 | #define RB_INIT(root) do { \ |
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305 | (root)->rbh_root = NULL; \ |
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306 | } while (/*CONSTCOND*/ 0) |
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307 | |
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308 | #define RB_BLACK 0 |
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309 | #define RB_RED 1 |
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310 | #define RB_ENTRY(type) \ |
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311 | struct { \ |
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312 | struct type *rbe_left; /* left element */ \ |
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313 | struct type *rbe_right; /* right element */ \ |
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314 | struct type *rbe_parent; /* parent element */ \ |
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315 | int rbe_color; /* node color */ \ |
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316 | } |
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317 | |
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318 | #define RB_LEFT(elm, field) (elm)->field.rbe_left |
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319 | #define RB_RIGHT(elm, field) (elm)->field.rbe_right |
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320 | #define RB_PARENT(elm, field) (elm)->field.rbe_parent |
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321 | #define RB_COLOR(elm, field) (elm)->field.rbe_color |
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322 | #define RB_ROOT(head) (head)->rbh_root |
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323 | #define RB_EMPTY(head) (RB_ROOT(head) == NULL) |
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324 | |
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325 | #define RB_SET(elm, parent, field) do { \ |
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326 | RB_PARENT(elm, field) = parent; \ |
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327 | RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \ |
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328 | RB_COLOR(elm, field) = RB_RED; \ |
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329 | } while (/*CONSTCOND*/ 0) |
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330 | |
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331 | #define RB_SET_BLACKRED(black, red, field) do { \ |
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332 | RB_COLOR(black, field) = RB_BLACK; \ |
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333 | RB_COLOR(red, field) = RB_RED; \ |
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334 | } while (/*CONSTCOND*/ 0) |
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335 | |
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336 | #ifndef RB_AUGMENT |
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337 | #define RB_AUGMENT(x) do {} while (0) |
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338 | #endif |
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339 | |
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340 | #define RB_ROTATE_LEFT(head, elm, tmp, field) do { \ |
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341 | (tmp) = RB_RIGHT(elm, field); \ |
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342 | if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) { \ |
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343 | RB_PARENT(RB_LEFT(tmp, field), field) = (elm); \ |
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344 | } \ |
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345 | RB_AUGMENT(elm); \ |
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346 | if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \ |
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347 | if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \ |
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348 | RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \ |
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349 | else \ |
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350 | RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \ |
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351 | } else \ |
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352 | (head)->rbh_root = (tmp); \ |
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353 | RB_LEFT(tmp, field) = (elm); \ |
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354 | RB_PARENT(elm, field) = (tmp); \ |
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355 | RB_AUGMENT(tmp); \ |
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356 | if ((RB_PARENT(tmp, field))) \ |
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357 | RB_AUGMENT(RB_PARENT(tmp, field)); \ |
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358 | } while (/*CONSTCOND*/ 0) |
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359 | |
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360 | #define RB_ROTATE_RIGHT(head, elm, tmp, field) do { \ |
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361 | (tmp) = RB_LEFT(elm, field); \ |
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362 | if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) { \ |
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363 | RB_PARENT(RB_RIGHT(tmp, field), field) = (elm); \ |
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364 | } \ |
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365 | RB_AUGMENT(elm); \ |
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366 | if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \ |
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367 | if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \ |
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368 | RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \ |
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369 | else \ |
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370 | RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \ |
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371 | } else \ |
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372 | (head)->rbh_root = (tmp); \ |
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373 | RB_RIGHT(tmp, field) = (elm); \ |
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374 | RB_PARENT(elm, field) = (tmp); \ |
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375 | RB_AUGMENT(tmp); \ |
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376 | if ((RB_PARENT(tmp, field))) \ |
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377 | RB_AUGMENT(RB_PARENT(tmp, field)); \ |
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378 | } while (/*CONSTCOND*/ 0) |
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379 | |
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380 | /* Generates prototypes and inline functions */ |
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381 | #define RB_PROTOTYPE(name, type, field, cmp) \ |
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382 | RB_PROTOTYPE_INTERNAL(name, type, field, cmp,) |
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383 | #define RB_PROTOTYPE_STATIC(name, type, field, cmp) \ |
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384 | RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static) |
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385 | #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr) \ |
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386 | attr void name##_RB_INSERT_COLOR(struct name *, struct type *); \ |
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387 | attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\ |
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388 | attr struct type *name##_RB_REMOVE(struct name *, struct type *); \ |
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389 | attr struct type *name##_RB_INSERT(struct name *, struct type *); \ |
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390 | attr struct type *name##_RB_FIND(struct name *, struct type *); \ |
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391 | attr struct type *name##_RB_NFIND(struct name *, struct type *); \ |
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392 | attr struct type *name##_RB_NEXT(struct type *); \ |
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393 | attr struct type *name##_RB_PREV(struct type *); \ |
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394 | attr struct type *name##_RB_MINMAX(struct name *, int); \ |
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395 | \ |
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396 | |
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397 | /* Main rb operation. |
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398 | * Moves node close to the key of elm to top |
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399 | */ |
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400 | #define RB_GENERATE(name, type, field, cmp) \ |
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401 | RB_GENERATE_INTERNAL(name, type, field, cmp,) |
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402 | #define RB_GENERATE_STATIC(name, type, field, cmp) \ |
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403 | RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static) |
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404 | #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr) \ |
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405 | attr void \ |
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406 | name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \ |
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407 | { \ |
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408 | struct type *parent, *gparent, *tmp; \ |
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409 | while ((parent = RB_PARENT(elm, field)) != NULL && \ |
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410 | RB_COLOR(parent, field) == RB_RED) { \ |
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411 | gparent = RB_PARENT(parent, field); \ |
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412 | if (parent == RB_LEFT(gparent, field)) { \ |
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413 | tmp = RB_RIGHT(gparent, field); \ |
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414 | if (tmp && RB_COLOR(tmp, field) == RB_RED) { \ |
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415 | RB_COLOR(tmp, field) = RB_BLACK; \ |
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416 | RB_SET_BLACKRED(parent, gparent, field);\ |
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417 | elm = gparent; \ |
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418 | continue; \ |
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419 | } \ |
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420 | if (RB_RIGHT(parent, field) == elm) { \ |
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421 | RB_ROTATE_LEFT(head, parent, tmp, field);\ |
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422 | tmp = parent; \ |
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423 | parent = elm; \ |
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424 | elm = tmp; \ |
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425 | } \ |
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426 | RB_SET_BLACKRED(parent, gparent, field); \ |
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427 | RB_ROTATE_RIGHT(head, gparent, tmp, field); \ |
---|
428 | } else { \ |
---|
429 | tmp = RB_LEFT(gparent, field); \ |
---|
430 | if (tmp && RB_COLOR(tmp, field) == RB_RED) { \ |
---|
431 | RB_COLOR(tmp, field) = RB_BLACK; \ |
---|
432 | RB_SET_BLACKRED(parent, gparent, field);\ |
---|
433 | elm = gparent; \ |
---|
434 | continue; \ |
---|
435 | } \ |
---|
436 | if (RB_LEFT(parent, field) == elm) { \ |
---|
437 | RB_ROTATE_RIGHT(head, parent, tmp, field);\ |
---|
438 | tmp = parent; \ |
---|
439 | parent = elm; \ |
---|
440 | elm = tmp; \ |
---|
441 | } \ |
---|
442 | RB_SET_BLACKRED(parent, gparent, field); \ |
---|
443 | RB_ROTATE_LEFT(head, gparent, tmp, field); \ |
---|
444 | } \ |
---|
445 | } \ |
---|
446 | RB_COLOR(head->rbh_root, field) = RB_BLACK; \ |
---|
447 | } \ |
---|
448 | \ |
---|
449 | attr void \ |
---|
450 | name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \ |
---|
451 | { \ |
---|
452 | struct type *tmp; \ |
---|
453 | while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && \ |
---|
454 | elm != RB_ROOT(head)) { \ |
---|
455 | if (RB_LEFT(parent, field) == elm) { \ |
---|
456 | tmp = RB_RIGHT(parent, field); \ |
---|
457 | if (RB_COLOR(tmp, field) == RB_RED) { \ |
---|
458 | RB_SET_BLACKRED(tmp, parent, field); \ |
---|
459 | RB_ROTATE_LEFT(head, parent, tmp, field);\ |
---|
460 | tmp = RB_RIGHT(parent, field); \ |
---|
461 | } \ |
---|
462 | if ((RB_LEFT(tmp, field) == NULL || \ |
---|
463 | RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\ |
---|
464 | (RB_RIGHT(tmp, field) == NULL || \ |
---|
465 | RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\ |
---|
466 | RB_COLOR(tmp, field) = RB_RED; \ |
---|
467 | elm = parent; \ |
---|
468 | parent = RB_PARENT(elm, field); \ |
---|
469 | } else { \ |
---|
470 | if (RB_RIGHT(tmp, field) == NULL || \ |
---|
471 | RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\ |
---|
472 | struct type *oleft; \ |
---|
473 | if ((oleft = RB_LEFT(tmp, field)) \ |
---|
474 | != NULL) \ |
---|
475 | RB_COLOR(oleft, field) = RB_BLACK;\ |
---|
476 | RB_COLOR(tmp, field) = RB_RED; \ |
---|
477 | RB_ROTATE_RIGHT(head, tmp, oleft, field);\ |
---|
478 | tmp = RB_RIGHT(parent, field); \ |
---|
479 | } \ |
---|
480 | RB_COLOR(tmp, field) = RB_COLOR(parent, field);\ |
---|
481 | RB_COLOR(parent, field) = RB_BLACK; \ |
---|
482 | if (RB_RIGHT(tmp, field)) \ |
---|
483 | RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\ |
---|
484 | RB_ROTATE_LEFT(head, parent, tmp, field);\ |
---|
485 | elm = RB_ROOT(head); \ |
---|
486 | break; \ |
---|
487 | } \ |
---|
488 | } else { \ |
---|
489 | tmp = RB_LEFT(parent, field); \ |
---|
490 | if (RB_COLOR(tmp, field) == RB_RED) { \ |
---|
491 | RB_SET_BLACKRED(tmp, parent, field); \ |
---|
492 | RB_ROTATE_RIGHT(head, parent, tmp, field);\ |
---|
493 | tmp = RB_LEFT(parent, field); \ |
---|
494 | } \ |
---|
495 | if ((RB_LEFT(tmp, field) == NULL || \ |
---|
496 | RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\ |
---|
497 | (RB_RIGHT(tmp, field) == NULL || \ |
---|
498 | RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\ |
---|
499 | RB_COLOR(tmp, field) = RB_RED; \ |
---|
500 | elm = parent; \ |
---|
501 | parent = RB_PARENT(elm, field); \ |
---|
502 | } else { \ |
---|
503 | if (RB_LEFT(tmp, field) == NULL || \ |
---|
504 | RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\ |
---|
505 | struct type *oright; \ |
---|
506 | if ((oright = RB_RIGHT(tmp, field)) \ |
---|
507 | != NULL) \ |
---|
508 | RB_COLOR(oright, field) = RB_BLACK;\ |
---|
509 | RB_COLOR(tmp, field) = RB_RED; \ |
---|
510 | RB_ROTATE_LEFT(head, tmp, oright, field);\ |
---|
511 | tmp = RB_LEFT(parent, field); \ |
---|
512 | } \ |
---|
513 | RB_COLOR(tmp, field) = RB_COLOR(parent, field);\ |
---|
514 | RB_COLOR(parent, field) = RB_BLACK; \ |
---|
515 | if (RB_LEFT(tmp, field)) \ |
---|
516 | RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\ |
---|
517 | RB_ROTATE_RIGHT(head, parent, tmp, field);\ |
---|
518 | elm = RB_ROOT(head); \ |
---|
519 | break; \ |
---|
520 | } \ |
---|
521 | } \ |
---|
522 | } \ |
---|
523 | if (elm) \ |
---|
524 | RB_COLOR(elm, field) = RB_BLACK; \ |
---|
525 | } \ |
---|
526 | \ |
---|
527 | attr struct type * \ |
---|
528 | name##_RB_REMOVE(struct name *head, struct type *elm) \ |
---|
529 | { \ |
---|
530 | struct type *child, *parent, *old = elm; \ |
---|
531 | int color; \ |
---|
532 | if (RB_LEFT(elm, field) == NULL) \ |
---|
533 | child = RB_RIGHT(elm, field); \ |
---|
534 | else if (RB_RIGHT(elm, field) == NULL) \ |
---|
535 | child = RB_LEFT(elm, field); \ |
---|
536 | else { \ |
---|
537 | struct type *left; \ |
---|
538 | elm = RB_RIGHT(elm, field); \ |
---|
539 | while ((left = RB_LEFT(elm, field)) != NULL) \ |
---|
540 | elm = left; \ |
---|
541 | child = RB_RIGHT(elm, field); \ |
---|
542 | parent = RB_PARENT(elm, field); \ |
---|
543 | color = RB_COLOR(elm, field); \ |
---|
544 | if (child) \ |
---|
545 | RB_PARENT(child, field) = parent; \ |
---|
546 | if (parent) { \ |
---|
547 | if (RB_LEFT(parent, field) == elm) \ |
---|
548 | RB_LEFT(parent, field) = child; \ |
---|
549 | else \ |
---|
550 | RB_RIGHT(parent, field) = child; \ |
---|
551 | RB_AUGMENT(parent); \ |
---|
552 | } else \ |
---|
553 | RB_ROOT(head) = child; \ |
---|
554 | if (RB_PARENT(elm, field) == old) \ |
---|
555 | parent = elm; \ |
---|
556 | (elm)->field = (old)->field; \ |
---|
557 | if (RB_PARENT(old, field)) { \ |
---|
558 | if (RB_LEFT(RB_PARENT(old, field), field) == old)\ |
---|
559 | RB_LEFT(RB_PARENT(old, field), field) = elm;\ |
---|
560 | else \ |
---|
561 | RB_RIGHT(RB_PARENT(old, field), field) = elm;\ |
---|
562 | RB_AUGMENT(RB_PARENT(old, field)); \ |
---|
563 | } else \ |
---|
564 | RB_ROOT(head) = elm; \ |
---|
565 | RB_PARENT(RB_LEFT(old, field), field) = elm; \ |
---|
566 | if (RB_RIGHT(old, field)) \ |
---|
567 | RB_PARENT(RB_RIGHT(old, field), field) = elm; \ |
---|
568 | if (parent) { \ |
---|
569 | left = parent; \ |
---|
570 | do { \ |
---|
571 | RB_AUGMENT(left); \ |
---|
572 | } while ((left = RB_PARENT(left, field)) != NULL); \ |
---|
573 | } \ |
---|
574 | goto color; \ |
---|
575 | } \ |
---|
576 | parent = RB_PARENT(elm, field); \ |
---|
577 | color = RB_COLOR(elm, field); \ |
---|
578 | if (child) \ |
---|
579 | RB_PARENT(child, field) = parent; \ |
---|
580 | if (parent) { \ |
---|
581 | if (RB_LEFT(parent, field) == elm) \ |
---|
582 | RB_LEFT(parent, field) = child; \ |
---|
583 | else \ |
---|
584 | RB_RIGHT(parent, field) = child; \ |
---|
585 | RB_AUGMENT(parent); \ |
---|
586 | } else \ |
---|
587 | RB_ROOT(head) = child; \ |
---|
588 | color: \ |
---|
589 | if (color == RB_BLACK) \ |
---|
590 | name##_RB_REMOVE_COLOR(head, parent, child); \ |
---|
591 | return (old); \ |
---|
592 | } \ |
---|
593 | \ |
---|
594 | /* Inserts a node into the RB tree */ \ |
---|
595 | attr struct type * \ |
---|
596 | name##_RB_INSERT(struct name *head, struct type *elm) \ |
---|
597 | { \ |
---|
598 | struct type *tmp; \ |
---|
599 | struct type *parent = NULL; \ |
---|
600 | int comp = 0; \ |
---|
601 | tmp = RB_ROOT(head); \ |
---|
602 | while (tmp) { \ |
---|
603 | parent = tmp; \ |
---|
604 | comp = (cmp)(elm, parent); \ |
---|
605 | if (comp < 0) \ |
---|
606 | tmp = RB_LEFT(tmp, field); \ |
---|
607 | else if (comp > 0) \ |
---|
608 | tmp = RB_RIGHT(tmp, field); \ |
---|
609 | else \ |
---|
610 | return (tmp); \ |
---|
611 | } \ |
---|
612 | RB_SET(elm, parent, field); \ |
---|
613 | if (parent != NULL) { \ |
---|
614 | if (comp < 0) \ |
---|
615 | RB_LEFT(parent, field) = elm; \ |
---|
616 | else \ |
---|
617 | RB_RIGHT(parent, field) = elm; \ |
---|
618 | RB_AUGMENT(parent); \ |
---|
619 | } else \ |
---|
620 | RB_ROOT(head) = elm; \ |
---|
621 | name##_RB_INSERT_COLOR(head, elm); \ |
---|
622 | return (NULL); \ |
---|
623 | } \ |
---|
624 | \ |
---|
625 | /* Finds the node with the same key as elm */ \ |
---|
626 | attr struct type * \ |
---|
627 | name##_RB_FIND(struct name *head, struct type *elm) \ |
---|
628 | { \ |
---|
629 | struct type *tmp = RB_ROOT(head); \ |
---|
630 | int comp; \ |
---|
631 | while (tmp) { \ |
---|
632 | comp = cmp(elm, tmp); \ |
---|
633 | if (comp < 0) \ |
---|
634 | tmp = RB_LEFT(tmp, field); \ |
---|
635 | else if (comp > 0) \ |
---|
636 | tmp = RB_RIGHT(tmp, field); \ |
---|
637 | else \ |
---|
638 | return (tmp); \ |
---|
639 | } \ |
---|
640 | return (NULL); \ |
---|
641 | } \ |
---|
642 | \ |
---|
643 | /* Finds the first node greater than or equal to the search key */ \ |
---|
644 | attr struct type * \ |
---|
645 | name##_RB_NFIND(struct name *head, struct type *elm) \ |
---|
646 | { \ |
---|
647 | struct type *tmp = RB_ROOT(head); \ |
---|
648 | struct type *res = NULL; \ |
---|
649 | int comp; \ |
---|
650 | while (tmp) { \ |
---|
651 | comp = cmp(elm, tmp); \ |
---|
652 | if (comp < 0) { \ |
---|
653 | res = tmp; \ |
---|
654 | tmp = RB_LEFT(tmp, field); \ |
---|
655 | } \ |
---|
656 | else if (comp > 0) \ |
---|
657 | tmp = RB_RIGHT(tmp, field); \ |
---|
658 | else \ |
---|
659 | return (tmp); \ |
---|
660 | } \ |
---|
661 | return (res); \ |
---|
662 | } \ |
---|
663 | \ |
---|
664 | /* ARGSUSED */ \ |
---|
665 | attr struct type * \ |
---|
666 | name##_RB_NEXT(struct type *elm) \ |
---|
667 | { \ |
---|
668 | if (RB_RIGHT(elm, field)) { \ |
---|
669 | elm = RB_RIGHT(elm, field); \ |
---|
670 | while (RB_LEFT(elm, field)) \ |
---|
671 | elm = RB_LEFT(elm, field); \ |
---|
672 | } else { \ |
---|
673 | if (RB_PARENT(elm, field) && \ |
---|
674 | (elm == RB_LEFT(RB_PARENT(elm, field), field))) \ |
---|
675 | elm = RB_PARENT(elm, field); \ |
---|
676 | else { \ |
---|
677 | while (RB_PARENT(elm, field) && \ |
---|
678 | (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\ |
---|
679 | elm = RB_PARENT(elm, field); \ |
---|
680 | elm = RB_PARENT(elm, field); \ |
---|
681 | } \ |
---|
682 | } \ |
---|
683 | return (elm); \ |
---|
684 | } \ |
---|
685 | \ |
---|
686 | /* ARGSUSED */ \ |
---|
687 | attr struct type * \ |
---|
688 | name##_RB_PREV(struct type *elm) \ |
---|
689 | { \ |
---|
690 | if (RB_LEFT(elm, field)) { \ |
---|
691 | elm = RB_LEFT(elm, field); \ |
---|
692 | while (RB_RIGHT(elm, field)) \ |
---|
693 | elm = RB_RIGHT(elm, field); \ |
---|
694 | } else { \ |
---|
695 | if (RB_PARENT(elm, field) && \ |
---|
696 | (elm == RB_RIGHT(RB_PARENT(elm, field), field))) \ |
---|
697 | elm = RB_PARENT(elm, field); \ |
---|
698 | else { \ |
---|
699 | while (RB_PARENT(elm, field) && \ |
---|
700 | (elm == RB_LEFT(RB_PARENT(elm, field), field)))\ |
---|
701 | elm = RB_PARENT(elm, field); \ |
---|
702 | elm = RB_PARENT(elm, field); \ |
---|
703 | } \ |
---|
704 | } \ |
---|
705 | return (elm); \ |
---|
706 | } \ |
---|
707 | \ |
---|
708 | attr struct type * \ |
---|
709 | name##_RB_MINMAX(struct name *head, int val) \ |
---|
710 | { \ |
---|
711 | struct type *tmp = RB_ROOT(head); \ |
---|
712 | struct type *parent = NULL; \ |
---|
713 | while (tmp) { \ |
---|
714 | parent = tmp; \ |
---|
715 | if (val < 0) \ |
---|
716 | tmp = RB_LEFT(tmp, field); \ |
---|
717 | else \ |
---|
718 | tmp = RB_RIGHT(tmp, field); \ |
---|
719 | } \ |
---|
720 | return (parent); \ |
---|
721 | } |
---|
722 | |
---|
723 | #define RB_NEGINF -1 |
---|
724 | #define RB_INF 1 |
---|
725 | |
---|
726 | #define RB_INSERT(name, x, y) name##_RB_INSERT(x, y) |
---|
727 | #define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y) |
---|
728 | #define RB_FIND(name, x, y) name##_RB_FIND(x, y) |
---|
729 | #define RB_NFIND(name, x, y) name##_RB_NFIND(x, y) |
---|
730 | #define RB_NEXT(name, x, y) name##_RB_NEXT(y) |
---|
731 | #define RB_PREV(name, x, y) name##_RB_PREV(y) |
---|
732 | #define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF) |
---|
733 | #define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF) |
---|
734 | |
---|
735 | #define RB_FOREACH(x, name, head) \ |
---|
736 | for ((x) = RB_MIN(name, head); \ |
---|
737 | (x) != NULL; \ |
---|
738 | (x) = name##_RB_NEXT(x)) |
---|
739 | |
---|
740 | #define RB_FOREACH_FROM(x, name, y) \ |
---|
741 | for ((x) = (y); \ |
---|
742 | ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \ |
---|
743 | (x) = (y)) |
---|
744 | |
---|
745 | #define RB_FOREACH_SAFE(x, name, head, y) \ |
---|
746 | for ((x) = RB_MIN(name, head); \ |
---|
747 | ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \ |
---|
748 | (x) = (y)) |
---|
749 | |
---|
750 | #define RB_FOREACH_REVERSE(x, name, head) \ |
---|
751 | for ((x) = RB_MAX(name, head); \ |
---|
752 | (x) != NULL; \ |
---|
753 | (x) = name##_RB_PREV(x)) |
---|
754 | |
---|
755 | #define RB_FOREACH_REVERSE_FROM(x, name, y) \ |
---|
756 | for ((x) = (y); \ |
---|
757 | ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \ |
---|
758 | (x) = (y)) |
---|
759 | |
---|
760 | #define RB_FOREACH_REVERSE_SAFE(x, name, head, y) \ |
---|
761 | for ((x) = RB_MAX(name, head); \ |
---|
762 | ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \ |
---|
763 | (x) = (y)) |
---|
764 | |
---|
765 | #endif /* _SYS_TREE_H_ */ |
---|