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160
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1 /*-
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2 * Copyright 2002 Niels Provos <[email protected]>
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3 * All rights reserved.
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4 *
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5 * Redistribution and use in source and binary forms, with or without
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6 * modification, are permitted provided that the following conditions
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7 * are met:
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8 * 1. Redistributions of source code must retain the above copyright
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9 * notice, this list of conditions and the following disclaimer.
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10 * 2. Redistributions in binary form must reproduce the above copyright
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11 * notice, this list of conditions and the following disclaimer in the
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12 * documentation and/or other materials provided with the distribution.
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13 *
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14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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15 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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16 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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17 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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18 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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19 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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20 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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21 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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22 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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23 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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24 */
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25
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26 #ifndef UV_TREE_H_
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27 #define UV_TREE_H_
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28
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29 #ifndef UV__UNUSED
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30 # if __GNUC__
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31 # define UV__UNUSED __attribute__((unused))
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32 # else
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33 # define UV__UNUSED
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34 # endif
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35 #endif
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36
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37 /*
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38 * This file defines data structures for red-black trees.
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39 * A red-black tree is a binary search tree with the node color as an
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40 * extra attribute. It fulfills a set of conditions:
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41 * - every search path from the root to a leaf consists of the
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42 * same number of black nodes,
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43 * - each red node (except for the root) has a black parent,
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44 * - each leaf node is black.
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45 *
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46 * Every operation on a red-black tree is bounded as O(lg n).
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47 * The maximum height of a red-black tree is 2lg (n+1).
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48 */
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49
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50 /* Macros that define a red-black tree */
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51 #define RB_HEAD(name, type) \
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52 struct name { \
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53 struct type *rbh_root; /* root of the tree */ \
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54 }
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55
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56 #define RB_INITIALIZER(root) \
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57 { NULL }
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58
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59 #define RB_INIT(root) do { \
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60 (root)->rbh_root = NULL; \
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61 } while (/*CONSTCOND*/ 0)
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62
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63 #define RB_BLACK 0
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64 #define RB_RED 1
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65 #define RB_ENTRY(type) \
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66 struct { \
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67 struct type *rbe_left; /* left element */ \
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68 struct type *rbe_right; /* right element */ \
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69 struct type *rbe_parent; /* parent element */ \
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70 int rbe_color; /* node color */ \
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71 }
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72
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73 #define RB_LEFT(elm, field) (elm)->field.rbe_left
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74 #define RB_RIGHT(elm, field) (elm)->field.rbe_right
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75 #define RB_PARENT(elm, field) (elm)->field.rbe_parent
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76 #define RB_COLOR(elm, field) (elm)->field.rbe_color
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77 #define RB_ROOT(head) (head)->rbh_root
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78 #define RB_EMPTY(head) (RB_ROOT(head) == NULL)
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79
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80 #define RB_SET(elm, parent, field) do { \
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81 RB_PARENT(elm, field) = parent; \
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82 RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \
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83 RB_COLOR(elm, field) = RB_RED; \
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84 } while (/*CONSTCOND*/ 0)
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85
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86 #define RB_SET_BLACKRED(black, red, field) do { \
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87 RB_COLOR(black, field) = RB_BLACK; \
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88 RB_COLOR(red, field) = RB_RED; \
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89 } while (/*CONSTCOND*/ 0)
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90
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91 #ifndef RB_AUGMENT
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92 #define RB_AUGMENT(x) do {} while (0)
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93 #endif
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94
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95 #define RB_ROTATE_LEFT(head, elm, tmp, field) do { \
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96 (tmp) = RB_RIGHT(elm, field); \
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97 if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) { \
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98 RB_PARENT(RB_LEFT(tmp, field), field) = (elm); \
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99 } \
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100 RB_AUGMENT(elm); \
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101 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \
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102 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
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103 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
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104 else \
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105 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
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106 } else \
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107 (head)->rbh_root = (tmp); \
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108 RB_LEFT(tmp, field) = (elm); \
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109 RB_PARENT(elm, field) = (tmp); \
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110 RB_AUGMENT(tmp); \
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111 if ((RB_PARENT(tmp, field))) \
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112 RB_AUGMENT(RB_PARENT(tmp, field)); \
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113 } while (/*CONSTCOND*/ 0)
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114
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115 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do { \
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116 (tmp) = RB_LEFT(elm, field); \
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117 if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) { \
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118 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm); \
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119 } \
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120 RB_AUGMENT(elm); \
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121 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \
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122 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
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123 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
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124 else \
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125 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
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126 } else \
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127 (head)->rbh_root = (tmp); \
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128 RB_RIGHT(tmp, field) = (elm); \
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129 RB_PARENT(elm, field) = (tmp); \
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130 RB_AUGMENT(tmp); \
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131 if ((RB_PARENT(tmp, field))) \
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132 RB_AUGMENT(RB_PARENT(tmp, field)); \
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133 } while (/*CONSTCOND*/ 0)
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134
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135 /* Generates prototypes and inline functions */
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136 #define RB_PROTOTYPE(name, type, field, cmp) \
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137 RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)
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138 #define RB_PROTOTYPE_STATIC(name, type, field, cmp) \
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139 RB_PROTOTYPE_INTERNAL(name, type, field, cmp, UV__UNUSED static)
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140 #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr) \
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141 attr void name##_RB_INSERT_COLOR(struct name *, struct type *); \
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142 attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
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143 attr struct type *name##_RB_REMOVE(struct name *, struct type *); \
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144 attr struct type *name##_RB_INSERT(struct name *, struct type *); \
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145 attr struct type *name##_RB_FIND(struct name *, struct type *); \
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146 attr struct type *name##_RB_NFIND(struct name *, struct type *); \
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147 attr struct type *name##_RB_NEXT(struct type *); \
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148 attr struct type *name##_RB_PREV(struct type *); \
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149 attr struct type *name##_RB_MINMAX(struct name *, int); \
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150 \
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151
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152 /* Main rb operation.
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153 * Moves node close to the key of elm to top
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154 */
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155 #define RB_GENERATE(name, type, field, cmp) \
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156 RB_GENERATE_INTERNAL(name, type, field, cmp,)
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157 #define RB_GENERATE_STATIC(name, type, field, cmp) \
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158 RB_GENERATE_INTERNAL(name, type, field, cmp, UV__UNUSED static)
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159 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr) \
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160 attr void \
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161 name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \
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162 { \
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163 struct type *parent, *gparent, *tmp; \
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164 while ((parent = RB_PARENT(elm, field)) != NULL && \
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165 RB_COLOR(parent, field) == RB_RED) { \
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166 gparent = RB_PARENT(parent, field); \
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167 if (parent == RB_LEFT(gparent, field)) { \
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168 tmp = RB_RIGHT(gparent, field); \
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169 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
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170 RB_COLOR(tmp, field) = RB_BLACK; \
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171 RB_SET_BLACKRED(parent, gparent, field); \
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172 elm = gparent; \
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173 continue; \
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174 } \
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175 if (RB_RIGHT(parent, field) == elm) { \
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176 RB_ROTATE_LEFT(head, parent, tmp, field); \
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177 tmp = parent; \
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178 parent = elm; \
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179 elm = tmp; \
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180 } \
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181 RB_SET_BLACKRED(parent, gparent, field); \
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182 RB_ROTATE_RIGHT(head, gparent, tmp, field); \
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183 } else { \
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184 tmp = RB_LEFT(gparent, field); \
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185 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
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186 RB_COLOR(tmp, field) = RB_BLACK; \
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187 RB_SET_BLACKRED(parent, gparent, field); \
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188 elm = gparent; \
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189 continue; \
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190 } \
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191 if (RB_LEFT(parent, field) == elm) { \
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192 RB_ROTATE_RIGHT(head, parent, tmp, field); \
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193 tmp = parent; \
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194 parent = elm; \
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195 elm = tmp; \
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196 } \
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197 RB_SET_BLACKRED(parent, gparent, field); \
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198 RB_ROTATE_LEFT(head, gparent, tmp, field); \
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199 } \
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200 } \
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201 RB_COLOR(head->rbh_root, field) = RB_BLACK; \
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202 } \
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203 \
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204 attr void \
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205 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, \
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206 struct type *elm) \
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207 { \
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208 struct type *tmp; \
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209 while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && \
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210 elm != RB_ROOT(head)) { \
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211 if (RB_LEFT(parent, field) == elm) { \
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212 tmp = RB_RIGHT(parent, field); \
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213 if (RB_COLOR(tmp, field) == RB_RED) { \
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214 RB_SET_BLACKRED(tmp, parent, field); \
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215 RB_ROTATE_LEFT(head, parent, tmp, field); \
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216 tmp = RB_RIGHT(parent, field); \
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217 } \
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218 if ((RB_LEFT(tmp, field) == NULL || \
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219 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) && \
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220 (RB_RIGHT(tmp, field) == NULL || \
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221 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) { \
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222 RB_COLOR(tmp, field) = RB_RED; \
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223 elm = parent; \
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224 parent = RB_PARENT(elm, field); \
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225 } else { \
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226 if (RB_RIGHT(tmp, field) == NULL || \
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227 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) { \
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228 struct type *oleft; \
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229 if ((oleft = RB_LEFT(tmp, field)) \
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230 != NULL) \
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231 RB_COLOR(oleft, field) = RB_BLACK; \
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232 RB_COLOR(tmp, field) = RB_RED; \
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233 RB_ROTATE_RIGHT(head, tmp, oleft, field); \
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234 tmp = RB_RIGHT(parent, field); \
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235 } \
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236 RB_COLOR(tmp, field) = RB_COLOR(parent, field); \
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237 RB_COLOR(parent, field) = RB_BLACK; \
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238 if (RB_RIGHT(tmp, field)) \
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239 RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK; \
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240 RB_ROTATE_LEFT(head, parent, tmp, field); \
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241 elm = RB_ROOT(head); \
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242 break; \
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243 } \
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244 } else { \
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245 tmp = RB_LEFT(parent, field); \
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246 if (RB_COLOR(tmp, field) == RB_RED) { \
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247 RB_SET_BLACKRED(tmp, parent, field); \
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248 RB_ROTATE_RIGHT(head, parent, tmp, field); \
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249 tmp = RB_LEFT(parent, field); \
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250 } \
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251 if ((RB_LEFT(tmp, field) == NULL || \
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252 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) && \
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253 (RB_RIGHT(tmp, field) == NULL || \
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254 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) { \
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255 RB_COLOR(tmp, field) = RB_RED; \
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256 elm = parent; \
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257 parent = RB_PARENT(elm, field); \
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258 } else { \
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259 if (RB_LEFT(tmp, field) == NULL || \
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260 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) { \
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261 struct type *oright; \
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262 if ((oright = RB_RIGHT(tmp, field)) \
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263 != NULL) \
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264 RB_COLOR(oright, field) = RB_BLACK; \
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265 RB_COLOR(tmp, field) = RB_RED; \
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266 RB_ROTATE_LEFT(head, tmp, oright, field); \
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267 tmp = RB_LEFT(parent, field); \
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268 } \
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269 RB_COLOR(tmp, field) = RB_COLOR(parent, field); \
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270 RB_COLOR(parent, field) = RB_BLACK; \
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271 if (RB_LEFT(tmp, field)) \
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272 RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK; \
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273 RB_ROTATE_RIGHT(head, parent, tmp, field); \
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274 elm = RB_ROOT(head); \
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275 break; \
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276 } \
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277 } \
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278 } \
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279 if (elm) \
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280 RB_COLOR(elm, field) = RB_BLACK; \
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281 } \
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282 \
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283 attr struct type * \
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284 name##_RB_REMOVE(struct name *head, struct type *elm) \
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285 { \
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286 struct type *child, *parent, *old = elm; \
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287 int color; \
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288 if (RB_LEFT(elm, field) == NULL) \
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289 child = RB_RIGHT(elm, field); \
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290 else if (RB_RIGHT(elm, field) == NULL) \
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291 child = RB_LEFT(elm, field); \
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292 else { \
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293 struct type *left; \
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294 elm = RB_RIGHT(elm, field); \
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295 while ((left = RB_LEFT(elm, field)) != NULL) \
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296 elm = left; \
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297 child = RB_RIGHT(elm, field); \
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298 parent = RB_PARENT(elm, field); \
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299 color = RB_COLOR(elm, field); \
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300 if (child) \
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301 RB_PARENT(child, field) = parent; \
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302 if (parent) { \
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303 if (RB_LEFT(parent, field) == elm) \
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304 RB_LEFT(parent, field) = child; \
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305 else \
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306 RB_RIGHT(parent, field) = child; \
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307 RB_AUGMENT(parent); \
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308 } else \
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309 RB_ROOT(head) = child; \
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310 if (RB_PARENT(elm, field) == old) \
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311 parent = elm; \
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312 (elm)->field = (old)->field; \
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313 if (RB_PARENT(old, field)) { \
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314 if (RB_LEFT(RB_PARENT(old, field), field) == old) \
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315 RB_LEFT(RB_PARENT(old, field), field) = elm; \
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316 else \
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317 RB_RIGHT(RB_PARENT(old, field), field) = elm; \
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318 RB_AUGMENT(RB_PARENT(old, field)); \
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319 } else \
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320 RB_ROOT(head) = elm; \
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321 RB_PARENT(RB_LEFT(old, field), field) = elm; \
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322 if (RB_RIGHT(old, field)) \
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323 RB_PARENT(RB_RIGHT(old, field), field) = elm; \
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324 if (parent) { \
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325 left = parent; \
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326 do { \
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327 RB_AUGMENT(left); \
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328 } while ((left = RB_PARENT(left, field)) != NULL); \
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329 } \
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330 goto color; \
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331 } \
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332 parent = RB_PARENT(elm, field); \
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333 color = RB_COLOR(elm, field); \
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334 if (child) \
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335 RB_PARENT(child, field) = parent; \
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336 if (parent) { \
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337 if (RB_LEFT(parent, field) == elm) \
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338 RB_LEFT(parent, field) = child; \
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339 else \
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340 RB_RIGHT(parent, field) = child; \
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341 RB_AUGMENT(parent); \
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342 } else \
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343 RB_ROOT(head) = child; \
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344 color: \
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345 if (color == RB_BLACK) \
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346 name##_RB_REMOVE_COLOR(head, parent, child); \
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347 return (old); \
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348 } \
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349 \
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350 /* Inserts a node into the RB tree */ \
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351 attr struct type * \
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352 name##_RB_INSERT(struct name *head, struct type *elm) \
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353 { \
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354 struct type *tmp; \
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355 struct type *parent = NULL; \
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356 int comp = 0; \
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357 tmp = RB_ROOT(head); \
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358 while (tmp) { \
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359 parent = tmp; \
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360 comp = (cmp)(elm, parent); \
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361 if (comp < 0) \
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362 tmp = RB_LEFT(tmp, field); \
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363 else if (comp > 0) \
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364 tmp = RB_RIGHT(tmp, field); \
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365 else \
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366 return (tmp); \
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367 } \
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368 RB_SET(elm, parent, field); \
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369 if (parent != NULL) { \
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370 if (comp < 0) \
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371 RB_LEFT(parent, field) = elm; \
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372 else \
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373 RB_RIGHT(parent, field) = elm; \
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374 RB_AUGMENT(parent); \
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375 } else \
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376 RB_ROOT(head) = elm; \
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377 name##_RB_INSERT_COLOR(head, elm); \
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378 return (NULL); \
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379 } \
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380 \
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381 /* Finds the node with the same key as elm */ \
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382 attr struct type * \
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383 name##_RB_FIND(struct name *head, struct type *elm) \
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384 { \
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385 struct type *tmp = RB_ROOT(head); \
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386 int comp; \
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387 while (tmp) { \
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388 comp = cmp(elm, tmp); \
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389 if (comp < 0) \
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390 tmp = RB_LEFT(tmp, field); \
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391 else if (comp > 0) \
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392 tmp = RB_RIGHT(tmp, field); \
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393 else \
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394 return (tmp); \
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395 } \
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396 return (NULL); \
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397 } \
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398 \
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399 /* Finds the first node greater than or equal to the search key */ \
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400 attr struct type * \
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401 name##_RB_NFIND(struct name *head, struct type *elm) \
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402 { \
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403 struct type *tmp = RB_ROOT(head); \
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404 struct type *res = NULL; \
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405 int comp; \
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406 while (tmp) { \
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407 comp = cmp(elm, tmp); \
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408 if (comp < 0) { \
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409 res = tmp; \
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410 tmp = RB_LEFT(tmp, field); \
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|
411 } \
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412 else if (comp > 0) \
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413 tmp = RB_RIGHT(tmp, field); \
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414 else \
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|
415 return (tmp); \
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|
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416 } \
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417 return (res); \
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|
|
418 } \
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|
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419 \
|
|
|
420 /* ARGSUSED */ \
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|
|
421 attr struct type * \
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|
|
422 name##_RB_NEXT(struct type *elm) \
|
|
|
423 { \
|
|
|
424 if (RB_RIGHT(elm, field)) { \
|
|
|
425 elm = RB_RIGHT(elm, field); \
|
|
|
426 while (RB_LEFT(elm, field)) \
|
|
|
427 elm = RB_LEFT(elm, field); \
|
|
|
428 } else { \
|
|
|
429 if (RB_PARENT(elm, field) && \
|
|
|
430 (elm == RB_LEFT(RB_PARENT(elm, field), field))) \
|
|
|
431 elm = RB_PARENT(elm, field); \
|
|
|
432 else { \
|
|
|
433 while (RB_PARENT(elm, field) && \
|
|
|
434 (elm == RB_RIGHT(RB_PARENT(elm, field), field))) \
|
|
|
435 elm = RB_PARENT(elm, field); \
|
|
|
436 elm = RB_PARENT(elm, field); \
|
|
|
437 } \
|
|
|
438 } \
|
|
|
439 return (elm); \
|
|
|
440 } \
|
|
|
441 \
|
|
|
442 /* ARGSUSED */ \
|
|
|
443 attr struct type * \
|
|
|
444 name##_RB_PREV(struct type *elm) \
|
|
|
445 { \
|
|
|
446 if (RB_LEFT(elm, field)) { \
|
|
|
447 elm = RB_LEFT(elm, field); \
|
|
|
448 while (RB_RIGHT(elm, field)) \
|
|
|
449 elm = RB_RIGHT(elm, field); \
|
|
|
450 } else { \
|
|
|
451 if (RB_PARENT(elm, field) && \
|
|
|
452 (elm == RB_RIGHT(RB_PARENT(elm, field), field))) \
|
|
|
453 elm = RB_PARENT(elm, field); \
|
|
|
454 else { \
|
|
|
455 while (RB_PARENT(elm, field) && \
|
|
|
456 (elm == RB_LEFT(RB_PARENT(elm, field), field))) \
|
|
|
457 elm = RB_PARENT(elm, field); \
|
|
|
458 elm = RB_PARENT(elm, field); \
|
|
|
459 } \
|
|
|
460 } \
|
|
|
461 return (elm); \
|
|
|
462 } \
|
|
|
463 \
|
|
|
464 attr struct type * \
|
|
|
465 name##_RB_MINMAX(struct name *head, int val) \
|
|
|
466 { \
|
|
|
467 struct type *tmp = RB_ROOT(head); \
|
|
|
468 struct type *parent = NULL; \
|
|
|
469 while (tmp) { \
|
|
|
470 parent = tmp; \
|
|
|
471 if (val < 0) \
|
|
|
472 tmp = RB_LEFT(tmp, field); \
|
|
|
473 else \
|
|
|
474 tmp = RB_RIGHT(tmp, field); \
|
|
|
475 } \
|
|
|
476 return (parent); \
|
|
|
477 }
|
|
|
478
|
|
|
479 #define RB_NEGINF -1
|
|
|
480 #define RB_INF 1
|
|
|
481
|
|
|
482 #define RB_INSERT(name, x, y) name##_RB_INSERT(x, y)
|
|
|
483 #define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y)
|
|
|
484 #define RB_FIND(name, x, y) name##_RB_FIND(x, y)
|
|
|
485 #define RB_NFIND(name, x, y) name##_RB_NFIND(x, y)
|
|
|
486 #define RB_NEXT(name, x) name##_RB_NEXT(x)
|
|
|
487 #define RB_PREV(name, x) name##_RB_PREV(x)
|
|
|
488 #define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF)
|
|
|
489 #define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF)
|
|
|
490
|
|
|
491 #define RB_FOREACH(x, name, head) \
|
|
|
492 for ((x) = RB_MIN(name, head); \
|
|
|
493 (x) != NULL; \
|
|
|
494 (x) = name##_RB_NEXT(x))
|
|
|
495
|
|
|
496 #define RB_FOREACH_FROM(x, name, y) \
|
|
|
497 for ((x) = (y); \
|
|
|
498 ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \
|
|
|
499 (x) = (y))
|
|
|
500
|
|
|
501 #define RB_FOREACH_SAFE(x, name, head, y) \
|
|
|
502 for ((x) = RB_MIN(name, head); \
|
|
|
503 ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \
|
|
|
504 (x) = (y))
|
|
|
505
|
|
|
506 #define RB_FOREACH_REVERSE(x, name, head) \
|
|
|
507 for ((x) = RB_MAX(name, head); \
|
|
|
508 (x) != NULL; \
|
|
|
509 (x) = name##_RB_PREV(x))
|
|
|
510
|
|
|
511 #define RB_FOREACH_REVERSE_FROM(x, name, y) \
|
|
|
512 for ((x) = (y); \
|
|
|
513 ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \
|
|
|
514 (x) = (y))
|
|
|
515
|
|
|
516 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y) \
|
|
|
517 for ((x) = RB_MAX(name, head); \
|
|
|
518 ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \
|
|
|
519 (x) = (y))
|
|
|
520
|
|
|
521 #endif /* UV_TREE_H_ */
|
