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1
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2 /*
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3 * Copyright (C) Igor Sysoev
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4 */
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5
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6
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7 #include <ngx_config.h>
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8 #include <ngx_core.h>
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9
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10
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11 /*
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12 * The code is based on the algorithm described in the "Introduction
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13 * to Algorithms" by Cormen, Leiserson and Rivest.
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14 */
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15
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16 #define ngx_rbt_red(node) ((node)->color = 1)
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17 #define ngx_rbt_black(node) ((node)->color = 0)
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18 #define ngx_rbt_is_red(node) ((node)->color)
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19 #define ngx_rbt_is_black(node) (!ngx_rbt_is_red(node))
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20 #define ngx_rbt_copy_color(n1, n2) (n1->color = n2->color)
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21
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22
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16
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23 static ngx_inline void ngx_rbtree_left_rotate(ngx_rbtree_t **root,
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42
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24 ngx_rbtree_t *sentinel, ngx_rbtree_t *node);
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16
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25 static ngx_inline void ngx_rbtree_right_rotate(ngx_rbtree_t **root,
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42
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26 ngx_rbtree_t *sentinel, ngx_rbtree_t *node);
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0
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27
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28
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42
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29 void
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30 ngx_rbtree_insert(ngx_rbtree_t **root, ngx_rbtree_t *sentinel,
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31 ngx_rbtree_t *node)
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0
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32 {
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33 ngx_rbtree_t *temp;
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34
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35 /* a binary tree insert */
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36
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37 if (*root == sentinel) {
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38 node->parent = NULL;
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39 node->left = sentinel;
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40 node->right = sentinel;
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41 ngx_rbt_black(node);
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42 *root = node;
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43
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44 return;
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45 }
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46
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47 temp = *root;
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48
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49 for ( ;; ) {
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106
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50
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51 /* node->key < temp->key */
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52
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53 if ((ngx_rbtree_key_int_t) node->key - (ngx_rbtree_key_int_t) temp->key
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54 < 0)
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55 {
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0
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56 if (temp->left == sentinel) {
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57 temp->left = node;
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58 break;
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59 }
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60
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61 temp = temp->left;
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62 continue;
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63 }
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64
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65 if (temp->right == sentinel) {
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66 temp->right = node;
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67 break;
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68 }
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69
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70 temp = temp->right;
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71 continue;
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72 }
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73
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74 node->parent = temp;
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75 node->left = sentinel;
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76 node->right = sentinel;
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77
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78
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79 /* re-balance tree */
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80
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81 ngx_rbt_red(node);
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82
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83 while (node != *root && ngx_rbt_is_red(node->parent)) {
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84
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85 if (node->parent == node->parent->parent->left) {
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86 temp = node->parent->parent->right;
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87
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88 if (ngx_rbt_is_red(temp)) {
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89 ngx_rbt_black(node->parent);
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90 ngx_rbt_black(temp);
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91 ngx_rbt_red(node->parent->parent);
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92 node = node->parent->parent;
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93
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94 } else {
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95 if (node == node->parent->right) {
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96 node = node->parent;
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97 ngx_rbtree_left_rotate(root, sentinel, node);
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98 }
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99
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100 ngx_rbt_black(node->parent);
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101 ngx_rbt_red(node->parent->parent);
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102 ngx_rbtree_right_rotate(root, sentinel, node->parent->parent);
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103 }
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104
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105 } else {
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106 temp = node->parent->parent->left;
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107
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108 if (ngx_rbt_is_red(temp)) {
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109 ngx_rbt_black(node->parent);
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110 ngx_rbt_black(temp);
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111 ngx_rbt_red(node->parent->parent);
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112 node = node->parent->parent;
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113
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114 } else {
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115 if (node == node->parent->left) {
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116 node = node->parent;
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117 ngx_rbtree_right_rotate(root, sentinel, node);
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118 }
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119
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120 ngx_rbt_black(node->parent);
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121 ngx_rbt_red(node->parent->parent);
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122 ngx_rbtree_left_rotate(root, sentinel, node->parent->parent);
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123 }
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124 }
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125
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126 }
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127
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128 ngx_rbt_black(*root);
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129 }
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130
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131
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42
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132 void
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133 ngx_rbtree_delete(ngx_rbtree_t **root, ngx_rbtree_t *sentinel,
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134 ngx_rbtree_t *node)
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0
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135 {
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136 ngx_int_t is_red;
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137 ngx_rbtree_t *subst, *temp, *w;
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138
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139 /* a binary tree delete */
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140
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141 if (node->left == sentinel) {
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142 temp = node->right;
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143 subst = node;
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144
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145 } else if (node->right == sentinel) {
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146 temp = node->left;
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147 subst = node;
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148
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149 } else {
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150 subst = ngx_rbtree_min(node->right, sentinel);
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151
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152 if (subst->left != sentinel) {
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153 temp = subst->left;
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154 } else {
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155 temp = subst->right;
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156 }
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157 }
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158
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159 if (subst == *root) {
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160 *root = temp;
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161 ngx_rbt_black(temp);
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162
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163 /* DEBUG stuff */
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164 node->left = NULL;
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165 node->right = NULL;
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166 node->parent = NULL;
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167 node->key = 0;
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168
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169 return;
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170 }
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171
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172 is_red = ngx_rbt_is_red(subst);
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173
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174 if (subst == subst->parent->left) {
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175 subst->parent->left = temp;
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176
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177 } else {
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178 subst->parent->right = temp;
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179 }
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180
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181 if (subst == node) {
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182
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183 temp->parent = subst->parent;
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184
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185 } else {
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186
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187 if (subst->parent == node) {
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188 temp->parent = subst;
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189
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190 } else {
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191 temp->parent = subst->parent;
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192 }
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193
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194 subst->left = node->left;
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195 subst->right = node->right;
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196 subst->parent = node->parent;
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197 ngx_rbt_copy_color(subst, node);
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198
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199 if (node == *root) {
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200 *root = subst;
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201
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202 } else {
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203 if (node == node->parent->left) {
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204 node->parent->left = subst;
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205 } else {
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206 node->parent->right = subst;
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207 }
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208 }
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209
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210 if (subst->left != sentinel) {
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211 subst->left->parent = subst;
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212 }
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213
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214 if (subst->right != sentinel) {
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215 subst->right->parent = subst;
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216 }
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217
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218 /* DEBUG stuff */
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219 node->left = NULL;
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220 node->right = NULL;
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221 node->parent = NULL;
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222 node->key = 0;
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223 }
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224
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225 if (is_red) {
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226 return;
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227 }
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228
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229 /* a delete fixup */
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230
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231 while (temp != *root && ngx_rbt_is_black(temp)) {
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232
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233 if (temp == temp->parent->left) {
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234 w = temp->parent->right;
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235
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236 if (ngx_rbt_is_red(w)) {
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237 ngx_rbt_black(w);
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238 ngx_rbt_red(temp->parent);
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239 ngx_rbtree_left_rotate(root, sentinel, temp->parent);
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240 w = temp->parent->right;
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241 }
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242
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243 if (ngx_rbt_is_black(w->left) && ngx_rbt_is_black(w->right)) {
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244 ngx_rbt_red(w);
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245 temp = temp->parent;
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246
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247 } else {
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248 if (ngx_rbt_is_black(w->right)) {
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249 ngx_rbt_black(w->left);
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250 ngx_rbt_red(w);
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251 ngx_rbtree_right_rotate(root, sentinel, w);
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252 w = temp->parent->right;
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253 }
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254
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255 ngx_rbt_copy_color(w, temp->parent);
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256 ngx_rbt_black(temp->parent);
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257 ngx_rbt_black(w->right);
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258 ngx_rbtree_left_rotate(root, sentinel, temp->parent);
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259 temp = *root;
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260 }
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261
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262 } else {
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263 w = temp->parent->left;
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264
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265 if (ngx_rbt_is_red(w)) {
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266 ngx_rbt_black(w);
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267 ngx_rbt_red(temp->parent);
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268 ngx_rbtree_right_rotate(root, sentinel, temp->parent);
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269 w = temp->parent->left;
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270 }
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271
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272 if (ngx_rbt_is_black(w->left) && ngx_rbt_is_black(w->right)) {
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273 ngx_rbt_red(w);
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274 temp = temp->parent;
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275
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276 } else {
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277 if (ngx_rbt_is_black(w->left)) {
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278 ngx_rbt_black(w->right);
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279 ngx_rbt_red(w);
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280 ngx_rbtree_left_rotate(root, sentinel, w);
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281 w = temp->parent->left;
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282 }
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283
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284 ngx_rbt_copy_color(w, temp->parent);
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285 ngx_rbt_black(temp->parent);
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286 ngx_rbt_black(w->left);
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287 ngx_rbtree_right_rotate(root, sentinel, temp->parent);
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288 temp = *root;
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289 }
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290 }
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291 }
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292
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293 ngx_rbt_black(temp);
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294 }
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295
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296
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42
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297 static ngx_inline void
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298 ngx_rbtree_left_rotate(ngx_rbtree_t **root, ngx_rbtree_t *sentinel,
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299 ngx_rbtree_t *node)
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0
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300 {
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301 ngx_rbtree_t *temp;
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302
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303 temp = node->right;
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304 node->right = temp->left;
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305
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306 if (temp->left != sentinel) {
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307 temp->left->parent = node;
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308 }
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309
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310 temp->parent = node->parent;
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311
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312 if (node == *root) {
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313 *root = temp;
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314
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315 } else if (node == node->parent->left) {
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316 node->parent->left = temp;
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317
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318 } else {
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319 node->parent->right = temp;
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320 }
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321
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322 temp->left = node;
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323 node->parent = temp;
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324 }
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325
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326
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42
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327 static ngx_inline void
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328 ngx_rbtree_right_rotate(ngx_rbtree_t **root, ngx_rbtree_t *sentinel,
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329 ngx_rbtree_t *node)
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0
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330 {
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331 ngx_rbtree_t *temp;
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332
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333 temp = node->left;
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334 node->left = temp->right;
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335
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336 if (temp->right != sentinel) {
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337 temp->right->parent = node;
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338 }
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339
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340 temp->parent = node->parent;
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341
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342 if (node == *root) {
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343 *root = temp;
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344
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345 } else if (node == node->parent->right) {
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346 node->parent->right = temp;
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347
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348 } else {
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349 node->parent->left = temp;
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350 }
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351
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352 temp->right = node;
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353 node->parent = temp;
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354 }
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