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