算法导论第三版--红黑树
红黑树是满足如下条件的二叉搜索树。
1、每个节点要么是红色的，要么是黑色的。
2、根节点是黑色。
3、每个叶子节点是黑色的。
4、如果一个节点是红色的，那么它的2个子节点是黑色的。
5、对每个节点，从它到它的后代叶子节点的简单路径上，均包含相同数目的黑色节点。
练习完这些代码，我感觉我把stl的rbtree抄了一遍。。。
1 enum RB { 2 RED, 3 BLACK 4 }; 5 6 template<typename T> 7 struct rb_node_cls { 8 typedef rb_node_cls<T> __node; 9 __node* parent; 10 __node* left; 11 __node* right; 12 T key; 13 RB color; 14 void *data; 15 }; 16 17 template<typename T> using rbt_node = rb_node_cls<T>; 18 19 template<typename T> 20 struct rb_tree_cls { 21 rbt_node<T>* root; 22 }; 23 24 template<typename T> using rb_tree = rb_tree_cls<T>; 25 26 template<typename T> 27 void left_rotate(rb_tree<T>& tree, rbt_node<T>* x) { 28 rbt_node<T>* y = x->right; 29 30 x->right = y->left; 31 if (y->left != nullptr) { 32 y->left->parent = x; 33 } 34 35 y->parent = x->parent; 36 if(x->parent == nullptr) { 37 tree.root = y; 38 } else if(x == x->parent->left) { 39 x->parent->left = y; 40 } else { 41 x->parent->right = y; 42 } 43 44 y->left = x; 45 x->parent = y; 46 } 47 48 template<typename T> 49 void right_rotate(rb_tree<T>& tree, rbt_node<T>* x) { 50 rbt_node<T>* y = x->left; 51 52 y->left = x->right; 53 54 if(x->right != nullptr) { 55 x->right->parent = y; 56 } 57 58 x->parent = y->parent; 59 if(y->parent == nullptr) { 60 tree.root = y; 61 } else if (y == y->parent->left) { 62 y->parent->left = x; 63 } else { 64 x->parent->right = x; 65 } 66 67 x->right = y; 68 y->parent = x; 69 } 70 71 template<typename T> 72 void rb_insert_fixup(rb_tree<T>& tree, rbt_node<T>* z) { 73 while(z->parent->color == RED) { 74 if(z->parent == z->parent->parent->left) { 75 rbt_node<T>* y = z->parent->parent->right; 76 if(y->color == RED){ 77 z->parent->color = BLACK; 78 y->color = BLACK; 79 z->parent->parent = RED; 80 z = z->parent->parent; 81 } else if(z == z->parent->right) { 82 z = z->parent; 83 left_rotate(tree, z); 84 } 85 z->parent->color = BLACK; 86 z->parent->parent->color = RED; 87 right_rotate(tree, z->parent->parent); 88 } else { 89 rbt_node<T>* y = z->parent->parent->left; 90 if(y->color == RED) { 91 z->parent->color = BLACK; 92 y->color = BLACK; 93 z->parent->parent = RED; 94 z = z->parent->parent; 95 } else if(z == z->parent->left) { 96 z = z->parent; 97 right_rotate(tree, z); 98 } 99 z->parent->color = BLACK; 100 z->parent->parent->color = RED; 101 left_rotate(tree, z->parent->parent); 102 } 103 } 104 tree.root->color = BLACK; 105 } 106 107 template<typename T> 108 void rb_insert(rb_tree<T>& tree, rbt_node<T>* z) { 109 rbt_node<T>* y = nullptr; 110 rbt_node<T>* x = tree.root; 111 112 while(x != nullptr) { 113 y = x; 114 x = (z->key < x->key) ? x->left : x->right; 115 } 116 117 z->parent = y; 118 if(y == nullptr){ 119 tree.root = z; 120 } else if(z->key < y->key) { 121 y->left = z; 122 } else { 123 y->right = z; 124 } 125 126 z->left = nullptr; 127 z->right = nullptr; 128 z->color = RED; 129 rb_insert_fixup(tree, z); 130 } 131 132 template<typename T> 133 void rb_transplant(rb_tree<T>& tree, rbt_node<T>* u, rbt_node<T>* v) { 134 if(u->parent == nullptr) { 135 tree.root = v; 136 } else if (u == u->parent->left) { 137 u->parent->left = v; 138 } else { 139 u->parent->right = v; 140 } 141 if(v != nullptr) 142 v->parent = u->parent; 143 } 144 145 template<typename T> 146 rbt_node<T>* tree_minimum(rbt_node<T>* node) { 147 while(node->left != nullptr) 148 node = node->left; 149 return node; 150 } 151 152 template<typename T> 153 void rb_delete_fixup(rb_tree<T>& tree, rbt_node<T>* x) { 154 while(x != tree.root && x->color == BLACK) { 155 if(x == x->parent->left) { 156 rbt_node<T>* w = x->parent->right; 157 if(w->color == RED) { 158 w->color = BLACK; 159 x->parent->color = RED; 160 left_rotate(tree, x->parent); 161 w = x->parent->right; 162 } 163 164 if(w->left->color == BLACK && w->right->color == BLACK) { 165 w->color = RED; 166 x = x->parent; 167 } else if(w->right->color == BLACK) { 168 w->left->color = BLACK; 169 w->color = RED; 170 right_rotate(tree, w); 171 w = x->parent->right; 172 } 173 174 w->color = x->parent->color; 175 x->parent->color = BLACK; 176 w->right->color = BLACK; 177 left_rotate(tree, x->parent); 178 x = tree.root; 179 } else { 180 rbt_node<T>* w = x->parent->left; 181 if(w->color == RED) { 182 w->color = BLACK; 183 x->parent->color = RED; 184 right_rotate(tree, x->parent); 185 w = x->parent->left; 186 } 187 188 if(w->right->color == BLACK && w->left->color == BLACK) { 189 w->color = RED; 190 x = x->parent; 191 } else if (w->left->color == BLACK) { 192 w->right->color = BLACK; 193 w->color = RED; 194 left_rotate(tree, w); 195 w = x->parent->left; 196 } 197 198 w->color = x->parent->color; 199 x->parent->color = BLACK; 200 x->left->color = BLACK; 201 right_rotate(tree, x->parent); 202 x = tree.root; 203 } 204 } 205 x->color = BLACK; 206 } 207 208 template<typename T> 209 void rb_delete(rb_tree<T>& tree, rbt_node<T>* z) { 210 rbt_node<T>* y = z; 211 rbt_node<T>* x = nullptr; 212 RB y_original_color = y->color; 213 214 if(z->left == nullptr) { 215 x = z->right; 216 rb_transplant(tree, z, z->right); 217 } else if(z->right == nullptr) { 218 x = z->left; 219 rb_transplant(tree, z, z->left); 220 } else { 221 y = tree_minimum(z->right); 222 y_original_color = y->color; 223 x = y->right; 224 if(y->parent == z){ 225 x->parent = y; 226 } else { 227 rb_transplant(tree, y, y->right); 228 y->right = z->right; 229 y->right->parent = y; 230 } 231 rb_transplant(tree, z, y); 232 y->left = z->left; 233 y->left->parent = y; 234 y->color = z->color; 235 } 236 if(y_original_color == BLACK){ 237 rb_delete_fixup(tree, x); 238 } 239 }
