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| 1 | +class TreeNode: |
| 2 | + def __init__(self, key=None, value=None, parent=None, left=None, right=None, |
| 3 | + left_subtree_height: int = 0, right_subtree_height: int = 0, balance_factor: int = 0): |
| 4 | + self.key = key |
| 5 | + self.value = value |
| 6 | + self.parent = parent |
| 7 | + self.left = left |
| 8 | + self.right = right |
| 9 | + self.left_subtree_height: int = left_subtree_height |
| 10 | + self.right_subtree_height: int = right_subtree_height |
| 11 | + self.balance_factor : int = balance_factor |
| 12 | + |
| 13 | + def has_left_child(self) -> bool: |
| 14 | + return self.left is not None |
| 15 | + |
| 16 | + def has_right_child(self) -> bool: |
| 17 | + return self.right is not None |
| 18 | + |
| 19 | + def has_both_children(self) -> bool: |
| 20 | + return self.has_left_child() and self.has_right_child() |
| 21 | + |
| 22 | + def is_leaf(self) -> bool: |
| 23 | + return not self.has_left_child() and not self.has_right_child() |
| 24 | + |
| 25 | + def is_root(self) -> bool: |
| 26 | + return self.parent is None |
| 27 | + |
| 28 | + def has_parent(self) -> bool: |
| 29 | + return self.parent is not None |
| 30 | + |
| 31 | + def is_left_child(self) -> bool: |
| 32 | + return self.parent.left == self |
| 33 | + |
| 34 | + def is_right_child(self) -> bool: |
| 35 | + return self.parent.right == self |
| 36 | + |
| 37 | + def find_min(self): |
| 38 | + if self is None: |
| 39 | + return None |
| 40 | + if self.has_left_child(): |
| 41 | + return self.left.find_min() |
| 42 | + else: |
| 43 | + return self |
| 44 | + |
| 45 | + def find_max(self): |
| 46 | + if self is None: |
| 47 | + return None |
| 48 | + node = self |
| 49 | + while node.right is not None: |
| 50 | + node = node.right |
| 51 | + return node |
| 52 | + |
| 53 | + |
| 54 | +class BinarySearchTree: |
| 55 | + def __init__(self): |
| 56 | + self.root: TreeNode = None |
| 57 | + self.elements: int = 0 |
| 58 | + |
| 59 | + def size(self) -> int: |
| 60 | + return self.elements |
| 61 | + |
| 62 | + def is_empty(self) -> bool: |
| 63 | + return self.root is None |
| 64 | + |
| 65 | + def put(self, key, value): |
| 66 | + if self.is_empty(): |
| 67 | + self.root = TreeNode(key, value) |
| 68 | + self.elements += 1 |
| 69 | + else: |
| 70 | + self._put(self.root, key, value) |
| 71 | + |
| 72 | + def _put(self, root: TreeNode, key, value): |
| 73 | + if root.key == key: |
| 74 | + root.value = value |
| 75 | + elif key < root.key: |
| 76 | + if root.has_left_child(): |
| 77 | + self._put(root.left, key, value) |
| 78 | + else: |
| 79 | + root.left = TreeNode(key, value, root) |
| 80 | + self.elements += 1 |
| 81 | + self._update_balance_factor(root) |
| 82 | + else: |
| 83 | + if root.has_right_child(): |
| 84 | + self._put(root.right, key, value) |
| 85 | + else: |
| 86 | + root.right = TreeNode(key, value, root) |
| 87 | + self.elements += 1 |
| 88 | + self._update_balance_factor(root) |
| 89 | + |
| 90 | + def get(self, key) -> TreeNode: |
| 91 | + if self.is_empty(): |
| 92 | + return None |
| 93 | + else: |
| 94 | + return self._get(self.root, key) |
| 95 | + |
| 96 | + def _get(self, root: TreeNode, key) -> TreeNode: |
| 97 | + if root.key == key: |
| 98 | + return root |
| 99 | + elif key < root.key: |
| 100 | + if root.has_left_child(): |
| 101 | + return self._get(root.left, key) |
| 102 | + else: |
| 103 | + return None |
| 104 | + else: |
| 105 | + if root.has_right_child(): |
| 106 | + return self._get(root.right, key) |
| 107 | + else: |
| 108 | + return None |
| 109 | + |
| 110 | + def contains(self, key) -> bool: |
| 111 | + if self.is_empty(): |
| 112 | + return None |
| 113 | + found: bool = False |
| 114 | + node: TreeNode = self.root |
| 115 | + while node is not None and not found: |
| 116 | + if node.key == key: |
| 117 | + found = True |
| 118 | + elif key < node.key: |
| 119 | + node = node.left |
| 120 | + else: |
| 121 | + node = node.right |
| 122 | + return found |
| 123 | + |
| 124 | + def delete(self, key): |
| 125 | + node_to_delete: TreeNode = self.get(key) |
| 126 | + if node_to_delete is None: |
| 127 | + return |
| 128 | + if node_to_delete.is_root(): |
| 129 | + if node_to_delete.is_leaf(): |
| 130 | + self.root = None |
| 131 | + self.elements -= 1 |
| 132 | + elif node_to_delete.has_both_children(): |
| 133 | + max_node: TreeNode = node_to_delete.left.find_max() |
| 134 | + tmp_key = max_node.key |
| 135 | + tmp_value = max_node.value |
| 136 | + self.delete(tmp_key) |
| 137 | + # keep pointer to that node, not root, root might change |
| 138 | + node_to_delete.key = tmp_key |
| 139 | + node_to_delete.value = tmp_value |
| 140 | + else: |
| 141 | + if node_to_delete.has_left_child(): |
| 142 | + self.root = node_to_delete.left |
| 143 | + else: |
| 144 | + self.root = node_to_delete.right |
| 145 | + self.root.parent = None |
| 146 | + self.elements -= 1 |
| 147 | + else: |
| 148 | + parent: TreeNode = None |
| 149 | + if node_to_delete.is_leaf(): |
| 150 | + parent = node_to_delete.parent |
| 151 | + if node_to_delete.is_left_child(): |
| 152 | + node_to_delete.parent.left = None |
| 153 | + else: |
| 154 | + node_to_delete.parent.right = None |
| 155 | + self.elements -= 1 |
| 156 | + elif node_to_delete.has_both_children(): |
| 157 | + max_node: TreeNode = node_to_delete.left.find_max() |
| 158 | + tmp_key = max_node.key |
| 159 | + tmp_value = max_node.value |
| 160 | + self.delete(tmp_key) |
| 161 | + node_to_delete.key = tmp_key |
| 162 | + node_to_delete.value = tmp_value |
| 163 | + elif node_to_delete.has_left_child(): |
| 164 | + parent = node_to_delete.parent |
| 165 | + self.elements -= 1 |
| 166 | + if node_to_delete.is_left_child(): |
| 167 | + node_to_delete.parent.left = node_to_delete.left |
| 168 | + else: |
| 169 | + node_to_delete.parent.right = node_to_delete.left |
| 170 | + node_to_delete.left.parent = node_to_delete.parent |
| 171 | + else: |
| 172 | + parent = node_to_delete.parent |
| 173 | + self.elements -= 1 |
| 174 | + if node_to_delete.is_left_child(): |
| 175 | + node_to_delete.parent.left = node_to_delete.right |
| 176 | + else: |
| 177 | + node_to_delete.parent.right = node_to_delete.right |
| 178 | + node_to_delete.right.parent = node_to_delete.parent |
| 179 | + if parent is not None: |
| 180 | + self._update_balance_factor(parent) |
| 181 | + |
| 182 | + def find_min(self) -> TreeNode: |
| 183 | + if self.is_empty(): |
| 184 | + return None |
| 185 | + node: TreeNode = self.root |
| 186 | + while node.left is not None: |
| 187 | + node = node.left |
| 188 | + return node |
| 189 | + |
| 190 | + def find_max(self) -> TreeNode: |
| 191 | + if self.is_empty(): |
| 192 | + return None |
| 193 | + node: TreeNode = self.root |
| 194 | + while node.right is not None: |
| 195 | + node = node.right |
| 196 | + return node |
| 197 | + |
| 198 | + def _update_balance_factor(self, root: TreeNode): |
| 199 | + old_balance_factor: int = root.balance_factor |
| 200 | + if root.has_left_child(): |
| 201 | + root.left_subtree_height = max(root.left.left_subtree_height, root.left.right_subtree_height) + 1 |
| 202 | + else: |
| 203 | + root.left_subtree_height = 0 |
| 204 | + if root.has_right_child(): |
| 205 | + root.right_subtree_height = max(root.right.left_subtree_height, root.right.right_subtree_height) + 1 |
| 206 | + else: |
| 207 | + root.right_subtree_height = 0 |
| 208 | + root.balance_factor = root.left_subtree_height - root.right_subtree_height |
| 209 | + if root.balance_factor < -1 or root.balance_factor > 1: |
| 210 | + self._rebalance(root) |
| 211 | + return |
| 212 | + if root.balance_factor != old_balance_factor and root.has_parent(): |
| 213 | + self._update(root.parent) |
| 214 | + |
| 215 | + def _rebalance(self, root: TreeNode): |
| 216 | + if root.balance_factor < 0: |
| 217 | + if root.right.balance_factor > 0: |
| 218 | + self._rotate_right(root.right) |
| 219 | + else: |
| 220 | + self._rotate_left(root) |
| 221 | + else: |
| 222 | + if root.left.balance_factor < 0: |
| 223 | + self._rotate_left(root.left) |
| 224 | + else: |
| 225 | + self._rotate_right(root) |
| 226 | + |
| 227 | + def _rotate_left(self, root: TreeNode): |
| 228 | + old_root: TreeNode = root |
| 229 | + new_root: TreeNode = old_root.right |
| 230 | + old_root.right = new_root.left |
| 231 | + if new_root.has_left_child(): |
| 232 | + new_root.left.parent = old_root |
| 233 | + new_root.parent = old_root.parent |
| 234 | + if old_root.has_parent(): |
| 235 | + if old_root.is_left_child(): |
| 236 | + old_root.parent.left = new_root |
| 237 | + else: |
| 238 | + old_root.parent.right = new_root |
| 239 | + else: |
| 240 | + self.root = new_root |
| 241 | + old_root.parent = new_root |
| 242 | + new_root.left = old_root |
| 243 | + self._update_balance_factor(old_root) |
| 244 | + |
| 245 | + def _rotate_right(self, root: TreeNode): |
| 246 | + old_root: TreeNode = root |
| 247 | + new_root: TreeNode = old_root.left |
| 248 | + old_root.left = new_root.right |
| 249 | + if new_root.has_right_child(): |
| 250 | + new_root.right.parent = old_root |
| 251 | + new_root.parent = old_root.parent |
| 252 | + if old_root.has_parent(): |
| 253 | + if old_root.is_left_child(): |
| 254 | + old_root.parent.left = new_root |
| 255 | + else: |
| 256 | + old_root.parent.right = new_root |
| 257 | + else: |
| 258 | + self.root = new_root |
| 259 | + old_root.parent = new_root |
| 260 | + new_root.right = old_root |
| 261 | + self._update_balance_factor(old_root) |
| 262 | + |
| 263 | + |
| 264 | + |
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