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avl-tree.py
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class TreeNode:
def __init__(self, key=None, value=None, parent=None, left=None, right=None,
left_subtree_height: int = 0, right_subtree_height: int = 0, balance_factor: int = 0):
self.key = key
self.value = value
self.parent = parent
self.left = left
self.right = right
self.left_subtree_height: int = left_subtree_height
self.right_subtree_height: int = right_subtree_height
self.balance_factor : int = balance_factor
def has_left_child(self) -> bool:
return self.left is not None
def has_right_child(self) -> bool:
return self.right is not None
def has_both_children(self) -> bool:
return self.has_left_child() and self.has_right_child()
def is_leaf(self) -> bool:
return not self.has_left_child() and not self.has_right_child()
def is_root(self) -> bool:
return self.parent is None
def has_parent(self) -> bool:
return self.parent is not None
def is_left_child(self) -> bool:
return self.parent.left == self
def is_right_child(self) -> bool:
return self.parent.right == self
def find_min(self):
if self is None:
return None
if self.has_left_child():
return self.left.find_min()
else:
return self
def find_max(self):
if self is None:
return None
node = self
while node.right is not None:
node = node.right
return node
class AVLTree:
def __init__(self):
self.root: TreeNode = None
self.elements: int = 0
def size(self) -> int:
return self.elements
def is_empty(self) -> bool:
return self.root is None
def put(self, key, value):
if self.is_empty():
self.root = TreeNode(key, value)
self.elements += 1
else:
self._put(self.root, key, value)
def _put(self, root: TreeNode, key, value):
if root.key == key:
root.value = value
elif key < root.key:
if root.has_left_child():
self._put(root.left, key, value)
else:
root.left = TreeNode(key, value, root)
self.elements += 1
self._update_balance_factor(root)
else:
if root.has_right_child():
self._put(root.right, key, value)
else:
root.right = TreeNode(key, value, root)
self.elements += 1
self._update_balance_factor(root)
def get(self, key) -> TreeNode:
if self.is_empty():
return None
else:
return self._get(self.root, key)
def _get(self, root: TreeNode, key) -> TreeNode:
if root.key == key:
return root
elif key < root.key:
if root.has_left_child():
return self._get(root.left, key)
else:
return None
else:
if root.has_right_child():
return self._get(root.right, key)
else:
return None
def contains(self, key) -> bool:
if self.is_empty():
return None
found: bool = False
node: TreeNode = self.root
while node is not None and not found:
if node.key == key:
found = True
elif key < node.key:
node = node.left
else:
node = node.right
return found
def delete(self, key):
node_to_delete: TreeNode = self.get(key)
if node_to_delete is None:
return
if node_to_delete.is_root():
if node_to_delete.is_leaf():
self.root = None
self.elements -= 1
elif node_to_delete.has_both_children():
max_node: TreeNode = node_to_delete.left.find_max()
tmp_key = max_node.key
tmp_value = max_node.value
self.delete(tmp_key)
# keep pointer to that node, not root, root might change
node_to_delete.key = tmp_key
node_to_delete.value = tmp_value
else:
if node_to_delete.has_left_child():
self.root = node_to_delete.left
else:
self.root = node_to_delete.right
self.root.parent = None
self.elements -= 1
else:
parent: TreeNode = None
if node_to_delete.is_leaf():
parent = node_to_delete.parent
if node_to_delete.is_left_child():
node_to_delete.parent.left = None
else:
node_to_delete.parent.right = None
self.elements -= 1
elif node_to_delete.has_both_children():
max_node: TreeNode = node_to_delete.left.find_max()
tmp_key = max_node.key
tmp_value = max_node.value
self.delete(tmp_key)
node_to_delete.key = tmp_key
node_to_delete.value = tmp_value
elif node_to_delete.has_left_child():
parent = node_to_delete.parent
self.elements -= 1
if node_to_delete.is_left_child():
node_to_delete.parent.left = node_to_delete.left
else:
node_to_delete.parent.right = node_to_delete.left
node_to_delete.left.parent = node_to_delete.parent
else:
parent = node_to_delete.parent
self.elements -= 1
if node_to_delete.is_left_child():
node_to_delete.parent.left = node_to_delete.right
else:
node_to_delete.parent.right = node_to_delete.right
node_to_delete.right.parent = node_to_delete.parent
if parent is not None:
self._update_balance_factor(parent)
def find_min(self) -> TreeNode:
if self.is_empty():
return None
node: TreeNode = self.root
while node.left is not None:
node = node.left
return node
def find_max(self) -> TreeNode:
if self.is_empty():
return None
node: TreeNode = self.root
while node.right is not None:
node = node.right
return node
def _update_balance_factor(self, root: TreeNode):
old_balance_factor: int = root.balance_factor
if root.has_left_child():
root.left_subtree_height = max(root.left.left_subtree_height, root.left.right_subtree_height) + 1
else:
root.left_subtree_height = 0
if root.has_right_child():
root.right_subtree_height = max(root.right.left_subtree_height, root.right.right_subtree_height) + 1
else:
root.right_subtree_height = 0
root.balance_factor = root.left_subtree_height - root.right_subtree_height
if root.balance_factor < -1 or root.balance_factor > 1:
self._rebalance(root)
return
if root.balance_factor != old_balance_factor and root.has_parent():
self._update(root.parent)
def _rebalance(self, root: TreeNode):
if root.balance_factor < 0:
if root.right.balance_factor > 0:
self._rotate_right(root.right)
else:
self._rotate_left(root)
else:
if root.left.balance_factor < 0:
self._rotate_left(root.left)
else:
self._rotate_right(root)
def _rotate_left(self, root: TreeNode):
old_root: TreeNode = root
new_root: TreeNode = old_root.right
old_root.right = new_root.left
if new_root.has_left_child():
new_root.left.parent = old_root
new_root.parent = old_root.parent
if old_root.has_parent():
if old_root.is_left_child():
old_root.parent.left = new_root
else:
old_root.parent.right = new_root
else:
self.root = new_root
old_root.parent = new_root
new_root.left = old_root
self._update_balance_factor(old_root)
def _rotate_right(self, root: TreeNode):
old_root: TreeNode = root
new_root: TreeNode = old_root.left
old_root.left = new_root.right
if new_root.has_right_child():
new_root.right.parent = old_root
new_root.parent = old_root.parent
if old_root.has_parent():
if old_root.is_left_child():
old_root.parent.left = new_root
else:
old_root.parent.right = new_root
else:
self.root = new_root
old_root.parent = new_root
new_root.right = old_root
self._update_balance_factor(old_root)