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201 lines
6.8 KiB
201 lines
6.8 KiB
"""
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File: avl_tree.py
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Created Time: 2022-12-20
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Author: a16su (lpluls001@gmail.com)
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"""
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import sys
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from pathlib import Path
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sys.path.append(str(Path(__file__).parent.parent))
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from modules import TreeNode, print_tree
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class AVLTree:
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"""AVL tree"""
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def __init__(self):
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"""Constructor"""
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self._root = None
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def get_root(self) -> TreeNode | None:
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"""Get binary tree root node"""
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return self._root
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def height(self, node: TreeNode | None) -> int:
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"""Get node height"""
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# Empty node height is -1, leaf node height is 0
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if node is not None:
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return node.height
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return -1
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def update_height(self, node: TreeNode | None):
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"""Update node height"""
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# Node height equals the height of the tallest subtree + 1
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node.height = max([self.height(node.left), self.height(node.right)]) + 1
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def balance_factor(self, node: TreeNode | None) -> int:
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"""Get balance factor"""
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# Empty node balance factor is 0
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if node is None:
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return 0
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# Node balance factor = left subtree height - right subtree height
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return self.height(node.left) - self.height(node.right)
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def right_rotate(self, node: TreeNode | None) -> TreeNode | None:
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"""Right rotation operation"""
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child = node.left
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grand_child = child.right
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# Rotate node to the right around child
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child.right = node
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node.left = grand_child
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# Update node height
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self.update_height(node)
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self.update_height(child)
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# Return the root of the subtree after rotation
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return child
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def left_rotate(self, node: TreeNode | None) -> TreeNode | None:
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"""Left rotation operation"""
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child = node.right
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grand_child = child.left
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# Rotate node to the left around child
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child.left = node
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node.right = grand_child
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# Update node height
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self.update_height(node)
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self.update_height(child)
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# Return the root of the subtree after rotation
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return child
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def rotate(self, node: TreeNode | None) -> TreeNode | None:
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"""Perform rotation operation to restore balance to the subtree"""
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# Get the balance factor of node
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balance_factor = self.balance_factor(node)
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# Left-leaning tree
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if balance_factor > 1:
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if self.balance_factor(node.left) >= 0:
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# Right rotation
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return self.right_rotate(node)
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else:
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# First left rotation then right rotation
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node.left = self.left_rotate(node.left)
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return self.right_rotate(node)
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# Right-leaning tree
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elif balance_factor < -1:
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if self.balance_factor(node.right) <= 0:
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# Left rotation
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return self.left_rotate(node)
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else:
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# First right rotation then left rotation
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node.right = self.right_rotate(node.right)
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return self.left_rotate(node)
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# Balanced tree, no rotation needed, return
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return node
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def insert(self, val):
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"""Insert node"""
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self._root = self.insert_helper(self._root, val)
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def insert_helper(self, node: TreeNode | None, val: int) -> TreeNode:
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"""Recursively insert node (helper method)"""
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if node is None:
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return TreeNode(val)
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# 1. Find insertion position and insert node
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if val < node.val:
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node.left = self.insert_helper(node.left, val)
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elif val > node.val:
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node.right = self.insert_helper(node.right, val)
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else:
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# Do not insert duplicate nodes, return
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return node
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# Update node height
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self.update_height(node)
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# 2. Perform rotation operation to restore balance to the subtree
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return self.rotate(node)
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def remove(self, val: int):
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"""Remove node"""
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self._root = self.remove_helper(self._root, val)
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def remove_helper(self, node: TreeNode | None, val: int) -> TreeNode | None:
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"""Recursively remove node (helper method)"""
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if node is None:
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return None
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# 1. Find and remove the node
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if val < node.val:
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node.left = self.remove_helper(node.left, val)
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elif val > node.val:
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node.right = self.remove_helper(node.right, val)
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else:
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if node.left is None or node.right is None:
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child = node.left or node.right
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# Number of child nodes = 0, remove node and return
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if child is None:
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return None
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# Number of child nodes = 1, remove node
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else:
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node = child
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else:
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# Number of child nodes = 2, remove the next node in in-order traversal and replace the current node with it
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temp = node.right
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while temp.left is not None:
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temp = temp.left
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node.right = self.remove_helper(node.right, temp.val)
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node.val = temp.val
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# Update node height
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self.update_height(node)
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# 2. Perform rotation operation to restore balance to the subtree
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return self.rotate(node)
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def search(self, val: int) -> TreeNode | None:
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"""Search node"""
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cur = self._root
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# Loop find, break after passing leaf nodes
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while cur is not None:
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# Target node is in cur's right subtree
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if cur.val < val:
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cur = cur.right
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# Target node is in cur's left subtree
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elif cur.val > val:
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cur = cur.left
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# Found target node, break loop
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else:
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break
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# Return target node
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return cur
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"""Driver Code"""
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if __name__ == "__main__":
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def test_insert(tree: AVLTree, val: int):
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tree.insert(val)
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print("\nInsert node {} after, AVL tree is".format(val))
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print_tree(tree.get_root())
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def test_remove(tree: AVLTree, val: int):
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tree.remove(val)
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print("\nRemove node {} after, AVL tree is".format(val))
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print_tree(tree.get_root())
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# Initialize empty AVL tree
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avl_tree = AVLTree()
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# Insert node
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# Notice how the AVL tree maintains balance after inserting nodes
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for val in [1, 2, 3, 4, 5, 8, 7, 9, 10, 6]:
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test_insert(avl_tree, val)
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# Insert duplicate node
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test_insert(avl_tree, 7)
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# Remove node
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# Notice how the AVL tree maintains balance after removing nodes
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test_remove(avl_tree, 8) # Remove node with degree 0
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test_remove(avl_tree, 5) # Remove node with degree 1
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test_remove(avl_tree, 4) # Remove node with degree 2
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result_node = avl_tree.search(7)
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print("\nFound node object is {}, node value = {}".format(result_node, result_node.val))
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