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* Retranslate the complete English edition from Simplified Chinese * Polish three English explanations after reader-focused review
201 lines
6.9 KiB
Python
201 lines
6.9 KiB
Python
"""
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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 the root of the binary tree"""
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return self._root
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def height(self, node: TreeNode | None) -> int:
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"""Get the node height"""
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# An empty subtree has height -1; a leaf has height 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 the node height"""
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# The node height equals the height of its taller 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 the balance factor"""
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# An empty subtree has balance factor 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"""
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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 the 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 rotated subtree
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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"""
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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 the 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 rotated subtree
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return child
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def rotate(self, node: TreeNode | None) -> TreeNode | None:
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"""Perform rotations to restore balance in this 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-heavy tree
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if balance_factor > 1:
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if self.balance_factor(node.left) >= 0:
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# Rotate right
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return self.right_rotate(node)
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else:
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# Rotate left, then right
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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-heavy tree
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elif balance_factor < -1:
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if self.balance_factor(node.right) <= 0:
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# Rotate left
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return self.left_rotate(node)
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else:
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# Rotate right, then left
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node.right = self.right_rotate(node.right)
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return self.left_rotate(node)
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# The tree is balanced; return without rotating
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return node
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def insert(self, val):
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"""Insert a 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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"""Insert a node recursively (helper method)"""
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if node is None:
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return TreeNode(val)
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# 1. Find the insertion position and insert the 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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# Return without inserting a duplicate node
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return node
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# Update the node height
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self.update_height(node)
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# 2. Perform rotations to restore balance in this subtree
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return self.rotate(node)
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def remove(self, val: int):
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"""Remove a 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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"""Remove a node recursively (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 children = 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 children = 1: remove node directly
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else:
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node = child
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else:
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# Number of children = 2: remove the inorder successor and use its value to replace the current node value
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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 the node height
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self.update_height(node)
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# 2. Perform rotations to restore balance in this subtree
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return self.rotate(node)
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def search(self, val: int) -> TreeNode | None:
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"""Find a node"""
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cur = self._root
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# Search in a loop, stopping if cur becomes None
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while cur is not None:
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# If present, the target node lies in the right subtree of cur
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if cur.val < val:
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cur = cur.right
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# If present, the target node lies in the left subtree of cur
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elif cur.val > val:
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cur = cur.left
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# The target node was found; exit the loop
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else:
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break
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# Return the target node, or None if it was not found
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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("\nAVL tree after inserting node {}:".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("\nAVL tree after removing node {}:".format(val))
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print_tree(tree.get_root())
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# Initialize an empty AVL tree
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avl_tree = AVLTree()
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# Insert a node
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# Observe how the AVL tree maintains balance after a node is inserted
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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 a duplicate node
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test_insert(avl_tree, 7)
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# Remove a node
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# Observe how the AVL tree maintains balance after a node is removed
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test_remove(avl_tree, 8) # Remove a node with 0 children
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test_remove(avl_tree, 5) # Remove a node with 1 child
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test_remove(avl_tree, 4) # Remove a node with 2 children
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result_node = avl_tree.search(7)
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print("\nFound node object: {}, node value = {}".format(result_node, result_node.val))
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