|
|
"""
|
|
|
File: avl_tree.py
|
|
|
Created Time: 2022-12-20
|
|
|
Author: a16su (lpluls001@gmail.com)
|
|
|
"""
|
|
|
|
|
|
import sys
|
|
|
from pathlib import Path
|
|
|
|
|
|
sys.path.append(str(Path(__file__).parent.parent))
|
|
|
from modules import TreeNode, print_tree
|
|
|
|
|
|
|
|
|
class AVLTree:
|
|
|
"""AVL 樹"""
|
|
|
|
|
|
def __init__(self):
|
|
|
"""建構子"""
|
|
|
self._root = None
|
|
|
|
|
|
def get_root(self) -> TreeNode | None:
|
|
|
"""獲取二元樹根節點"""
|
|
|
return self._root
|
|
|
|
|
|
def height(self, node: TreeNode | None) -> int:
|
|
|
"""獲取節點高度"""
|
|
|
# 空節點高度為 -1 ，葉節點高度為 0
|
|
|
if node is not None:
|
|
|
return node.height
|
|
|
return -1
|
|
|
|
|
|
def update_height(self, node: TreeNode | None):
|
|
|
"""更新節點高度"""
|
|
|
# 節點高度等於最高子樹高度 + 1
|
|
|
node.height = max([self.height(node.left), self.height(node.right)]) + 1
|
|
|
|
|
|
def balance_factor(self, node: TreeNode | None) -> int:
|
|
|
"""獲取平衡因子"""
|
|
|
# 空節點平衡因子為 0
|
|
|
if node is None:
|
|
|
return 0
|
|
|
# 節點平衡因子 = 左子樹高度 - 右子樹高度
|
|
|
return self.height(node.left) - self.height(node.right)
|
|
|
|
|
|
def right_rotate(self, node: TreeNode | None) -> TreeNode | None:
|
|
|
"""右旋操作"""
|
|
|
child = node.left
|
|
|
grand_child = child.right
|
|
|
# 以 child 為原點，將 node 向右旋轉
|
|
|
child.right = node
|
|
|
node.left = grand_child
|
|
|
# 更新節點高度
|
|
|
self.update_height(node)
|
|
|
self.update_height(child)
|
|
|
# 返回旋轉後子樹的根節點
|
|
|
return child
|
|
|
|
|
|
def left_rotate(self, node: TreeNode | None) -> TreeNode | None:
|
|
|
"""左旋操作"""
|
|
|
child = node.right
|
|
|
grand_child = child.left
|
|
|
# 以 child 為原點，將 node 向左旋轉
|
|
|
child.left = node
|
|
|
node.right = grand_child
|
|
|
# 更新節點高度
|
|
|
self.update_height(node)
|
|
|
self.update_height(child)
|
|
|
# 返回旋轉後子樹的根節點
|
|
|
return child
|
|
|
|
|
|
def rotate(self, node: TreeNode | None) -> TreeNode | None:
|
|
|
"""執行旋轉操作，使該子樹重新恢復平衡"""
|
|
|
# 獲取節點 node 的平衡因子
|
|
|
balance_factor = self.balance_factor(node)
|
|
|
# 左偏樹
|
|
|
if balance_factor > 1:
|
|
|
if self.balance_factor(node.left) >= 0:
|
|
|
# 右旋
|
|
|
return self.right_rotate(node)
|
|
|
else:
|
|
|
# 先左旋後右旋
|
|
|
node.left = self.left_rotate(node.left)
|
|
|
return self.right_rotate(node)
|
|
|
# 右偏樹
|
|
|
elif balance_factor < -1:
|
|
|
if self.balance_factor(node.right) <= 0:
|
|
|
# 左旋
|
|
|
return self.left_rotate(node)
|
|
|
else:
|
|
|
# 先右旋後左旋
|
|
|
node.right = self.right_rotate(node.right)
|
|
|
return self.left_rotate(node)
|
|
|
# 平衡樹，無須旋轉，直接返回
|
|
|
return node
|
|
|
|
|
|
def insert(self, val):
|
|
|
"""插入節點"""
|
|
|
self._root = self.insert_helper(self._root, val)
|
|
|
|
|
|
def insert_helper(self, node: TreeNode | None, val: int) -> TreeNode:
|
|
|
"""遞迴插入節點（輔助方法）"""
|
|
|
if node is None:
|
|
|
return TreeNode(val)
|
|
|
# 1. 查詢插入位置並插入節點
|
|
|
if val < node.val:
|
|
|
node.left = self.insert_helper(node.left, val)
|
|
|
elif val > node.val:
|
|
|
node.right = self.insert_helper(node.right, val)
|
|
|
else:
|
|
|
# 重複節點不插入，直接返回
|
|
|
return node
|
|
|
# 更新節點高度
|
|
|
self.update_height(node)
|
|
|
# 2. 執行旋轉操作，使該子樹重新恢復平衡
|
|
|
return self.rotate(node)
|
|
|
|
|
|
def remove(self, val: int):
|
|
|
"""刪除節點"""
|
|
|
self._root = self.remove_helper(self._root, val)
|
|
|
|
|
|
def remove_helper(self, node: TreeNode | None, val: int) -> TreeNode | None:
|
|
|
"""遞迴刪除節點（輔助方法）"""
|
|
|
if node is None:
|
|
|
return None
|
|
|
# 1. 查詢節點並刪除
|
|
|
if val < node.val:
|
|
|
node.left = self.remove_helper(node.left, val)
|
|
|
elif val > node.val:
|
|
|
node.right = self.remove_helper(node.right, val)
|
|
|
else:
|
|
|
if node.left is None or node.right is None:
|
|
|
child = node.left or node.right
|
|
|
# 子節點數量 = 0 ，直接刪除 node 並返回
|
|
|
if child is None:
|
|
|
return None
|
|
|
# 子節點數量 = 1 ，直接刪除 node
|
|
|
else:
|
|
|
node = child
|
|
|
else:
|
|
|
# 子節點數量 = 2 ，則將中序走訪的下個節點刪除，並用該節點替換當前節點
|
|
|
temp = node.right
|
|
|
while temp.left is not None:
|
|
|
temp = temp.left
|
|
|
node.right = self.remove_helper(node.right, temp.val)
|
|
|
node.val = temp.val
|
|
|
# 更新節點高度
|
|
|
self.update_height(node)
|
|
|
# 2. 執行旋轉操作，使該子樹重新恢復平衡
|
|
|
return self.rotate(node)
|
|
|
|
|
|
def search(self, val: int) -> TreeNode | None:
|
|
|
"""查詢節點"""
|
|
|
cur = self._root
|
|
|
# 迴圈查詢，越過葉節點後跳出
|
|
|
while cur is not None:
|
|
|
# 目標節點在 cur 的右子樹中
|
|
|
if cur.val < val:
|
|
|
cur = cur.right
|
|
|
# 目標節點在 cur 的左子樹中
|
|
|
elif cur.val > val:
|
|
|
cur = cur.left
|
|
|
# 找到目標節點，跳出迴圈
|
|
|
else:
|
|
|
break
|
|
|
# 返回目標節點
|
|
|
return cur
|
|
|
|
|
|
|
|
|
"""Driver Code"""
|
|
|
if __name__ == "__main__":
|
|
|
|
|
|
def test_insert(tree: AVLTree, val: int):
|
|
|
tree.insert(val)
|
|
|
print("\n插入節點 {} 後，AVL 樹為".format(val))
|
|
|
print_tree(tree.get_root())
|
|
|
|
|
|
def test_remove(tree: AVLTree, val: int):
|
|
|
tree.remove(val)
|
|
|
print("\n刪除節點 {} 後，AVL 樹為".format(val))
|
|
|
print_tree(tree.get_root())
|
|
|
|
|
|
# 初始化空 AVL 樹
|
|
|
avl_tree = AVLTree()
|
|
|
|
|
|
# 插入節點
|
|
|
# 請關注插入節點後，AVL 樹是如何保持平衡的
|
|
|
for val in [1, 2, 3, 4, 5, 8, 7, 9, 10, 6]:
|
|
|
test_insert(avl_tree, val)
|
|
|
|
|
|
# 插入重複節點
|
|
|
test_insert(avl_tree, 7)
|
|
|
|
|
|
# 刪除節點
|
|
|
# 請關注刪除節點後，AVL 樹是如何保持平衡的
|
|
|
test_remove(avl_tree, 8) # 刪除度為 0 的節點
|
|
|
test_remove(avl_tree, 5) # 刪除度為 1 的節點
|
|
|
test_remove(avl_tree, 4) # 刪除度為 2 的節點
|
|
|
|
|
|
result_node = avl_tree.search(7)
|
|
|
print("\n查詢到的節點物件為 {}，節點值 = {}".format(result_node, result_node.val))
|
