AVL樹是一種特殊的二叉搜索樹 (BST樹)，數據極端情況下, 二叉搜索樹會退化成爲單鏈表，但是AVL樹通過旋轉操作規避了這個問題。
查找平均複雜度：O（logn）
# AVL樹不適於刪除的情況
class AVLTreeNode(object):
def __init__(self, data):
self.data = data # 數據
self.left: AVLTreeNode = None # 左子樹
self.right: AVLTreeNode = None # 右子樹
self.height = 1 # 樹高度
def get_data(node: AVLTreeNode):
return node.data
def set_data(node: AVLTreeNode, data):
node.data = data
# 獲得樹形結構
def get_left_node(node: AVLTreeNode):
return node.left
def get_right_node(node: AVLTreeNode):
return node.right
def get_height(node: AVLTreeNode):
if node is None:
return 0
return node.height
def get_max_node(node: AVLTreeNode):
temp_node = node
if temp_node.right is not None:
return get_max_node(temp_node.right)
else:
return temp_node
def get_min_node(node: AVLTreeNode):
temp_node = node
if temp_node.left is not None:
return get_min_node(temp_node.left)
else:
return temp_node
def get_node(node: AVLTreeNode, data):
temp_node: AVLTreeNode = node
while temp_node:
if data < temp_node.data:
temp_node = temp_node.left
elif data > temp_node.data:
temp_node = temp_node.right
else:
return temp_node
return None
# 右旋：先記錄待旋轉節點的左節點，然後將左節點的right指向待旋轉節點即可
def right_rotate(node: AVLTreeNode):
head_node: AVLTreeNode = node.left
node.left = head_node.right # 將父節點的右側放在待旋轉節點的左側
head_node.right = node # 將父節點的右指針指向待旋轉節點
node.height = max(get_height(node.left), get_height(node.right)) + 1
head_node.height = max(get_height(head_node.left), get_height(head_node.right)) + 1
return head_node
def left_rotate(node: AVLTreeNode):
head_node: AVLTreeNode = node.right
node.right = head_node.left
head_node.left = node
node.height = max(get_height(node.left), get_height(node.right)) + 1
head_node.height = max(get_height(head_node.left), get_height(head_node.right)) + 1
return head_node
# 先左旋，再右旋
def left_right_rotate(node: AVLTreeNode):
son_node = left_rotate(node.left)
node.left = son_node
return right_rotate(node)
def right_left_rotate(node: AVLTreeNode):
son_node = right_rotate(node.right)
node.right = son_node
return left_rotate(node)
# 左子樹與右子樹差距最大爲1，否則及時調整
def adjust_height(node: AVLTreeNode):
if get_height(node.right) - get_height(node.left) > 1:
if get_height(node.right.right) > get_height(node.right.left):
node = left_rotate(node)
else:
node = right_left_rotate(node)
elif get_height(node.left) - get_height(node.right) > 1:
if get_height(node.left.left) > get_height(node.left.right):
node = right_rotate(node)
else:
node = left_right_rotate(node)
else:
pass
return node
def insert_node(node: AVLTreeNode, data):
if node is None:
return AVLTreeNode(data)
if (node.data is not None) and (data < node.data): # 向左插入
node.left = insert_node(node.left, data)
node.height = max(get_height(node.left), get_height(node.right)) + 1
node = adjust_height(node)
elif (node.data is not None) and (data > node.data): # 向右插入
node.right = insert_node(node.right, data)
node.height = max(get_height(node.left), get_height(node.right)) + 1
node = adjust_height(node)
else:
print('Can not insert same value')
return node
def delete_node(node: AVLTreeNode, data):
if node is None:
return None
if (node is not None) and (data < node.data): # 左側查詢
node.left = delete_node(node.left, data)
node = adjust_height(node)
elif (node is not None) and (data > node.data): # 右側查詢
node.right = delete_node(node.right, data)
node = adjust_height(node)
else: # 在這裏刪除
if (node.left is not None) and (node.right is not None): # 左右節點都不爲空
node.data = get_min_node(node.right).data
node.right = delete_node(node.right, node.data)
elif node.left is not None: # 左節點不爲空，右節點爲空
node = node.left
else: # 左節點爲空，右節點未知
node = node.right
if node is not None:
node.height = max(get_height(node.left), get_height(node.right)) + 1
adjust_height(node)
return node
def get_all(node: AVLTreeNode):
values = []
def add_values(values, node: AVLTreeNode):
if node is not None:
values = add_values(values, node.left)
values.append(node.data)
values = add_values(values, node.right)
return values
return add_values(values, node)
def main():
root = AVLTreeNode(10)
number_list = (3, 2, 1, 4, 5, 6, 7, 15, 26, 17)
for number in number_list:
root = insert_node(root, number)
all_values = get_all(root)
del_note = delete_node(root, 3)
all_values = get_all(root)
pass
if __name__ == '__main__':
main()