在Python中实现AVL树,需要定义一个TreeNode类来表示树的节点,然后定义一个AVLTree类来实现AVL树的操作。
class TreeNode:
def __init__(self, key):
self.key = key
self.left = None
self.right = None
self.height = 1
class AVLTree:
def __init__(self):
self.root = None
def insert(self, key):
self.root = self._insert(self.root, key)
def _insert(self, node, key):
if not node:
return TreeNode(key)
if key < node.key:
node.left = self._insert(node.left, key)
else:
node.right = self._insert(node.right, key)
node.height = 1 + max(self._get_height(node.left), self._get_height(node.right))
balance = self._get_balance(node)
# 左旋
if balance > 1 and key < node.left.key:
return self._rotate_right(node)
# 右旋
if balance < -1 and key > node.right.key:
return self._rotate_left(node)
# 左右旋
if balance > 1 and key > node.left.key:
node.left = self._rotate_left(node.left)
return self._rotate_right(node)
# 右左旋
if balance < -1 and key < node.right.key:
node.right = self._rotate_right(node.right)
return self._rotate_left(node)
return node
def _get_height(self, node):
if not node:
return 0
return node.height
def _get_balance(self, node):
if not node:
return 0
return self._get_height(node.left) - self._get_height(node.right)
def _rotate_left(self, z):
y = z.right
T2 = y.left
y.left = z
z.right = T2
z.height = 1 + max(self._get_height(z.left), self._get_height(z.right))
y.height = 1 + max(self._get_height(y.left), self._get_height(y.right))
return y
def _rotate_right(self, z):
y = z.left
T3 = y.right
y.right = z
z.left = T3
z.height = 1 + max(self._get_height(z.left), self._get_height(z.right))
y.height = 1 + max(self._get_height(y.left), self._get_height(y.right))
return y
以上是AVL树的Python实现代码,包括了插入节点和旋转操作。可以根据需要进一步实现删除节点、查找节点等操作。