mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-26 13:16:28 +08:00
281 lines
8.2 KiB
Python
281 lines
8.2 KiB
Python
import sys, os.path as osp
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import typing
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sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
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from include import *
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class AVLTreeNode:
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def __init__(
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self,
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val=None,
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height: int = 0,
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left: typing.Optional["AVLTreeNode"] = None,
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right: typing.Optional["AVLTreeNode"] = None,
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):
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self.val = val
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self.height = height
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self.left = left
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self.right = right
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def __str__(self):
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val = self.val
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left_val = self.left.val if self.left else None
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right_val = self.right.val if self.right else None
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return "<AVLTreeNode: {}, leftAVLTreeNode: {}, rightAVLTreeNode: {}>".format(
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val, left_val, right_val
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)
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class AVLTree:
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def __init__(self, root: typing.Optional[AVLTreeNode] = None):
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self.root = root
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@staticmethod
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def height(node: typing.Optional[AVLTreeNode]) -> int:
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"""
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获取结点高度
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Args:
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node:起始结点
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Returns: 高度 or -1
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"""
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# 空结点高度为 -1 ，叶结点高度为 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: AVLTreeNode):
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"""
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更新结点高度
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Args:
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node: 要更新高度的结点
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Returns: None
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"""
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# 结点高度等于最高子树高度 + 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: AVLTreeNode) -> int:
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"""
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获取结点平衡因子
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Args:
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node: 要获取平衡因子的结点
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Returns: 平衡因子
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"""
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# 空结点平衡因子为 0
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if node is None:
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return 0
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# 结点平衡因子 = 左子树高度 - 右子树高度
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return self.height(node.left) - self.height(node.right)
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def __right_rotate(self, node: AVLTreeNode) -> AVLTreeNode:
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child = node.left
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grand_child = child.right
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# 以 child 为原点，将 node 向右旋转
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child.right = node
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node.left = grand_child
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# 更新结点高度
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self.__update_height(node)
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self.__update_height(child)
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# 返回旋转后子树的根节点
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return child
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def __left_rotate(self, node: AVLTreeNode) -> AVLTreeNode:
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child = node.right
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grand_child = child.left
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# 以 child 为原点，将 node 向左旋转
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child.left = node
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node.right = grand_child
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# 更新结点高度
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self.__update_height(node)
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self.__update_height(child)
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# 返回旋转后子树的根节点
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return child
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def rotate(self, node: AVLTreeNode):
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"""
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执行旋转操作，使该子树重新恢复平衡
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Args:
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node: 要旋转的根结点
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Returns: 旋转后的根结点
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"""
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# 获取结点 node 的平衡因子
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balance_factor = self.balance_factor(node)
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# 左偏树
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if balance_factor > 1:
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if self.balance_factor(node.left) >= 0:
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# 右旋
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return self.__right_rotate(node)
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else:
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# 先左旋后右旋
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node.left = self.__left_rotate(node.left)
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return self.__right_rotate(node)
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# 右偏树
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elif balance_factor < -1:
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if self.balance_factor(node.right) <= 0:
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# 左旋
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return self.__left_rotate(node)
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else:
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# 先右旋后左旋
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node.right = self.__right_rotate(node.right)
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return self.__left_rotate(node)
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# 平衡树，无需旋转，直接返回
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return node
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def insert(self, val) -> AVLTreeNode:
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"""
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插入结点
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Args:
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val: 结点的值
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Returns:
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node: 插入结点后的根结点
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"""
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self.root = self.insert_helper(self.root, val)
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return self.root
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def insert_helper(
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self, node: typing.Optional[AVLTreeNode], val: int
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) -> AVLTreeNode:
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"""
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递归插入结点（辅助函数）
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Args:
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node: 要插入的根结点
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val: 要插入的结点的值
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Returns: 插入结点后的根结点
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"""
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if node is None:
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return AVLTreeNode(val)
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# 1. 查找插入位置，并插入结点
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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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# 重复结点不插入，直接返回
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return node
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# 更新结点高度
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self.__update_height(node)
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# 2. 执行旋转操作，使该子树重新恢复平衡
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return self.rotate(node)
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def remove(self, val: int):
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"""
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删除结点
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Args:
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val: 要删除的结点的值
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Returns:
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"""
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root = self.remove_helper(self.root, val)
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return root
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def remove_helper(
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self, node: typing.Optional[AVLTreeNode], val: int
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) -> typing.Optional[AVLTreeNode]:
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"""
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递归删除结点（辅助函数）
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Args:
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node: 删除的起始结点
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val: 要删除的结点的值
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Returns: 删除目标结点后的起始结点
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"""
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if node is None:
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return None
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# 1. 查找结点，并删除之
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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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# 子结点数量 = 0 ，直接删除 node 并返回
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if child is None:
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return None
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# 子结点数量 = 1 ，直接删除 node
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else:
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node = child
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else: # 子结点数量 = 2 ，则将中序遍历的下个结点删除，并用该结点替换当前结点
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temp = self.min_node(node.right)
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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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# 更新结点高度
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self.__update_height(node)
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# 2. 执行旋转操作，使该子树重新恢复平衡
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return self.rotate(node)
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def min_node(
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self, node: typing.Optional[AVLTreeNode]
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) -> typing.Optional[AVLTreeNode]:
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# 获取最小结点
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if node is None:
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return None
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# 循环访问左子结点，直到叶结点时为最小结点，跳出
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while node.left is not None:
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node = node.left
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return node
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def search(self, val: int):
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cur = self.root
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while cur is not None:
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if cur.val < val:
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cur = cur.right
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elif cur.val > val:
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cur = cur.left
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else:
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break
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return cur
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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("\n插入结点 {} 后，AVL 树为".format(val))
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print_tree(tree.root)
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def test_remove(tree: AVLTree, val: int):
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tree.remove(val)
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print("\n删除结点 {} 后，AVL 树为".format(val))
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print_tree(tree.root)
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# 初始化空 AVL 树
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avl_tree = AVLTree()
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# 插入结点
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# 请关注插入结点后，AVL 树是如何保持平衡的
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test_insert(avl_tree, 1)
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test_insert(avl_tree, 2)
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test_insert(avl_tree, 3)
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test_insert(avl_tree, 4)
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test_insert(avl_tree, 5)
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test_insert(avl_tree, 8)
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test_insert(avl_tree, 7)
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test_insert(avl_tree, 9)
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test_insert(avl_tree, 10)
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test_insert(avl_tree, 6)
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# 插入重复结点
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test_insert(avl_tree, 7)
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# 删除结点
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# 请关注删除结点后，AVL 树是如何保持平衡的
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test_remove(avl_tree, 8) # 删除度为 0 的结点
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test_remove(avl_tree, 5) # 删除度为 1 的结点
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test_remove(avl_tree, 4) # 删除度为 2 的结点
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result_node = avl_tree.search(7)
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print("\n查找到的结点对象为 {}，结点值 = {}".format(result_node, result_node.val))
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