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206 lines
7.1 KiB
Python
206 lines
7.1 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, os.path as osp
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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 AVLTree:
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def __init__(self, root: Optional[TreeNode] = None):
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self.root = root
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""" 获取结点高度 """
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def height(self, node: Optional[TreeNode]) -> int:
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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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""" 更新结点高度 """
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def __update_height(self, node: Optional[TreeNode]):
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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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""" 获取平衡因子 """
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def balance_factor(self, node: Optional[TreeNode]) -> int:
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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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""" 右旋操作 """
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def __right_rotate(self, node: Optional[TreeNode]) -> TreeNode:
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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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""" 左旋操作 """
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def __left_rotate(self, node: Optional[TreeNode]) -> TreeNode:
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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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""" 执行旋转操作，使该子树重新恢复平衡 """
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def __rotate(self, node: Optional[TreeNode]) -> TreeNode:
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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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""" 插入结点 """
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def insert(self, val) -> TreeNode:
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self.root = self.__insert_helper(self.root, val)
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return self.root
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""" 递归插入结点（辅助函数）"""
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def __insert_helper(self, node: Optional[TreeNode], val: int) -> TreeNode:
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if node is None:
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return TreeNode(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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""" 删除结点 """
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def remove(self, val: int):
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root = self.__remove_helper(self.root, val)
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return root
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""" 递归删除结点（辅助函数） """
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def __remove_helper(self, node: Optional[TreeNode], val: int) -> Optional[TreeNode]:
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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.__get_inorder_next(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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""" 获取中序遍历中的下一个结点（仅适用于 root 有左子结点的情况） """
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def __get_inorder_next(self, node: Optional[TreeNode]) -> Optional[TreeNode]:
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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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""" 查找结点 """
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def search(self, val: int):
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cur = self.root
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# 循环查找，越过叶结点后跳出
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while cur is not None:
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# 目标结点在 cur 的右子树中
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if cur.val < val:
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cur = cur.right
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# 目标结点在 cur 的左子树中
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elif cur.val > val:
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cur = cur.left
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# 找到目标结点，跳出循环
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else:
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break
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# 返回目标结点
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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("\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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