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* Revised the book * Update the book with the second revised edition * Revise base on the manuscript of the first edition
200 lines
6.6 KiB
Python
200 lines
6.6 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
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from pathlib import Path
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sys.path.append(str(Path(__file__).parent.parent))
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from modules import TreeNode, print_tree
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class AVLTree:
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"""AVL 树"""
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def __init__(self):
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"""构造方法"""
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self._root = None
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def get_root(self) -> TreeNode | None:
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"""获取二叉树根节点"""
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return self._root
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def height(self, node: TreeNode | None) -> int:
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"""获取节点高度"""
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# 空节点高度为 -1 ，叶节点高度为 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: TreeNode | None):
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"""更新节点高度"""
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# 节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: TreeNode | None) -> int:
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"""获取平衡因子"""
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# 空节点平衡因子为 0
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if node is None:
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return 0
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# 节点平衡因子 = 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: TreeNode | None) -> TreeNode | None:
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"""右旋操作"""
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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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# 更新节点高度
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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: TreeNode | None) -> TreeNode | None:
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"""左旋操作"""
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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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# 更新节点高度
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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: TreeNode | None) -> TreeNode | None:
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"""执行旋转操作，使该子树重新恢复平衡"""
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# 获取节点 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，无须旋转，直接返回
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return node
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def insert(self, val):
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"""插入节点"""
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self._root = self.insert_helper(self._root, val)
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def insert_helper(self, node: TreeNode | None, val: int) -> TreeNode:
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"""递归插入节点（辅助方法）"""
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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节点
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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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# 重复节点不插入，直接返回
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return node
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# 更新节点高度
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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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"""删除节点"""
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self._root = self.remove_helper(self._root, val)
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def remove_helper(self, node: TreeNode | None, val: int) -> TreeNode | None:
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"""递归删除节点（辅助方法）"""
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if node is None:
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return None
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# 1. 查找节点并删除
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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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# 子节点数量 = 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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# 子节点数量 = 1 ，直接删除 node
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else:
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node = child
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else:
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# 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点
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temp = node.right
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while temp.left is not None:
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temp = temp.left
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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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# 更新节点高度
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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 search(self, val: int) -> TreeNode | None:
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"""查找节点"""
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cur = self._root
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# 循环查找，越过叶节点后跳出
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while cur is not None:
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# 目标节点在 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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# 目标节点在 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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# 找到目标节点，跳出循环
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else:
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break
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# 返回目标节点
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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插入节点 {} 后，AVL 树为".format(val))
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print_tree(tree.get_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删除节点 {} 后，AVL 树为".format(val))
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print_tree(tree.get_root())
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# 初始化空 AVL 树
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avl_tree = AVLTree()
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# 插入节点
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# 请关注插入节点后，AVL 树是如何保持平衡的
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for val in [1, 2, 3, 4, 5, 8, 7, 9, 10, 6]:
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test_insert(avl_tree, val)
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# 插入重复节点
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test_insert(avl_tree, 7)
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# 删除节点
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# 请关注删除节点后，AVL 树是如何保持平衡的
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test_remove(avl_tree, 8) # 删除度为 0 的节点
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test_remove(avl_tree, 5) # 删除度为 1 的节点
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test_remove(avl_tree, 4) # 删除度为 2 的节点
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result_node = avl_tree.search(7)
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print("\n查找到的节点对象为 {}，节点值 = {}".format(result_node, result_node.val))
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