From e6c8a35841af4fe7b8cda915f5b9a82ca0d5e1b1 Mon Sep 17 00:00:00 2001 From: LJK <3477715681@qq.com> Date: Wed, 27 May 2026 19:48:40 +0800 Subject: [PATCH] feat: Add Splay Tree implementation --- data_structures/binary_tree/splay_tree.py | 191 ++++++++++++++++++++++ 1 file changed, 191 insertions(+) create mode 100644 data_structures/binary_tree/splay_tree.py diff --git a/data_structures/binary_tree/splay_tree.py b/data_structures/binary_tree/splay_tree.py new file mode 100644 index 000000000000..7d73d809a342 --- /dev/null +++ b/data_structures/binary_tree/splay_tree.py @@ -0,0 +1,191 @@ +# 文件名：data_structures/binary_tree/splay_tree.py +from __future__ import annotations + +class Node: + """Splay树节点类""" + def __init__(self, key: int): + self.key = key + self.left: Node | None = None + self.right: Node | None = None + +class SplayTree: + """ + 伸展树（Splay Tree）实现 + 特性：每次访问节点后，将该节点旋转到根位置，优化局部性访问性能 + """ + def __init__(self): + self.root: Node | None = None + + def _right_rotate(self, x: Node) -> Node: + """右旋操作（zig）""" + y = x.left + x.left = y.right + y.right = x + return y + + def _left_rotate(self, x: Node) -> Node: + """左旋操作（zig）""" + y = x.right + x.right = y.left + y.left = x + return y + + def _splay(self, root: Node | None, key: int) -> Node | None: + """ + 核心伸展操作：将包含key的节点旋转到根 + 包含zig、zig-zig、zig-zag三种模式 + """ + if root is None or root.key == key: + return root + + # 目标节点在左子树 + if key < root.key: + if root.left is None: + return root + # Zig-Zig模式：左-左 + if key < root.left.key: + root.left.left = self._splay(root.left.left, key) + root = self._right_rotate(root) + # Zig-Zag模式：左-右 + elif key > root.left.key: + root.left.right = self._splay(root.left.right, key) + if root.left.right: + root.left = self._left_rotate(root.left) + return root.left if root.left is None else self._right_rotate(root) + + # 目标节点在右子树 + else: + if root.right is None: + return root + # Zig-Zig模式：右-右 + if key > root.right.key: + root.right.right = self._splay(root.right.right, key) + root = self._left_rotate(root) + # Zig-Zag模式：右-左 + elif key < root.right.key: + root.right.left = self._splay(root.right.left, key) + if root.right.left: + root.right = self._right_rotate(root.right) + return root.right if root.right is None else self._left_rotate(root) + + def search(self, key: int) -> bool: + """搜索指定key，存在返回True，不存在返回False""" + self.root = self._splay(self.root, key) + return self.root is not None and self.root.key == key + + def insert(self, key: int) -> None: + """插入新节点""" + if self.root is None: + self.root = Node(key) + return + + self.root = self._splay(self.root, key) + if self.root.key == key: + return # 已存在，无需插入 + + new_node = Node(key) + if key < self.root.key: + new_node.right = self.root + new_node.left = self.root.left + self.root.left = None + else: + new_node.left = self.root + new_node.right = self.root.right + self.root.right = None + self.root = new_node + + def delete(self, key: int) -> None: + """删除指定key的节点""" + if self.root is None: + return + + self.root = self._splay(self.root, key) + if self.root.key != key: + return # 节点不存在 + + # 左右子树合并 + if self.root.left is None: + self.root = self.root.right + else: + temp = self.root.right + self.root = self.root.left + self.root = self._splay(self.root, key) + self.root.right = temp + + def find_min(self) -> int | None: + """查找树中最小值""" + if self.root is None: + return None + current = self.root + while current.left: + current = current.left + self.root = self._splay(self.root, current.key) + return current.key + + def find_max(self) -> int | None: + """查找树中最大值""" + if self.root is None: + return None + current = self.root + while current.right: + current = current.right + self.root = self._splay(self.root, current.key) + return current.key + + def inorder_traversal(self, root: Node | None, result: list[int]) -> None: + """中序遍历（有序输出）""" + if root: + self.inorder_traversal(root.left, result) + result.append(root.key) + self.inorder_traversal(root.right, result) + + def get_size(self, root: Node | None) -> int: + """获取树的节点总数""" + if root is None: + return 0 + return 1 + self.get_size(root.left) + self.get_size(root.right) + + def get_height(self, root: Node | None) -> int: + """获取树的高度""" + if root is None: + return -1 + return 1 + max(self.get_height(root.left), self.get_height(root.right)) + + def print_tree(self, root: Node | None, indent: str = "", last: bool = True) -> None: + """可视化打印树结构""" + if root: + print(indent + ("└── " if last else "├── ") + str(root.key)) + indent += " " if last else "│ " + self.print_tree(root.left, indent, False) + self.print_tree(root.right, indent, True) + +# 测试用例 +if __name__ == "__main__": + tree = SplayTree() + # 插入测试 + for key in [10, 20, 30, 40, 50, 25]: + tree.insert(key) + print("中序遍历:", end=" ") + traversal_result = [] + tree.inorder_traversal(tree.root, traversal_result) + print(traversal_result) + + # 搜索测试（访问后节点会被伸展到根） + print("\n搜索25:", tree.search(25)) + print("搜索后根节点:", tree.root.key) + + # 删除测试 + tree.delete(30) + print("\n删除30后中序遍历:", end=" ") + traversal_result = [] + tree.inorder_traversal(tree.root, traversal_result) + print(traversal_result) + + # 辅助方法测试 + print("\n树大小:", tree.get_size(tree.root)) + print("树高度:", tree.get_height(tree.root)) + print("最小值:", tree.find_min()) + print("最大值:", tree.find_max()) + + print("\n树结构:") + tree.print_tree(tree.root) \ No newline at end of file