build

docs/chapter_tree/avl_tree.md

@@ -229,7 +229,7 @@ AVL 树既是二叉搜索树也是平衡二叉树，同时满足这两类二叉
             return node.height
         return -1
 
-    def __update_height(self, node: TreeNode | None):
+    def update_height(self, node: TreeNode | None):
         """更新节点高度"""
         # 节点高度等于最高子树高度 + 1
         node.height = max([self.height(node.left), self.height(node.right)]) + 1
@@ -636,7 +636,7 @@ AVL 树的特点在于“旋转”操作，它能够在不影响二叉树的中
 === "Python"
 
     ```python title="avl_tree.py"
-    def __right_rotate(self, node: TreeNode | None) -> TreeNode | None:
+    def right_rotate(self, node: TreeNode | None) -> TreeNode | None:
         """右旋操作"""
         child = node.left
         grand_child = child.right
@@ -644,8 +644,8 @@ AVL 树的特点在于“旋转”操作，它能够在不影响二叉树的中
         child.right = node
         node.left = grand_child
         # 更新节点高度
-        self.__update_height(node)
-        self.__update_height(child)
+        self.update_height(node)
+        self.update_height(child)
         # 返回旋转后子树的根节点
         return child
     ```
@@ -873,7 +873,7 @@ AVL 树的特点在于“旋转”操作，它能够在不影响二叉树的中
 === "Python"
 
     ```python title="avl_tree.py"
-    def __left_rotate(self, node: TreeNode | None) -> TreeNode | None:
+    def left_rotate(self, node: TreeNode | None) -> TreeNode | None:
         """左旋操作"""
         child = node.right
         grand_child = child.left
@@ -881,8 +881,8 @@ AVL 树的特点在于“旋转”操作，它能够在不影响二叉树的中
         child.left = node
         node.right = grand_child
         # 更新节点高度
-        self.__update_height(node)
-        self.__update_height(child)
+        self.update_height(node)
+        self.update_height(child)
         # 返回旋转后子树的根节点
         return child
     ```
@@ -1135,7 +1135,7 @@ AVL 树的特点在于“旋转”操作，它能够在不影响二叉树的中
 === "Python"
 
     ```python title="avl_tree.py"
-    def __rotate(self, node: TreeNode | None) -> TreeNode | None:
+    def rotate(self, node: TreeNode | None) -> TreeNode | None:
         """执行旋转操作，使该子树重新恢复平衡"""
         # 获取节点 node 的平衡因子
         balance_factor = self.balance_factor(node)
@@ -1143,20 +1143,20 @@ AVL 树的特点在于“旋转”操作，它能够在不影响二叉树的中
         if balance_factor > 1:
             if self.balance_factor(node.left) >= 0:
                 # 右旋
-                return self.__right_rotate(node)
+                return self.right_rotate(node)
             else:
                 # 先左旋后右旋
-                node.left = self.__left_rotate(node.left)
-                return self.__right_rotate(node)
+                node.left = self.left_rotate(node.left)
+                return self.right_rotate(node)
         # 右偏树
         elif balance_factor < -1:
             if self.balance_factor(node.right) <= 0:
                 # 左旋
-                return self.__left_rotate(node)
+                return self.left_rotate(node)
             else:
                 # 先右旋后左旋
-                node.right = self.__right_rotate(node.right)
-                return self.__left_rotate(node)
+                node.right = self.right_rotate(node.right)
+                return self.left_rotate(node)
         # 平衡树，无须旋转，直接返回
         return node
     ```
@@ -1552,24 +1552,24 @@ AVL 树的节点插入操作与二叉搜索树在主体上类似。唯一的区
     ```python title="avl_tree.py"
     def insert(self, val):
         """插入节点"""
-        self.root = self.__insert_helper(self.root, val)
+        self._root = self.insert_helper(self._root, val)
 
-    def __insert_helper(self, node: TreeNode | None, val: int) -> TreeNode:
+    def insert_helper(self, node: TreeNode | None, val: int) -> TreeNode:
         """递归插入节点（辅助方法）"""
         if node is None:
             return TreeNode(val)
         # 1. 查找插入位置，并插入节点
         if val < node.val:
-            node.left = self.__insert_helper(node.left, val)
+            node.left = self.insert_helper(node.left, val)
         elif val > node.val:
-            node.right = self.__insert_helper(node.right, val)
+            node.right = self.insert_helper(node.right, val)
         else:
             # 重复节点不插入，直接返回
             return node
         # 更新节点高度
-        self.__update_height(node)
+        self.update_height(node)
         # 2. 执行旋转操作，使该子树重新恢复平衡
-        return self.__rotate(node)
+        return self.rotate(node)
     ```
 
 === "C++"
@@ -1904,17 +1904,17 @@ AVL 树的节点插入操作与二叉搜索树在主体上类似。唯一的区
     ```python title="avl_tree.py"
     def remove(self, val: int):
         """删除节点"""
-        self.root = self.__remove_helper(self.root, val)
+        self._root = self.remove_helper(self._root, val)
 
-    def __remove_helper(self, node: TreeNode | None, val: int) -> TreeNode | None:
+    def remove_helper(self, node: TreeNode | None, val: int) -> TreeNode | None:
         """递归删除节点（辅助方法）"""
         if node is None:
             return None
         # 1. 查找节点，并删除之
         if val < node.val:
-            node.left = self.__remove_helper(node.left, val)
+            node.left = self.remove_helper(node.left, val)
         elif val > node.val:
-            node.right = self.__remove_helper(node.right, val)
+            node.right = self.remove_helper(node.right, val)
         else:
             if node.left is None or node.right is None:
                 child = node.left or node.right
@@ -1929,12 +1929,12 @@ AVL 树的节点插入操作与二叉搜索树在主体上类似。唯一的区
                 temp = node.right
                 while temp.left is not None:
                     temp = temp.left
-                node.right = self.__remove_helper(node.right, temp.val)
+                node.right = self.remove_helper(node.right, temp.val)
                 node.val = temp.val
         # 更新节点高度
-        self.__update_height(node)
+        self.update_height(node)
         # 2. 执行旋转操作，使该子树重新恢复平衡
-        return self.__rotate(node)
+        return self.rotate(node)
     ```
 
 === "C++"