Update 0701.二叉搜索树中的插入操作.md

problems/0701.二叉搜索树中的插入操作.md

@@ -256,132 +256,103 @@ class Solution {
 -----
 ## Python 
 
-**递归法** - 有返回值
-
+递归法（版本一）
 ```python
-# Definition for a binary tree node.
-# class TreeNode:
-#     def __init__(self, val=0, left=None, right=None):
-#         self.val = val
-#         self.left = left
-#         self.right = right
 class Solution:
-    def insertIntoBST(self, root: TreeNode, val: int) -> TreeNode:
-        # 返回更新后的以当前root为根节点的新树，方便用于更新上一层的父子节点关系链
+    def __init__(self):
+        self.parent = None
 
-        # Base Case
-        if not root: return TreeNode(val)
+    def traversal(self, cur, val):
+        if cur is None:
+            node = TreeNode(val)
+            if val > self.parent.val:
+                self.parent.right = node
+            else:
+                self.parent.left = node
+            return
 
-        # 单层递归逻辑:
-        if val < root.val: 
-            # 将val插入至当前root的左子树中合适的位置
-            # 并更新当前root的左子树为包含目标val的新左子树
-            root.left = self.insertIntoBST(root.left, val)
+        self.parent = cur
+        if cur.val > val:
+            self.traversal(cur.left, val)
+        if cur.val < val:
+            self.traversal(cur.right, val)
 
-        if root.val < val:
-            # 将val插入至当前root的右子树中合适的位置
-            # 并更新当前root的右子树为包含目标val的新右子树
-            root.right = self.insertIntoBST(root.right, val)
-
-        # 返回更新后的以当前root为根节点的新树
+    def insertIntoBST(self, root, val):
+        self.parent = TreeNode(0)
+        if root is None:
+            return TreeNode(val)
+        self.traversal(root, val)
         return root
+
 ```
 
-**递归法** - 无返回值
+递归法（版本二）
 ```python
 class Solution:
-    def insertIntoBST(self, root: TreeNode, val: int) -> TreeNode:
-        if not root: 
+    def insertIntoBST(self, root, val):
+        if root is None:
             return TreeNode(val)
         parent = None
-        def __traverse(cur: TreeNode, val: int) -> None: 
-            # 在函数运行的同时把新节点插入到该被插入的地方. 
-            nonlocal parent
-            if not cur: 
-                new_node = TreeNode(val)
-                if parent.val < val: 
-                    parent.right = new_node
-                else: 
-                    parent.left = new_node
-                return 
-
-            parent = cur # 重点: parent的作用只有运行到上面if not cur:才会发挥出来.
-            if cur.val < val: 
-                __traverse(cur.right, val)
-            else: 
-                __traverse(cur.left, val)
-            return
-        __traverse(root, val)
-        return root
-```
-
-**递归法** - 无返回值 - another easier way
-```python
-class Solution:
-    def insertIntoBST(self, root: Optional[TreeNode], val: int) -> Optional[TreeNode]:
-        newNode = TreeNode(val)
-        if not root: return newNode
-        
-        if not root.left and val < root.val:
-            root.left = newNode
-        if not root.right and val > root.val:
-            root.right = newNode
-        
-        if val < root.val:
-            self.insertIntoBST(root.left, val)
-        if val > root.val:
-            self.insertIntoBST(root.right, val)
-        
-        return root
-```
-
-**递归法** - 无返回值 有注释 不用Helper function
-```python
-class Solution:
-    def insertIntoBST(self, root: Optional[TreeNode], val: int) -> Optional[TreeNode]:
-        if not root:    # for root==None
-            return TreeNode(val)
-        if root.val<val:
-            if root.right==None:    # find the parent
-                root.right = TreeNode(val)
-            else:   # not found, keep searching
-                self.insertIntoBST(root.right, val)
-        if root.val>val:
-            if root.left==None: # found the parent
-                root.left = TreeNode(val)
-            else:   # not found, keep searching
-                self.insertIntoBST(root.left, val)
-        # return the final tree
-        return root
-```
-
-**迭代法**  
-与无返回值的递归函数的思路大体一致 
-```python
-class Solution:
-    def insertIntoBST(self, root: TreeNode, val: int) -> TreeNode:
-        if not root: 
-            return TreeNode(val)
-        parent = None # 此步可以省略
         cur = root
-
-        # 用while循环不断地找新节点的parent
-        while cur: 
-            parent = cur  # 首先保存当前非空节点作为下一次迭代的父节点
-            if cur.val < val: 
-                cur = cur.right
-            elif cur.val > val: 
+        while cur:
+            parent = cur
+            if val < cur.val:
                 cur = cur.left
-
-        # 运行到这意味着已经跳出上面的while循环, 
-        # 同时意味着新节点的parent已经被找到.
-        # parent已被找到, 新节点已经ready. 把两个节点黏在一起就好了. 
-        if parent.val > val: 
+            else:
+                cur = cur.right
+        if val < parent.val:
             parent.left = TreeNode(val)
-        else: 
+        else:
             parent.right = TreeNode(val)
-        
         return root
+```
+
+递归法（版本三）
+```python
+class Solution:
+    def insertIntoBST(self, root: Optional[TreeNode], val: int) -> Optional[TreeNode]:
+        if root is None or root.val == val:
+            return TreeNode(val)
+        elif root.val > val:
+            if root.left is None:
+                root.left = TreeNode(val)
+            else:
+                self.insertIntoBST(root.left, val)
+        elif root.val < val:
+            if root.right is None:
+                root.right = TreeNode(val)
+            else:
+                self.insertIntoBST(root.right, val)
+        return root
+```
+
+
+
+迭代法
+```python
+class Solution:
+    def insertIntoBST(self, root, val):
+        if root is None:  # 如果根节点为空，创建新节点作为根节点并返回
+            node = TreeNode(val)
+            return node
+
+        cur = root
+        parent = root  # 记录上一个节点，用于连接新节点
+        while cur is not None:
+            parent = cur
+            if cur.val > val:
+                cur = cur.left
+            else:
+                cur = cur.right
+
+        node = TreeNode(val)
+        if val < parent.val:
+            parent.left = node  # 将新节点连接到父节点的左子树
+        else:
+            parent.right = node  # 将新节点连接到父节点的右子树
+
+        return root
+
             
 ```
 -----