# 669. Trim a Binary Search Tree

#### Medium

***

Given the `root` of a binary search tree and the lowest and highest boundaries as `low` and `high`, trim the tree so that all its elements lies in `[low, high]`. Trimming the tree should **not** change the relative structure of the elements that will remain in the tree (i.e., any node's descendant should remain a descendant). It can be proven that there is a **unique answer**.

Return *the root of the trimmed binary search tree*. Note that the root may change depending on the given bounds.

 

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/09/09/trim1.jpg)

```
Input: root = [1,0,2], low = 1, high = 2
Output: [1,null,2]
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2020/09/09/trim2.jpg)

```
Input: root = [3,0,4,null,2,null,null,1], low = 1, high = 3
Output: [3,2,null,1]
```

 

**Constraints:**

* The number of nodes in the tree in the range `[1, 104]`.
* `0 <= Node.val <= 104`
* The value of each node in the tree is **unique**.
* `root` is guaranteed to be a valid binary search tree.
* `0 <= low <= high <= 104`

```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 trimBST(self, root: Optional[TreeNode], low: int, high: int) -> Optional[TreeNode]:
        if not root or (root.left is None and root.right is None and (root.val < low or root.val > high)):
            return None
        if root.val < low:
            return self.trimBST(root.right, low, high)
        elif root.val > high:
            return self.trimBST(root.left, low, high)
        # Check for left value
        if root.left and root.left.val < low:
            root.left = self.trimBST(root.left.right, low, high)
        else:
            root.left = self.trimBST(root.left, low, high)
        # Check for right value
        if root.right and root.right.val > high:
            root.right = self.trimBST(root.right.left, low, high)
        else:
            root.right = self.trimBST(root.right, low, high)
        return root
            
            
         
```

#### More Clean Solution

If you will check above solution you might notice that Line 17 & 22 are being handled by  Line 12 & 14 respectively.

```python
class Solution:
    def trimBST(self, root: Optional[TreeNode], low: int, high: int) -> Optional[TreeNode]:
        if not root:
            return None
        if root.val < low:
            return self.trimBST(root.right, low, high)
        elif root.val > high:
            return self.trimBST(root.left, low, high)
        root.left = self.trimBST(root.left, low, high)
        root.right = self.trimBST(root.right, low, high)
        return root
```