# 669 Trim a Binary Search Tree

Given a binary search tree and the lowest and highest boundaries as L and R, trim the tree so that all its elements lies in \[L, R] (R >= L). You might need to change the root of the tree, so the result should return the new root of the trimmed binary search tree.

Example 1:

```
Input: 
    1
   / \
  0   2

  L = 1
  R = 2

Output: 
    1
      \
       2
```

Example 2:

```
Input: 
    3
   / \
  0   4
   \
    2
   /
  1

  L = 1
  R = 3

Output: 
      3
     / 
   2   
  /
 1
```

**The Idea:** Rebuild the tree. If the root value is less than the minimum (L), then we can entirely ignore the left half. In the same way, we can entirely ignore the right half if the root is greater than the maximum element.

**Complexity:** O(N) time and space

```python
def trimBST(self, root, L, R):
    """
    :type root: TreeNode
    :type L: int
    :type R: int
    :rtype: TreeNode
    """

    if not root:
        return None
    if root.val < L:
        return self.trimBST(root.right, L, R)
    elif root.val > R:
        return self.trimBST(root.left, L, R)
    root.left = self.trimBST(root.left, L, R)
    root.right = self.trimBST(root.right, L, R)
    return root
```


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