# 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

# Solution

Approach 1: recursive.

Approach 2: iterative.

# Code (Python)

Approach 1:

    def trimBST(self, root, L, R):
        """
        :type root: TreeNode
        :type L: int
        :type R: int
        :rtype: TreeNode
        """
        # recursive
        if not root:
            return None
        if root.val < L:
            return self.trimBST(root.right, L, R)
        if 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

Approach 2:

    def trimBST(self, root, L, R):
        # iterative
        if not root:
            return None
        # find the root node to return
        while root and root.val < L or root.val > R:
            if root.val < L:
                root = root.right
            if root.val > R:
                root = root.left
        if root.val < L or root.val > R:
            return None
        # trim left subtree
        node = root
        while node:
            while node.left and node.left.val < L:
                node.left = node.left.right # only the right subtree has the chance to fit into the range
            node = node.left # subsequent subtrees
        # trim right subtree
        node = root
        while node:
            while node.right and node.right.val > R:
                node.right = node.right.left
            node = node.right
        return root

# Code (C++)

Approach 1:

Approach 2: