Given a binary search tree, write a functionkthSmallestto find thekth smallest element in it.

Note:
You may assume k is always valid, 1 ? k ? BST's total elements.

Follow up:
What if the BST is modified (insert/delete operations) often and you need to find the kth smallest frequently? How would you optimize the kthSmallest routine?

Recursive Code with InOrder Traversal(Accepted):

# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
    def kthSmallest(self, root, k):
        """
        :type root: TreeNode
        :type k: int
        :rtype: int
        """
        def inorder(root,result=[]):
            if root.left: inorder(root.left,result)
            result.append(root.val)
            if root.right: inorder(root.right,result)
            return result
        result = inorder(root)
        return result[k-1]