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# 230 Kth Smallest Element in a BST

Given a binary search tree, write a function`kthSmallest`to find the**k**th 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?

**The Idea:** Just do inorder traversal until the kth element is reached. Admitted, this is terrible python code (with the use of references), but it surprising scored in the top percentile range.

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

```python
# 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
        """
        count = [k]
        stop = [False]
        val = [0]
        self.in_order_to_k(root, count, stop, val)
        return val[0]


    def in_order_to_k(self, root, cnt, stop, val):
        """
        :type root: TreeNode
        :type cnt: int
        :rtype: void
        """
        if (root and not stop[0]):
            self.in_order_to_k(root.left, cnt, stop, val)
            cnt[0] -= 1
            if (cnt[0] == 0 and not stop[0] and root):
                val[0] = root.val
                stop[0] = True
            self.in_order_to_k(root.right, cnt, stop, val)
```


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