"""
230. Kth Smallest Element in a BST
Difficulty: Medium
https://leetcode.com/problems/kth-smallest-element-in-a-bst/

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Given the root of a binary search tree, and an integer k, return the
k^th smallest value (1-indexed) of all the values of the nodes in the
tree.



Example 1:

Input: root = [3,1,4,null,2], k = 1
Output: 1

Example 2:

Input: root = [5,3,6,2,4,null,null,1], k = 3
Output: 3



Constraints:

        • The number of nodes in the tree is n.

        • 1 <= k <= n <= 10^4

        • 0 <= Node.val <= 10^4



Follow up: If the BST is modified often (i.e., we can do insert and
delete operations) and you need to find the kth smallest frequently,
how would you optimize?
"""


# 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 kthSmallest(self, root: Optional[TreeNode], k: int) -> int:
        n = 0
        stack = []
        cur = root

        while cur or stack:
            while cur:
                stack.append(cur)
                cur = cur.left

            cur = stack.pop()
            n += 1
            if n == k:
                return cur.val
            cur = cur.right