230. Kth Smallest Element in a BST

Medium

---

Given the root of a binary search tree, and an integer k, return the kth 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 <= 104

• 0 <= Node.val <= 104

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:
        l = [0]
        result = root.val
        def traverse(root, l):
            nonlocal result
            if root is None:
                return
            traverse(root.left, l)
            l[0] = l[0]+1
            if l[0] == k:
                result = root.val
                return # Making little but fast return
            traverse(root.right, l)
        traverse(root, l)
        return result