0230: Kth Smallest Element in a BST

Problem Statement

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?

Code Solution

class Solution:
    def kthSmallest(self, root, k):
	    
        res = None
        def rec(node):
            nonlocal res, k
            if not node:
                return
            rec(node.left)
            if k == 1:
                res = node.val
                k = k - 1
                return
            k = k - 1
            rec(node.right)
        
        rec(root)
        return res