Kth Smallest Element in a BST

Description

Given a binary search tree, write a function kthSmallest to find the kth smallest element in it.

 

Example 1:

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

Example 2:

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

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?

 

Constraints:

• The number of elements of the BST is between 1 to 10^4.
• You may assume k is always valid, 1 ≤ k ≤ BST's total elements.

Solution(javascript)

function TreeNode(val) {
  this.val = val
  this.left = null
  this.right = null
}

const kthSmallest = (root, k) => {
  const result = []
  const aux = (node) => {
    if (node) {
      aux(node.left)
      result.push(node.val)
      aux(node.right)
    }
  }
  aux(root)
  return result[k - 1]
}