 Time Flying  ### 230. Kth Smallest Element in a BST

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.

### Analyze

``````/**
* Definition for a binary tree node.
* function TreeNode(val, left, right) {
*     this.val = (val===undefined ? 0 : val)
*     this.left = (left===undefined ? null : left)
*     this.right = (right===undefined ? null : right)
* }
*/
/**
* @param {TreeNode} root
* @param {number} k
* @return {number}
*/
var kthSmallest = function(root, k) {
const countResult = { value: 0 }
return analyzeCount(root, k, countResult)
}

var analyzeCount = function(node, k, count) {
if (!node) return null
const pickLeft = analyzeCount(node.left, k, count)
if (typeof pickLeft === 'number') return pickLeft
count.value = count.value + 1
if (k === count.value) {
return node.val
}
const pickRight = analyzeCount(node.right, k, count)
if (typeof pickRight === 'number') return pickRight
}``````