# LeetCode 230. Kth Smallest Element in a BST

## Description

https://leetcode.com/problems/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
```

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`.

## Explanation

traverse and sorting.

## Python Solution

``````# 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: TreeNode, k: int) -> int:

values = []

self.helper(root, values)

return heapq.nsmallest(k, values)[-1]

def helper(self, root, values):

if root == None:
return

values.append(root.val)
self.helper(root.left, values)
self.helper(root.right, values)``````
• Time complexity: O(N).
• Space complexity: O(N).