---
title: '230. Kth Smallest Element in a BST'
description: Given the root of a binary search tree, and an integer k, return the k^th smallest value (1-indexed) of all the values of the nodes in the tree
sidebar:
  label: 'Kth Smallest Element in a BST'
  badge: 'Medium'
---

<Badge variant="accent">Binary Search Tree</Badge>

::::warning
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?
::::

### 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 <= 10^4`
- `0 <= Node.val <= 10^4`

## Solution

```py
# 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:
        n = 0
        stack = []
        cur = root

        while cur or stack:
            while cur:
                stack.append(cur)
                cur = cur.left

            cur = stack.pop()
            n += 1
            if n == k:
                return cur.val
            cur = cur.right
```