# [Solved] 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.

## Question

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?

## 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
def inorder(root,res,k):
if root==None:return
heapq.heappush(res,-root.val)
if len(res)>k:heapq.heappop(res)
inorder(root.left,res,k)
inorder(root.right,res,k)

class Solution:
def kthSmallest(self, root: TreeNode, k: int) -> int:
res = []
heapq.heapify(res)
inorder(root,res,k)
return -res[0]```