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apps/docs/content/binary-search-tree/230-kth-smallest-element-in-a-bst.mdx

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+---
+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">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`
+
+## Approach
+
+```mermaid
+flowchart TD
+  S(["kthSmallest(root, k)"]) --> I["n = 0, stack = [], cur = root"]
+  I --> W{"cur or stack?"}
+  W -- no --> E(["fall off the loop — unreachable, k <= n"])
+  W -- yes --> L{"cur?"}
+  L -- yes --> P["stack.append(cur), cur = cur.left — push the whole left spine"]
+  P --> L
+  L -- no --> O["cur = stack.pop(), n += 1 — nodes pop in ascending order"]
+  O --> K{"n == k?"}
+  K -- yes --> R(["return cur.val"])
+  K -- no --> N["cur = cur.right"]
+  N --> W
+```
+
+## 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
+```
+
+## Explanation
+
+<YouTube id="5LUXSvjmGCw" title="Kth Smallest Element in a BST - Leetcode 230 - Python" />