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78. Kth Smallest Element in a BST

mediumAsked at Reddit

Find the kth smallest in a BST. Reddit uses this to test inorder + early termination — relevant for ranked-paginated retrieval from an in-memory BST of upvote scores.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Source citations

Public interview reports confirming this problem appears in Reddit loops.

  • Glassdoor (2026-Q1)— Reddit phone screen, BST canonical.

Problem

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.

Constraints

  • The number of nodes in the tree is n.
  • 1 <= k <= n <= 10^4
  • 0 <= Node.val <= 10^4

Examples

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

Approaches

1. Full inorder + index

Build full inorder list, return list[k-1].

Time
O(n)
Space
O(n)
function kthSmallest(root, k) {
  const list = [];
  function inorder(n) { if (!n) return; inorder(n.left); list.push(n.val); inorder(n.right); }
  inorder(root);
  return list[k - 1];
}

Tradeoff: Linear time but builds full list.

2. Iterative inorder with early-stop (optimal)

Use an explicit stack; stop as soon as we've popped k elements.

Time
O(h + k)
Space
O(h)
function kthSmallest(root, k) {
  const stack = [];
  let cur = root;
  while (cur || stack.length) {
    while (cur) { stack.push(cur); cur = cur.left; }
    cur = stack.pop();
    if (--k === 0) return cur.val;
    cur = cur.right;
  }
}

Tradeoff: Doesn't traverse the whole tree. Sublinear when k << n.

Reddit-specific tips

Reddit interviewers want the early-stop version. Bonus signal: discuss how the answer changes if the BST is modified frequently — Morris traversal preserves O(1) extra space, or maintain a size attribute per node for O(log n) selection.

Common mistakes

  • Forgetting that k is 1-indexed.
  • Recursing right before left (gives kth largest).
  • Building the full list when iterative early-stop is asked for.

Follow-up questions

An interviewer at Reddit may pivot to one of these next:

  • Kth largest in BST.
  • What if the BST is modified often? (Maintain rank — augmented BST.)
  • Kth smallest in sorted matrix (LC 378).

Solve it now

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Output

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FAQ

Why is iterative better here?

Early-stop saves work when k is small. Recursive needs to track 'how many remaining' through return values.

What about Morris traversal?

O(1) extra space using threading. More code, same complexity.

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