Skip to content
MediumTreesAI interview only

Lowest Common Ancestor of a Binary Search Tree

Asked atamazonmetamicrosoftlinkedinapple

01 · Problem

Given a binary search tree (BST), find the lowest common ancestor (LCA) node of two given nodes in the BST.

According to the definition of LCA on Wikipedia: "The lowest common ancestor is defined between two nodes p and q as the lowest node in T that has both p and q as descendants (where we allow a node to be a descendant of itself)."

02 · Examples

Example 01
        6
       / \
      2   8
     / \ / \
    0  4 7  9
      / \
     3   5
Input
root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 8
Output
6

The LCA of nodes 2 and 8 is 6. Node 2 is in the left subtree and node 8 is in the right subtree, so the root (6) is their lowest common ancestor.

Example 02
        6
       / \
      2   8
     / \ / \
    0  4 7  9
      / \
     3   5
Input
root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 4
Output
2

The LCA of nodes 2 and 4 is 2. Node 4 is a descendant of node 2, and a node can be a descendant of itself according to the LCA definition.

Example 03
Input
root = [2,1], p = 2, q = 1
Output
2

The root node 2 is the ancestor of node 1, and since a node is its own descendant, the LCA is 2.

03 · Constraints

  • 01The number of nodes in the tree is in the range [2, 105].
  • 02-109 <= Node.val <= 109
  • 03All Node.val are unique.
  • 04p != q
  • 05p and q will exist in the BST.

04 · Optimal complexity

Time
O(h)
Space
O(1)
05 · Two ways to work on it

Practice it alone or rehearse it as an interview.

Practice Mode gives you an editor and test runs, nothing else. AI Interview Mode puts a voice interviewer on the other side, adds a clock, and ends with a scored summary of the round.

Start a voice interview on this problem