235. Lowest Common Ancestor of a Binary Search Tree

At a Glance

• Topic: Tree
• Pattern: Analyze Pattern
• Difficulty: Medium
• LeetCode: 235

Problem Statement

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).”

Example 1:

Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 8 Output: 6 Explanation: The LCA of nodes 2 and 8 is 6.

Example 2:

Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 4 Output: 2 Explanation: The LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.

Example 3:

Input: root = [2,1], p = 2, q = 1 Output: 2

Constraints:

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

Approach & Solution Steps

Leverage the BST property. If both target nodes are smaller than the current node, search the left subtree. If both are larger, search the right subtree. Otherwise, the current node is the LCA.

Optimal JS Solution

function lowestCommonAncestor(root, p, q) {
  let curr = root;
  while (curr) {
    if (p.val < curr.val && q.val < curr.val) curr = curr.left;
    else if (p.val > curr.val && q.val > curr.val) curr = curr.right;
    else return curr;
  }
  return null;
}

Edge Cases & Pitfalls

• Always consider empty or null inputs.
• Watch out for off-by-one index errors.