Lowest Common Ancestor of a BST – Solution & Complexity

Solution Walkthrough

  1. Step 1: Recognize the Pattern

    The key pattern is: BST ordering identifies where search paths split. Identify the state and invariant before coding.

  2. Step 2: Build the Algorithm

    Advance one state transition at a time. Mark or update state before exploring dependent work.

  3. Step 3: Check Edge Cases

    Test empty or minimal input, skewed shapes, duplicates where allowed, and impossible outcomes.

  4. Step 4: Solution and Complexity

    Time: O(h). Space: O(1).

    Java/Go/Rust below are reference solutions for learning the pattern in those languages; only Python and JavaScript can be run and submitted for this problem, since the remote judge doesn't support the TreeNode structure yet.

    def lowest_common_ancestor(root: TreeNode, p: int, q: int) -> int:
        low, high = min(p, q), max(p, q)
        node = root
        while node.val < low or node.val > high:
            node = node.right if node.val < low else node.left
        return node.val

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