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Microsoft·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
May 2026

Summary

Microsoft SWE interview with a tree problem. Pretty standard algorithmic round, nothing too wild, but the LCA question has more edge cases than it looks like at first glance.

Questions Asked (1)

Q1

Given a binary tree with two nodes p and q, find their lowest common ancestor (the deepest node that has both p and q as descendants, where a node can be its own descendant).

Algorithms & Data Structures
Author's notes

My first instinct was to just do a recursive DFS and return the node when I found either p or q.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem constraints (e.g., whether it's a binary search tree, if parent pointers exist, and if nodes are guaranteed to be present). Then present a recursive solution that traverses the tree, returning the node if it matches p or q, and otherwise combining results from left and right subtrees. Analyze time and space complexity, and discuss iterative alternatives or optimizations.

Pro tip: Mention edge cases like when p or q is the root, or when one is an ancestor of the other, and explain how your solution handles them. Also, briefly discuss how the approach changes if the tree is a BST or if parent pointers are available, showing adaptability.

1. Clarify the problem

Ask about assumptions: Is it a binary search tree? Are parent pointers available? Are p and q guaranteed to be in the tree? This shows attention to detail.

2. Outline the recursive approach

Explain that you'll traverse the tree, and at each node, check if it's p or q. Recursively search left and right subtrees, and use the results to determine the LCA.

3. Detail the base and recursive cases

Base case: if node is null or matches p or q, return node. Recursive case: if both left and right return non-null, current node is LCA; otherwise return the non-null child.

4. Analyze complexity

State that time complexity is O(n) in the worst case, and space complexity is O(h) due to recursion stack, where h is tree height.

5. Discuss edge cases and alternatives

Cover cases like p or q being the root, or one being ancestor of the other. Mention iterative solutions using parent pointers or path-to-root if applicable.

Key Points to Mention

  • Definition of LCA: deepest node that has both p and q as descendants, allowing a node to be its own descendant.
  • Recursive post-order traversal: process left and right subtrees before the current node.
  • Handling of cases where one node is an ancestor of the other.
  • Time and space complexity analysis: O(n) time, O(h) space.
  • Alternative approaches for BSTs (using value comparisons) or with parent pointers (finding intersection of paths).
  • Edge cases: empty tree, p or q not present, p == q.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.