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Microsoft·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Apr 2026

Summary

Microsoft SWE coding round, one tree DP problem the whole time. Pretty standard session, nothing fancy, but the problem had enough depth to keep you on your toes if you hadn't seen the pattern before.

Questions Asked (1)

Q1

Given the root of a binary tree where each node holds a non-negative integer, return the maximum sum you can collect such that no two directly connected nodes (parent and child) are both included.

Algorithms & Data Structures
Author's notes

I knew this was a tree DP problem pretty quickly, which helped.

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AI HintsAI Generated

Suggested Approach

Use dynamic programming on the tree, where for each node you compute two values: the maximum sum when the node is included (and children excluded) and when it is excluded (children may be included or excluded). Then combine these values bottom-up via post-order traversal to get the global maximum.

Pro tip: Clearly define the two states and explain the recurrence before coding; this shows structured thinking and avoids confusion. Also, mention that the solution runs in O(n) time and O(h) space, which is optimal.

1. Define states

For each node, define two values: include (max sum if node is included) and exclude (max sum if node is excluded).

2. Derive recurrence

If node is included, its children must be excluded, so include = node.val + sum(child.exclude). If node is excluded, children can be either included or excluded, so exclude = sum(max(child.include, child.exclude)).

3. Choose traversal

Use post-order DFS to compute these values bottom-up, returning a pair (include, exclude) for each subtree.

4. Compute final answer

At the root, the maximum sum is max(root.include, root.exclude).

5. Analyze complexity

Time complexity is O(n) since each node is visited once; space complexity is O(h) for recursion stack, where h is tree height.

Key Points to Mention

  • Dynamic programming on trees with two states per node
  • Post-order traversal to process children before parent
  • Recurrence relations for include and exclude cases
  • Time and space complexity analysis (O(n) time, O(h) space)
  • Handling of base cases (null nodes return (0,0))
  • Comparison with naive approach (exponential) to highlight efficiency

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