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Early-stage Startup·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say
May 2026

Summary

Got a tree problem in what felt like a coding round and completely bombed the optimization part. Ended up going down a rabbit hole learning about rerooting DP and binary lifting after the fact, which left me wondering how much of this stuff actually matters for the day-to-day job.

Questions Asked (1)

Q1

Given a tree, re-root it at every node and compute some answer for each possible root. Optimize your solution.

Algorithms & Data Structures
Author's notes

My first solution worked but was way too slow, and they pushed me to optimize it.

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AI HintsAI Generated

Suggested Approach

Use a two-pass DFS technique: first compute the answer for an arbitrary root (e.g., node 0) via post-order traversal, then perform a pre-order traversal to 'reroot' the tree, updating the answer for each child based on the parent's answer. This achieves O(n) time by avoiding recomputation for each root.

Pro tip: Emphasize that the rerooting technique works for any associative and commutative aggregation (like sums, counts, max/min) and that the key is to define a transition function that updates the answer when moving the root from a parent to a child.

1. Understand the problem and define the answer

Clarify what 'answer' means for a given root (e.g., sum of distances to all nodes, subtree sizes, etc.). Identify if the answer can be computed from children's answers and the node itself.

2. Compute initial answer for an arbitrary root

Pick any node as root (e.g., 0) and perform a post-order DFS to compute the answer for that root. Also compute any auxiliary data needed for rerooting (e.g., subtree sizes, sums).

3. Derive rerooting transition

Determine how the answer changes when the root moves from a parent to a child. For example, for sum of distances, the child's answer = parent's answer + (n - 2*subtree_size[child]).

4. Perform pre-order DFS to compute answers for all roots

Traverse the tree from the initial root, and for each child, compute its answer using the transition from the parent's answer. Store the result for each node.

5. Analyze complexity and edge cases

Confirm O(n) time and O(n) space. Discuss handling of large trees, recursion depth (use iterative DFS if needed), and special cases like n=1.

Key Points to Mention

  • Two-pass DFS: post-order for initial root, pre-order for rerooting.
  • Rerooting transition formula derived from the specific problem (e.g., sum of distances).
  • Time complexity O(n) and space complexity O(n).
  • Avoiding O(n^2) by not recomputing from scratch for each root.
  • Handling recursion depth with iterative DFS or increasing recursion limit.
  • Generalization to other tree DP problems (e.g., maximum independent set, centroid).

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