Snowflake·Software Engineer·Technical Phone Screen·Senior

Senior

Jun 2026

Summary

Snowflake technical phone screen with a tree DP problem that sounds manageable until you realize there's a second optimization layer on top of the first. The kind of question where getting the basic structure right is only half the battle.

Questions Asked (1)

Given a rooted tree and an integer N, find the minimum number of node deletions (each deletion removes a node and its entire subtree) needed to cap the tree's maximum depth at N. Among all ways to achieve that minimum deletion count, find the one that maximizes the total depth of deleted nodes in the original tree. Return that maximum sum.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The first part clicked pretty fast, standard subtree DP.

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AI HintsAI Generated

Suggested Approach

Use a bottom-up dynamic programming approach on the tree, where for each node you compute the minimum deletions needed to cap the depth at N and the maximum sum of depths of deleted nodes for that minimum. Combine children results by considering whether to delete the node or keep it, ensuring depth constraints are met.

Pro tip: Clarify that 'depth' is measured from the root (root depth 0 or 1) and confirm the definition of 'total depth of deleted nodes'—whether it's the sum of original depths of all nodes in deleted subtrees or just the roots of deleted subtrees. This shows attention to detail and avoids off-by-one errors.

1. Clarify definitions and constraints

Confirm the definition of depth (root depth 0 or 1) and what 'total depth of deleted nodes' means (sum of original depths of all nodes in deleted subtrees). Also, check if N can be 0 or if the tree depth is already ≤ N.

2. Define DP state

For each node u, define dp[u][d] = (min_deletions, max_sum) where d is the depth of u from the root (or relative depth from u's parent). Alternatively, define DP based on the maximum allowed depth from u to any leaf in its subtree.

3. Formulate transitions

For a node u, consider two options: delete u (cost 1 deletion, sum = sum of depths of all nodes in subtree(u)), or keep u and combine children's DP states such that the maximum depth from u to a leaf ≤ N - depth(u). For each child, choose the best state that satisfies the depth constraint.

4. Compute bottom-up

Perform a post-order traversal to compute DP values for each node. For each node, merge children's DP arrays by taking the minimum deletions and, for ties, the maximum sum. Use prefix/suffix maxima to efficiently combine children while respecting depth limits.

5. Return final answer

The answer is the max_sum from the DP state at the root that achieves the minimum deletions while capping the overall depth at N. If the tree depth is already ≤ N, the answer is 0 deletions and sum 0.

Key Points to Mention

Dynamic programming on trees (tree DP) with state representing depth constraints
Trade-off between minimizing deletions and maximizing sum of depths of deleted nodes
Post-order traversal for bottom-up computation
Handling of depth constraints by limiting the maximum depth from a node to a leaf
Efficient merging of children's DP states using prefix/suffix maxima or knapsack-like combination
Edge cases: N=0, tree depth already ≤ N, skewed trees, and large N

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