Snowflake·Software Engineer·Technical Phone Screen·Senior

Senior

Jun 2026

Summary

Snowflake technical phone screen with a tree DP problem that looked like a standard tree traversal until you realized it was basically a knapsack on a tree. Harder than I expected for a phone screen.

Questions Asked (1)

Given a rooted tree where each node has a non-negative weight, you can delete any node along with its entire subtree (but not the root). With a total weight budget W for kept nodes, maximize the depth of the resulting tree. Return the max depth and which nodes to delete.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I spent the first few minutes thinking about greedy approaches and they all fell apart pretty fast.

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AI HintsAI Generated

Suggested Approach

Clarify the problem constraints and define the objective precisely, then propose a dynamic programming solution on trees that computes for each node the minimum weight needed to achieve a given depth. Use binary search or direct DP to find the maximum depth within budget, and reconstruct deletions via backtracking.

Pro tip: Discuss the trade-off between time and space complexity, and mention that the problem is NP-hard in general if the tree is not rooted or if weights can be negative, but here the non-negative weights and rooted structure allow a polynomial DP.

1. Clarify and Restate

Confirm the problem details: rooted tree, non-negative weights, delete node and its subtree, cannot delete root, budget W for kept nodes, maximize depth. Ask about input size and expected output format.

2. Define DP State

Define DP[v][d] = minimum total weight of kept nodes in subtree of v to achieve depth d from v (or from root). Consider depth as number of edges from root to deepest kept node.

3. Derive Recurrence

For a leaf, DP[v][0] = weight(v). For internal node, combine children: to achieve depth d, either keep v and one child with depth d-1, or keep v and multiple children? Actually depth is max over children, so DP[v][d] = weight(v) + min over children c of (DP[c][d-1] + sum of other children's minimal weights to keep them at any depth ≤ d-1? Wait, we need to keep all children? No, we can delete entire subtrees. So we can choose to keep a subset of children. To maximize depth, we need at least one child with depth d-1, and for other children we can either delete them (cost 0) or keep them with any depth ≤ d-1, but we want to minimize total weight. So for each child, we can compute the minimum weight to keep that child's subtree with depth at most d-1 (or delete it). Let minCost[c][k] = min_{0≤i≤k} DP[c][i]. Then DP[v][d] = weight(v) + min_{c} (DP[c][d-1] + sum_{c'≠c} minCost[c'][d-1]).

4. Compute and Optimize

Compute DP bottom-up. For each node, compute minCost arrays. Then find max d such that DP[root][d] ≤ W. Use binary search on d if monotonic, or compute all d up to height. Reconstruct deletions by tracking choices.

5. Reconstruct and Analyze

Backtrack from root to identify which nodes to delete (those not kept). Analyze time complexity: O(n * height^2) or O(n^2) worst case, space O(n * height). Discuss potential optimizations like heavy-light or greedy if weights are uniform.

Key Points to Mention

Dynamic programming on trees with state (node, depth) and minimizing weight.
The recurrence involves combining children and taking the minimum over which child provides the maximum depth.
Use of prefix/suffix sums or precomputed minCost to efficiently compute the sum of other children's costs.
Binary search on depth if the minimum weight is monotonic with depth (it is non-decreasing).
Reconstruction of deleted nodes via backtracking the DP choices.
Complexity analysis: O(n * h^2) time, O(n * h) space, where h is tree height; can be optimized to O(n * h) with careful merging.

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