Amazon·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

Apr 2026

Summary

Amazon ML engineer interview with a dynamic programming batch optimization problem. The question was more involved than I expected for a phone screen, required both an optimal answer and reconstructing the actual partition.

Questions Asked (1)

Given an array of K document lengths and G available GPUs, partition the documents into at most G non-empty batches to minimize total padding waste, where padding waste is defined as the sum over batches of (batch size times max length in batch minus sum of lengths in batch). Return the minimum waste and one valid partition. Handle edge cases where K is 0 or G is at least K.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I knew sorting was the right first move since grouping similar lengths reduces padding, but formalizing the DP recurrence took me longer than I'd like to admit.

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AI HintsAI Generated

Suggested Approach

First clarify the problem and edge cases, then propose a dynamic programming solution that sorts the lengths and computes the minimum waste for partitioning the first i documents into j batches. Explain the recurrence and how to reconstruct the partition, and discuss time/space complexity and potential optimizations.

Pro tip: Mention that sorting is valid because in an optimal solution each batch consists of a contiguous segment of sorted lengths, which simplifies the DP and reduces the state space. Also, proactively discuss how to handle large K or G with optimizations like divide-and-conquer DP or convex hull trick.

1. Clarify and handle edge cases

Confirm definitions and constraints, and explicitly handle K=0 (return 0 waste and empty partition) and G>=K (each document in its own batch, waste=0).

2. Sort and justify contiguity

Sort the lengths ascending. Argue that an optimal partition can be formed by contiguous segments in sorted order, because swapping elements to make batches contiguous does not increase waste.

3. Define DP state and recurrence

Let dp[i][j] be the minimum waste for partitioning the first i documents into j batches. Recurrence: dp[i][j] = min_{p<j..i-1} dp[p][j-1] + waste(p+1..i), where waste(l..r) = (r-l+1)*len[r] - sum_{t=l}^r len[t].

4. Compute and reconstruct

Fill the DP table bottom-up, keeping parent pointers to reconstruct one optimal partition. Return dp[K][min(G,K)] and the batches.

5. Analyze complexity and optimizations

State O(K^2 * G) time and O(K*G) space; mention that prefix sums allow O(1) waste computation, and discuss possible optimizations like divide-and-conquer DP or convex hull trick if needed.

Key Points to Mention

Edge cases: K=0 and G>=K, with appropriate return values.
Sorting the lengths and the contiguity property in optimal partitions.
Dynamic programming state definition and recurrence relation.
Efficient waste computation using prefix sums.
Reconstruction of the partition using parent pointers.
Time and space complexity, and potential optimizations for large inputs.

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