Amazon·Research Scientist·Technical Phone Screen·Senior

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May 2026

Summary

Amazon Applied Scientist phone screen for an RS role, centered entirely on a single partition DP problem about batching documents onto GPUs to minimize padding. The interviewer flagged it as a low pass-rate question upfront, which was not exactly reassuring. Brutal if you haven't drilled partition DP before.

Questions Asked (1)

You have K documents of varying lengths and G GPU batches. After sorting the documents by length, partition them into exactly G contiguous groups to minimize total cost, where each group's cost is its size multiplied by its maximum element. Derive the recurrence, implement the DP, and reconstruct the actual partition boundaries.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The interviewer nudged me toward G=2 first, which helped.

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AI HintsAI Generated

Suggested Approach

First, define the DP state and recurrence clearly, explaining how the cost of a group is computed. Then, outline the bottom-up DP implementation with O(K^2 G) time, and finally describe how to reconstruct the partition boundaries using a parent pointer array.

Pro tip: Mention that the sorted order is crucial for the contiguous grouping to be optimal, and discuss potential optimizations like divide-and-conquer DP or Knuth's optimization if the interviewer probes further.

1. Define DP State and Recurrence

Let dp[i][g] be the minimum cost to partition the first i documents into g groups. The recurrence is dp[i][g] = min_{j < i} (dp[j][g-1] + (i - j) * max_{j+1..i} length).

2. Precompute Group Costs

Precompute the maximum length for all contiguous subarrays to allow O(1) cost lookup, or compute on the fly using a running maximum.

3. Implement Bottom-Up DP

Initialize dp[0][0] = 0 and others to infinity. Iterate over number of groups g from 1 to G, and for each i from 1 to K, compute dp[i][g] using the recurrence.

4. Reconstruct Partition Boundaries

Maintain a parent array parent[i][g] storing the optimal j for dp[i][g]. After filling the DP table, backtrack from dp[K][G] to find the group boundaries.

5. Analyze Complexity and Discuss Trade-offs

State time complexity O(G K^2) and space O(G K). Mention possible optimizations like divide-and-conquer DP or Knuth's optimization if applicable.

Key Points to Mention

Sorting the documents is a prerequisite for the contiguous grouping to be optimal.
The cost function is group size multiplied by the maximum element in the group.
DP state: dp[i][g] = min cost for first i documents in g groups.
Recurrence: dp[i][g] = min_{j < i} (dp[j][g-1] + (i - j) * max_{j+1..i} length).
Reconstruction using a parent pointer array to trace back the optimal partitions.
Time complexity O(G K^2) and space O(G K), with possible optimizations.

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