Amazon·Software Engineer·Online Assessment (OA)·Intermediate

Intermediate

May 2026

Summary

Amazon SWE online assessment with an array/algorithm problem involving logistics machine capacity sequences. Pretty niche problem framing but the core idea isn't too wild once you strip away the story.

Questions Asked (1)

Given an integer array representing machine capacities, the efficiency is defined as the sum of absolute differences between consecutive elements. Find the minimum number of machines you can keep (must keep at least one) such that the sum of absolute differences remains the same. If it's not possible, return the original array length.

Algorithms & Data Structures

Author's notes

Took me a while to realize that a lot of machines in the middle can be redundant without affecting the total absolute difference sum.

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AI HintsAI Generated

Suggested Approach

First, clarify the problem and edge cases, then identify that the sum of absolute differences is invariant under removing elements that lie on a monotonic segment between two kept elements. The goal reduces to selecting a subsequence that preserves the total variation, which can be solved by dynamic programming or by finding the minimum number of local extrema (peaks and valleys) needed to maintain the sum.

Pro tip: Mention that the minimum number of machines corresponds to the number of local extrema in the array (including endpoints), as these are the only points where the direction of change reverses. This insight simplifies the problem and shows deep understanding.

1. Understand the problem and edge cases

Restate the problem to ensure clarity: we need the smallest subsequence (keeping order) with the same sum of absolute differences as the original array. Consider edge cases: array of length 1, all equal elements, strictly increasing/decreasing arrays.

2. Identify the invariant

The sum of absolute differences is the total variation. Removing an element that lies on a straight monotonic segment between two kept elements does not change the total variation. Thus, we only need to keep elements that are necessary to preserve the direction changes.

3. Reduce to local extrema

The minimal subsequence must include the first and last elements, and all local extrema (peaks and valleys) where the sign of the difference changes. Any other element can be removed without affecting the sum.

4. Count the required elements

Count the number of local extrema plus the endpoints. If the array has no direction changes (monotonic), the minimum is 2 (or 1 if all elements are equal). If the array length is 1, return 1.

5. Handle impossibility and return result

If the computed minimum is greater than the original length (which shouldn't happen), return the original length. Otherwise, return the count. Verify with examples.

Key Points to Mention

The sum of absolute differences is the total variation of the sequence.
Removing elements on a monotonic segment does not change the total variation.
The minimal subsequence must include all local extrema (peaks and valleys) and the endpoints.
For a strictly monotonic array, the minimum is 2 (or 1 if all elements are equal).
Edge cases: single element array, all equal elements, and arrays with multiple equal consecutive elements.
Time complexity: O(n) to scan and count extrema, which is optimal.

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