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luma ai·Machine Learning Engineer·Technical Phone Screen·Senior

Senior
May 2026

Summary

Coding round for an MLE role at Luma AI. Just one algorithmic problem, pretty focused on array manipulation and geometry basics.

Questions Asked (1)

Q1

Given an array of positive integers, return a binary array of length n-2 where each element indicates whether the corresponding triple of consecutive values can form a valid triangle.

Algorithms & Data Structures
Author's notes

The triangle inequality part is straightforward once you remember you need all three checks, not just one.

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AI HintsAI Generated

Suggested Approach

Clarify the problem and edge cases, then propose an O(n) solution that checks each consecutive triple using the triangle inequality. Emphasize that for positive integers, only the sum of the two smaller sides needs to exceed the largest side, which simplifies the check.

Pro tip: Mention that since the array is positive, you can avoid sorting each triple by just checking if the sum of the two smaller elements (min and mid) is greater than the max. This shows optimization awareness and mathematical insight.

1. Clarify the problem

Confirm that the output length is n-2, each element corresponds to a triple starting at index i (0 ≤ i ≤ n-3), and that a valid triangle requires the sum of any two sides to be greater than the third.

2. Identify the triangle condition

For positive integers, the triangle inequality reduces to checking if the sum of the two smaller sides is greater than the largest side. This avoids checking all three inequalities.

3. Design the algorithm

Iterate through the array from index 0 to n-3. For each triple, find the min, mid, and max values (or sort the triple) and check if min + mid > max. Append 1 if true, else 0.

4. Analyze complexity

The algorithm runs in O(n) time with O(n) space for the output (or O(1) extra space if output is not counted). Sorting each triple would be O(n log 3) = O(n) but with higher constant; direct comparison is better.

5. Handle edge cases

If n < 3, return an empty array. Also consider large integers and potential overflow (though Python handles big ints natively).

Key Points to Mention

  • Triangle inequality: a + b > c, a + c > b, b + c > a; for positive numbers, only the largest side needs to be checked.
  • Time complexity: O(n) single pass, space complexity: O(n) for output.
  • Edge cases: n < 3 returns empty array; n = 3 returns array of length 1.
  • Optimization: avoid sorting each triple by using min/max comparisons or a single pass to find the largest and sum of the other two.
  • Potential pitfalls: integer overflow in languages like C++/Java (though not in Python), and ensuring correct indexing for triples.
  • Real-world relevance: similar sliding window or triple-check patterns appear in ML pipelines for feature validation or data quality checks.

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