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MathWorks·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Jul 2026

Summary

MathWorks software engineer interview with a focused algorithmic problem around array pair removal. Pretty standard coding round but they pushed hard on complexity analysis and wanted you to actually justify your approach, not just code it up.

Questions Asked (1)

Q1

Given an integer array and a target value k, you can remove pairs of indices where the two elements sum to k. Each index can only be used once. What is the maximum number of such pair removals you can perform? They also asked you to design an O(n) or O(n log n) solution, discuss the space-time trade-offs, and write working code.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

The core idea clicked pretty fast: use a frequency map, iterate through the array, and for each element check if its complement exists.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem constraints and edge cases, then propose a hash map-based solution that counts frequencies of each element to greedily form pairs, achieving O(n) time. Discuss the trade-offs between time and space, and be prepared to write clean, efficient code with proper handling of duplicates and the k/2 case.

Pro tip: Demonstrate awareness of the k/2 edge case where an element pairs with itself, and mention that sorting with two pointers is an alternative O(n log n) approach with O(1) extra space, showing you understand multiple solutions.

1. Clarify the problem

Ask about constraints: array size, element range, whether elements can be negative, and if k can be negative. Confirm that each index can be used only once and that pairs are unordered.

2. Propose an O(n) hash map solution

Use a frequency map to count occurrences of each number. For each unique number x, if k-x exists, form as many pairs as possible, being careful when x == k-x (use floor(count/2)).

3. Discuss time and space trade-offs

Explain that the hash map approach uses O(n) extra space for O(n) time. Mention that sorting the array and using two pointers gives O(n log n) time with O(1) extra space (if in-place sort allowed), which is better for memory-constrained environments.

4. Write clean code

Implement the chosen solution with clear variable names, handle edge cases (empty array, no pairs), and test with examples. If writing in an interview, start with the hash map solution as it's straightforward.

5. Analyze and optimize

After coding, walk through a small example to verify correctness. Discuss potential optimizations, such as early termination if remaining elements cannot form pairs, or using a set if each element is unique.

Key Points to Mention

  • Hash map frequency counting to achieve O(n) time complexity.
  • Handling the special case where x == k-x (element pairs with itself).
  • Space-time trade-off: O(n) space for O(n) time vs O(1) space for O(n log n) time with sorting.
  • Edge cases: empty array, no valid pairs, negative numbers, large k.
  • Greedy pairing is optimal because each pair uses two elements and we want to maximize count.
  • Code should be modular and testable, with clear comments.

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