MathWorks·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

MathWorks software engineer interview with a tricky array manipulation problem that looks straightforward but has a subtle edge case worth thinking through carefully.

Questions Asked (1)

You have an array of integers and a number K. You must perform exactly K operations, where each operation decrements any single element by 1. After using all K operations, what is the maximum possible value of the minimum element in the array?

Algorithms & Data Structures

Author's notes

The first instinct is binary search on the answer, which is right, but I almost missed the 'exactly K' part.

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AI HintsAI Generated

Suggested Approach

First, clarify the problem and constraints, then explain that the optimal strategy is to binary search on the answer X, checking if it's possible to make all elements at least X using at most K decrements. For a given X, compute the total decrements needed as sum(max(0, a_i - X)) and compare with K.

Pro tip: Mention that the answer is monotonic: if X is achievable, any smaller value is also achievable, which justifies binary search. Also, note that the problem is equivalent to finding the largest X such that the sum of excesses above X is ≤ K.

1. Clarify the problem

Restate the problem in your own words and confirm with the interviewer: we need to maximize the minimum element after exactly K decrements. Ask about constraints (e.g., array size, value ranges) to determine the expected time complexity.

2. Identify the monotonic property

Explain that if we can achieve a minimum value of X, we can also achieve any value less than X by simply not using all decrements or by decrementing further. This monotonicity allows binary search on the answer.

3. Design the feasibility check

For a candidate minimum X, compute the total number of decrements needed to make every element at least X: sum(max(0, a_i - X)). If this sum is ≤ K, then X is feasible.

4. Binary search for the maximum X

Set low = min(array) - K (or 0 if negative) and high = min(array). While low ≤ high, check mid; if feasible, move low up, else move high down. Return the largest feasible X.

5. Analyze complexity and edge cases

Time complexity: O(n log(max_value)) due to binary search and O(n) check. Space: O(1). Discuss edge cases: K=0, K very large (answer can be negative), all elements equal, etc.

Key Points to Mention

Binary search on the answer (the minimum value) because feasibility is monotonic.
Feasibility check: sum of (a_i - X) for elements greater than X must be ≤ K.
The answer can be negative if K is large enough to decrement all elements below zero.
Time complexity: O(n log(max_val)) which is efficient for large arrays.
Alternative approach: sort and use a greedy strategy, but binary search is simpler and optimal.
Clarify that we must perform exactly K operations, but extra decrements can be wasted on any element without affecting the minimum.

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