LinkedIn·Machine Learning Engineer·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

LinkedIn ML engineer interview with a math-meets-coding problem that felt more like a puzzle than a typical coding screen. Not what I expected going in.

Questions Asked (1)

Given a sorted array, apply the quadratic formula to each element and return the results in sorted order.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was to just map the formula and re-sort at the end, which works but they clearly wanted something smarter.

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AI HintsAI Generated

Suggested Approach

First, clarify the problem: the quadratic formula is f(x) = ax^2 + bx + c, and we need to apply it to each element of a sorted array, then return the results sorted. Recognize that if a > 0, the function is convex (U-shaped), so the sorted order of outputs can be obtained by merging two sorted sequences: one from the left end (decreasing) and one from the right end (increasing). If a < 0, the function is concave (inverted U), so the maximum is at the vertex, and the sorted order can be obtained by splitting at the vertex and merging. If a = 0, it's linear, so order is preserved or reversed depending on b. Implement an O(n) two-pointer approach to merge the two sorted halves.

Pro tip: Mention that this is a common pattern for applying monotonic functions to sorted arrays, and that handling the vertex (where the function changes direction) is key to achieving O(n) time. Also, note that if the array contains negative numbers, the vertex may lie within the array, so you need to find the split point where the function's derivative changes sign.

1. Clarify the problem and assumptions

Ask whether the quadratic formula means f(x) = ax^2 + bx + c with given coefficients, and confirm that the input array is sorted in ascending order. Also, check if the array can contain negative numbers and if the coefficients are fixed.

2. Analyze the function's monotonicity

Determine the shape of the quadratic: if a > 0, it's convex with a minimum at the vertex; if a < 0, it's concave with a maximum at the vertex. The vertex x = -b/(2a) divides the array into two monotonic parts.

3. Find the split point (vertex) in the sorted array

Use binary search to find the index where the array values cross the vertex, or simply find the point where the function's derivative changes sign. This splits the array into two parts: one where f is decreasing and one where f is increasing (or vice versa).

4. Merge the two sorted sequences

Apply f to each element in both parts. The left part (if decreasing) will produce values in decreasing order, and the right part (if increasing) will produce values in increasing order. Use two pointers to merge these into a single sorted array in O(n) time.

5. Handle edge cases and discuss trade-offs

Consider cases where a = 0 (linear function), the vertex is outside the array, or the array has duplicates. Discuss the time complexity (O(n) after O(log n) for finding the vertex) and space complexity (O(n) for the output).

Key Points to Mention

The quadratic function's monotonicity depends on the sign of 'a' and the vertex location.
For a > 0, the function is convex, so the minimum is at the vertex; the array splits into a decreasing part (left of vertex) and an increasing part (right of vertex).
For a < 0, the function is concave, so the maximum is at the vertex; the array splits into an increasing part (left of vertex) and a decreasing part (right of vertex).
Use binary search to find the vertex index in O(log n) time, then merge the two sorted halves in O(n) time.
Edge cases: a = 0 (linear), vertex outside the array, empty array, and duplicate values.
This approach is optimal because sorting the transformed array naively would take O(n log n), but we can achieve O(n) by exploiting the structure.

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