Two Sigma·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Jun 2026

Summary

Two Sigma coding round, got a math-flavored array problem that looked approachable until I actually had to think about the direction of the sweep. Not a brutal interview but it required more careful reasoning than I expected for what seemed like a simple transformation task.

Questions Asked (1)

You're given a sorted integer array and three coefficients for a quadratic function. Apply the function to every element and return the results in sorted order. You need to do this in O(n) time.

Algorithms & Data Structures

Author's notes

My first instinct was to just map and sort, which is O(n log n) and obviously not what they wanted.

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AI HintsAI Generated

Suggested Approach

Recognize that applying a quadratic function to a sorted array produces a sequence that is either monotonic or bitonic (first decreasing then increasing) depending on the sign of the leading coefficient. Use a two-pointer technique from both ends of the array, comparing the transformed values and placing the larger (or smaller) one at the end of the result array to achieve O(n) time.

Pro tip: Clarify edge cases upfront, such as when a=0 (linear function) or when the array contains duplicates, and mention that the two-pointer approach naturally handles them without extra code. Also, discuss how you would verify the result with a brute-force O(n log n) solution for small inputs.

1. Understand the problem and constraints

Restate the problem: given a sorted array and quadratic coefficients a, b, c, apply f(x)=ax^2+bx+c to each element and return the results sorted in O(n) time. Note that the input array is sorted, which is key to achieving O(n).

2. Analyze the shape of the transformed sequence

Determine that the transformed values form a sequence that is either monotonic (if a=0) or bitonic (if a≠0). The vertex of the parabola is at x = -b/(2a), and the sequence decreases then increases if a>0, or increases then decreases if a<0.

3. Choose the appropriate two-pointer strategy

If a>0, the maximum transformed value is at one of the ends, so fill the result array from the end by comparing the transformed values at the two pointers and placing the larger one. If a<0, the minimum is at one of the ends, so fill from the end by placing the smaller one (or equivalently, fill from the start by placing the larger one).

4. Implement and handle edge cases

Write the code with two pointers (left=0, right=n-1) and an index for the result array. Handle a=0 (linear function) by simply transforming and returning the array (since it remains sorted). Also consider integer overflow and use appropriate data types.

5. Test and verify

Test with small examples, including negative numbers, duplicates, and a=0. Compare with a brute-force O(n log n) approach to ensure correctness. Discuss time and space complexity: O(n) time and O(n) space for the result.

Key Points to Mention

The transformed sequence is bitonic (or monotonic) due to the quadratic function's shape.
Two-pointer technique from both ends of the sorted array to achieve O(n) time.
Handling of edge cases: a=0 (linear), negative coefficients, duplicates, and integer overflow.
Time complexity: O(n) because each element is processed once; space complexity: O(n) for the output array.
Comparison of transformed values at the two pointers to decide placement in the result array.
The vertex of the parabola at x = -b/(2a) determines the turning point, but explicit computation is not needed for the two-pointer approach.

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