Upstart·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Jul 2026

Summary

Interviewed for a software engineering role at Upstart and got the classic two-sum problem. Pretty standard coding screen, nothing too wild, but the follow-up about doing it in linear time is where things get interesting.

Questions Asked (1)

Given an array of integers and a target value, return the indices of the two numbers that sum to the target. Then solve it in O(n) time.

Algorithms & Data Structures

Author's notes

Started with the brute force nested loop thing because my brain just goes there first.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem constraints (e.g., exactly one solution, cannot use same element twice) and discussing brute force O(n^2) as a baseline. Then introduce a hash map to store each number's complement and index, achieving O(n) time and O(n) space. Walk through a concrete example to demonstrate correctness and edge cases.

Pro tip: Mention that the hash map approach trades space for time, and if the array is sorted, a two-pointer approach could achieve O(n) time with O(1) space—showing you consider trade-offs. Also, explicitly state that you assume exactly one solution exists, as per common problem statements.

1. Clarify requirements and constraints

Ask if there is exactly one solution, if the same element can be used twice, and if the array is sorted. Confirm input/output types and edge cases like empty array or no solution.

2. Discuss brute force and its complexity

Explain the naive O(n^2) approach using nested loops to check all pairs. This sets a baseline and shows you can analyze time complexity.

3. Introduce hash map for O(n) solution

Iterate through the array once, storing each number and its index in a hash map. For each element, check if its complement (target - current) exists in the map; if so, return the indices.

4. Walk through an example and edge cases

Use a small example like [2,7,11,15] with target 9 to show how the hash map works. Mention edge cases: duplicate numbers, negative numbers, and ensuring indices are distinct.

5. Analyze complexity and discuss trade-offs

State that time complexity is O(n) and space complexity is O(n). Optionally mention that if the array is sorted, a two-pointer approach uses O(1) space, but sorting would take O(n log n).

Key Points to Mention

Hash map stores value-to-index mapping for O(1) lookups.
Check for complement before inserting current element to avoid using the same index twice.
Time complexity: O(n) single pass; space complexity: O(n) for the hash map.
Edge cases: no solution, multiple solutions, negative numbers, and duplicates.
Alternative two-pointer approach if array is sorted (O(n) time, O(1) space).
Assumption of exactly one solution simplifies return logic.

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