Scale AI·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Scale AI SWE interview that was basically a math problem dressed up as a coding question. The base version seemed manageable but they kept layering on follow-ups until I was doing floating point arithmetic for milliseconds on an analog clock, which felt a bit absurd.

Questions Asked (1)

Given a time string in 'HH:MM' format (24-hour clock), compute the smallest positive angle in degrees between the hour and minute hands on an analog clock. Then extend your solution to handle seconds ('HH:MM:SS') and finally milliseconds ('HH:MM:SS.mmm'), with continuous hand movement throughout.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The base case felt fine.

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AI HintsAI Generated

Suggested Approach

Start by deriving the formula for the angle between the hands for the simplest case (HH:MM), then generalize to include seconds and milliseconds by treating each hand's position as a continuous function of time. Emphasize the importance of modular arithmetic and handling floating-point precision, and discuss trade-offs between precision and performance.

Pro tip: Mention that the smallest angle is always ≤ 180°, so you can take min(angle, 360 - angle). Also, highlight that using floating-point for milliseconds may introduce precision issues, so consider using integer arithmetic (e.g., milliseconds since midnight) to avoid errors.

1. Understand the problem and define variables

Clarify the input format and the requirement for continuous hand movement. Define variables for hours, minutes, seconds, and milliseconds, and note that each hand moves continuously.

2. Derive the angle formula for HH:MM

Calculate the minute hand angle as (minutes * 6) degrees (since 360/60 = 6). Calculate the hour hand angle as (hours % 12 * 30) + (minutes * 0.5) degrees (since 360/12 = 30 and 30/60 = 0.5). Then compute the absolute difference and take the minimum of that difference and 360 minus the difference.

3. Extend to seconds and milliseconds

Add the contribution of seconds to the minute hand: seconds * 0.1 degrees (since 6/60 = 0.1). Add the contribution of seconds to the hour hand: seconds * (0.5/60) = seconds * (1/120) degrees. For milliseconds, add milliseconds * 0.0001 degrees to the minute hand (since 0.1/1000 = 0.0001) and milliseconds * (1/120000) degrees to the hour hand. Alternatively, compute total time in milliseconds and use continuous formulas.

4. Handle precision and edge cases

Use floating-point carefully; consider using integer arithmetic by converting everything to milliseconds since midnight. Ensure the result is always positive and ≤ 180. Test edge cases like 12:00:00.000 (angle 0) and 6:00:00.000 (angle 180).

5. Discuss trade-offs and optimizations

Compare approaches: direct formula vs. converting to milliseconds and using modular arithmetic. Discuss time complexity (O(1)) and space complexity (O(1)). Mention potential precision issues with floating-point and how to mitigate them.

Key Points to Mention

Continuous movement: each hand moves smoothly, so seconds and milliseconds affect both hour and minute hands.
Angle formulas: minute hand = 6 * (minutes + seconds/60 + milliseconds/60000) degrees; hour hand = 30 * (hours%12 + minutes/60 + seconds/3600 + milliseconds/3600000) degrees.
Smallest angle: take min(|hour_angle - minute_angle|, 360 - |hour_angle - minute_angle|).
Modular arithmetic: use modulo 360 to keep angles within [0, 360).
Precision: floating-point errors can accumulate; using integer milliseconds since midnight avoids this.
Edge cases: 12:00:00.000, 6:00:00.000, and times near midnight/noon.

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