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Scale Digit-Square Convergence Requests

AppleSoftware Engineer · Technical Screen
MediumSoftware EngineerTechnical ScreenSystem Design

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This question evaluates a candidate's competency in designing scalable, low-latency distributed services that combine algorithmic optimization and caching to handle massive request volumes for a numerical convergence operation.

Design a service that receives very high request volume for the digit-square convergence operation.

For each request, the input is a positive integer n. The service repeatedly replaces n with the sum of the squares of its decimal digits and returns whether the sequence eventually reaches 1.

Requirements:

  • Handle billions of requests over time.
  • Keep request latency low.
  • Avoid expensive repeated computation for common states.
  • Use the observation that after a small number of transformations, fixed-width integers collapse into a small numeric range, such as values below 1,000 or another small bound chosen by the implementation.