Apple·Software Engineer·Onsite - System Design / Architecture·Senior

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Apr 2026

Summary

Apple system design round for a software engineer role. One question, pretty focused, but it had enough layers to keep me busy for the whole session.

Questions Asked (1)

Design a high-throughput service that accepts a positive integer and determines whether repeatedly replacing it with the sum of its squared digits eventually reaches 1. The service needs to handle billions of requests efficiently, with low latency and minimal redundant computation.

System DesignAlgorithms & Data StructuresTechnical Trade-offs

Author's notes

I went straight to caching and that was the right instinct, but I fumbled explaining why the cache stays small.

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AI HintsAI Generated

Suggested Approach

Start by clarifying requirements and scale, then propose a multi-layer solution: precompute the happy number status for all numbers up to a reasonable bound (e.g., 1 million) using cycle detection, and for larger inputs, use memoization with a cache (e.g., Redis) to avoid redundant computation. Finally, discuss how to distribute the workload across multiple servers and optimize for low latency and high throughput.

Pro tip: Emphasize that the happy number problem has a small state space (numbers quickly reduce to a few digits), so caching and precomputation can reduce most requests to O(1) lookups. Also, mention that you would use a bloom filter or similar to quickly reject numbers that are known to be unhappy, further reducing latency.

1. Clarify Requirements and Constraints

Ask about expected request rate, latency targets, input size distribution, and whether the service needs to be stateless or can use shared caches. Confirm that the input is a positive integer and that the output is a boolean (happy or not).

2. Design Core Algorithm with Precomputation

Explain that for any number, the sum of squared digits quickly reduces to a small number (e.g., under 1000 for 64-bit integers). Precompute the happy status for all numbers up to a certain limit (e.g., 1 million) using cycle detection (Floyd's or a set). For larger numbers, compute the sum of squared digits once and then look up the result in the precomputed table.

3. Introduce Caching and Memoization

Use a distributed cache (e.g., Redis) to store results for numbers that are frequently requested but not in the precomputed range. Implement a write-through or read-through cache with TTL to handle billions of requests. Consider using a Bloom filter to quickly identify numbers that are definitely unhappy, reducing cache lookups.

4. Scale and Distribute the Service

Deploy the service as a stateless microservice behind a load balancer. Use consistent hashing to route requests for the same number to the same cache shard to improve cache hit rates. Autoscale based on request rate and ensure the precomputed table is replicated across all instances.

5. Optimize for Latency and Throughput

Use in-memory data structures for the precomputed table (e.g., a bitset) to minimize memory and maximize lookup speed. Batch requests if possible, and use asynchronous I/O. Monitor cache hit rates and adjust precomputation range or cache size accordingly.

Key Points to Mention

Precomputation of happy numbers up to a bound (e.g., 1 million) to reduce most requests to O(1) lookups.
Cycle detection algorithms (Floyd's tortoise and hare or hash set) for determining happy numbers.
Use of distributed caching (e.g., Redis) with consistent hashing to avoid redundant computation across servers.
Bloom filters to quickly reject known unhappy numbers and reduce cache misses.
Stateless service design with horizontal scaling and load balancing for high throughput.
Trade-offs between precomputation range, memory usage, and cache size; and how to handle numbers larger than the precomputed bound.

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