Started with the naive approach, checking every number up to n by dividing it by all smaller numbers.
Start by clarifying the problem: confirm whether n is inclusive, the expected input range, and if the result should be a list or array. Then explain the Sieve of Eratosthenes algorithm, which is the optimal approach for generating all primes up to n, and discuss its time and space complexity. Finally, walk through a code implementation, handling edge cases like n < 2.
Pro tip: At Apple, interviewers value clean, efficient code and clear communication. Mention that the Sieve of Eratosthenes is the standard for this problem, but also briefly note the trade-offs with a trial division approach for very small n or memory-constrained environments.
Ask if n is inclusive, the expected input range, and the desired output format (e.g., list, array). Confirm edge cases like n < 2.
Select the Sieve of Eratosthenes for optimal O(n log log n) time complexity. Briefly mention alternative approaches like trial division and their trade-offs.
Describe how the sieve works: create a boolean array of size n+1, mark multiples of each prime starting from 2, and collect unmarked numbers.
Write clean code, handling edge cases (n < 2 returns empty list). Use efficient loops and avoid unnecessary operations.
State time and space complexity (O(n log log n) time, O(n) space). Walk through a small example (e.g., n=10) to verify correctness.
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