Pinterest·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Pinterest data scientist interview with a coding problem that looked straightforward until I actually had to think about the complexity constraints. The sieve angle was a bit unexpected for a DS role, but I guess they wanted to see if you could write clean, efficient code under pressure.

Questions Asked (1)

Write a function that returns the first n prime numbers in ascending order, using an efficient sieve approach with a tight upper bound estimate rather than trial division. Include unit tests and discuss the time and space complexity.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was trial division and I basically started going down that path before catching myself.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem and constraints, then explain the sieve approach with a tight upper bound estimate (e.g., using the nth prime approximation). Write clean code with unit tests, and analyze time and space complexity, discussing trade-offs.

Pro tip: Mention that for large n, the sieve of Eratosthenes with a bound like n(ln n + ln ln n) is efficient, but for very large n, a segmented sieve or incremental sieve can reduce memory usage. Also, note that unit tests should cover edge cases like n=0, n=1, and small n.

1. Clarify requirements and constraints

Ask about input range, expected output format, and any performance constraints. Confirm that n is a non-negative integer and that the function should return a list of the first n primes.

2. Choose the algorithm and bound

Explain that you'll use the sieve of Eratosthenes with an upper bound estimated from the nth prime approximation (e.g., n(ln n + ln ln n) for n >= 6). Justify why this is more efficient than trial division.

3. Implement the function

Write code that creates a boolean array up to the bound, marks composites, and collects primes until n are found. Handle edge cases (n=0, n=1) and ensure the bound is sufficient.

4. Write unit tests

Include tests for n=0, n=1, n=5, n=10, and a larger n to verify correctness. Also test that the function returns primes in ascending order and that the count matches n.

5. Analyze complexity and discuss trade-offs

State that time complexity is O(m log log m) and space is O(m), where m is the upper bound. Discuss potential improvements like segmented sieve for memory efficiency and note that the bound is an estimate but safe for n >= 6.

Key Points to Mention

Sieve of Eratosthenes is more efficient than trial division for generating multiple primes.
Use the nth prime approximation: p_n ~ n(ln n + ln ln n) for n >= 6, and add a safety margin.
Time complexity: O(m log log m), space complexity: O(m), where m is the upper bound.
Edge cases: n=0 returns empty list, n=1 returns [2], n=2 returns [2,3].
Unit tests should verify correctness, order, and count.
For very large n, consider segmented sieve to reduce memory usage.

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