The logic itself wasn't too bad to reason through.
Start by clarifying requirements and edge cases, then outline a two-phase algorithm: first filter eligible ads based on per-user display limits, then randomly sample without replacement to assign to positions. Discuss trade-offs between different sampling methods and how to update the state dictionary efficiently.
Pro tip: Mention that you would use a Fisher-Yates shuffle on the eligible ads and then take the first N, which is O(n) and unbiased, and note that if supply is less than positions, you should fill remaining positions with a fallback or leave empty, depending on product requirements.
Ask about the definition of display limits (per ad per user? global?), what to do when there are fewer eligible ads than positions, and whether the assignment should be deterministic given a seed.
Filter ads that have not exceeded their display limit, then randomly select without replacement up to the number of positions. If not enough ads, decide on a fallback strategy (e.g., repeat ads, leave positions empty, or use a default ad).
Use a Fisher-Yates shuffle on the eligible ads list and take the first N, or use reservoir sampling if the list is large and N is small. Update the state dictionary by incrementing counts for the selected ads.
Discuss time and space complexity: O(M) to filter, O(M) to shuffle (or O(N) with reservoir sampling), and O(N) to update state. Compare with alternative approaches like weighted random selection if ads have priorities.
Walk through test cases: normal case, insufficient ads, ads at limit, empty inputs. Verify randomness and that state updates correctly.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.