I recognized the base problem pretty fast but the per-round k array threw me for a second.
Model the circle as a circular linked list or use an order-statistics tree to efficiently handle eliminations. Simulate each round by advancing the current pointer by (count-1) steps modulo the current number of friends, then remove that friend. Continue until one friend remains.
Pro tip: Clarify the indexing and direction of counting upfront (e.g., 0-indexed, clockwise) to avoid off-by-one errors. Mention that if the count array is large, you can optimize by taking modulo the current circle size.
Ask questions to confirm: indexing (0 or 1), counting direction, whether the count includes the current person, and what happens if the count array is exhausted (e.g., repeat or stop).
Decide between a simple array with a list for O(n^2) simulation, a circular linked list for O(n*k) where k is number of rounds, or an order-statistics tree (e.g., Fenwick tree) for O(n log n).
Maintain the current position and the current circle size. For each count c, compute the index to remove as (current + c - 1) % size, remove that element, and update current to that index (which now points to the next person).
Consider n=1, empty count array, counts larger than current size, and negative counts (if allowed). Ensure the loop terminates correctly.
State the time and space complexity of your approach. If needed, propose optimizations like using a Fenwick tree to find the k-th remaining person in O(log n) per elimination.
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