Clarify the problem constraints and then propose an efficient solution using a max-heap to track the largest available gaps between occupied seats. For each assignment, pop the largest gap, place the employee at its midpoint, and push the two new sub-gaps back into the heap. Discuss time and space complexity, and consider edge cases like the first assignment and when seats are exhausted.
Pro tip: Mention that this is essentially the 'Exam Room' problem and that using a priority queue with a custom comparator (to break ties by smaller index) ensures deterministic and optimal placement. Also, note that the first assignment should always be seat 0 to maximize distance for subsequent placements.
Ask about the range of N, whether seats are 0-indexed, and if multiple assignments can happen concurrently. Confirm that the goal is to maximize the minimum distance to any occupied seat at each step.
Use a max-heap (priority queue) to store available intervals between occupied seats, prioritized by the maximum possible distance to the nearest neighbor. For each interval, store its start and end indices.
For an interval (left, right), the best seat is at mid = (left + right) / 2, and the distance to the nearest occupied seat is min(mid - left, right - mid). Handle edge cases: if left == -1 (before first seat), distance = right; if right == N (after last seat), distance = N - 1 - left.
On each call, pop the interval with the largest distance (break ties by smaller index). Place the employee at the computed seat, then push the two new intervals (left, seat) and (seat, right) back into the heap. Return the assigned seat.
Time complexity: O(log N) per assignment due to heap operations. Space: O(N) for the heap. Discuss handling of first assignment (seat 0), last seat, and when no seats are left.
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