The core logic is pretty clean once you see it: for each value just do integer division by the bucket width and clamp to the last bucket index.
Clarify the bucket boundaries and overflow handling, then design a single-pass algorithm that computes each element's bucket index in O(1) time. Handle edge cases like negative numbers, values below the first bucket, and values exceeding the regular range, ensuring the last bucket catches all overflow.
Pro tip: Explicitly discuss how to handle negative values and values below the first bucket, as many candidates forget that the first bucket may also need a catch-all for underflow. Also, mention that the algorithm should be O(n) time and O(1) extra space (besides the output array).
Ask about bucket boundaries, whether buckets are inclusive/exclusive, how negative numbers and values below the first bucket are handled, and confirm the overflow behavior for the last bucket.
Derive a formula to map a value to its bucket index, e.g., index = (value - min_value) / bucket_width, with adjustments for negative values and clamping to the last bucket for overflow.
Iterate through the sorted array once, compute the bucket index for each element, and increment the corresponding count. Use the sorted property to potentially early-exit or optimize if needed.
Ensure that values exceeding the regular range are placed in the last bucket, and consider if a similar catch-all is needed for values below the first bucket (e.g., if negative values are allowed).
State that the time complexity is O(n) and space complexity is O(k) for the output. Walk through examples, including edge cases like empty array, all elements in one bucket, and overflow.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.