Model the hand as a sliding window of fixed size (the hand span) over the sorted unique keys, and greedily extend the window as far as possible to cover consecutive keys. Count the number of windows needed to cover all keys; each new window after the first represents a hand reposition. For the follow-up, record the keys covered by each window and print them when moving to the next window, plus the final window at the end.
Pro tip: Clarify the hand span upfront—it's a crucial parameter that might be implied by the example (e.g., span=5 for [1,2,3,4,5]). Also, discuss edge cases like duplicate keys, unsorted input, and keys outside the piano range to show thoroughness.
Ask about the hand span (number of keys the hand can cover), whether the array can contain duplicates, and if the keys are within a standard piano range (e.g., 1-88). Confirm that the hand can be placed anywhere on the keyboard.
Sort the array in ascending order and remove duplicates, as playing the same key multiple times doesn't require repositioning. This simplifies the problem to covering a set of unique keys with intervals of length equal to the hand span.
Initialize a window starting at the smallest key. Extend the window to cover as many consecutive keys as possible within the hand span. When the next key exceeds the current window's end, increment the move count and start a new window at that key. Repeat until all keys are covered.
During the greedy process, store the keys covered by each window. When moving to a new window, print the previous window's keys. After processing all keys, print the final window's keys.
State that sorting takes O(n log n) time and the greedy pass takes O(n) time, so overall O(n log n). Test with edge cases: empty array, single key, all keys within one span, keys exactly at span boundaries, and large gaps.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.