How should I practice Minimum Piano Hand Raises and Thumb Positions?

Start by reading the full statement, solve the visible examples, then compare the pattern against related Google phone screen and onsite interview problems in FastPrep.

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Minimum Piano Hand Raises and Thumb Positions

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Problem statement

Source note: Two reports describe this Google question. Both ask to play a sequence of notes with one hand that spans five neighboring keys, moving the hand as rarely as possible, with the first position free. An earlier onsite report also asked for the thumb position of each group; a later phone-screen report asked for each note's finger counted from the lowest note of its group, which puts the thumb on that lowest note.

The reports do not give the keyboard size or a tie rule between equally short plans. Practice choices: keys run from 0 to 87, each group is extended as far as it fits, and the result lists the raise count followed by the thumb positions. Putting each thumb on its group's lowest note follows the later report. The per-note fingers are explained in the editorial but not judged.

The judged task matches the reports at about 90%.

For this exercise, assume a piano keyboard has keys numbered 0 through 87. One hand placement puts the thumb on some key p and covers the five consecutive keys p through p + 4, one per finger: finger 0 (the thumb) on p up to finger 4 (the little finger) on p + 4.

Play the notes in their given order. The first hand placement is free, and each move to another placement is one hand raise. Find the minimum number of raises.

The problem statement continues

Pro

Examples

Example 1

notes = [0,4,5,9,10]return = [2,0,5,10]

The longest fitting segments are [0, 4], [5, 9] and [10]. Their lowest notes are 0, 5 and 10, so those are the thumb positions. Three placements need two raises. In the first segment, note 4 is played by finger 4 - 0 = 4.

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