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Took me a minute to even parse what the penalty function was doing.
First, restate the problem in your own words to confirm understanding, then propose an efficient algorithm. Use prefix sums to compute penalties for all possible closing times in O(n) time, and track the earliest index that achieves the minimum penalty.
Pro tip: Mention that you can compute the penalty in a single pass by maintaining counts of empty hours and customers after the current index, and update the minimum penalty and earliest index dynamically. This shows you can optimize both time and space.
Confirm that the string represents hourly arrivals, with 'Y' meaning a customer arrives and 'N' meaning no customer. The penalty for closing at hour j is the number of 'N's before j plus the number of 'Y's after j.
Let n be the length of the string. For a closing time j (0-indexed), penalty(j) = count of 'N' in s[0..j-1] + count of 'Y' in s[j..n-1]. Note that closing at j means the store is open for hours 0 to j-1.
Precompute total number of 'Y's. Traverse the string from left to right, maintaining the count of 'N's seen so far and the count of 'Y's remaining. At each index j, compute penalty(j) and update the minimum penalty and earliest index if a new minimum is found.
Consider closing at time 0 (all customers after are penalized) and closing at time n (all empty hours before are penalized). Also handle empty string or all 'Y'/'N' strings.
After the traversal, return the earliest index j that gives the minimum penalty. If multiple indices yield the same minimum, the first one encountered is the earliest.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.