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naraburns  nihil supernum  1yr ago (text post)   35417 thread views

Culture War Roundup for the week of October 3, 2022

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Out of curiosity, did you expect the warmup to be addressed with something like:

Compare two middlemost entries; the max lies in the half of the array containing the greater of the two. Return this half of the array. Repeat until the remaining array has length 1 (with the max entry guaranteed).

Or is there a better way? Conversely, suppose the interviewee does the obvious thing and compares consecutive pairs until a decreasing pair is found. Would they have any chance of getting hired?

More or less. It's essentially a binary search, where you're looking for a local maximum instead of an exact value. It's optimal.

Usually competitive candidates see this immediately. If someone suggests a linear scan, I'll ask if we can do better and they eventually get to the binary search. That's not in itself something that results in a NH recommendation, but in practice the people who get the binary search right away tend to do better on later parts.

Or is there a better way?

The max can be any one of N entries. So in order to specify its position, you need the number of bits in N. Any search which allows you to find the max in fewer than that many bits would imply that you can specify the position of the max in fewer than that many bits, and is therefore impossible.

If a query on the list just gives you a single bit of information, you're right, giving us the log2 bound. I have seen the claim made in an interview that a quantum speedup is possible to improve on that. (Cf https://web.mit.edu/rsi/www/pdfs/papers/2003/2003-brianj.pdf for a quantum search on an ordered list).

Would love for someone well-versed in quantum algorithms to confirm.

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