Asking this question in a real interview, if the candidate missed the summation approach and used an array to keep counts, I'd simply say "That sounds good. What if we were really worried about memory use? Could we do it with less memory?"
This is what it's supposed to feel like when Interview Cake offers the "gotcha" that we can solve the problem with O(1) additional memory after you say you have an answer, before showing you the final solution. In real life I wouldn't fault the candidate for needing the nudge.
Another flow I've considered is to make the question multi-part, with the second part (the "follow-up" question) adding the O(1) time constraint. I'm worried that with this flow, in the case where you do jump right to the summation approach, the app will feel naive because it will pose a whole new question that you've already answered.
So far I think the best approach is to keep the current flow but use a less harsh word than "gotcha." What do you think? Do you still think the question is just fundamentally too much of an "aha"?
(I agree that if the candidate jumped right to the summation answer on this one it's a weak signal. I wouldn't ask this question in an interview--it's not my favorite either, and it's unfortunate that it's a common one. My favorites aren't on the site yet because they're hard to explain without pictures. Adding those pictures is the next project!)
Nitpicking because this tripped me up: You can do this in-place and in O(n) time by repeatedly partitioning the array in half (by value) and discarding the smaller half. I'd have needed a hint that you can do it in one pass to have noticed the summation approach.
This is what it's supposed to feel like when Interview Cake offers the "gotcha" that we can solve the problem with O(1) additional memory after you say you have an answer, before showing you the final solution. In real life I wouldn't fault the candidate for needing the nudge.
Another flow I've considered is to make the question multi-part, with the second part (the "follow-up" question) adding the O(1) time constraint. I'm worried that with this flow, in the case where you do jump right to the summation approach, the app will feel naive because it will pose a whole new question that you've already answered.
So far I think the best approach is to keep the current flow but use a less harsh word than "gotcha." What do you think? Do you still think the question is just fundamentally too much of an "aha"?
(I agree that if the candidate jumped right to the summation answer on this one it's a weak signal. I wouldn't ask this question in an interview--it's not my favorite either, and it's unfortunate that it's a common one. My favorites aren't on the site yet because they're hard to explain without pictures. Adding those pictures is the next project!)