Missing number(s) Interview Question Redux

Question

The common interview problem of determining the missing value in a range from 1 to N has been done a thousand times over. Variations include 2 missing values up to K missing val

Answer 1

My question is that seeing as the [...] cases converge at roughly something larger than O(nlogn) [...]

In 2011 (after you posted this question) Caf posted a simple answer that solves the problem in O(n) time and O(k) space [where the array size is n - k].

Importantly, unlike in other solutions, Caf's answer has no hidden memory requirements (using bit array's, adding numbers to elements, multiplying elements by -1 - these would all require O(log(n)) space).

Note: The question here (and the original question) didn't ask about the streaming version of the problem, and the answer here doesn't handle that case.

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Regarding the other answers: I agree that many of the proposed "solutions" to this problem have dubious complexity claims, and if their time complexities aren't better in some way than either:

• count sort (O(n) time and space)
• compare (heap) sort (O(n*log(n)) time, O(1) space)

...then you may as well just solve the problem by sorting.

However, we can get better complexities (and more importantly, genuinely faster solutions):