On an array of $n = 2^k$ numbers, where $k$ is a non-negative integer, the $k = \log n$ order statistics $1, 2, 4, 8,\ldots, 2^k$ can all be determined in a total of $Θ(n)$ time in the worst case.
I think that this statement is wrong because the loop will take $k$ iterations. So, the time should be $Θ(\log(n))$. But, I'm not sure my guess is correct. Could you tell me whether or not my guess is correct?