What is the best-case cost of Shellsort for an array whose size n is a power of 2 when using divide-by-twos increments?

\Theta(n \log n)
  • \Theta(n^2)
  • \Theta(n)
  • \Theta(2^n)
  • \Theta(\log n)

Think about whether the sorted list is a best-case input or not.

Sorted input is the best case.

How many increments are there for the divide-by-two increment series?

With divide-by-two increments, there are \log n increments.

\log n passes over an array of length n must cost n \log n.