big o - what the running time of this recursive algorithm? - 


search_item(a,item,c)  index <- c     if (a[index] > item)        index <- 2 * index       search_item(a, item, index) else if (a[index] < item)        index <- 2 * index + 1       search_item(a, item, index) else  return index

you gave little (no) information. sad, give answer , hope show more effort in other questions, show effort in answering question.

the algorithm posted seems incomplete. think there returns missing. however:

the simplest complexity analysis this:
work on array a. let n number of elements in a. in every recursive call either multiplying current index 2 (and make recursive call) or return current index.
assuming algorithm correct, can have k recursive calls 2k < n. k < log₂(n) holds.

this means algorithm has time-complexity of o(log n).

since algorithm named "search" algorithm, looks array a representation of binary search tree , search algorithm recursive binary search.
fits complexity calculated.


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