Suppose that, even unrealistically, we are to search a list of 700 million items using Binary Search, Recursive (Algorithm 2.1). What is the maximum number of comparisons that this algorithm must perform before finding a given item or concluding that it is not in the list

"Suppose that, in a divide-and-conquer algorithm, we always divide an instance of size n of a problem into n subinstances of size n/3, and the dividing and combining steps take linear time. Write a recurrence equation for the running time T(n), and solve this recurrence equation for T(n). Show your solution in order notation."

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Explanation:

Since we are talking about binary search, let's assume that the items are sorted according to some criteria.

Time complexity of binary search is O(logN) in worst case, best case and average case as well. That means it can search for an item in Log N time where N is size of the input. Here problem talks about the item not getting found. So, this is a worst case scenario. Even in this case, binary search runs in O(logN) time.

N = 700000000.

So, number of comparisions can be log(N) = 29.3 = 29.

So, in the worst case it does comparisions 29 times

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