Consider linear search again (see Exercise 2.1-3). How many elements of the input sequence need to be checked on the average, assuming that the element being searched for is equally likely to be any element in the array? How about in the worst case? What are the average-case and worst-case running times of linear search in \(\Theta\)-notation? Justify your answers.
On average, half the the elements in array \(A\) will be checked before \(v\) is found in it. And in the worst case (\(v\) is not present in \(A\)), all the elements needs to be checked.
In either case, the running time will be proportional to \(n\), i.e. \(\Theta(n)\).