Use the master method to show that the solution to the binary-search recurrence T (n) = T (n/2) + (1) is T (n) = (lg

Use the master method to show that the solution to the binary-search recurrence T (n) = T (n/2) + Θ(1) is T (n) = Θ(lg n).

Exercise 2.3-5

Referring back to the searching problem (see Exercise 2.1-3), observe that if the  sequence A is sorted, we can check the midpoint of the sequence against ν and eliminate half of the sequence from further consideration. The binary search algorithm repeats this procedure, halving the size of the remaining portion of the sequence each time. Write pseudocode, either iterative or recursive, for binary search. Argue that the worst-case running time of binary search is Θ(lg n).