• April 10th, 2016

Mathematics

Paper, Order, or Assignment Requirements

  1. (20) Given a sorted (in increasing order) array A[1..n] of distinct integers, (a) use the divide-and-conquer technique to design an algorithm that in o(n) (i.e. sublinear) time, determines whether there exists an i, 1 ≤ i ≤ n, such that A[i] = i; For example, for array [2, 3, 9, 11, 19], the answer is no while the answer is yes for [−10, −5, 1, 4, 10, 20, 30, 50] since A[4] = 4. (2) let t(n) be the running time of your algorithm, give a recurrence for t(n) and solve it using all four different methods covered. Solutions to incorrect recurrence will only get partial credit. You can use this and the next page for Q1. Describe your algorithm in English or very high level pseudo code.

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