Given a collection of sorted arrays A1, A2, A3, ..., Ak of numbers, such that the size of the first array (i.e., A1 ))is n and the sizes of the remaining arrays are geometrically decreasing. Specifically|A|| = |Ai1| for i 2, 3, ..., k. Design an O(n) time algorithm to compute the number of distinct numbers numbers across all arrays. In other-words, compute the size of the set S = {A; [j] | i E [1, k] and je [1, Ai|]}. Provide a clear presentation of your algorithm, as well as the analysis of running time. Let A [1, n] be an array of n numbers such that, A [i] n0.3 Design an efficient algorithm (the best asymptotic running time possible) to check if a given number 3 is in A. Provide a clear presentation of your algorithm, as well as the analysis of running time. Given a collection of sorted arrays A1, A2, A3, ..., Ak of numbers, such that the size of the first array (i.e., A1 ))is n and the sizes of the remaining arrays are geometrically decreasing. Specifically|A|| = |Ai1| for i 2, 3, ..., k. Design an O(n) time algorithm to compute the number of distinct numbers numbers across all arrays. In other-words, compute the size of the set S = {A; [j] | i E [1, k] and je [1, Ai|]}. Provide a clear presentation of your algorithm, as well as the analysis of running time. Let A [1, n] be an array of n numbers such that, A [i] n0.3 Design an efficient algorithm (the best asymptotic running time possible) to check if a given number 3 is in A. Provide a clear presentation of your algorithm, as well as the analysis of running time