Problem 2: Finding an element. (i) Let n be an even positive integer. Let A be an array containing n not necessary different integers. Elements in A are not necessary sorted. Describe an algorithm which in time O(n) tests whether there exists an element x in A that appears in A at least n/2 times. (ii) Let S be a set containing n integers. An element x ∈ S is an approximate median of S, if |{y ∈ S | y < x}| ≥ n/4 and |{y ∈ S | y > x}| ≥ n/4 Given an array A containing n different integers, not necessary sorted, describe an algorithm which in time O(n) finds all approximate medians of the set {A[i] | i = 1, 2, . . . , n}.

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A: answer is given below

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Basic operations

A computer is an electronic machine that processes data by performing operations on it. Computer operations are actions performed by the computer to complete a given task. A computer can take input, store values/ information, process information and produce output.