The following algorithm adds all the entries in a square n × n array A. Analyze this algorithm where the work unit is the addition operation. sum = 0 for i = 1 to n do for j = 1 to n do sum = sum + A[i, j] end for end for write ("Total of all array elements is", sum)

a. Analyze the following algorithm where the work unit is the output statement. Assume that n = 2m for some positive integer m. integer j, k for k = 1 to n do j = n; while j ≥ 2 do write j j = j/2 end while end for
b. In one part of algorithm SelectionSort, the index of the maximum item in a list must be found. This requires comparisons between list elements. In an n-element (unsorted) list, how many such comparisons are needed in the worst case to find the maximum element? How many such comparisons are needed in the average case?