Using the following reference string apply Optimal Page, Least Recently Used and FIFO algorithms to the sequence for a memory with 4 frames. Write the number of page faults for each. 1, 4, 8, 5, 2, 7, 0, 4, 3, 4, 1, 8, 2, 5, 6, 9, 5, 4, 0, 7, 3, 4, 8, 1

Suppose we wish to sort the following values: 84, 22, 19, 11, 60, 68, 31, 29, 58, 23, 45, 93, 48, 31, 7. Assume that: we have three pages of memory for sorting; we will use an external sorting algorithm with a 2-way merge; a page only holds two values. We do not use double buffering and we use quick sort in pass 0 to produce the initial runs. For each sorting pass, show the contents of all temporary files except that you should fully utilize the buffers by sorting every 3 pages into a run in pass 0. Could you show step by step detailed explaination for this?

(b) Consider the two sorting algorithms below, which each take as input array A] indexed from s to f. SwapSort2(A, s, f) SwapSort1(A, s, f) swapped = true while (swapped) swapped = false for i = s to f-2 swapped = true while (swapped) swapped = false for i = s to f-2 if A[i] > A[i+2] Swap A[i] and A[i+2] swapped = true if A[i] > Ali+2] Swap A[i] and A[i+2] swapped = true swapped = true while (swapped) swapped = false for i = s to f-1 if A[i] > A[i+1] Swap A[i] and A[i+1] swapped = true • Execute SwapSort1 on array A = [7,6, 5, 4, 3, 2, 1] indexed from s = 1 to f = 7. • Which of the above two algorithms is correct?. Justify your answer. • What is the worst-case number of comparisons are made by SwapSort2 when the input array A has length n and is sorted in reverse order? • Does your result from above represent the worst-case number of comparisons made by SwapSort2? Justify your answer. • Justify that the worst-case runtime of SwapSort2 is of the form T(n) a, b, c. = an? + bn +c for…