The algorithm S(A,n,I) selects all the jut smallest element from an array A of n elements by using linear select to select each of the jug smallest elements. Clearly one could also implement S alternatively as T(A,n,I), which first sort A and then select the first I elements. Please compare the average case complexities of the two algorithms.

Suppose arrays A and B are both sorted in increasing order and both contain n elements. What is the time complexity to find the median of A U B, i.e., the set of elements in A or B?

During each iteration of Quick Sort algorithm, the first element of array is selected as a pivot. The algorithm for Quick Sort is given below. Modify it in such a way that last element of array should be selected as a pivot at each iteration. Also explain the advantages.

The recursive algorithm below takes as input an array A of distinct integers, indexed between s andf, and an integer k. The algorithm returns the index of the integer k in the array A, or ?1 if the integerk is not contained within A. Complete the missing portion of the algorithm in such a way that you makethree recursive calls to subarrays of approximately one third the size of A.• Write and justify a recurrence for the runtime T(n) of the above algorithm.• Use the recursion tree to show that the algorithm runs in time O(n).FindK(A,s,f,k)if s < fif f = s + 1if k = A[s] return sif k = A[f] return felseq1 = b(2s + f)=3cq2 = b(q1 + 1 + f)=2c... to be continued.else... to be continued.