Please explain and show your work

5.11. Consider the array S consisting of 8 elements in the follow ing order: 6,4,8, 1,5,7,2,3. Find the total number of comparisons that each of the following algorithms take on the above input SimpleSort (Algorithm 7) . MergeSort (Algorithm 8) Quicksort (Algorithm 11) Show the steps of the algorithm when calculating the number of compar- isons. Exercise 5.12. Given two sORTED (in ascending order) arrays A[L.n] and B1.n], each containingn numbers, give anO(log n)-time algorithm (again, counting the number of comparisons) to find the median of all the 2n ele- ments in arrays A and B Exercise 5.13. Given three SORTED (in ascending order) arrays All.nBI.. and C[1.n], each containing n numbers, give an O(log n)-time algorithm again, counting the number of comparisons) to find the nth smallest zum- ber of all 3n elements in arrays A, B, and C Exercise 5.14. Show how to modify QuickSort algorithm so that it runs in worst case O(n log n) time. (Hint: The modification is choosing the pivot in a better way. How?) Exercise 5.15. Givenn points on the s-axis line (in some arbitrary order), find the closest pair of points in" logn) time. . Show that the problem can be solved using sorting Give a divide and conquer algorithm that does not use sorting, (The advantage of this approach is that it generalizes to points in higher dimensions, e.g. 2 dimensions). Hint: Partition the points into two subproblems of equal size. recursively solve the subproblems, and ficiently combine them to solve the riginal problem: exploit the fact