"1. (15pt) the algorithm for selection sort of the ith largest element of a list with guaranteed (n) performance that was given in class and in the book divides the file into groups of d elements with d=5. it then computes the median of the subgroup medians to produce the pivot. a) (7 pt) the subgroup median calculation in the book’s method would be easier if d=3. show that if d=3, the number of elements greater than the median is at most 2n/3. b) (2 pt) show that the performance of the selection method given in the book with d=3 is bounded above in performance by the recurrence equation t(n) = t(n/3) +t(2n/3) + (n). c) (6 pt) what is the solution of the recurrence equation in part b? show your work. first, find the solution using some form of the master theorem. then check your solution using substitution. what does this solution say about the choice between the method with d=3 and that with d=5?