algorthims please solve b and c both of them with good hand write

1. Quicksort Analysis. (a) (5 points) Using the deterministic quicksort, if the median of the elements in the array was chosen as the pivot, what would be the recurrence T(n) and the solution to this recurrence? (b) (5 points) Using the deterministic quicksort, if the second largest element of the elements in the array was chosen as the pivot, what would be the recurrence 7(n) and the solution to this recurrence? (e) (Bonus +5 points): In class we showed that the expected running time of randomized quicksort is Onlgn). Show that the expected running time is also Sl(n Ign). Hint: think about the minimum work that the algorithm must do