Average$-$Case Analysis. Consider the deterministic $($i$.$e$.$ non$-$randomized$)$ version of quicksort that we saw in class which takes the last element in the array as thepivot to partition the rest of the elements around.

$($a$)(5$ points$)$ In the best case, the pivot always splits the array in half for all recursive calls. Give an example of a sequence of $7$ distinct numbers that cause this best$-$case behavior.

$($b$)(5$ points$)$ Suppose that all the elements in the array are equal. Write down the

recurrence and solve it to find the running time of quicksort in this case.