1. In class (Sept 4) we discussed a deterministic linear-time
algorithm for finding the median (or kth smallest element) of an
unsorted array.  Suppose we changed the algorithm so that rather than
breaking up the array into groups of size 5, we used groups of size 7
instead.

(a) What is the recurrence that results?

(b) What does this solve to, and why?

2. Consider a deterministic Quicksort algorithm that chooses the pivot
by running a deterministic linear-time median-finding algorithm, like
the one discussed in class.  (After all, the median element is the best
pivot).

(a) Write a recurrence for the running time T(n) of this algorithm on an
array of size n.  [Note: you should just view the median-finding
algorithm as a linear-time black box; your recurrence shouldn't go
into the innards of that algorithm] 

(b) Solve the recurrence in Theta() notation.