Problem $17.$ Suppose in the above solution instead of subdividing into groups of size $5,$ we divide

the array into groups of size $7.$ Derive and prove the recurrence for the runtime of this modified.

Problem $18.$ Earlier we showed that the runtime of QuickSort depends upon the quality $($rank$)$

of the pivot in the corresponding subarray. Suppose we always select pivot by selecting the median

of the subarray using the above algorithm. for median. Show that the runtime of this $$modified$$

algorithm is O$($nlogn$).$