$4-1-$ Let array locations $A[0],$dots,$A[7]$ hold numbers $A=\{12,10,8,7,6,5,4,2\}.$ Carry out by hand one call of the partition function of Quick Sort on the array A above. You must trace the actions of partition on this array carefully. After this single call to partition, answer the questions:

What is the initial index of the pivot element? Wrat is its value?

Where does the pivot end up$?($What is its index st the end?$)$

How many non$-$trivial interchanges are there? $($Interchanges of two distin elements.$)$

How many empty interchanges are there? $($Interchanges of an element with itself.$).$

What value is returned by this call to partition?

What is the result after this single call to partition? Identify the left sub$-$array of the partition and the right sub$-$array of the partition.

Suppose we continue with the quicksort algorithm beyond this initial call to partition. Briefly describe with this specific example how the rest of the sorting goes, until the array is sorted.