Following is a function 'QuickSort$($A$,$p$,$r$)\text{'}$ to sort an array A from index p to r$.$

QuickSort$($A$,$ p$,$ r$)$

$$ if p $<$ r

$$ q $=$ Partition$($A$,$ p$,$ r$)$

$$ QuickSort$($A$,$ p$,$ q$-1)$

$$ QuickSort$($A$,$ q$+1,$ r$)$

Given an array A $=[2,8,7,1,3],$ the function calls will be made in the following order.

QuickSort$($A$,1,5)$

Partition$($A$,1,5)$

QuickSort$($A$,1,2)$

Partition$($A$,1,2)$

QuickSort$($A$,1,0)$

QuickSort$($A$,2,2)$

QuickSort$($A$,4,5)$

Partition$($A$,4,5),$ A$=[1,2,3,7,8]$

QuickSort$($A$,4,3)$

QuickSort$($A$,5,5)$

The array A will be $[2,1,3,8,7]$ at the end of Partition$($A$,1,5)$

The array A will be $[1,2,3,8,7]$ at the end of Partition$($A$,1,2)$

The array A will be $[1,2,3,7,8]$ at the end of Partition$($A$,4,5)$

Here is the question.

Given the array A $=[1,5,6,7,2],$

Show the function calls with parameters in the correct order and

show what the array A will be at the end of each Partition$()$