$//$ PLEASE DRAW AND SHOW ALL THE STEPS NEEDED$//////$

$($a$).$Construct an essentially complete binary tree of the larrax $4,5,8,13,13,3,6,19,29,5,31$

$($b$).$ Transform the essentially complete binary tree of $($a$)$ to a binary search tree. Show

all the steps!

$($c$).$ Transform the binary search tree of $($b$)$ to a min heap. Show all the steps!

$($d$).$ Transform the essentially complete binary tree of $($a$)$ to a min heap using the "static"

heap construction approach. Show all the steps, including the changes in the array for

each iteration. Are the min heaps of $($c$)$ and $($d$)$ the same?

$($e $-15$ pts$)$ Sort the array of Q$1$ in the decreasing order of the values of the elements using the

min heap of $($d$).$ Show all the steps, including the changes in the array for each iteration.

$($f $-20$ pts$)$ Construct a min heap of the array generated in Q$1$ using the "dynamic" heap

construction approach. Are the min heaps of $($d$)$ and $($f$)$ the same?

$(g-8pts)$ Delete the root node of the min heap of $($f$)$ and rearrange the remaining nodes to

restore the min heap