Given a sequence of numbers: $8,5,23,12,16,3,20,$ insert them into two different data structures, a max$-$heap and a binary search tree $($BST$),$ in the given order.

$(1)$ Start with an empty max$-$heap. Insert the numbers sequentially by calling the Max$-$Heap$-$Insert procedure.What is the resulting max$-$heap $($in array representation$)$ after all the numbers have been inserted? Please format your answer as a sequence of numbers separated by commas $($e$.$g$.$: $1,2,3,4,5,6,7).$A

What is the height of this max$-$heap?

A

$(2)$ Start with an empty BST$.$ Insert the same set of numbers in the given order by calling the Tree$-$Insert procedure.What is the height of the BST after all the numbers have been inserted?A