$($a$)$ What are the differences if any between a Heap array and a sorted array?

What are the main advantages of a binary Heap compared to both an unsorted array and

a sorted array from the point of view of insert$()$ and remove$()$ operations?

$(6$ marks$)$

$($b$)$ Draw the following heap array as a two$-$dimensional binary tree data structure:

Also, assuming another array hPos$[]$ is used to store the position of each key in the

heap, show the contents of hPos$[]$ for this heap.

$(6$ marks$)$

$($c$)$ By using tree and array diagrams, illustrate the effect of inserting a node whose key is

$13$ into the heap in the array of part $($b$).$ You can ignore effects on $h$ Pos$[].$

$(9$ marks$)$

$($d$)$ By using tree diagrams, illustrate the effect of a remove operation on the modified heap

from part $($c$).$

$(5$ marks$)$

$($e$)$ Write in pseudocode a recursive version, maxHeapify$($int k$),$ of the siftDown$($int k$)$

Heap operation.

$(7$ marks$)$