$($a$)$ Using diagrams, show the detailed workings for the first two passes of the outer loop of

a bubble sort on the following array.

Use your resulting array diagram to point out in your own words a significant flaw in

bubble sort.

$(6$ marks$)$

$($b$)$ What is the basic idea behind comb sort that makes it an improvement on bubble sort.

Apply comb sort to the array in part $($a$)$ until it becomes bubble sort..

$(8$ marks$)$

$($c$)$ Show the first two partitionings that occur when quick sort is applied to the array in part

$($a$).$

$(7$ marks$)$

$($d$)$ Provide a simple example which shows quick sort at its worst. What is the complexity

of quick sort at its worst?

$(5$ marks$)$

$($e$)$ Write down the complexity of heap sort and outline how it is arrived at$.$ In your own

words, contrast it with that of bubble sort and quick sort.

$(7$ marks$)$