a$.$ The operation convertToMinHeap$(h)$ converts a maximum heap into a minimum heap. Design an algorithm of convertToMinHeap that runs in $O(nlgn)$ time. Show that your algorithm runs in $O(nlgn).$

$(10\mathrm{.}0$ marks$)$

b$.$ Given the following maximum heap, illustrate the process of converting it into a minimum heap using your algorithm described in $($a$).$ You need to show the intermediate processes.

$(10\mathrm{.}0$ marks$)$