Question $1(30\mathrm{.}0$ marks$)$

a$.$ Show the steps that a quicksort with middle$-$of$-$three $($mean$)$ pivot selection takes

when sorting the array, shown below, in ascending order. Note the parameters to

determine the mid position are as follow: low $=0,$ high $=n-1,$ and mid $={|}_{{?}_{?}}\frac{\text{l}\text{o}\text{w}+\text{h}\text{i}\text{g}\text{h}}{(2{)}_{{?}_{?}}}|,$

where $n$ is the number of data in the array.

$(15\mathrm{.}0$ marks$)$

b$.$ Show the steps that a heapsort takes when sorting the array in ascending order.

Note, you can choose to start the first node as node $0$ or node $1.$ It is up to you.

$(15\mathrm{.}0$ marks$)$