Run the algorithm for n $=32$ and for each of the following cases:

$(1)$ Worst$-$case data input; $(2)$ Best$-$case data input; $(3)$ Random data input. $($Performance on random

data represents average$-$case.$)$

For each case, print n$,$ input array, output array $($sorted data$),$ and the number of key$-$comparisons. Does

the number of key$-$comparisons agree with the theoretical values? Theoretically, the worst$-$cse number of

key comparisons is $($n$2$ n$)/2,$ and the average number is $($n$2$ n$)/4,$ which is half of the worst$-$case