$1$: $2$: $3$: $4$: $5$: $6$: $7$: $8$: $9$:

$10$: $11$: $12$:

Consider the following algorithm:

function EpicCount$($A : array$)$ letnbethelengthofA count $0$ forifrom$0$ton$1$do

for j from i $+1$ to n $1$ do

if A$[$i$]<$ A$[$j$]$ A$[$i$]>$ A$[$j$]$ then

count $$ count $+1$ end if

end for end for

return count end function

Question $1($a$)$ Derive a closed$-$form T $($n$)$ for the number of array accesses, where n is the length of the input array. Note: Do not consider short$-$circuit evaluation for T$($n$).$

$($b$)$ Does the closed$-$form T$($n$)$ change if the condition for the if statement is $($A$[$i$])=$ A$[$j$])$ instead?

$($c$)$ Describe the output of the algorithm in a single sentence.

$($d$)$ What is the lowest possible value for count?

$($e$)$ What is the highest possible value for count?