Question $1$

Consider the following algorithm:

function : array$)$

let $n$ be the length of $A$

count larr$0$

for i from $0$ to $n-1$ do

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

if larrT$(n)nT(n)T(n)(A[i])A[j]A[i]$ then

count larr count $+1$

end $if$

end for

end for

return count

end function

$(a)$ Derive a closed$-$form $T(n)$ for the number $of$ array accesses, where $nis$ 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 $is(A[i])A[j]$