Consider the following algorithm.

ALGORITHM Mystery $(A[0..n-1,0..n-1])$

for $i=0ton-2$ :

for $j=i+1ton-1$ :

$ifA[i,j]A[j,i]$

return false

return true

$($a$)$ What does this algorithm compute?

$($b$)$ What is its basic operation?

$($c$)$ Determine the worst$-$case recurrence relation for this algorithm and perform an analysis

to determine its complexity class.

$($d$)$ State the input for the best$-$case and worst$-$case.

$($e$)$ Suggest an improvement, if possible, or a better algorithm altogether, and indicate its

efficiency class.