Sample $3$: Suppose we are to find the minimum among n numbers $($n is very large$).$ We divide the numbers among p processors $($p $<<$ n$).$ Each processor is going to find the minimum of $($n$/$p$)$ numbers and then use MPI$\_$Reduce$()$ to find the true global minimum.

$($a$)$ What is the sequential run time of the finding minimum algorithm $($using the O notation$)?($b$)$ What$$s the communication time of the algorithm $($using the O notation$)?($c$)$ What$$s the parallel overhead? $($d$)$ What$$s the iso$-$efficiency relation? $($e$)$ What$$s the scalability of the algorithm?