Algorithm

$(26)$ Let $f(n)$ designate the

the number of steps that will

be executed in the Algorithm

to the right. Designate everyone

of $($a$)-($h$)$ below that are

TRUE for $f(n).$

Input $n$

$x$:$=0$;$y$:$=0$

For $k=1$ to $n-1$

For $j=1$ to $k+1$

$x$:$=a[k]+b[j]$

Next j

Next i

return $x$

$($a$)f(n)=O(lo{g}_{10}n),i.e.,f(n)$ is of order at most $O(lo{g}_{10}n).$

$($b$)f(n)=O(\sqrt[\phantom{2}]{n}),$ i$.$e$.,f(n)$ is of order at most $o(\sqrt[\phantom{2}]{n}).$

$($c$)f(n)=O(1),$ i$.$e$.,f(n)$ is of order at most $O(1).$

$($d$)f(n)=O(n),$ i$.$e$.,f(n)$ is of order at most $o(n).$

$($e$)f(n)=O(n^2),$ i$.$e$.,f(n)$ is of order at most $O(n^2).$

$($f$)f(n)=O(n^3),$ i$.$e$.,f(n)$ is of order at most $O(n^3).$

$($g$)f(n)=O(n^4),$ i$.$e$.,f(n)$ is of order at most $O(n^4).$

$($h$)f(n)=O(2^n),$ i$.$e$.,f(n)$ is of order at most $o(2^n).$