Question

Consider the following three function:
$f_1$ = ${10}^n$, $f_2$ = $n^{logn}$, $f_3$ = $n^{\sqrt{n}}$
Which one of the following options arrange the functions in the increasing order of asympotic growth rate?

• A. $f_2$, $f_3$, $f_1$
• B. $f_1$, $f_2$, $f_3$
• C. $f_2$, $f_1$, $f_3$
• D. $f_3$, $f_3$, $f_1$

Answer 1

The correct option is A $f_2$, $f_3$, $f_1$

$f_2$ : $n^{logn}$ $f_3$ : $n^{\sqrt{n}}$
log ($n^{logn}$) log $n^{\sqrt{n}}$ = (log n) . (log n) = $\sqrt{n}$ . log n
$\therefore$ $n^{logn}$ = O($n^{\sqrt{n}}$) ($f_2$ < $f_3$)
$\therefore$ $f_1$ > $f_3$ > $f_2$
In increasing order of asympotic growth rate.