Questions

$[3pts,1pt$ each$]$ For each group of functions, sort the functions in increasing order of asymptotic $($big$-$O$)$ complexity.

A$)$ Group A

$f_1(n)=n^{0\mathrm{.}9999}logn$

$f_2(n)=n^{1\mathrm{.}9999}$

$f_3(n)=n^{1\mathrm{.}0001}$

$f_4(n)={1\mathrm{.}00001}^n$

B$)$ Group B

$f_1(n)=n^{100}*2^{\frac{n}{4}}$

$f_2(n)=(2n)!$

$f_3(n)=n*2^{2n}$

$f_4(n)=n^{\sqrt[\phantom{2}]{n}}$

C$)$ Group C

$f_1(n)=3^{100n}$

$f_2(n)=n\sqrt[\phantom{2}]{nlogn}$

$f_3(n)=2^{100n}$

$f_4(n)=2^{2^n}$