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Which of the following is the correct order if they are ordered by asymptotic growth rates?



$F_3:(lg\,n)^{lg\, n}$


$F_3$ can be re-written as $n^{lg\,lgn}$ using property $a^{log_bc}=c^{log_ba}$

So, $F_4 \gt F_2 \gt F_1=F_3$

Is my order correct?
in Algorithms by Boss (29k points) | 89 views
How would you decide between $F_2$ and $F_3$?
Ayush your order is spot on.

@srestha F4 comes first, followed by F2, not the other way around. Comment below in case you need explanation.
yes, got it
one is power of log n

and another is power of n

So, power of n will be greater
Yes, but one is constant to some power and the other is a variable.

How do you decide then?
@goxul-$F_2$ is exponential and $F_3$ is polynomial. Exponential grow faster than polynomial

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