Question Id : 18857 |
Context : UGC NET Computer Science Nov 2021 (Paper II)
Which of the given options provides the increasing order of asymptotic complexity of functions $f_1,\ f_2,\ f_3$ and $f_4$?
A. $f_1(n)=2^n$
B. $f_2(n)=n^{3/2}$
C. $f_3(n)=n\log n$
D. $f_4(n)=n^{\log n}$
Choose the correct answer from the options given below.
🎥 Video solution / Text Solution of this question is given below:
Compare the growth rates:
$n\log n$ grows slower than $n^{3/2}$.
So,
$f_3(n)<f_2(n)$
Now, $n^{\log n}$ grows faster than any polynomial like $n^{3/2}$.
But $2^n$ grows faster than $n^{\log n}$.
So, increasing order is:
$f_3,\ f_2,\ f_4,\ f_1$
That is:
C, B, D, A
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