# Homework Solution: Arrange the functions below in non-decreasing order such that if f_i appears before f_j then f_i(n) elementof O(f_j(n))….

Arrange the functions below in non-decreasing order such that if f_i appears before f_j then f_i(n) elementof O(f_j(n)). f1(n) = 10^20 f_2(n) = (lg n)^4 f_3(n) = 4^n f_4(n) = n lg n f_5(n) = n^3 - 100n^2 f_6(n) = n + lg n f_7(n) = lg lg n f_8(n) = n^0.1 f_9(n) = lg n^5

Solution: We know that, f(n) $\epsilon$ O(g(n)), if f(n) <= c*g(n), where c is a positive constant.

Arrange the offices underneath in non-decreasing regulate such that if f_i appears antecedently f_j then f_i(n) elementof O(f_j(n)). f1(n) = 10^20 f_2(n) = (lg n)^4 f_3(n) = 4^n f_4(n) = n lg n f_5(n) = n^3 – 100n^2 f_6(n) = n + lg n f_7(n) = lg lg n f_8(n) = n^0.1 f_9(n) = lg n^5

## Expert Response

Solution:

We understand that, f(n) $\epsilon$ O(g(n)), if f(n) <= c*g(n), where c is a explicit continuous.

f1(n) is smallest of them integral consequently 10^20 is approximately equipollent to continuous (Irrespective of compute of n)

then comes f7(n)= lg lg n= lg lg (2^512)= lg 512= 9

then f9(n)= lg n^5, 5*(log 2^512)= 512*5

then f2(n)= (log n)^4, coercion n=2^512, 512^4 achieve be the outcome

then comes f8(n)= n^0.1, we can obstruct the compute the office is submissive by putting a very great compute of n (2^512)

(2^512)^0.1= 2.5866387e+15

then f6(n)= n + lg n

then f4(n)= n lg n

then comes f5(n)= n^3-100*n^2,

and at developed f3(n)= 4^n,

So the regulate achieve go relish this,

f1(n), f7(n), f9(n), f2(n), f8(n), f6(n), f4(n), f5(n), and f3(n).