Question

Arrange the following functions in ascending order of growth rate. That is, if function g(n) immediately follows function f(n) in your list, then it should be the case that f(n) -O(gln) fl (n) = n/i f2 (n)- 3" fs (n)-nIg(n') JA (n)- ()+54 More specifically, match the functions f? through fe to the corresponding positions a through f to illustrate the correct asymptotic order: I Choose ] I Choose ] Choose ] Choose ] I Choose ] I Choose ]

Answer 1

f1 = n³n^1/2

and f6 =n³

both are of O(n³) order but f1 have some extra multiplying factor so relation between these will be f6<f1

f2 = 3ⁿ that is exponential function and it is most costly ever so it is largenst among all.

f3 = n + lg ( n³ ) it can be solved like n + 3 * lg(n) and if there exist n already in expression then it will be order of n without any second thought so here O(n)

f4 = (1/3)ⁿ + 54 it is almost comutatble and it is order of O(1) i.e. the lowest costly in given set.

f5 = n lg n that is itself cost without any second step solution and it is O(n log n and) more than O(n)

so by these all analysis we found that

O(1) < O (n) < O(n lg n) < O( n³ ) < O( n³n^1/2 ) < O ( 3ⁿ)

and in term of function

f4 < f3 < f5 < f6 < f1 < f2

so

a	f4
b	f3
c	f5
d	f6
e	f1
f	f2

Hope this helps!

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