1
    T(n) =  (n!n+n^3)(n^2+7logn)

How to find the expression (constant) that bounds n!n^3 ?

Simon Leung
  • 25
  • 4
  • 1
    Please clarify your question. It is not at all clear to me what you are asking. There are (infinitely) many expressions (functions) that bound the expression (function) `n!n^3`. That is a trivial statement. But none of them is constant in `n`. – walnut Feb 19 '20 at 16:25
  • Are you perhaps asking for an upper bound not involving factorial (!)? Perhaps involving just polynomial and exponential and logarithmic functions? – Patrick87 Feb 19 '20 at 18:28
  • T(n) <= c(gn) We have g(n) = O(n!n^3). How to find c in my case ? – Simon Leung Feb 19 '20 at 23:48
  • since T(n) <= n!n^3 + n!n^3 + n!n^3 + n!n^3. Hence O(n!n^3) and constant will be 4, correct ? – Simon Leung Feb 20 '20 at 00:08
  • @SimonLeung That is correct. Didn't you ask this same question already and get this answer there? – Patrick87 Feb 20 '20 at 13:36

1 Answers1

0

n! is O(n^n) so if

T(n) = (n!n+n^3)(n^2+7logn)

then T(n) is O(n^(n+3))

jwezorek
  • 3,125
  • 1
  • 19
  • 30