Asymptotic Question

Asked Apr 16 '19 at 12:09

Active Apr 16 '19 at 12:09

Viewed 22 times

Hi how do I find the asymptotic bound for the recurrence T(n) = T(n/2) + T(n/4) + T(n/8) + n?

Can I use master theorem or Substitution method only? If so, I need some help for substitution method. My attempt is as below:

Sub T(n/2) into T(n/2) + j(n) = T(n/(2^2) + j(n/2) T(n) = T(n/(2^2) + j(n/2) + j(n)

Sub T(n/2^2) into T(n/2) + j(n) = T(n/(2^3) + j(n/2^3) T(n) = T(n/(2^3) + j(n/2^3) + j(n) = T(n/2^i) + (n/2^k)

ok then I'm not sure what to do from here...

asked Apr 16 '19 at 12:09

spidermarn

1

Use the Akra-Bazzi theorem. You can also prove that $T(n)=O(n)$ by induction. – Yuval Filmus Apr 16 '19 at 13:04
The master theorem only applies to recurrences of the form $T(n)=aT(n/b)+f(n)$, which is not what you have here. – David Richerby Apr 16 '19 at 14:34
See here. – ryan Apr 16 '19 at 22:39

0 Answers0