0

I have a recurrence relation of the form $T(n) = 2T(n/2)+O(1)$

I'm not sure how to deal with the big $O$-notation in the problem in order to start solving it ? Any help would be appreciated.

John L.
  • 38,985
  • 4
  • 33
  • 90
Adam Carroll
  • 1

1 Answers1

0

Hint: can you solve it for $n = 2^k$ where we replace $O(1)$ with constant $c$ and let $f(1) = c$? Then you have:

$$f(2^k) = 2f(2^{k-1}) + c$$

Then the pattern starts $f(1) = c$, $f(2) = 3c$, $f(4) = 7c$, $f(8) = 15c$... any guesses?

orlp
  • 13,386
  • 1
  • 24
  • 40