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.
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$\begingroup$ Use the master theorem. $\endgroup$ – Yuval Filmus May 25 '19 at 18:56
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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?
