How to prove the asymptotic upper bound for $T(n) = 2T(\lfloor n/2\rfloor + 17) + n$ is $O(n \log n)$?

Asked Jun 24 '13 at 14:43

Active Jun 27 '13 at 18:45

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I met the problem

Show that the solution to $T(n) = 2T(\lfloor n/2\rfloor + 17) + n$ is $O(n \log n)$

while reading Introduction to Algorithm. It's a question about the substitution method for solving recurrences.

Should I just assume $T(n/2 + 17) \leq O((n/2 + 17) \log(n/2 + 17))$ and then prove $T(n) \leq O(n \log n)$? Is this inductive assumption enough to solve it?

edited Jun 27 '13 at 18:45

Alejandro Sazo

asked Jun 24 '13 at 14:43

Aobo Yang

3

Please check out our related reference questions and see whether you can answer yourself. – Raphael Jun 24 '13 at 18:44
2

Did you try using this inductive assumption? Let us know if it works. – Yuval Filmus Jun 24 '13 at 22:21

How to prove the asymptotic upper bound for $T(n) = 2T(\lfloor n/2\rfloor + 17) + n$ is $O(n \log n)$?

0 Answers0