Proof of the base case of Big Theta using induction

Asked Oct 21 '14 at 00:00

Active Oct 21 '14 at 04:21

Viewed 36 times

Here is a recursive definition for the runtime of some unspecified function. a and c are positive constants.

$T(n)=a$, if $n=2$

$T(n)=2T(n/2)+cn$ if $n>2$

Use induction to prove that $T(n)=\theta(n\log(n))$

How should I do my base case? It is not a number, so how do I find my n0?

edited Oct 21 '14 at 04:21

InformedA

asked Oct 21 '14 at 00:00

Carol Doner

Try to spend more time on it yourself. We are not going to spell out the answer for you. – Yuval Filmus Oct 21 '14 at 01:09
@YuvalFilmus You already answered the question anyway. – G. Bach Oct 21 '14 at 01:13
@G.Bach Not this aspect, though. – Yuval Filmus Oct 21 '14 at 01:14

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