I've searched online for this but I only seem to find answers for a similar equation:
T(n) = T(n/3) + T(2n/3) + cn
But the one I'm trying to solve is:
T(n) = T(n/3) + T(2n/3)
Base case: We can assume
T(a) = Theta(1) for any constant
I've succeeded in proving (by induction) that
T(n) = O(n*log(n)). I thought the answer should be
Theta(n*log(n)), but I cannot prove that
T(n) = Omega(n*log(n)).
So my question is - am I correct that the answer is
O(n*log(n)), and NOT
Theta(n*log(n))? IF that's true that would really be great...
If I'm wrong I will of course explain where I'm stuck in the induction process...
P.S. If you need to, please try to explain using induction, because I haven't learned all methods for solving these problems yet.