0

Here we have $T(1)=1$ and $$T(n)=T(n-1)+T\left(\left\lfloor\frac{n}{2}\right\rfloor\right)+n.$$ How to show its asymptotics? I suppose it's $n^{\Theta(\log n)}$, but not sure.

For the question here, there's no term $n$ in the summation, and I found it hard to reduce my question to it. Thanks a lot for your help.

Community
  • 1
Wei Zhan
  • 740
  • 1
    http://math.stackexchange.com/questions/475081/upper-bound-for-tn-tn-1-tn-2-n-with-recursion-tree – Prahlad Vaidyanathan Oct 15 '13 at 12:19
  • 1
    @Vaidyanathan Thank you. My question might be duplicated. But in your link, there's no detail for the derivation of this bound. What's the thinking process? – Wei Zhan Oct 15 '13 at 12:30
  • In 2015 the linked question also was marked as a duplicate of this question. It has four answers, but has $n/2$ instead of $\lfloor n/2\rfloor$, so I am not perfectly sure that they are suitable for this question. – Alex Ravsky May 10 '19 at 02:13

0 Answers0