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Proving this recurrence is $n \log n$
I need to prove that $T(n)$ is $\mathcal O(n\log n)$ with the substitution method.
$$ T(n)\leq 3\log n + n + \frac{6}{n}\sum^{2n/3}_{n/3}T(i).$$
This is my attempt: I assume $T(n) \leq c n \log n$ and …
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3
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Upper bounding this expression
I need to prove that the following expression is $\mathcal O(n \log n)$ with the substitution method: $$ T(n) \leq 3\log n + n + \frac{6}{n}\sum^{n - \frac{\log n}{3}}_{i=\frac{\log n}{3}} T(i)$$
This …