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Considering the runtime analysis (with the master theorem) of the function below

$T(n) = 12T(\frac{n}{4}) + 2\sqrt{n} + \log^4(n)$.

As I could not figure out a way to get the equation in the form $T(n)=aT(\frac{n}{b}) + \theta(n^d)$, I aimed to get the equation in the form of $T(n)=aT(\frac{n}{b})+\theta(n^k\log^pn)$ as listed here.

My idea is to drop the $2\sqrt{n}$ term (as $\forall n>\approx 2.5: \log^4(n)>2\sqrt{n}$), and then give the final runtime analysis in big O notation as opposed to $\theta$ notation. Is this a valid solution?

Note: this is similar to a problem in a homework assignment I am doing, but I have changed things in the equation as I am solely posting to help my understanding and not to cheat.

Glorfindel
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Mini
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1 Answers1

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I suspect you have missed that $\sqrt{n} = n^{1/2}$.

D.W.
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