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There's a part in the solution that I can't understand, I think it's just something basic that I'm missing. In the solution it says:

$$T(k) \leq 2(c(k/2)^2 \log(k/2)) + k^2$$

Then it became

$$T(k) \leq ( ck^2 \log(k/2) ) / 2 + k^2$$

P.S: I forgot how to do StackExchange latex again, I am so sorry.

Inquest
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Gannicus
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  • For future reference: http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – Inquest Jul 10 '13 at 21:04

1 Answers1

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\begin{align} T(k) &\leq 2(c(k/2)^2 \log(k/2)) + k^2\\ &= 2(c(k^2/4) \log(k/2)) + k^2\\ &= (c(k^2/2) \log(k/2)) + k^2\\ &= (ck^2 \log(k/2))/2 + k^2\\ \end{align}

Inquest
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  • Brilliant. This is the part of Math I suck the most.. I didn't see that square coming. Thanks, very much appreciated. :) – Gannicus Jul 11 '13 at 01:09