this is for holding javascript data
Mazdak Farrokhzad added stuff.tex
about 10 years ago
Commit id: 1961088bd75b4a6fc852c270c76643ce6b4dbc73
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Given that:
\[T(2^n) = n(5 * 2^(2(n-1)))\]
Then:
\begin{equation}
\begin{split}
T(2^(n+1)) = 5 * B(2^n) + (2^2) T(2^n) = 5 * 2^(2n) + (2^2)(n(5 * 2^(2(n-1)))) = 5 * 2^(2n) + n(5 * 2^(2 + 2(n-1))) = 5 * 2^(2n) + n(5 * 2^(2n)) = (n + 1)(5 * 2^(2n))
T(n) = (log n)(5 * 2^(2(log(n) - 1))) = (log n)(5 * 2^(2(log(n) - 1))) = (log n)(5 * 2^(2 log(n) - 2))) = (log n)(5 * 2^(2 log(n)) * 2^(-2)) = (log n)(5 * (2^log(n))^2 * 2^(-2)) = (log n)(n^2/2^2)
T(n) = O(n^2 log n)
\end{split}
\end{equation}
