this is for holding javascript data
Mazdak Farrokhzad edited b) Algorithm.tex
almost 10 years ago
Commit id: ff7080019fc2fb5da8b34ed34c96fb94f86d2b15
deletions | additions
diff --git a/b) Algorithm.tex b/b) Algorithm.tex
index db2c949..a019db4 100644
--- a/b) Algorithm.tex
+++ b/b) Algorithm.tex
...
\begin{align*}
T_{\mathtt{min}}(m, n) &= \sum_{i=1}^{2^n}{\left[m^2(i - 1)\right]}\\
&= m^22^{n-1}\left(2^n - 1\right)\\
T_{\mathtt{max}}(m, n) &=
\sum_{i=1}^{2^{n+1}-1}{\left[\floor{\log_2((2^{m+1}-1)^{i-1})} \sum_{i=1}^{2^{n+1}-1}{\left[\floor{\log_2\big((2^{m+1}-1)^{i-1}\big)} \cdot \floor{\log_2(2^{m+1}-1)} \right]}\\
&< \sum_{i=1}^{2^{n+1}}{\left[ (m+1)^2(i-1) \right]}\\
&= (m+1)^22^{n}\left(2^{n+1} - 1\right)
\end{align*}