Mazdak Farrokhzad edited b) Algorithm.tex  almost 10 years ago

Commit id: ff7080019fc2fb5da8b34ed34c96fb94f86d2b15

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\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*}