Mazdak Farrokhzad edited a) As few classrooms as possible.tex  almost 10 years ago

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T(n) &= c_0 + n\log{n} + \sum_{i=1}^{n-1} \left[ c_1 + \log{i} + \sum_{j=1}^i \Big[ c_2 \Big] \right]  + 1 \left[ c_1 + \sum_{i=1}^{n-1} \Big[ \log{i} \Big] + \log{1} \right]\\  &= c_0 + n\log{n} + \sum_{i=1}^{n-1} \left[ c_1 + \log{i} + c_2i \right]  +1  \left[ c_1 + \sum_{i=1}^{n-1} \Big[ \log{i} \Big] + \log{1} \right]\\ &= c_0 + n\log{n} + (n-1)c_1 nc_1  + \sum_{i=1}^{n-1} \left[ c_1 + \log{i} + c_2i \right] +1  \left[c_1 +  \sum_{i=1}^{n-1} \Big[ \log{i} \Big] + \log{1} \right]\\ \end{align*}  \end{subequations}