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Little_Mouse

Time Complexity Guide

Feb 13th, 2022 (edited)
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  1. \documentclass{article}
  2. \usepackage{array}
  3. \begin{document}
  4. \begin{center}
  5. \begin{tabular}{ | m{5em} | m{5cm}| }
  6.  \hline
  7.   $n \leq 10$ & $\mathcal{O}(n!)$\\
  8.  \hline
  9.   $n \leq 20$ & $\mathcal{O}(2^{n})$\\
  10.  \hline
  11.   $n \leq 50$ & $\mathcal{O}(n^{5})$\\
  12.  \hline
  13.   $n \leq 100$ & $\mathcal{O}(n^{4})$\\
  14.  \hline
  15.   $n \leq 500$ & $\mathcal{O}(n^{3})$\\
  16.  \hline
  17.   $n \leq 3000$ & $\mathcal{O}(n^{2}\cdot \log{n})$\\
  18.  \hline
  19.   $n \leq 5000$ & $\mathcal{O}(n^{2})$\\
  20.  \hline
  21.   $n \leq 10^{5}$ & $\mathcal{O}(n\cdot \log{n}) \sim \mathcal{O}(n\cdot \sqrt{n})$\\
  22.  \hline
  23.   $n \leq 10^{6}$ & $\mathcal{O}(n\cdot \log{n}) \sim \mathcal{O}(n)$\\
  24.  \hline
  25.   $n \leq 10^{12}$ & $\mathcal{O}(\sqrt{n})$\\
  26.  \hline
  27.   $n \leq 10^{18}$ & $\mathcal{O}(\log{n})$\\
  28.  \hline
  29. \end{tabular}
  30. \end{center}
  31. \end{document}
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