# 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}