How to make enumerate items and a table side by side like the effect in the image which is from CLRS P.61.
I have tried to make every row a table in each enumerate item, but the effect is not the same as what I expect.
And manually adding a. b. c. in the first column of a table could not solve the problem either because it will make the indentation wrong. Here is a MWE to show the wrong indentation.
\documentclass{article}
\usepackage{array}
\usepackage{showframe}
\usepackage{enumitem}
\usepackage{amsmath}
\newcolumntype{C}[1]{>{\centering\arraybackslash$}p{#1}<{$}}
\newcolumntype{L}[1]{>{\raggedright\arraybackslash$}p{#1}<{$}}
\begin{document}
$\begin{array}{L{1em}C{3em}*{6}{C{3em}|}}
& A & B & O & o & \Omega & \omega & \Theta \\ \hline
a. & {\lg^k{n}} & n^{\epsilon} & & & & & \\ \hline
b. & n^k & c^n & & & & & \\ \hline
c. & \sqrt{n} & n^{\sin{n}} & & & & & \\ \hline
\end{array}$
\begin{enumerate}[label=\textbf{\textit{\alph*}}.]
\item $\displaystyle\lim_{n \to \infty} (1+\frac{1}{n})^n = e$
\item $\displaystyle\lim_{n \to \infty} (1+\frac{1}{n})^n = e$
\item $\displaystyle\lim_{n \to \infty} (1+\frac{1}{n})^n = e$
\end{enumerate}
\end{document}
In the image above ,the first red line could not be horizontally aligned with the second red line.