enumerate items and table side by side

Question

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.

Answer 1

This uses a new column type called E (like enumerate) and a counter called rowcounter which increases in each row, the first row is omitted here. The table column is left aligned, but r - type might be better!

Please note that this will fail after 26 rows of course since the \alph output cannot handle counter values larger than 26. The \alphalph command from alphalph package could be useful then.

Please fill in in the math content yourself.

\documentclass{article}

\usepackage{array}

\newcounter{rowcounter}
\newcolumntype{E}{>{\bfseries \ifnum\value{rowcounter} > 0 \alph{rowcounter}.\fi\stepcounter{rowcounter}}l}
\begin{document}

\begin{tabular}{E*{7}{c}}
  & A & B & C & D & E & F & G\tabularnewline
  & \tabularnewline
  & \tabularnewline
  & \tabularnewline
  & \tabularnewline
\end{tabular}



\end{document}

Update

\documentclass{article}

\usepackage{array}
\usepackage{showframe}
\usepackage{enumitem}
\usepackage{amsmath}

\newcounter{rowcounter}
\newcolumntype{D}{>{\ifnum\value{rowcounter} > 0 \text{\textbf{\textit{\alph{rowcounter}}}.}\fi\stepcounter{rowcounter}}r}
\newcolumntype{C}[1]{>{\centering\arraybackslash$}p{#1}<{$}}
\newcolumntype{L}[1]{>{\raggedright\arraybackslash$}p{#1}<{$}}


\newlength{\enumindent}
\setlength{\enumindent}{\leftmargin}
\addtolength{\enumindent}{1.7\tabcolsep}



\begin{document}
$
\begin{array}{DC{3em}*{6}{C{3em}|}}
   & A & B & O & o & \Omega & \omega & \Theta \\ \hline
 & {\lg^k{n}} & n^{\epsilon} &  &  &  &  &  \\ \hline
 & n^k & c^n &  &  &  &  &  \\ \hline
 & \sqrt{n} & n^{\sin{n}} &  &  &  &  &  \\ \hline
\end{array}
$

\begin{enumerate}[label=\textbf{\textit{\alph*}}.,leftmargin=\enumindent]
\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}