An example of construction of a double array.

double-array-build.tex

\documentclass[t]{beamer}
\usepackage{palatino}
\usepackage{amssymb,amsmath}
\usepackage{tikz}
\usepackage{color}
\usepackage{colortbl}


\def\drawtrie{
  \begin{tikzpicture}[->,thick,vertex/.style={circle,fill=white,draw=black, text=black,minimum size=13pt}]
    \node[vertex] (0) at (0,0) {0};
    \node[vertex] (1) at (-2, -1.5) {1};
    \node[vertex] (2) at (0, -1.5)  {2};
    \node[vertex] (3) at (2, -1.5)  {3};
    \node[vertex] (4) at (-3, -3) {4};
    \node[vertex] (5) at (-1, -3)  {5};
    \node[vertex] (6) at (2, -3)  {6};

    \path (0) edge node [above left] {a} (1);
    \path (0) edge node [left] {b} (2);
    \path (0) edge node [above right] {d} (3);

    \path (1) edge node [above left] {b} (4);
    \path (1) edge node [above right] {c} (5);
    \path (3) edge node [right] {a} (6);
  \end{tikzpicture}}

\begin{document}

\begin{frame}
  \begin{center}
    \drawtrie
  \vspace{4mm}
  \begin{tabular}{c|c|c|c|c|c|c|c|c|c}
    {} & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline
    base &  &  &  &  &  &  &  &  &  \\ \hline
    check &  &  &  &  &  &  &  &  &
  \end{tabular}

  \vspace{4mm}
  'a' $\rightarrow$ 1, 'b' $\rightarrow$ 2, 'c' $\rightarrow$ 3, ...
  \end{center}
\end{frame}

\begin{frame}
  \begin{center}
    \drawtrie
  \vspace{4mm}
  \begin{tabular}{c|c|c|c|c|c|c|c|c|c}
    {} & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline
    base & \only<3->{0} &  &  &  &  &  &  &  &  \\ \hline
    check &  & \only<4->{0} & \only<5->{0} &  & \only<6->{0}  &  &  &  &
  \end{tabular}

  \vspace{4mm}
  \only<1>{{children(0) = \{1,2,3\}}}%
  \only<2,3>{n = 0, m = 1
    \begin{align*}
      base[n] &= m - k1 \\
              &= 1 - \textsf{'a'} = 1 - 1 = 0
    \end{align*}%
  }
  \only<4>{check[1] = 0}
  \only<5>{check[1-'a'+'b'] = check[1-1+2] = check[2] = 0}
  \only<6>{check[1-'a'+'d'] = check[\alert{4}] = 0}
\end{center}
\end{frame}

\begin{frame}
  \begin{center}
    \drawtrie
  \vspace{4mm}
  \begin{tabular}{c|c|c|c|c|c|c|c|c|c}
    {} & 0 & 1 & 2 & 3 & 4 & \only<1>{5}\only<2->{\cellcolor{red!30!white}5} & 6 & 7 & 8 \\ \hline
    base & 0 & \only<3>{\alert{3}}\only<4->{3} &  &  &  &  &  &  &  \\ \hline
    check &  & {0} & {0} &  & {0} & \only<4>{\alert{1}}\only<5>{1} & \only<5>{\alert{1}} &  &
  \end{tabular}

  \vspace{4mm}
  \only<1>{{children(1) = \{4,5\}}}%
  \only<2,3>{m = 5\\}%
  \only<3>{base[1] = m - 'b' = 5 - 2 = 3}
  \only<4>{check[5] = 1}
  \only<5>{check[5-'b'+'c'] = check[6] = 1}
\end{center}
\end{frame}

\begin{frame}
  \begin{center}
    \drawtrie
  \vspace{4mm}
  \begin{tabular}{c|c|c|c|c|c|c|c|c|c}
    {} & 0 & 1 & 2 & \only<1>{3}\only<2->{\cellcolor{red!30!white}3} & 4 & {5} & 6 & 7 & 8 \\ \hline
    base & 0 & 3 &  & & \only<3>{\alert{2}}\only<4>{2} &  &  &  &  \\ \hline
    check &  & 0 & 0 & \only<4>{\alert{4}} & 0 & 1 & 1 &  &
  \end{tabular}

  \vspace{4mm}
  \only<1>{children(3) = 6 (n = 4)}%
  \only<2,3>{n = 4, m = 3\\}%
  \only<3>{base[4] = m - 'b' = 3 - 1 = 2}
  \only<4>{check[3] = 4}
  % \only<5>{check[5-'b'+'c'] = check[6] = 1}
\end{center}
\end{frame}

\end{document}

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