Count the number of elements of each size in a list

Question

Comment: The following question is somewhat similar to "Position of largest element in a list" but I'm (unfortunately) not familiar what LaTeX 3 programming so I'm forced to ask. :(

Code: Consider the following example:

\documentclass{beamer}

\usepackage[danish]{babel}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{booktabs}
\usepackage{siunitx}

\begin{document}

\def\elevA{6}
\def\elevB{0}
\def\elevC{0}
\def\elevD{3}
\def\elevE{0}
\def\elevF{2}
\def\elevG{1}
\def\elevH{1}
\def\elevI{1}
\def\elevJ{5}
\def\elevK{0}
\def\elevL{3}
\def\elevM{7}
\def\elevN{3}
\def\elevO{1}
\def\elevP{1}
\def\elevQ{0}
\def\elevR{0}
\def\elevS{0}
\def\elevT{2}
\def\elevU{1}
\def\elevV{2}
\def\elevW{0}
\def\elevX{2}
\def\elevY{1}
\def\elevZ{1}
\def\elevAa{4}
\def\elevAb{6}
\def\elevAc{1}
\def\elevAd{1}
\def\elevAe{6}
\def\elevAf{2}
\def\elevAg{0}
\def\elevAh{3}
\def\elevAi{2}
\def\elevAj{1}
\def\elevAk{0}
\def\elevAl{0}
\def\elevAm{0}
\def\elevAn{0}
\def\elevAo{0}
\def\elevAp{4}

\begin{frame}

\begin{table}
\centering
\small
  \begin{tabular}{*{14}{c}}
   \toprule
    \elevA  & \elevB  & \elevC  & \elevD  & \elevE  & \elevF  & \elevG  &
    \elevH  & \elevI  & \elevJ  & \elevK  & \elevL  & \elevM  & \elevN    \\[0.5ex]
    \elevO  & \elevP  & \elevQ  & \elevR  & \elevS  & \elevT  & \elevU  &
    \elevV  & \elevW  & \elevX  & \elevY  & \elevZ  & \elevAa & \elevAb   \\[0.5ex]
    \elevAc & \elevAd & \elevAe & \elevAf & \elevAg & \elevAh & \elevAi &
    \elevAj & \elevAk & \elevAl & \elevAm & \elevAn & \elevAo & \elevAp   \\
   \bottomrule
  \end{tabular}
\end{table}
\end{frame}

\end{document}

Output:

Question: How do I make LaTeX count the number of entries with each value (here it's 0, 1, ..., 7)? What I mean is, how many times in the list does a 0 occur, how many times in the list does a 1 occur and so forth.

If a macro like \HowMany can be created and then use, say, \HowMany{0} with the reture value 14, it will be really nice!

Notes:

• It doesn't have to be a LaTeX 3 solution, but I need to compile the original document (i.e., the one I need the solution for) via latex --> dvips --> ps2pdf.
• The input numbers are via the \def method.
• I can find the minimum value (here it's 0) and maximum value (here it's 7) myself but if LaTeX can do it, it will (of course) be preferable.

Answer 1

A more complicated approach, showing how giving more structure to your macros can give less problems.

Instead of several \elevXY macros, I define just one that takes the letters as argument. The corresponding values are stored in a property list.

The standard behavior of \elev is to print the corresponding number (in this incarnation it is fully expandable). However, after the \countappearances declaration, besides printing the number it will update another property list storing the number of appearances until then. This property list is initialized to store 0 for each number. The declaration is local, so its effects will vanish as soon as the table (or frame environment, if table is not used) ends.

Finally, \HowMany accesses the property corresponding to the number. The values are stored in the counting property list in a global fashion, so they'll be accessible until the next \countappearances declaration.

\documentclass{beamer}

\usepackage[danish]{babel}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{booktabs}
\usepackage{siunitx}
\usepackage{xparse}

\ExplSyntaxOn
\prop_new:N \g_svend_elev_prop
\prop_gput:Nnn \g_svend_elev_prop {A} {6}
\prop_gput:Nnn \g_svend_elev_prop {B} {0}
\prop_gput:Nnn \g_svend_elev_prop {C} {0}
\prop_gput:Nnn \g_svend_elev_prop {D} {3}
\prop_gput:Nnn \g_svend_elev_prop {E} {0}
\prop_gput:Nnn \g_svend_elev_prop {F} {2}
\prop_gput:Nnn \g_svend_elev_prop {G} {1}
\prop_gput:Nnn \g_svend_elev_prop {H} {1}
\prop_gput:Nnn \g_svend_elev_prop {I} {1}
\prop_gput:Nnn \g_svend_elev_prop {J} {5}
\prop_gput:Nnn \g_svend_elev_prop {K} {0}
\prop_gput:Nnn \g_svend_elev_prop {L} {3}
\prop_gput:Nnn \g_svend_elev_prop {M} {7}
\prop_gput:Nnn \g_svend_elev_prop {N} {3}
\prop_gput:Nnn \g_svend_elev_prop {O} {1}
\prop_gput:Nnn \g_svend_elev_prop {P} {1}
\prop_gput:Nnn \g_svend_elev_prop {Q} {0}
\prop_gput:Nnn \g_svend_elev_prop {R} {0}
\prop_gput:Nnn \g_svend_elev_prop {S} {0}
\prop_gput:Nnn \g_svend_elev_prop {T} {2}
\prop_gput:Nnn \g_svend_elev_prop {U} {1}
\prop_gput:Nnn \g_svend_elev_prop {V} {2}
\prop_gput:Nnn \g_svend_elev_prop {W} {0}
\prop_gput:Nnn \g_svend_elev_prop {X} {2}
\prop_gput:Nnn \g_svend_elev_prop {Y} {1}
\prop_gput:Nnn \g_svend_elev_prop {Z} {1}
\prop_gput:Nnn \g_svend_elev_prop {Aa} {4}
\prop_gput:Nnn \g_svend_elev_prop {Ab} {6}
\prop_gput:Nnn \g_svend_elev_prop {Ac} {1}
\prop_gput:Nnn \g_svend_elev_prop {Ad} {1}
\prop_gput:Nnn \g_svend_elev_prop {Ae} {6}
\prop_gput:Nnn \g_svend_elev_prop {Af} {2}
\prop_gput:Nnn \g_svend_elev_prop {Ag} {0}
\prop_gput:Nnn \g_svend_elev_prop {Ah} {3}
\prop_gput:Nnn \g_svend_elev_prop {Ai} {2}
\prop_gput:Nnn \g_svend_elev_prop {Aj} {1}
\prop_gput:Nnn \g_svend_elev_prop {Ak} {0}
\prop_gput:Nnn \g_svend_elev_prop {Al} {0}
\prop_gput:Nnn \g_svend_elev_prop {Am} {0}
\prop_gput:Nnn \g_svend_elev_prop {An} {0}
\prop_gput:Nnn \g_svend_elev_prop {Ao} {0}
\prop_gput:Nnn \g_svend_elev_prop {Ap} {4}

\prop_new:N \g_svend_count_prop
\prop_new:N \g_svend_count_zero_prop
\prop_gput:Nnn \g_svend_count_zero_prop { 0 } { 0 }
\prop_gput:Nnn \g_svend_count_zero_prop { 1 } { 0 }
\prop_gput:Nnn \g_svend_count_zero_prop { 2 } { 0 }
\prop_gput:Nnn \g_svend_count_zero_prop { 3 } { 0 }
\prop_gput:Nnn \g_svend_count_zero_prop { 4 } { 0 }
\prop_gput:Nnn \g_svend_count_zero_prop { 5 } { 0 }
\prop_gput:Nnn \g_svend_count_zero_prop { 6 } { 0 }
\prop_gput:Nnn \g_svend_count_zero_prop { 7 } { 0 }
\prop_gset_eq:NN \g_svend_count_prop \g_svend_count_zero_prop

\tl_new:N \l_svend_number_tl
\tl_new:N \l_svend_count_tl

\DeclareExpandableDocumentCommand{\elev}{m}
 {
  \svend_get_item:n { #1 }
 }

\NewDocumentCommand{\countappearances}{}
 {
  % now \elev will also count
  \cs_set_eq:NN \elev \svend_get_item_count:n
  % reinitialize the counter property list
  \prop_set_eq:NN \g_svend_count_prop \g_svend_count_zero_prop
 }

\DeclareExpandableDocumentCommand{\HowMany}{m}
 {
  \prop_item:Nn \g_svend_count_prop { #1 }
 }

\cs_new:Npn \svend_get_item:n #1
 {
  \prop_item:Nn \g_svend_elev_prop { #1 }
 }

\cs_new_protected:Npn \svend_get_item_count:n #1
 {
  \tl_set:Nx \l_svend_number_tl { \svend_get_item:n { #1 } }
  % print the entry
  \tl_use:N \l_svend_number_tl
  % get the current count
  \tl_set:Nx \l_svend_count_tl
   {
    \prop_item:NV \g_svend_count_prop \l_svend_number_tl
   }
  % advance the count by 1
  \tl_set:Nx \l_svend_count_tl { \int_to_arabic:n { \l_svend_count_tl + 1 } }
  % update the property
  \prop_gput:NVV \g_svend_count_prop \l_svend_number_tl \l_svend_count_tl
 }

\cs_generate_variant:Nn \prop_item:Nn { NV }
\cs_generate_variant:Nn \prop_gput:Nnn { NVV }

\ExplSyntaxOff

\begin{document}

\begin{frame}

\begin{table}
\centering
\small
\countappearances

\begin{tabular}{*{14}{c}}
\toprule
\elev{A}  & \elev{B}  & \elev{C}  & \elev{D}  & \elev{E}  & \elev{F}  & \elev{G}  &
\elev{H}  & \elev{I}  & \elev{J}  & \elev{K}  & \elev{L}  & \elev{M}  & \elev{N}    \\[0.5ex]
\elev{O}  & \elev{P}  & \elev{Q}  & \elev{R}  & \elev{S}  & \elev{T}  & \elev{U}  &
\elev{V}  & \elev{W}  & \elev{X}  & \elev{Y}  & \elev{Z}  & \elev{Aa} & \elev{Ab}   \\[0.5ex]
\elev{Ac} & \elev{Ad} & \elev{Ae} & \elev{Af} & \elev{Ag} & \elev{Ah} & \elev{Ai} &
\elev{Aj} & \elev{Ak} & \elev{Al} & \elev{Am} & \elev{An} & \elev{Ao} & \elev{Ap}   \\
\bottomrule
\end{tabular}

\bigskip

\begin{tabular}{*{8}{c}}
\toprule
\multicolumn{8}{c}{How many} \\
\midrule
0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\HowMany{0} &
\HowMany{1} &
\HowMany{2} &
\HowMany{3} &
\HowMany{4} &
\HowMany{5} &
\HowMany{6} &
\HowMany{7} \\
\bottomrule
\end{tabular}

\end{table}
\end{frame}

\end{document}

Answer 2

\documentclass{beamer}

\usepackage[danish]{babel}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{booktabs}
\usepackage{siunitx}
\usepackage{array}

\def\zz\ignorespaces#1{%
\expandafter\xdef\csname zz#1\endcsname{%
\expandafter\ifx\csname zz#1\endcsname\relax
1%
\else
\the\numexpr\csname zz#1\endcsname+1\relax
\fi}%
#1}

\begin{document}

\def\elevA{6}
\def\elevB{0}
\def\elevC{0}
\def\elevD{3}
\def\elevE{0}
\def\elevF{2}
\def\elevG{1}
\def\elevH{1}
\def\elevI{1}
\def\elevJ{5}
\def\elevK{0}
\def\elevL{3}
\def\elevM{7}
\def\elevN{3}
\def\elevO{1}
\def\elevP{1}
\def\elevQ{0}
\def\elevR{0}
\def\elevS{0}
\def\elevT{2}
\def\elevU{1}
\def\elevV{2}
\def\elevW{0}
\def\elevX{2}
\def\elevY{1}
\def\elevZ{1}
\def\elevAa{4}
\def\elevAb{6}
\def\elevAc{1}
\def\elevAd{1}
\def\elevAe{6}
\def\elevAf{2}
\def\elevAg{0}
\def\elevAh{3}
\def\elevAi{2}
\def\elevAj{1}
\def\elevAk{0}
\def\elevAl{0}
\def\elevAm{0}
\def\elevAn{0}
\def\elevAo{0}
\def\elevAp{4}

\begin{frame}

\begin{table}
\centering
\small
  \begin{tabular}{
    *{14}{>\zz c}
  }
   \toprule
    \elevA  & \elevB  & \elevC  & \elevD  & \elevE  & \elevF  & \elevG  &
    \elevH  & \elevI  & \elevJ  & \elevK  & \elevL  & \elevM  & \elevN    \\[0.5ex]
    \elevO  & \elevP  & \elevQ  & \elevR  & \elevS  & \elevT  & \elevU  &
    \elevV  & \elevW  & \elevX  & \elevY  & \elevZ  & \elevAa & \elevAb   \\[0.5ex]
    \elevAc & \elevAd & \elevAe & \elevAf & \elevAg & \elevAh & \elevAi &
    \elevAj & \elevAk & \elevAl & \elevAm & \elevAn & \elevAo & \elevAp   \\
   \bottomrule
  \end{tabular}
\end{table}

{\count0=0
\loop
\the\count0:\csname zz\the\count0\endcsname\endgraf
\ifnum\count0<8
\advance\count0 1
\repeat
}
\end{frame}



\end{document}