Display Item list in sequential and random (without repetition) order

Question

There are list of exam questions (as example 1-20). This list is divided on two parts (1-10, 11-20). Examination ticket contain two questions, first from first part and second from second part. This questions have to choose randomly without repetitions. Question random choose without repetition is solved before with \pgfmathdeclarerandomlist command.

But before examination tickets will generated questions list have to displayed in sequential order. So list were defined as:

\listadd{\mIqlist}{}%
\forcsvlist{\listadd\mIqlist}{{This, is},{is},{a},{very},{long},{text},{split},{in},{many}}

\listadd{\mIIqlist}{}%
\forcsvlist{\listadd\mIIqlist}{{than},{thirty},{items},{in},{here,}{but},{he},{did},{not}}

And for random purpose:

%вопросы первого блока
\newcounter{firsttotal}
\newcounter{firstcurr}
\setcounter{firsttotal}{9} %общее кол-во вопросов должно совпадать с кол-вом вопросов в списке
\newcommand\declarefirst{
\pgfmathdeclarerandomlist{firstlist}{\mIqlist}}
\declarefirst

%вопросы второго блока
\newcounter{secondtotal}
\newcounter{secondcurr}
\setcounter{secondtotal}{9} %общее кол-во вопросов должно совпадать с кол-вом вопросов в списке
\newcommand\declaresecond{
\pgfmathdeclarerandomlist{secondlist}{\mIIqlist}}
\declaresecond

%макрос \prunelist для удаления уже выбраных из списка вопросов для избежания повторений в первой итерации
\makeatletter
\def\prunelist#1{
\expandafter\edef\csname pgfmath@randomlist@#1\endcsname
     {\the\numexpr\csname pgfmath@randomlist@#1\endcsname-1\relax}
\count@\pgfmath@randomtemp 
\loop
\expandafter\let
\csname pgfmath@randomlist@#1@\the\count@\expandafter\endcsname
\csname pgfmath@randomlist@#1@\the\numexpr\count@+1\relax\endcsname
\ifnum\count@<\csname pgfmath@randomlist@#1\endcsname\relax
\advance\count@\@ne
\repeat}
\makeatother

%печатать вопрос из первого списка (выбирается случайным образом)
\newcommand\printfirst{
\pgfmathrandomitem{\z}{firstlist}
\z
\prunelist{firstlist}
\addtocounter{firstcurr}{1}
\ifnum \value{firstcurr} = \value{firsttotal} \setcounter{firstcurr}{0}\declarefirst \fi
}

%печатать вопрос из второго списка (выбирается случайным образом)
\newcommand\printsecond{
\pgfmathrandomitem{\z}{secondlist}
\z
\prunelist{secondlist}
\addtocounter{secondcurr}{1}
\ifnum \value{secondcurr} = \value{secondtotal} \setcounter{secondcurr}{0}\declaresecond \fi
}

In document sequential list displayed as:

\begin{enumerate}[label={\arabic*.}]
\renewcommand*{\do}[1]{\item {#1}}
\dolistloop{\mIqlist}
\dolistloop{\mIIqlist}
\end{enumerate} 

And in exam ticket:

\forloop{ct}{0}{\value{ct} < \value{TotalNum}}
{
 ....
 1.\printfirst \newline\newline
 2.\printsecond \newline
 ....
}

But while compile error occurs:

! Missing $ inserted.
<inserted text> 
                $
l.101 }
       %forloop

This error occure while I try \printfirst or \printsecond. As I understand this error is associated with list separator | symbol. How can I fix it?

Answer 1

The easiest way to do arrays in LaTeX is to use \csname ...\endcsname. (You can also use the xstring package, but this is faster, albeit ugly.) The problem is that \csname has to be expanded before things like \let or \xdef, leading to lots of \expandafters. Also, \index0 is not a legal macro name and can only be implemented using \csname.

\documentclass{article}
\usepackage{tikz}

\newcommand{\mylist}{}% reserve global name

\begin{document}
\begin{tikzpicture}{overlay}% ignore spaces
\foreach \i in {0,...,5} {\expandafter\xdef\csname index\i\endcsname{\i}}% create indexes
\foreach \i in {0,...,5} {% randomise (last step redundant)
  \pgfmathparse{int(random(\i,5))}%
  \let\j=\pgfmathresult
  \expandafter\let\expandafter\tempa\csname index\i\endcsname
  \expandafter\let\expandafter\tempb\csname index\j\endcsname
  \global\expandafter\let\csname index\i\endcsname=\tempb
  \global\expandafter\let\csname index\j\endcsname=\tempa
}%
\xdef\mylist{\csname index0\endcsname}% create comma delimited list
\foreach \i in {1,...,5} {\xdef\mylist{\mylist,\csname index\i\endcsname}}%
\end{tikzpicture}

\noindent\mylist
\end{document}

Answer 2

Here is an implementation with the Knuth shuffle algorithm (https://tex.stackexchange.com/a/344488/4427)

\documentclass{article}
\usepackage[a6paper]{geometry}

\usepackage{xparse}

\ExplSyntaxOn

% user level commands

\NewDocumentCommand{\definefirstlist}{m}
 {
  \__konstantin_define_list:Nn \g_konstantin_firstlist_prop { #1 }
 }
\NewDocumentCommand{\definesecondlist}{m}
 {
  \__konstantin_define_list:Nn \g_konstantin_secondlist_prop { #1 }
 }

\NewDocumentCommand{\printlists}{ }
 {
  \section*{First~List}
  \__konstantin_print_list:N \g_konstantin_firstlist_prop
  \section*{Second~List}
  \__konstantin_print_list:N \g_konstantin_secondlist_prop
 }

\NewDocumentCommand{\maketickets}{}
 {
  % compute the number of questions
  \int_set:Nn \l__konstantin_index_int
   {
    \int_min:nn { \prop_count:N \g_konstantin_firstlist_prop }
                { \prop_count:N \g_konstantin_secondlist_prop }
   }
  % generate the identity permutation
  \int_step_inline:nnnn { 1 } { 1 } { \l__konstantin_index_int }
   {
    \prop_gput:Nnn \g_knuthshuffle_identity_prop { ##1 } { ##1 }
   }
  % generate a first permutation
  \knuthshuffle_generate:n { \l__konstantin_index_int }
  \seq_set_eq:NN \l_konstantin_firstquestion_seq \l_knuthshuffle_permutation_seq
  % generate a second permutation
  \knuthshuffle_generate:n { \l__konstantin_index_int }
  \seq_set_eq:NN \l_konstantin_secondquestion_seq \l_knuthshuffle_permutation_seq
  % print the tickets
  \int_step_inline:nnnn { 1 } { 1 } { \l__konstantin_index_int }
   {
    \konstantin_ticket:n { ##1 }
   }
 }

% variables
\int_new:N \l__konstantin_index_int
\prop_new:N \g_konstantin_firstlist_prop
\prop_new:N \g_konstantin_secondlist_prop

% internal functions
\cs_new_protected:Nn \__konstantin_define_list:Nn
 {
  \int_zero:N \l__konstantin_index_int
  \tl_map_inline:nn { #2 }
   {
    \int_incr:N \l__konstantin_index_int
    \prop_gput:Nfn #1 { \int_to_arabic:n { \l__konstantin_index_int } } { ##1 }
   }
 }
\cs_generate_variant:Nn \prop_gput:Nnn { Nf }

\cs_new_protected:Nn \__konstantin_print_list:N
 {
  \int_step_inline:nnnn { 1 } { 1 } { \prop_count:N #1 }
   {
    \noindent
    ##1.~
    \prop_item:Nn #1 { ##1 }
    \par
   }
 }

\cs_new_protected:Nn \konstantin_ticket:n
 {
  \clearpage
  \ticketheader{#1}
  \par
  \noindent\textbf{Question~1}:\\
  \prop_item:Nx \g_konstantin_firstlist_prop
   {
    \seq_item:Nn \l_konstantin_firstquestion_seq {#1}
   }
  \par
  \vspace*{\fill}
  \noindent\textbf{Question~2}:\\
  \prop_item:Nx \g_konstantin_secondlist_prop
   {
    \seq_item:Nn \l_konstantin_secondquestion_seq {#1}
   }
  \par
  \vspace*{\fill}
 }
\cs_generate_variant:Nn \prop_item:Nn { Nx }

%%% the Knuth shuffle macros https://tex.stackexchange.com/a/344488/4427

\prop_new:N \g_knuthshuffle_identity_prop
\prop_new:N \l_knuthshuffle_newperm_prop
\int_new:N \l_knuthshuffle_random_int
\seq_new:N \l_konstantin_firstquestion_seq
\seq_new:N \l_konstantin_secondquestion_seq

\cs_new:Nn \knuthshuffle_get_random:Nnn
 {
  \int_set:Nn #1 { \fp_eval:n { randint(#2,#3) } }
 }

\cs_new_protected:Nn \knuthshuffle_generate:n
 {
  \prop_set_eq:NN \l_knuthshuffle_newperm_prop \g_knuthshuffle_identity_prop
  \int_step_inline:nnnn { #1 } { -1 } { 2 }
   {
    \knuthshuffle_get_random:Nnn \l_knuthshuffle_random_int { 1 } { ##1 }
    \prop_get:NnN \l_knuthshuffle_newperm_prop { ##1 } \l_knuthshuffle_tempa_tl 
    \prop_get:NVN \l_knuthshuffle_newperm_prop \l_knuthshuffle_random_int \l_knuthshuffle_tempb_tl 
    \prop_put:NnV \l_knuthshuffle_newperm_prop { ##1 } \l_knuthshuffle_tempb_tl
    \prop_put:NVV \l_knuthshuffle_newperm_prop \l_knuthshuffle_random_int \l_knuthshuffle_tempa_tl
   }
  \seq_clear:N \l_knuthshuffle_permutation_seq
  \int_step_inline:nnnn { 1 } { 1 } { #1 }
   {
    \seq_put_right:Nx \l_knuthshuffle_permutation_seq
     {
      \prop_item:Nn \l_knuthshuffle_newperm_prop { ##1 }
     }
   }
  %\seq_show:N \l_knuthshuffle_permutation_seq % for debugging
 }


\ExplSyntaxOff

% define here the header for the question tickets
\newcommand{\ticketheader}[1]{% #1 is the ticket number
  \begin{center}
  \large\bfseries Ticket #1
  \end{center}
  \bigskip
}

% define the list of questions
\definefirstlist{
 {This, is}
 {is}
 {a}
 {very}
 {long}
 {text}
 {split}
 {in}
 {many}
}

\definesecondlist{
  {than}
  {thirty}
  {items}
  {in}
  {here}
  {but}
  {he}
  {did}
  {not}
}

\begin{document}

\printlists

\maketickets

\end{document}