How to find the position of a word in a jumbled sentence?

Question

I have an initial sentence:

The quick brown fox jumps over the lazy dog.

I have a new sentence (which is always a jumble of the original sentence):

The lazy dog jumps over the quick brown fox.

In the original sentence, for each word, I want to superscript the word position as according to the jumbled sentence. Can someone guide me as to how I can achieve this?

Any novel approach (using new packages) is appreciated. Thanks in advance. In the following MWE, I am obviously not achieving what I actually want.

\documentclass[12pt]{memoir}
\usepackage{listofitems}
\usepackage{amsmath}

\newcommand{\wordsI}
{   1. The,
    2. quick,
    3. brown,       
    4. fox      
    +
    5. jumps,
    6. over,
    7. the,
    8. lazy,
    9. dog
}

\newcommand{\wordsII}
{   The
    lazy
    dog         
    jumps
    over
    the
    quick
    brown
    fox
}

% Tokenize the words in order to display them
\newcommand{\tokenize}[1]
{%
    \setsepchar{+/,/./}
    \readlist*\textarray{#1}
    \foreachitem\groupoflines\in\textarray
    {
        \setsepchar{,}
        \readlist*\linearray{\groupoflines} 
        \foreachitem\line\in\linearray
        {  
            \setsepchar{.}
            \readlist*\wordarray{\line}
            $ \text{\wordarray[2]} ^ {\wordarray[1]} $
        }%
        \newline
    }
}

\begin{document}
\noindent
Actual sentence:
\newline
% The splitting of the sentence in 2 lines is intentional
\tokenize{\wordsI}

\noindent
Jumbled sentence:
\textbf{\wordsII}   
\end{document}

In this example, I will get the result I need if I have the following definition instead:

\newcommand{\wordsI}
{   1. The,
    7. quick,
    8. brown,       
    9. fox      
    +
    4. jumps,
    5. over,
    6. the,
    2. lazy,
    3. dog
}

But, I don't want to make the change manually. I am looking for a way to make it 'dynamic' based on the jumbled sentence.

EDIT: I want to achieve this even in scenarios like this:

Initial sentence:

the quick brown fox jumps over the lazy dog.

Jumbled sentence:

the lazy dog jumps over the quick brown fox.

In this case, I need to have some kind of 'tags' for the words in the initial sentence in order for the jumbled sentence to be non-ambiguous.

\newcommand{\wordsI}
{   1. the,
    2. quick,
    3. brown,       
    4. fox      
    +
    5. jumps,
    6. over,
    7. the,
    8. lazy,
    9. dog
}

\newcommand{\wordsII}
{   7. the
    8. lazy
    9. dog         
    5. jumps
    6. over
    1. the
    2. quick
    3. brown
    4. fox
}

Desired output:

Answer 1

Something like this?

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn

\seq_new:N \l_jsp_sentence_temp_seq
\seq_new:N \l_jsp_sentence_original_seq
\seq_new:N \l_jsp_sentence_jumbled_seq
\prop_new:N \l_jsp_sentence_original_ind_prop
\prop_new:N \l_jsp_sentence_jumbled_ind_prop
\int_new:N \l_jsp_sentence_word_int

\NewDocumentCommand{\parseoriginalsentence}{m}
 {
  \seq_set_split:Nnn \l_jsp_sentence_temp_seq { + } { #1 }
  \seq_clear:N \l_jsp_sentence_original_seq
  \prop_clear:N \l_jsp_sentence_original_ind_prop
  \seq_map_inline:Nn \l_jsp_sentence_temp_seq
   {
    \int_zero:N \l_jsp_sentence_word_int
    \clist_map_inline:nn { ##1 }
     {
      \int_incr:N \l_jsp_sentence_word_int
      \seq_put_right:Nn \l_jsp_sentence_original_seq { ####1 }
      \prop_put:Nnx \l_jsp_sentence_original_ind_prop
       { ####1 } { \int_to_arabic:n { \l_jsp_sentence_word_int } }
     }
    \seq_put_right:Nn \l_jsp_sentence_original_seq { + }
   }
 }
\NewDocumentCommand{\parsejumbledsentence}{m}
 {
  \prop_clear:N \l_jsp_sentence_jumbled_ind_prop
  \seq_set_split:Nnn \l_jsp_sentence_jumbled_seq { , } { #1 }
  \int_zero:N \l_jsp_sentence_word_int
  \seq_map_inline:Nn \l_jsp_sentence_jumbled_seq
   {
    \int_incr:N \l_jsp_sentence_word_int
    \prop_put:Nnx \l_jsp_sentence_jumbled_ind_prop
     { ##1 } { \int_to_arabic:n { \l_jsp_sentence_word_int } }
   }
 }

\NewDocumentCommand{\printoriginalsentence}{s}
 {
  \IfBooleanTF{#1}
   {
    \jsp_sentence_print_from_original:
   }
   {
    \jsp_sentence_print_from_jumbled:
   }
 }

\cs_new_protected:Nn \jsp_sentence_print_from_original:
 {
  \seq_map_inline:Nn \l_jsp_sentence_original_seq
   {
    \tl_if_eq:nnTF { ##1 } { + }
     {
      \par
     }
     {
      \prop_item:Nn \l_jsp_sentence_original_ind_prop { ##1 }.\nobreakspace ##1 ~
     }
   }
 }

\cs_new_protected:Nn \jsp_sentence_print_from_jumbled:
 {
  \seq_map_inline:Nn \l_jsp_sentence_original_seq
   {
    \tl_if_eq:nnTF { ##1 } { + }
     {
      \par
     }
     {
      \prop_item:Nn \l_jsp_sentence_jumbled_ind_prop { ##1 }.\nobreakspace ##1 ~
     }
   }
 }
\ExplSyntaxOff

\begin{document}

\parseoriginalsentence{
  The,
  quick,
  brown,
  fox
  +
  jumps,
  over,
  the,
  lazy,
  dog
}
\parsejumbledsentence{
  The,
  lazy,
  dog,
  jumps,
  over,
  the,
  quick,
  brown,
  fox
}

\printoriginalsentence*

\bigskip

\printoriginalsentence

\end{document}

Answer 2

IMO the most interesting thing about TeX is its typesetting and the worst thing is its programming facility, so it's best to do such programming outside of TeX (as far away as possible!), and use TeX solely for typesetting. Everything may be possible with TeX but it won't necessarily be the easiest / most maintainable solution.

Still, if using TeX, this sort of programming is easier to do with LuaTeX (at least for me, and I imagine for most people). Compile the following file with lualatex (I've let your “tags” be optional: you can tag every word like the(1) quick(2) ..., or tag only the duplicate words):

\documentclass[12pt]{memoir}
\usepackage{amsmath} % For \text

\newcommand{\printword}[2]{$\text{#1} ^ {#2}$\quad} % Or whatever formatting you like.
\newcommand{\linesep}{\newline}

\directlua{dofile('jumble.lua')}
\newcommand{\printjumble}[2]{
  \directlua{get_sentence1_lines()}{#1}
  \directlua{get_sentence2_words()}{#2}
  %
  \noindent
  Actual sentence:
  \newline
  \directlua{print_sentence1_lines()}

  \noindent
  Jumbled sentence:
  \textbf{\directlua{print_sentence2()}}
}

\begin{document}
\printjumble{
  the(1) quick brown fox
  +
  jumps over the(7) lazy dog
}{
  the(7) lazy dog jumps over the(1) quick brown fox
}
\end{document}

where jumble.lua (which could be inlined into the same .tex file, but I prefer to keep separate) is the following:

-- Expected from TeX: before calling print_sentence1_lines(),
--     call get_sentence1_lines() and get_sentence2_words()
--     define \printword and \linesep.
-- Globals: sentence2_words, position_for_word, sentence1_lines

function get_sentence1_lines()
   sentence1_lines = token.scan_string()
end

function get_sentence2_words()
   local sentence2 = token.scan_string()
   sentence2_words = {}
   position_for_word = {}
   local i = 0
   for word in string.gmatch(sentence2, "%S+") do
      i = i + 1
      assert(position_for_word[word] == nil, string.format('Duplicate word: %s', word))
      sentence2_words[i] = without_tags(word)
      position_for_word[word] = i
   end
end

function print_sentence2()
   for i, word in ipairs(sentence2_words) do
      tex.print(word)
   end
end

function print_sentence1_lines()
   for line in string.gmatch(sentence1_lines, "[^+]+") do
      for word in string.gmatch(line, "%S+") do
         position = position_for_word[word]
         assert(position_for_word[word] ~= nil, string.format('New word: %s', word))
         tex.print(string.format([[\printword{%s}{%s}]], without_tags(word), position))
      end
      tex.print([[\linesep]])
   end
end

function without_tags(word)
   local new_word = string.gsub(word, "%(.*%)", "")
   return new_word
end

This produces

as in the question.

Note that you can make this a bit shorter (e.g. see the first revision of this answer) by moving things around, but I find it cleanest to keep (as much as possible) the typesetting instructions in the .tex file and and the programming in the .lua file.