TeX: Depth-first search

main.tex

%#!latex
%  0-2-4-6-8
% 0#########  How many moves are
% :# #  #  #  needed to go
% 2#   ## ##  from (1,1) to (7,1) ?
% :### #   #
% 4#     # #
% :#########
\makeatletter
\newcount\my@x \newcount\my@y \newcount\my@m
\def\my@untr{-1}% untraversed
\@tfor\my@p:=%
    {1,1}{3,1}{4,1}{6,1}{7,1}{1,2}{2,2}{3,2}%
    {6,2}{3,3}{5,3}{6,3}{7,3}{1,4}{2,4}{3,4}%
    {4,4}{5,4}{7,4}\do{%
  \@namedef{my@(\my@p)}{-1}}
\def\my@nameedef#1{\expandafter\edef\csname#1\endcsname}
\def\my@one@step(#1,#2)#3\relax{%
  \my@x=#1 \my@y=#2 \def\my@pos@stack{#3}%
  \my@m=\numexpr\@nameuse{my@(#1,#2)}+1\relax
  \my@add@step{1}{0}\my@add@step{0}{1}%
  \my@add@step{-1}{0}\my@add@step{0}{-1}}
\def\my@add@step#1#2{%
  \def\my@p{\the\numexpr\my@x+#1,\the\numexpr\my@y+#2}%
  \expandafter\ifx\csname my@(\my@p)\endcsname\my@untr
    \my@nameedef{my@(\my@p)}{\the\my@m}%
    \edef\my@pos@stack{(\my@p)\my@pos@stack}%
  \fi}
\@namedef{my@(1,1)}{0}
\def\my@pos@stack{(1,1)}
\@whilesw\unless\ifx\my@pos@stack\@empty\fi{%
  \expandafter\my@one@step\my@pos@stack\relax}
% Show the answer!
\typeout{***Answer=\@nameuse{my@(7,1)}}
\stop