How to make a recursive macro in (La)TeX?

Question

The following MWE is the code of my attempt translating my working algorithm in C# to (La)TeX. I don't understand why it does not work. Can you probe the source of problem?

Remarks:

#1 is a list of binary elements. Either character 1 (move upward) or 0 (move to the right) will be appended to this list recursively. In the beginning it is an empty list.
#2 represents the remaining number of movements to the right.
#3 represents the remaining number of movements upward.

\documentclass{article}
\usepackage{ifthen,pgf}

\parindent=0pt

\newcommand{\Populate}[3]%
{%
        \ifthenelse{#2=0}% on the most left border?
        {% 
                \ifthenelse{#3=0}% on the most top border?
                {% 
                        #1\endgraf% I need to trim the most left comma later!
                }%
                {% 
                        % move upward
                        \pgfmathtruncatemacro{\ups}{#3-1}%
                        \Populate{#1,1}{#2}{\ups}%
                }%  
        }%      
        {% 
                \ifthenelse{#2=#3}% on the diagonal border?
                {%
                        % move to the right
                        \pgfmathtruncatemacro{\rights}{#2-1}%
                        \Populate{#1,0}{\rights}{#3}%
                }%
                {%
                        % move to the right
                        \pgfmathtruncatemacro{\rights}{#2-1}%
                        \Populate{#1,0}{\rights}{#3}%
                        % move upward
                        \pgfmathtruncatemacro{\ups}{#3-1}%
                        \Populate{#1,1}{#2}{\ups}%
                }%
        }%      
}


\begin{document}
\Populate{}{4}{4}
\end{document}

It produced a wrong output as follows:

,0,0,0,0,1,1,1,1
,0,0,0,1,1,1,1
,0,0,1,1,1,1
,0,1,1,1,1

The expected output must be as follows: (the leading comma will be removed later)

,0,0,0,0,1,1,1,1
,0,0,0,1,0,1,1,1
,0,0,0,1,1,0,1,1
,0,0,0,1,1,1,0,1
,0,0,1,0,0,1,1,1
,0,0,1,0,1,0,1,1
,0,0,1,0,1,1,0,1
,0,0,1,1,0,0,1,1
,0,0,1,1,0,1,0,1
,0,1,0,0,0,1,1,1
,0,1,0,0,1,0,1,1
,0,1,0,0,1,1,0,1
,0,1,0,1,0,0,1,1
,0,1,0,1,0,1,0,1

The last edit:

For N x N case, use \Populate{0}{N-1}{N} to avoid having an extra job to remove the leading commas above. (I just got this enlightenment)

Are you sure that tikz-pgf tag is necessary? ;-) – Paul Gaborit Jul 18 '12 at 07:10 — Paul Gaborit, Jul 18 '12 at 07:10
@PolGab: Maybe because of its scope behavior. :-) – kiss my armpit Jul 18 '12 at 07:16 — kiss my armpit, Jul 18 '12 at 07:16

score 7 · Accepted Answer · edited Jul 18 '12 at 12:28

You have to use more groups ({...}) to localize (re)definition of your macros \ups and rights:

\documentclass{article}
\usepackage{ifthen,pgf}

\parindent=0pt

\newcommand{\Populate}[3]%
{%
  \ifthenelse{#2=0}% on the most left border?
  {% 
    \ifthenelse{#3=0}% on the most top border?
    {% 
      #1\endgraf% I need to trim the most left comma later!
    }%
    {%
        % move upward
        \pgfmathtruncatemacro{\ups}{#3-1}%
        \Populate{#1,1}{#2}{\ups}%
    }%  
  }%      
  {% 
    \ifthenelse{#2=#3}% on the diagonal border?
    {%
        % move to the right
        \pgfmathtruncatemacro{\rights}{#2-1}%
        \Populate{#1,0}{\rights}{#3}%
    }%
    {%
      {% GROUP
        % move to the right
        \pgfmathtruncatemacro{\rights}{#2-1}%
        \Populate{#1,0}{\rights}{#3}%
      }%
        % move upward
        \pgfmathtruncatemacro{\ups}{#3-1}%
        \Populate{#1,1}{#2}{\ups}%
    }%
  }%      
}


\begin{document}
\Populate{}{4}{4}
\end{document}

Remark: a macro is not a function. Your question should be "How to make a recursive macro in (La)TeX?".

I prefer the control words \bgroup and \egroup to the curly braces { and } because I can avoid appending % and too deep nested scoping. — kiss my armpit, Jul 18 '12 at 07:20
@HiggsBoson \bgroup starts a new scope just the same as {. And it is longer than {%. — Ryan Reich, Jul 18 '12 at 07:51
@RyanReich: But my eyes locates the scoping pair much better when using \bgroup and \egroup. — kiss my armpit, Jul 18 '12 at 08:10

kiss my armpit · Answer 2 · 2012-07-18T12:53:56.630

The simplest version I can do. If you have more simpler one, please edit this answer.

\documentclass{minimal}

\newcount\u
\newcount\r

\def\d#1{\advance#1-1\relax}

\newcommand{\Populate}[3]{%
        \r#2\u#3%
        \ifnum\r=0
                \ifnum\u=0\relax
                        #1\endgraf
                \else
                        \d\u\Populate{#1,1}{#2}{\the\u}%
                \fi
        \else
                \ifnum\r=\u
                        \d\r\Populate{#1,0}{\the\r}{#3}%
                \else                       
                        {\d\r\Populate{#1,0}{\the\r}{#3}}% must be grouped!
                        \d\u\Populate{#1,1}{#2}{\the\u}%
                \fi
        \fi}


\begin{document}
\Populate{0}{3}{4}
\end{document}

How to make a recursive macro in (La)TeX?

2 Answers2