# Compound Pathway Problem with holes

The picture below is what I am trying to create.

I have asked a similar question before, and I got an excellent answer, but it's still not 100% what I am looking for. I know that I have to use \usepackage{tikz} and possibly \usepackage{xintexpr} and \usetikzlibrary{math} \documentclass[tikz,border=5]{article} \usepackage{tikz} \usepackage{xintexpr} \usetikzlibrary{math} \begin{document}

\begin{tikzpicture}[x=2cm,y=-2cm, node 0/.style={fill=red!20}]
\tikzmath{%
int \i, \j, \m, \n, \t;
\m = 5; \n = 5;
% Initialise board.
for \i in {0,...,\m}{
for \j in {0,...,\n}{
\t{\i,\j} = 0;
};
};
% Create holes.
\t{2,3} = -1;
\t{3,4} = -1;
\t{5,2} = -1;
% Perform calculations.
for \i1 in {0,...,\m}{
for \j1 in {0,...,\n}{
if (\t{\i1,\j1} == -1) then {
\t{\i1,\j1} = 0;
} else {
if (\i1 == 0 || \j1 == 0) then  {
\t{\i1,\j1} = 1;
} else {
\i2 = \i1 - 1;
\j2 = \j1 - 1;
\t{\i1,\j1} = \t{\i2,\j1} + \t{\i1,\j2};
};
};
};
};
% Draw nodes.
for \i1 in {0,...,\m}{
for \j1 in {0,...,\n}{
{ \node [circle, fill=blue!20, minimum size=1cm, node \t{\i1,\j1}/.try]
(n-\i1-\j1) at (\j1, \i1) {\t{\i1,\j1}}; };
};
};
% Draw edges.
for \i1 in {0,...,\m}{
for \j1 in {0,...,\n}{
\i2 = \i1 + 1;
\j2 = \j1 + 1;
if (\i1 < \m) then {
if (\t{\i2,\j1} > 0) then {
{ \draw [thick, -stealth] (n-\i1-\j1) -- (n-\i2-\j1); };
};
};
if (\j1 < \n) then {
if (\t{\i1,\j2} > 0) then {
{ \draw [thick, -stealth] (n-\i1-\j1) -- (n-\i1-\j2); };
};
};
};
};
}
\end{tikzpicture}

\end{document}


This code has the idea to what I am looking for, but what I want is to refine the code so it can look exactly like the picture included. I'm new to latex and the idea of programming/coding, but I am trying to learn.

Also my picture needs to fit into my homework problem setting

\documentclass[28pt]{article}
\usepackage{fancyhdr}

• Please post a compilable example that produces what you have by now. Jul 16, 2017 at 8:47

Ok, so an additional data structure is required to model the "routes" which have holes.

\documentclass[border=5]{standalone}
\usepackage{tikz}
\usetikzlibrary{math}
\begin{document}
\begin{tikzpicture}[x=2cm, y=-2cm]
\tikzmath{%
int \i, \j, \m, \n, \t, \r;
\m = 6; \n = 6;
% Initialise board.
for \i in {0,...,\m-1}{
for \j in {0,...,\n-1}{
\t{\i,\j} = 0;
};
};
for \i in {0,...,\m-1}{
for \j in {0,...,\n-1}{
\r{\i,\j} = 11;
};
};
% Starting point.
\t{0,0} = 1;
% Create holes in route.
% 01 can go east
% 10 can go south
% 11 can go east and south
\r{2,2} = 10;
\r{3,3} = 10;
\r{4,2} = 01;
% Perform calculations.
for \i1 in {0,...,\m-1}{
for \j1 in {0,...,\n-1}{
if (\i1 == 0 && \j1 == 0) then {
\t{0,0} = 1;
} else {
if (\j1 > 0) then {
\j2 = \j1 - 1;
if (mod(\r{\i1,\j2}, 2) == 1) then {
\t{\i1,\j1} = \t{\i1,\j1} + \t{\i1,\j2};
};
};
if (\i1 > 0) then {
\i2 = \i1 - 1;
if (mod(floor(\r{\i2,\j1} / 10), 2) == 1) then {
\t{\i1,\j1} = \t{\i1,\j1} + \t{\i2,\j1};
};
};
};
};
};
% Draw nodes.
for \i1 in {0,...,\m-1}{
for \j1 in {0,...,\n-1}{
{ \fill  (\j1, \i1) circle [radius=0.05]
node [above left] {\t{\i1,\j1}}; };
};
};
% Draw edges.
for \i1 in {0,...,\m-1}{
for \j1 in {0,...,\n-1}{
if (mod(\r{\i1,\j1}, 2) == 1 && \j1 < \n - 1) then {
{ \draw [thick, -stealth, shorten >=0.1cm] (\j1,\i1) -- ++(1, 0); };
};
if (mod(floor(\r{\i1,\j1} / 10), 2) == 1 && \i1 < \m - 1) then {
{ \draw [thick, -stealth,  shorten >=0.1cm] (\j1,\i1) -- ++(0,1); };
};
};
};
}
\end{tikzpicture}
\end{document} • This is good, however the "holes" that I need to create cannot so easily be done with your code. The picture above can show you exactly what I mean. Jul 17, 2017 at 5:08
• @Nixie777 see the updated answer. Jul 17, 2017 at 11:54
• This is perfect! I know I not suppose to say thank you in comments, but truly, thank you so much! This helps out so much! Jul 18, 2017 at 7:29

I hope this is what you want

\documentclass{standalone}
\usepackage{tikz}
\usepgfmodule{parser}
\begin{document}

\catcode\^^=12\relax\pgfparserdef{countpath}{initial}{the character ^^}{\nextcell}\catcode\^^=10\relax
\catcode\^^M=12\relax\pgfparserdef{countpath}{initial}{the character ^^M}{\nextline}\catcode\^^M=5\relax
\pgfparserdef{countpath}{all}{the character ;}{\endcountpath}
\pgfparserdef{countpath}{all}{the character +}{\nextcell\drawanode}
\pgfparserdef{countpath}{all}{the character |}{\nextcell\draw(\coordx,-\coordy)+(0,1)--+(0,-1);\expandafter\xdef\csname cp/\coordx/\coordy\endcsname{C}}
\pgfparserdef{countpath}{all}{the character -}{\nextcell\draw(\coordx,-\coordy)+(-1,0)--+(1,0);\expandafter\xdef\csname cp/\coordx/\coordy\endcsname{C}}
\def\countpath{
\begin{tikzpicture}[shorten <=9pt,shorten >=9pt]
\def\coordx{0}\def\coordy{0}
\catcode\^^M=12\relax\catcode\^^=12\relax
\pgfparserparse{countpath}%
}
\def\endcountpath{
\end{tikzpicture}
\pgfparserswitch{final}
}
\def\nextcell{\pgfmathtruncatemacro\coordx{\coordx+1}}
\def\nextline{\pgfmathtruncatemacro\coordy{\coordy+1}\def\coordx{0}}
\def\drawanode{
\def\numberofpaths{0}
\ifnum\coordy=1
\ifnum\coordx=1
\def\numberofpaths{1}
\fi
\fi
% check upper neighbor
\pgfmathtruncatemacro\coordyminusi{\coordy-1}
\expandafter\if\csname cp/\coordx/\coordyminusi\endcsname\relax\else
\pgfmathtruncatemacro\coordyminusii{\coordy-2}
\pgfmathtruncatemacro\numberofpaths{\numberofpaths+\csname cp/\coordx/\coordyminusii\endcsname}
\fi
% check left neighbor
\pgfmathtruncatemacro\coordxminusi{\coordx-1}
\expandafter\if\csname cp/\coordxminusi/\coordy\endcsname\relax\else
\pgfmathtruncatemacro\coordxminusii{\coordx-2}
\pgfmathtruncatemacro\numberofpaths{\numberofpaths+\csname cp/\coordxminusii/\coordy\endcsname}
\fi
\expandafter\xdef\csname cp/\coordx/\coordy\endcsname{\numberofpaths}
\draw(\coordx,-\coordy)node{\numberofpaths};
}

\countpath
+-+-+-+-+-+-+-+ +-+
| |   | | |   | | |
+-+ +-+-+ +-+-+-+-+
|   | | |   | | | |
+-+-+-+-+-+-+-+ +-+
| | | | |     | | |
+-+ +-+-+ +-+-+ +-+
|   | | |   | | | |
+-+-+-+-+-+-+-+-+-+
| |   | | |   | | |
+-+-+-+-+-+-+-+ +-+
|   | | | | | | | |
+-+-+-+-+-+-+-+-+-+
;

\end{document} • This is impressive. I'll use this as well to figure out another compound pathway I have. Jul 18, 2017 at 7:30
• SO I copied your code into sharelatex, but for some reason the output gives me the pathway, but with all the numbers are now zero. Jul 18, 2017 at 7:37
• I now know why: this site translates my tabs into spaces so the coordinates are shifted to the right by four units. I fixed the code (by deleting extra spaces.) Jul 19, 2017 at 3:19