私はラテックスでパスカルの三角形を使って穴のある通路グリッドを作成しようとしています。また、コンパス

Question

下の図は私が何をしようとしているのかを示しています。

また、この特定の質問にどのタグを使用すればよいかわかりません。

私が使用しているコード:

 \documentclass[28pt]{article}

 \usepackage{fancyhdr}

 \usepackage[includeheadfoot,margin=1.0cm]{geometry} 
 \usepackage{amsmath,amsthm,amssymb}
 \usepackage{enumitem}
 \usepackage{mathtools}
 \usepackage{framed}
 \usepackage{chessfss} %chess figure for HW #2
 \usepackage[english]{babel} %table for problem A.43
 \usepackage{multirow} %table for problem A.43
%\usepackage[table]{xcolor} color certain blocks in a table
%\usepackage[pass,showframe]{geometry}  just to show the margins
 \usepackage[makeroom]{cancel}
 \usepackage{array}  %BETWEEN TWO 2-DIGIT NUMBERS

 \newcommand{\N}{\mathbb{N}}
 \newcommand{\Z}{\mathbb{Z}}
 \newcommand{\thedate}{\today}

 \newtheoremstyle{case}{}{}{}{}{}{:}{ }{}
 \theoremstyle{case}
 \newtheorem{case}{Case}


 \newenvironment{theorem}[2][Theorem]{\begin{trivlist}
 \item[\hskip \labelsep {\bfseries #1}\hskip \labelsep {\bfseries #2.}]}{\end{trivlist}}
 \newenvironment{lemma}[2][Lemma]{\begin{trivlist}
 \item[\hskip \labelsep {\bfseries #1}\hskip \labelsep {\bfseries #2.}]}{\end{trivlist}}
 \newenvironment{exercise}[2][Exercise]{\begin{trivlist}
 \item[\hskip \labelsep {\bfseries #1}\hskip \labelsep {\bfseries #2.}]}{\end{trivlist}}
 \newenvironment{problem}[2][Problem]{\begin{trivlist}
 \item[\hskip \labelsep {\bfseries #1}\hskip \labelsep {\bfseries #2.}]}{\end{trivlist}}
 \newenvironment{question}[2][Question]{\begin{trivlist}
 \item[\hskip \labelsep {\bfseries #1}\hskip \labelsep {\bfseries #2.}]}{\end{trivlist}}
 \newenvironment{corollary}[2][Corollary]{\begin{trivlist}
 \item[\hskip \labelsep {\bfseries #1}\hskip \labelsep {\bfseries #2.}]}{\end{trivlist}}

 \begin{document}

 \end{document}

Answer 1

こうすればいいと思います:

\documentclass[tikz,border=5]{standalone}
\usetikzlibrary{math}
\begin{document}
\begin{tikzpicture}[x=2cm,y=-2cm, node 0/.style={fill=red!20}]
\tikzmath{%
  int \i, \j, \m, \n, \t;
  \m = 6; \n = 6;
  % Initialise board.
  for \i in {0,...,\m}{
    for \j in {0,...,\n}{
      \t{\i,\j} = 0;
    };
  };
  % Create holes.
  \t{0,3} = -1;
  \t{4,4} = -1;
  \t{5,1} = -1;
  \t{2,5} = -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}

「穴」がなければ、もっと簡単に行うことができます。

\documentclass[tikz,border=5]{standalone}
\usepackage{xintexpr}
\begin{document}
\begin{tikzpicture}[x=2cm,y=2cm]
\draw [help lines] grid [step=1] (6,-6);
\foreach \x in {0,...,6}
  \foreach \y in {0,...,6}
    \node [circle, fill=blue!20, minimum size=1cm]
      at (\x, -\y) {\xinttheiiexpr binomial(\x+\y,\x)\relax};
\end{tikzpicture}
\end{document}