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以编程方式说明排列

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以编程方式说明排列

以下是所谓的扩展排列（上半部分）的图示。它只是意味着信号路径不是直接通过（像下半部分，又称身份排列），而是被打乱，一些输入会分裂并导致多个输出（4 个输入 ↦ 6 个输出）。 在此处输入图片描述

以下是该代码：

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows,positioning}

\begin{document}
\begin{tikzpicture}[>=latex']

\tikzset{cross line/.style={preaction={draw=white, -, shorten >=1pt, shorten <=1pt, line width=3.33pt}}}
\tikzstyle{invisible_block} = [draw=none, minimum size=0.0mm, text centered, text width=1.9em]
\tikzstyle{bit} = [fill,shape=rectangle, minimum size=0.5mm, inner sep=0pt]

  \newcount\u

  %% Define all nodes:
  \foreach \i in {0,...,7} {
    \u=\i 
    \advance\u by 1
    \def\j{\number\u}
    %% 8 invisible boxes
    \node[invisible_block, xshift=\i*12mm] 
        (S\j) {}; 
    %% 6 above (inputs) 
    \foreach \m in {0,...,5}  {
      \node[bit,xshift=1mm,yshift=0.2mm,right=1.25*\m mm of S\j.north west] (S\j in\m) {};
      \node[bit,above=15mm of S\j in\m] (S\j inmid\m) {};
      \node[bit,above=4mm of S\j in\m] (S\j inclose\m) {};
    }
    %% 4 on top (inputs)
    \foreach \m in {1,...,4}  {
      \node[xshift=1mm,yshift=-0.2mm,right=1.25*\m mm of S\j.south west] (S\j out\m) {};
      \node[bit,above=4mm of S\j inmid\m] (S\j inext\m) {};
    }
  }

  %% crossed connections
  \foreach \i in {1,...,7} {
    \u=\i 
    \advance\u by 1
    \def\j{\number\u}

    \draw[-,very thin] (S\j inext1) -- (S\i inmid5);
    \draw[cross line,-,very thin] (S\i inext4) -- (S\j inmid0);
  }

  %% vertical connections
  \foreach \i in {0,...,7} {
    \u=\i 
    \advance\u by 1
    \def\j{\number\u}

    \foreach \m in {0,...,5}  {
      \draw[-,very thin] (S\j inclose\m) -- (S\j in\m);
      \draw[-,densely dotted,thin,color={black!40!white}] (S\j inclose\m) -- (S\j inmid\m);
    }
    \foreach \m in {1,...,4}  {
      \draw[-,very thin] (S\j inmid\m) -- (S\j inext\m);
    }
  }

  %% big loopy horizontal cables 
  %% nodes (invisible)
  \node[coordinate,right=2mm of S8inmid5] (afterS8) {};
  \node[coordinate,right=4mm of S8inmid5] (afterS8b) {};
  \node[coordinate, left=2mm of S1inmid0] (beforeS1) {};
  \node[coordinate, left=4mm of S1inmid0] (beforeS1b) {};
  %% lines (visible)
  \draw[cross line,-,very thin] (S1inext1.south west) to[out=200, in=120] (beforeS1b) to[out=300,in=270,distance=7mm] (afterS8) to[out=90,in=90,distance=1.8mm] (S8inmid5.north);
  \draw[cross line,-,very thin] (S8inext4.south east) to[out=330, in=60] (afterS8b) to[out=240,in=270,distance=10mm] (beforeS1) to[out=90,in=90,distance=1.8mm] (S1inmid0.north);

  %%% long horizontal chassis bars / lines/ edges
  \draw[-,thin] (S1inext1.north west)   -- node[above, near start] {} (S8inext4.north east);
  \draw[-,thin] (S1inmid0.south west)   -- (S8inmid5.south east);
  \draw[-,thin] (S1inclose0.north west) -- (S8inclose5.north east);
  \draw[-,thin] (S1in0.south west)      -- (S8in5.south east);

\end{tikzpicture}
\end{document}

它有一个很好的可预测、无缝、重复的模式。并非所有的排列都是这样的。这是我在维基百科上找到的一张图片。 在此处输入图片描述 下表显示了哪些节点映射到哪些节点。

      01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
      :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: ::
      09 17 23 31 13 28 02 18 24 16 30 06 26 20 10 01 08 14 25 03 04 29 11 19 32 12 22 07 05 27 15 21

我的问题是：我们如何才能方便地将这些数据合并到代码中，以便以相同（或类似）的风格进行说明。它不一定非得是这组数据，这只是我目前正在处理的数据集。我不想每次处理新的排列时都手动重新排列连接，而是希望能够简单地向它输入逗号分隔的值、元组数组、电子表格中的数据或类似的东西。

这听起来可能很复杂，但实际上它要做的就是在呈现一组值时将点连接起来。

最终结果可能看起来像这样：

在此处输入图片描述

我开始手动添加它们，例如：

\draw[-,very thin] (S1inclose0.south east) -- (S3in1.north west);
\draw[-,very thin] (S1inclose2.south east) -- (S4in1.north west);

然后决定必须有一个更好的方法，这就是我所得到的：

\foreach \x in {1,...,8} {
  \foreach \y in {1,...,4} {
    \draw[-,very thin] (S\x inclose\y.south east) -- ( ??? );

答案1

这将根据排列连接项目符号。它只绘制标01,02,...在顶行的节点，然后绘制标p(01),p(02),...在底行的节点，其中p(x)是排列x。在第二次运行中，它将x顶部与p(x)底部连接起来。您需要做的就是说

\pic{perms={09,17,23,31,13,28,02,18,24,16,30,06,26,20,10,01,08,14,25,03,04,29,11,19,32,12,22,07,05,27,15,21}};

和 Ti钾Z 将完成剩下的工作。您不限于 32 个条目。（此版本假设您始终有两位数字并希望用0s 填充。如果您想要不同的约定，这将很容易实现。此外，还可以添加控制图形尺寸的 pgf 键，但所有这些都需要您方面的一些输入。）

\documentclass[tikz,border=3.14mm]{standalone}
\tikzset{cross line/.style={preaction={draw=white, -, shorten >=1pt, shorten
<=1pt, line width=1.6pt}}}
\begin{document}

\begin{tikzpicture}[pics/perms/.style={code={
 \foreach \XX [count=\YY] in {#1} 
 {\node[blullet] (T\YY) at (\YY,5) {\ifnum\YY<10 0\fi\YY};
 \node[blullet] (B\the\numexpr\XX) at (\YY,-5) {\XX};}
 \foreach \XX [count=\YY] in {#1} 
 {\draw[cross line] (T\YY) -- (B\YY);}
 }},blullet/.style={circle,fill=blue,text=white,text width={width("33")},
 font=\sffamily,align=center},scale=0.5,transform shape]
 \pic{perms={09,17,23,31,13,28,02,18,24,16,30,06,26,20,10,01,08,14,25,03,04,29,11,19,32,12,22,07,05,27,15,21}};
\end{tikzpicture}
\end{document}

在此处输入图片描述

编辑：尝试解决评论问题。请让我知道您希望更改哪些内容。

\documentclass[tikz,border=3.14mm]{standalone}
\tikzset{cross line/.style={preaction={draw=white, -, shorten >=1pt, shorten
<=1pt, line width=1.6pt}}}
\begin{document}

\begin{tikzpicture}[pics/perms/.style={code={
 \foreach \XX [count=\YY] in {#1} 
 {\node[blullet] (T\YY) at ({\YY+int((\YY-1)/4)},10) {};
 \node[blullet] (M\YY) at ({\YY+int((\YY-1)/4)},5) {\ifnum\YY<10 0\fi\YY};
 \node[blullet] (B\the\numexpr\XX) at ({\YY+int((\YY-1)/4)},-5) {\XX};
 \xdef\Ymax{\YY}}
 \foreach \XX [count=\YY] in {#1} 
 {\draw[cross line] (M\YY) -- (B\YY);
 \ifnum\YY>1
 \ifnum\YY<\Ymax
 \pgfmathtruncatemacro{\YYp}{\YY+ifthenelse(int(\YY/4)==\YY/4,1,0)
 -ifthenelse(int((\YY-1)/4)==(\YY-1)/4,1,0)}
 \pgfmathtruncatemacro{\YYm}{\YY-ifthenelse(int((\YY+1)/4)==(\YY+1)/4,1,0)}
 \draw[cross line] (T\YYp) -- (M\YY);
 \else 
 \draw (T1.-135) to[out=-135,in=180] ([yshift=-2cm]M1.south)
 -- ([yshift=-2cm]M\Ymax.south) to[out=0,in=-45] (M\Ymax);
 \fi
 \else
 \draw (M1.-135) to[out=-135,in=180] ([yshift=-1cm]M1.south)
 -- ([yshift=-1cm]M\Ymax.south) to[out=0,in=-45] (T\Ymax);
 \fi
 }
 }},blullet/.style={circle,fill=blue,text=white,text width={width("33")},
 font=\sffamily,align=center},scale=0.5,transform shape]
 \pic{perms={09,17,23,31,13,28,02,18,24,16,30,06,26,20,10,01,08,14,25,03,04,29,11,19,32,12,22,07,05,27,15,21}};
\end{tikzpicture}
\end{document}

在此处输入图片描述

答案2

改编自tjt263s的回答：

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{shapes.geometric, calc}



\tikzset{,
,   cross line/.style={preaction={draw=white, -, shorten >=#1, shorten
<=#1, line width=2.5pt}, line width=1.5}
,square/.style={regular polygon,regular polygon sides=4}
,sqnode/.style={square,fill=black, text=white,align=center,inner sep=2pt}
}

\newcommand{\perms}[3]{
    \foreach \XX [count=\YY] in {#1} {
        \node[sqnode](#2-\the\numexpr\XX) at ($(top) + (\XX,\yDist)$) {};
        \coordinate (last) at ($(top) + (\YY,\yDist)$); % to connect first with last
        \node[sqnode](#3-\the\numexpr\XX) at ($(top) + (\YY,0)$) {};
        \draw[cross line=5pt] (#3-\the\numexpr\XX.center) -- (#2-\the\numexpr\XX.center);
    }
    \node[sqnode] (last) at (last) {};
    \draw[ultra thick] (#2-1.north west) -- (last.north east);    % connect top line
    \draw[ultra thick]($(#2-1.south west) - (0,\yDist)$) -- ($(last.south east) - (0,\yDist)$);
}

\begin{document}
\begin{tikzpicture}[scale=1.5,transform shape]

\def\yDist{5} % distance between top and bottom row

\coordinate (top) at (0,0); % location of top left node
\perms{1,2,4,5,3,6,7,8,9,10}{T1}{B1} % T1 = name of top row, T2 = name of bottom row
\coordinate (top) at (0,-8); % location of top left node
\perms{5,4,3,2,1,6,7,8,9,10}{T2}{B2} % T1 = name of top row, T2 = name of bottom row

\foreach \XX [count=\YY] in {1,2,4,5,3,6,7,8,9,10} { % has to be same permutation as top one
    \draw[dotted, very thick] (B1-\XX.south) -- (T2-\YY.north);    % connect top line
}

\end{tikzpicture}
\end{document}

样本

如果您需要元素组之间的特殊间距（如您的其中一张图片中所示），请调整这两行的at (\XX,“和”部分。at (\YY

    \node\[blullet\]    (B\the\numexpr\XX) at (\XX,\yDist) {};
    \node\[blullet\]    (T\the\numexpr\XX) at (\YY,0) {};

基本上你必须应用以下功能：

f(x) = x + floor(x/4)* 0.5

0.5每组点后添加一个空格4。不过我不确定如何在 tikz 坐标中实现这些类型的计算。

我尝试使用该库来实现分组math：

\documentclass[tikz,border=5mm]{standalone}
\usetikzlibrary{shapes.geometric, calc}
\usetikzlibrary{math}

\tikzset{,
,   cross line/.style={preaction={draw=white, -, shorten >=#1, shorten
<=#1, line width=2.5pt}, line width=1}
,square/.style={regular polygon,regular polygon sides=4}
,sqnode/.style={square,fill=black, text=white,align=center,inner sep=2pt}
}

\newcommand{\perms}[3]{
    \foreach \XX [count=\YY] in {#1} {
        \tikzmath{
            integer \m;
            real \tx;
            \offset = 1; % extra distance between groups
            \m1 = ((\XX - 1) * 0.25); % size of groups (0.25 => 4)
            \m2 = ((\YY - 1) * 0.25); % same
            \tx1 = \XX + \m1 * \offset; % calculate transformed x coord
            \tx2 = \YY + \m2 * \offset;
        };
        \node[sqnode](#2-\the\numexpr\XX) at ($(top) + (\tx{1},\yDist)$) {};
        \coordinate (last) at ($(top) + (\tx{1},\yDist)$); % to connect first with last
        \node[sqnode](#3-\the\numexpr\XX) at ($(top) + (\tx{2},0)$) {};
        \draw[cross line=5pt] (#3-\the\numexpr\XX.center) -- (#2-\the\numexpr\XX.center);
    }
    \node[sqnode] (last) at (last) {};
    \draw[ultra thick] (#2-1.north west) -- (last.north east);    % connect top line
    \draw[ultra thick]($(#2-1.south west) - (0,\yDist)$) -- ($(last.south east) - (0,\yDist)$);
}

\begin{document}
\begin{tikzpicture}[scale=1.0,transform shape]

\def\yDist{5} % distance between top and bottom row

\coordinate (top) at (0,0); % location of top left node
\perms{1,2,3,5,4,6,8,7,9,10}{T1}{B1} % T1 = name of top row, T2 = name of bottom row
\coordinate (top) at (0,-8); % location of top left node
\perms{4,3,2,1,6,5,8,7,9,10}{T2}{B2} % T1 = name of top row, T2 = name of bottom row

\foreach \XX [count=\YY] in {1,2,3,5,4,6,8,7,9,10} { % has to be same permutation as top one
    \draw[dotted, very thick] (B1-\XX.south) -- (T2-\YY.north);    % connect top line
}

\end{tikzpicture}
\end{document}

在此处输入图片描述

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