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如何在一张图片中组合自上而下和自下而上的二叉树？

tag-icon • tag-icon tikz-pgf trees
如何在一张图片中组合自上而下和自下而上的二叉树？

我想画一棵如下图所示的二叉树。不幸的是，我完全不知道如何从上到下画两棵树以匹配它们的叶子。任何帮助都将不胜感激。

在此处输入图片描述

答案1

一种选择：

在此处输入图片描述

代码：

\documentclass{article}
\usepackage{forest}
\usetikzlibrary{positioning,arrows.meta}

\newsavebox\Downtree
\newsavebox\Uptree

\tikzset{
  nleft/.style={text width=15pt,midway,left,font=\strut\scriptsize},
  nright/.style={text width=15pt,midway,right,font=\strut\scriptsize},
  }

\savebox\Downtree{\begin{forest}
for tree={
  s sep=25pt,
  l sep=20pt,
  where n children=0{inner ysep=0pt}{draw,circle},
  edge={->,>=latex}
}
[Y3
  [Y2,edge label={node[nleft]{yes}}
    [,edge label={node[nleft]{yes}}]
    [,edge label={node[nright]{no}}]
  ]
  [Y1,edge label={node[nright]{no}}
    [,edge label={node[nleft]{yes}}]
    [,edge label={node[nright]{no}}]
  ]
]
\end{forest}%
}
\savebox\Uptree{\begin{forest}
for tree={
  grow'=north,
  s sep=25pt,
  l sep=20pt,
  where n children=0{inner ysep=0pt}{draw,circle},
  edge={->,>=latex}
}
[X3
  [X4,edge label={node[nleft]{no}}
    [,edge label={node[nleft]{no}}]
    [,edge label={node[nright]{yes}}]
  ]
  [X1,edge label={node[nright]{yes}}
    [,edge label={node[nleft]{no}}]
    [,edge label={node[nright]{yes}}]
  ]
]
\end{forest}%
}

\begin{document}

\begin{tikzpicture}[>={Latex[open]}]
\node[inner sep=0pt] (Down) {\usebox\Downtree};
\coordinate (aux);
\node[inner sep=0pt,below=0pt of Down] (Up) {\usebox\Uptree};
\begin{scope}[red,->]
\draw
  ([xshift=-15pt,yshift=-10pt]Down.north) to[bend right] (Down.south west);
\draw
  ([xshift=-15pt,yshift=10pt]Up.south) to[bend left] (Up.north west);
\end{scope}
\begin{scope}[blue,->]
\draw
  ([xshift=15pt,yshift=-10pt]Down.north) to[bend left] (Down.south east);
\draw
  ([xshift=15pt,yshift=10pt]Up.south) to[bend right] (Up.north east);
\end{scope}
\begin{scope}[green,<->]
\draw
  ([xshift=-2pt]Down.south) 
  .. controls ++(-10pt,2cm) and ++(10pt,2cm) .. 
  ([xshift=2pt]Down.south);
\draw
  ([xshift=-2pt]Up.north) 
  .. controls ++(-10pt,-2cm) and ++(10pt,-2cm) .. 
  ([xshift=2pt]Up.north);
\end{scope}

\end{tikzpicture}

\end{document}

我用的是forest包来构建两棵独立的树；一棵向下生长，另一棵向上生长。首先将每棵树装箱，然后将箱子放在\nodes中，tikzpicture以便轻松绘制红色和绿色箭头。

答案2

虽然您想绘制树木，但无需使用Tikz trees、tikz-qtree、forest、 ... 来绘制它们。matrix类似下面的代码或只需正确定位节点即可完成相同的操作。

并且下一个代码不会tikzpicture在另一个代码中插入tikzpicture，这有时是不推荐的。

\documentclass[tikz,border=2mm]{standalone}

\usetikzlibrary{matrix, arrows.meta}

\begin{document}
\begin{tikzpicture}[>=latex]
\matrix (A) [matrix of nodes, nodes={circle,draw},
             row 3/.style={nodes={draw=none, inner sep=0pt},nodes in empty cells},
             row sep=.75cm, column sep=3mm]
{
&[4mm]&&&Y3&&&&[4mm]\\
&&Y2&&&&Y1&&\\
&&&&&&&&\\
&&X4&&&&X1&&\\
&&&&X3&&&&\\
};
\draw[->] (A-1-5)--  node[above left]{yes} (A-2-3);
\draw[->] (A-1-5)-- node[above right]{no} (A-2-7) ;
\draw[->] (A-2-3)--  node[above left]{yes} (A-3-2);
\draw[->] (A-2-3)-- node[above right]{no} (A-3-4) ;
\draw[->] (A-2-7)--  node[above left]{yes} (A-3-6);
\draw[->] (A-2-7)-- node[above right]{no} (A-3-8) ;

\draw[->] (A-5-5)--  node[below left]{no} (A-4-3);
\draw[->] (A-5-5)-- node[below right]{yes} (A-4-7) ;
\draw[->] (A-4-3)--  node[below left]{no} (A-3-2);
\draw[->] (A-4-3)-- node[below right]{yes} (A-3-4) ;
\draw[->] (A-4-7)--  node[below left]{no} (A-3-6);
\draw[->] (A-4-7)-- node[below right]{yes} (A-3-8) ;

\draw[red,->, >={Latex[open]},shorten <=3mm] (A-1-5.north) to[out=180,in=90] (A-3-1);
\draw[red,->, >={Latex[open]},shorten <=3mm] (A-5-5.south) to[out=180,in=-90] (A-3-1);
\draw[blue,->, >={Latex[open]},shorten <=3mm] (A-1-5.north) to[out=0,in=90] (A-3-9);
\draw[blue,->, >={Latex[open]},shorten <=3mm] (A-5-5.south) to[out=0,in=-90] (A-3-9);

\draw[green,<->, >={Latex[open]},shorten <=1mm, shorten >=1mm] (A-3-5) to[loop above,min distance=2cm] (A-3-5);
\draw[green,<->, >={Latex[open]},shorten <=1mm, shorten >=1mm] (A-3-5) to[loop below,min distance=2cm] (A-3-5);

\end{tikzpicture}
\end{document}

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