LaTeX 中的递归树

Question

如何在 LaTeX 中绘制以下递归树？

我曾尝试使用 Ti钾我用 Z 图片来做这个，但代码中还是会出错。请推荐一个更简单的代码。

Answer 1

您可以使用强大的forest包；你甚至可以把内容计算留给包：

代码：

\documentclass[border=5pt]{standalone}
\usepackage{amsmath}
\usepackage{forest}

\begin{document}

\begin{forest}
for tree={
  parent anchor=south,
  s sep=2pt
},
delay={for descendants={
  if n=1
    {draw,content/.wrap 2 pgfmath args=
      {$c\binom{n}{#2}^{2}$}{content}{int(2^level)}}
      {if n'=1{draw,content/.wrap 2 pgfmath args=
        {$c\binom{n}{#2}^{2}$}{content}{int(2^level)}}{}
      },  
     where n children={0}{draw,content=c}{}
  }
}
[$cn^{2}$,draw
  [
    [
      [
        []
        []
        []
      ]
      [
        [,phantom]
      ]
      [
        [,phantom]
      ]
      [
        []
        []
        []
      ]
    ]
    [
      [,phantom]
    ]
    [
      [,phantom]
    ]
    [
      [
        []
        []
        []
      ]
      [
        [,phantom]
      ]
      [
        [,phantom]
      ]
      [
        []
        []
        []
      ]
    ]
  ]
  [
    [,phantom [,phantom]]
  ]
  [
    [,phantom [,phantom]]
  ]
  [
    [
      [
        []
        []
        []
      ]
      [
        [,phantom]
      ]
      [
        [,phantom]
      ]
      [
        []
        []
        []
      ]
    ]
    [
      [,phantom]
    ]
    [
      [,phantom]
    ]
    [
      [
         []
        []
        []
     ]
      [
        [,phantom]
      ]
      [
        [,phantom]
      ]
      [
        []
        []
        []
      ]
    ]
  ]
]
\end{forest}

\end{document}

Answer 2

forest允许您使用标准括号表示法指定树。请参阅我对先前问题的回答了解如何使用括号表示法将树转换为规范。那里的其他答案涵盖了适合绘制简单树的其他软件包（如问题中所述）。所以如果你不喜欢forest，也许其他一个会适合你。

对于forest，这里有一个原型可以帮助您入门：

\documentclass[tikz,border=10pt]{standalone}
\usepackage{forest}
\begin{document}

\begin{forest}
  for tree={
    draw,
    align=center
  }
  [root
    [child
      [grandchild
        [great\\-grandchild]
        [great\\-grandchild]
        [great\\-grandchild]
      ]
      [grandchild, calign with current]
      [grandchild
        [great\\-grandchild]
        [great\\-grandchild]
        [great\\-grandchild]
      ]
    ]
    [child
      [grandchild
        [great\\-grandchild]
        [great\\-grandchild]
        [great\\-grandchild]
      ]
      [grandchild, calign with current]
      [grandchild
        [great\\-grandchild]
        [great\\-grandchild]
        [great\\-grandchild]
      ]
    ]
    [child
      [grandchild
        [great\\-grandchild]
        [great\\-grandchild]
        [great\\-grandchild]
      ]
      [grandchild, calign with current]
      [grandchild
        [great\\-grandchild]
        [great\\-grandchild]
        [great\\-grandchild]
      ]
    ]
    [child
      [grandchild
        [great\\-grandchild]
        [great\\-grandchild]
        [great\\-grandchild]
      ]
      [grandchild, calign with current]
      [grandchild
        [great\\-grandchild]
        [great\\-grandchild]
        [great\\-grandchild]
      ]
    ]
  ]
\end{forest}


\end{document}