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我如何从暴露的最右侧节点绘制箭头到右侧对齐的值。

\documentclass[landscape]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{tikz}
\usepackage{forest}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}

\begin{document}
$$
  \begin{array}{lr}
    \begin{forest}
    for tree={
        l sep=2.5em
    }
     [$cn^2$
      [$c\left(\frac{n}{4}\right)^2$
       [$c\left(\frac{n}{16}\right)^2$
        []
        []
        []
       ]
       [$c\left(\frac{n}{16}\right)^2$
        []
        []
        []
       ]
       [$c\left(\frac{n}{16}\right)^2$
        []
        []
        []
       ]
      ]
      [$c\left(\frac{n}{4}\right)^2$
       [$c\left(\frac{n}{16}\right)^2$
        []
        []
        []
       ]
       [$c\left(\frac{n}{16}\right)^2$
        []
        []
        []
       ]
       [$c\left(\frac{n}{16}\right)^2$
        []
        []
        []
       ]
      ]
      [$c\left(\frac{n}{4}\right)^2$
       [$c\left(\frac{n}{16}\right)^2$
        []
        []
        []
       ]
       [$c\left(\frac{n}{16}\right)^2$
        []
        []
        []
       ]
       [$c\left(\frac{n}{16}\right)^2$
        []
        []
        []
       ]
      ]
     ]
    \end{forest} &
    \quad\begin{aligned}
        &cn^2 \\ \\
        &\frac{3}{16}cn^2 \\ \\
        &\left(\frac{3}{16}\right)^2cn^2 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
    \end{aligned}
  \end{array}
$$
\end{document}

由此得出下图：

在此处输入图片描述

但我想要的是类似的东西：

在此处输入图片描述

我还希望右边的 3 个方程与它们对应的树上的级别对齐。

本质上，我正在尝试重新创建我的书中的图表 d)：

在此处输入图片描述

答案1

像这样？

在此处输入图片描述

我命名了最右边的森林节点，并在它们右边放置了方程式。然后连接线的绘制很简单：

\documentclass[landscape]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{positioning}

\usepackage{forest}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}

\begin{document}
\[
    \begin{forest}
    for tree={
        l sep=2.5em
    }
     [$cn^2$,name=L1
      [$c\left(\frac{n}{4}\right)^2$
       [$c\left(\frac{n}{16}\right)^2$
        []
        []
        []
       ]
       [$c\left(\frac{n}{16}\right)^2$
        []
        []
        []
       ]
       [$c\left(\frac{n}{16}\right)^2$
        []
        []
        []
       ]
      ]
      [$c\left(\frac{n}{4}\right)^2$
       [$c\left(\frac{n}{16}\right)^2$
        []
        []
        []
       ]
       [$c\left(\frac{n}{16}\right)^2$
        []
        []
        []
       ]
       [$c\left(\frac{n}{16}\right)^2$
        []
        []
        []
       ]
      ]
      [$c\left(\frac{n}{4}\right)^2$, name=L2
       [$c\left(\frac{n}{16}\right)^2$
        []
        []
        []
       ]
       [$c\left(\frac{n}{16}\right)^2$
        []
        []
        []
       ]
       [$c\left(\frac{n}{16}\right)^2$, name=L3
        []
        []
        []
       ]
      ]
     ]
    \node (a) [right=of L1 -| L3.east] {$cn^2$};
    \node (b) [right=of L2 -| L3.east] {$\frac{3}{16}cn^2$};
    \node (c) [right=of L3.east]       {$\left(\frac{3}{16}\right)^2 cn^2$};
    \draw[dashed,->] (L1) -- (a);
    \draw[dashed,->] (L2) -- (b);
    \draw[dashed,->] (L3) -- (c);
    \end{forest}
\]
\end{document}

答案2

此代码定义了level markers您希望标记级别的树的样式以及level mark定义标记的样式。level mark可以添加到相关级别的任何节点。代码要求该值需要数学模式。（如果您需要文本，这将很容易更改。）

新的 nodewalk 步骤，tier end移动到当前 上的最后一个节点tier。level markers样式设置tier以对应于树的级别。

\documentclass[border=10pt]{article}
\usepackage{forest}
\usetikzlibrary{arrows.meta}
\forestset{
  define long step={tier end}{}{
    group={
      while nodewalk valid={next on tier}{next on tier},
      current
    }
  },
  level markers/.style={
    tikz+={
      \coordinate (tree marker) at ([xshift=10pt]current bounding box.east);
    },    
    before typesetting nodes={
      for tree={
        tier/.option=level,
      },
    },
  },
  level mark/.style={
    before drawing tree={
      for tier end={
        tikz+={
          \node (b) [anchor=mid west] at (tree marker |- .mid) {$#1$};
          \draw [densely dashed, -LaTeX] (.east) -- (b.west |- .center);
        },
      },
    },
  }
}
\begin{document}
\begin{forest}
  for tree={
    l sep=2.5em,
    math content,
  },
  level markers,
  [cn^2, level mark=cn^2
    [c\left(\frac{n}{4}\right)^2, level mark=\frac{3}{16}cn^2
      [c\left(\frac{n}{16}\right)^2, level mark=\left(\frac{3}{15}\right)^2n^2
        []
        []
        []
      ]
      [c\left(\frac{n}{16}\right)^2
        []
        []
        []
      ]
      [c\left(\frac{n}{16}\right)^2
        []
        []
        []
      ]
    ]
    [c\left(\frac{n}{4}\right)^2
      [c\left(\frac{n}{16}\right)^2
        []
        []
        []
      ]
      [c\left(\frac{n}{16}\right)^2
        []
        []
        []
      ]
      [c\left(\frac{n}{16}\right)^2
        []
        []
        []
      ]
    ]
    [c\left(\frac{n}{4}\right)^2
      [c\left(\frac{n}{16}\right)^2
        []
        []
        []
      ]
      [c\left(\frac{n}{16}\right)^2
        []
        []
        []
      ]
      [c\left(\frac{n}{16}\right)^2
        []
        []
        []
      ]
    ]
  ]
\end{forest} 
\end{document}

结果树

编辑[根据修正后的水平标记]

此代码显示了如何自动绘制树。它定义了一个样式，auto level markers该样式需要 3 个参数：每个父级拥有的子级数/分母、分母以及要填充和标记的级别数。例如，要求 3 个级别将产生一个 4 级树，其中第四级由没有内容且没有级别标记的节点组成。

\documentclass[border=10pt,tikz]{standalone}
\usepackage{forest}
\usetikzlibrary{arrows.meta}
\forestset{
  define long step={tier end}{}{
    group={
      while nodewalk valid={next on tier}{next on tier},
      current
    }
  },
  level markers/.style={
    tikz+={
      \coordinate (tree marker) at ([xshift=10pt]current bounding box.east);
    },    
    before typesetting nodes={
      for tree={
        tier/.option=level,
      },
    },
  },
  level mark/.style={
    before drawing tree={
      for tier end={
        tikz+={
          \node (b) [anchor=mid west] at (tree marker |- .mid) {$#1$};
          \draw [densely dashed, -LaTeX] (.east) -- (b.west |- .center);
        },
      },
    },
  },
  declare count register={auto numerator},
  declare count register={auto denominator},
  declare count register={auto levels},
  declare count register={auto denominator squared},
  Autoforward register={auto denominator}{
    auto denominator squared=#1*#1,
  },
  auto numerator'=3,
  auto denominator'=4,
  auto levels'=3,
  auto level markers/.style n args=3{
    level markers,
    auto numerator=#1,
    auto denominator=#2,
    auto levels=#3,
    delay={
      tempcounta'=0,
      while={
        > RR< {tempcounta}{auto levels}
      }{
        where n children=0{
          repeat={
            >R{auto numerator}
          }{
            append={[]}
          }
        }{},
        do dynamics,
        tempcounta'+=1,
      }
    },
    before typesetting nodes={
      where={
        > OR<  {level} {auto levels}
      }{
        if level=0{
          content=cn^2,
          math content
        }{
          content/.process={
            OR w2+P w {level} {auto denominator} {int(##2^##1)} { c\left(\frac{n}{##1}\right)^2 }
          },
          math content
        }
      }{},
      for nodewalk={
        r,
        while={
          > ORw+n< {level} {auto levels} {##1-1}
        }{l}
      }{
        if level>=2{
          level mark/.process={ O R R w3 {level} {auto numerator} {auto denominator squared} {\left(\frac{##2}{##3}\right)^{##1}cn^2} }
        }{
          if level=1{
            level mark/.process={ R R w2 {auto numerator} {auto denominator squared} {\frac{##1}{##2}cn^2} }
          }{
            level mark=cn^2
          }
        }
      },
    },
    before packing={
      for tree={
        l sep'=2.5em
      },
    },
  },
}
\begin{document}
\begin{forest}
  auto level markers={3}{4}{3},
  []
\end{forest}
\begin{forest}
  auto level markers={2}{6}{4},
  []
\end{forest}
\end{document}

第一棵树是上面绘制的树的修正版本：

自动化和修正版本

第二个随机改变传递给样式的值，根据树所代表的内容，这可能是也可能没有意义的：

变化

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