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使用 Tikz 在樹中建立點/線括號

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使用 Tikz 在樹中建立點/線括號

我問自己是否可以用 tikz 創建如圖所示的點：

樹的例子

程式碼

\begin{tikzpicture}

\tikzstyle{level 1}=[sibling distance=60mm]
\tikzstyle{level 2}=[sibling distance=33mm]
\tikzstyle{level 3}=[sibling distance=10mm]
\tikzstyle{level 4}=[sibling distance=5mm]
\node {n} 
    child {node {$\frac{n}{3}$}
        child {node {$\frac{n}{9}$}
            child{node {$\frac{n}{27}$}}
            child{node {$\frac{n}{27}$}}
            child{node {$\frac{n}{27}$}}}
        child {node {$\frac{n}{9}$}
            child{node {$\frac{n}{27}$}}
            child{node {$\frac{n}{27}$}}
            child{node {$\frac{n}{27}$}}}}
        child {node {$\frac{n}{3}$}
        child {node {$\frac{n}{9}$}
            child{node {$\frac{n}{27}$}}
            child{node {$\frac{n}{27}$}}
            child{node {$\frac{n}{27}$}}}
        child {node {$\frac{n}{9}$}
                        child{node {$\frac{n}{27}$}}
            child{node {$\frac{n}{27}$}}
            child{node {$\frac{n}{27}$}}}}
        child {node {$\frac{n}{3}$}
            child{node{$\frac{n}{9}$}
                            child{node {$\frac{n}{27}$}}
            child{node {$\frac{n}{27}$}}
            child{node {$\frac{n}{27}$}}}
            child{node{$\frac{n}{9}$}
                            child{node {$\frac{n}{27}$}}
            child{node {$\frac{n}{27}$}}
            child{node {$\frac{n}{27}$}}}
    };

我想在最後一個子節點以及子節點之間開始點線。

答案1

這是使用 Tikz 的解決方案。該代碼很大程度上基於這個遞迴樹的例子，但也進行了大量修改以適合您的範例影像。不確定您是否想要cn/n實際的分數，但這很容易從下面的程式碼開始解決。

輸出

方案圖

程式碼

\documentclass[margin=10pt]{standalone} 
\usepackage{tikz}
\usepackage{tikz-qtree}
\usetikzlibrary{trees,calc,arrows.meta,positioning,decorations.pathreplacing,bending}

\tikzset{
    edge from parent/.style={draw, thick, blue!70!black},
    no edge from this parent/.style={
        every child/.append style={
        edge from parent/.style={draw=none}}},
    level 3/.style={yshift=5cm},
    level 4/.style={level distance=5mm} 
         }

\begin{document}

\begin{tikzpicture}[
    level/.style={sibling distance=40mm/#1},
    text=blue!70!black,
    >=latex,
    font=\sffamily
    ]

\node (z){cn} 
  child {node (a) {cn/2}
    child {node  (b) {cn/4}
      child {node (b1) {$\vdots$}[no edge from this parent]
       child {node (b11) {c}}
      }
      child {node (b2) {$\vdots$}[no edge from this parent]
       child {node (b12) {c}}
      }
    }
    child {node (g) {cn/4}
      child {node (g1) {$\vdots$}[no edge from this parent]
       child {node (g11) {c}}
      }
      child {node (g2) {$\vdots$}[no edge from this parent]
       child {node (g12) {c}}
      }
    }
  }
    child {node (d) {cn/2}
      child {node  (e) {cn/4}
        child {node (e1) {$\vdots$}[no edge from this parent]
         child {node (e11) {c}}
        }
        child {node (e2) {$\vdots$}[no edge from this parent]
         child {node (e12) {c}}
        }
      }
      child {node (f) {cn/4}
        child {node (f1) {$\vdots$}[no edge from this parent]
         child {node (f11) {c}}
        }
        child {node (f2) {$\vdots$}[no edge from this parent]
         child {node (f12) {c}
         }
         }
  }
};

\node[left=5 of z]  (ln1) {cn}[no edge from this parent]
    child {node (ln2) {cn}[no edge from this parent]
        child {node (ln3) {cn}[no edge from this parent]
            child {node (ln4) {}[no edge from this parent]
                child {node (ln5) {cn}}}}};

\path (b12.north east) -- (g11.north west) node [midway] {$\cdots$};
\path (e12.north east) -- (f11.north west) node [midway] {$\cdots$};

\coordinate (cd1) at ($(f12)+(1,0)$);
\coordinate (nb1) at ($(g12)!.5!(e11)$);

\draw[blue!70!black,thick,<->,] 
    (cd1) -- (cd1|-z.east) node [near start, fill=white] {log(n)};

\draw[blue!70!black,dashed,thick,->]    
    ($(z.west)+(-1em,0)$) -- (ln1);
\draw[blue!70!black,dashed,thick,->]    
    ($(a.west)+(-1em,0)$) -- (ln2.east);
\draw[blue!70!black,dashed,thick,->]    
    ($(b.west)+(-1em,0)$) -- (ln3);
\draw[blue!70!black,dashed,thick,->]    
    ($(b11.west)+(-1em,0)$) -- (ln5);

\draw[blue!70!black,thick,decorate,decoration={brace,amplitude=10pt,mirror},->,-{latex[flex=1pt]}] (b11.south west) -- (f12.south east);
\end{tikzpicture}
\end{document}

答案2

這是一個使用的解決方案forest。請注意，這採用目標圖像的“像這樣”極為嚴重地。這意味著主樹的實際規範非常非常緊湊：

   [c, name=node 1
     [, name=node 2 [, name=node 3 [][]][[][]]][[[][]][[][]]]
   ]

顯然，如果您想要一些不太通用的東西，您可以手動指定節點的內容。

另請注意，我實際上沒有理由以我的方式指定節點 4-13 的標籤。特別是，編號為 10-13 的節點的規範實際上只是因為我想嘗試節點遍歷。

\documentclass[tikz,border=5pt]{standalone}
\usepackage{forest,textcomp}
\usetikzlibrary{positioning,arrows.meta,decorations.pathreplacing}
\begin{document}
 \begin{forest}
   for tree={
     font=\sffamily,
     before typesetting nodes={
       if={level>0}{
         if n children=0{
           append/.wrap pgfmath arg={
             [#1, font=\sffamily, edge=dotted]
           }{content("!r")},
           content={},
         }{
           content/.wrap 2 pgfmath args={#2n\textfractionsolidus#1}{int(level()*2)}{content("!r")}
         }
       }{
         delay n=1{
           content/.wrap value={##1n},
           node walk={
             every step/.style={alias=node 4}, F,
             every step/.style={alias=node 10}, N,
             every step/.style={alias=node 11}, N,
             every step/.style={alias=node 9},
             node walk={
               rL,
               node walk={
                 every step/.style={alias=node 12}, P,
                 every step/.style={alias=node 13}, P}
             }
           }
         }
       }
     },
   }
   [c, name=node 1
     [, name=node 2 [, name=node 3 [][]][[][]]][[[][]][[][]]]
   ]
   \begin{scope}[font=\sffamily, >=Triangle]
     \node (node 5) [left=25pt of node 4] {cn};
     \foreach \i/\j in {6/3,7/2,8/1} \node (node \i) at (node 5 |- node \j) {cn};
     \foreach \i/\j in {1/8,2/7,3/6,4/5} \draw [densely dashed, ->] (node \i.west) -- (node \j.east);
     \path [draw, decorate, decoration={brace, amplitude=10pt}] (node 9.south east) -- (node 4.south west);
     \path [draw, <->] (node 9.south east) +(15pt,0) coordinate (c) -- (c |- node 1.north) node [pos=.4, fill=white] {log(n)};
   \end{scope}
   \draw [dotted] (node 10.north east) -- (node 11.north west) (node 13.north east) -- (node 12.north west);
  \end{forest}
\end{document}

節點行走樹

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