Creating dots/lines brackets in tree with Tikz

Question

I am asking myself if I can create dots like the ones in the picture with tikz:

tree example

Code

\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 {$\frac{n}{27}$}}}
    };

And I want to start the dot lines at last child nodes and between the child nodes.

Yes, you can. You can dot a line by writing \draw[dotted] .... — Alenanno, Apr 29 '15 at 15:34
If you post the code you are using for the tree, somebody can show you how to do the dotted lines. (I'm not clear which ones you mean right now - the horizontal or vertical ones?) — cfr, Apr 29 '15 at 15:56
I edited the main question with the code I am using and what I especially want. — , Apr 29 '15 at 17:05
This question reminds me of http://tex.stackexchange.com/a/120605 — Qrrbrbirlbel, Apr 29 '15 at 23:16

Alenanno · Accepted Answer · 2015-04-30T09:19:11.453

Here is a solution using Tikz. The code was heavily based on this example of a recursion tree, but also heavily modified to fit your example image. Not sure if you wanted the cn/n to be actual fractions, but that's easily fixable starting from the code below.

Output

scheme figure

Code

\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}

For the arrow, have you tried the arrows from arrows.meta library? (arrows is deprecated either-way.) By the way, your usage of -> and -latex is wrong (for lack of a better word). > is a short-cut and short-hand for an arrow tip that shall be used generally. Define >=latex (or >=Latex with the arrows.meta library) and then use only ->, <->, etc. — Qrrbrbirlbel, Apr 29 '15 at 22:28
@Qrrbrbirlbel Interesting. Thanks for the heads-up! I'm looking into it and fixing the code. By the way, >=latex and >=Latexseem to yield the same result, or am I missing something? — Alenanno, Apr 29 '15 at 22:46
Yes, I forgot to mention the flex and the bend options for arrows. Needs the bending library. Though, OP has used a much smaller arrow tip in relation to the curvature of the brace. — Qrrbrbirlbel, Apr 29 '15 at 22:51
@Qrrbrbirlbel Those are for rotating the arrow tip, correct? I was also interested in the various arrow tips available for arrows.meta, since I haven't found anything in the Tikz manual about this. — Alenanno, Apr 29 '15 at 22:55
Rotating: Kind of. It provides solutions for paths that are curved where a "straight" arrow tip should be placed. If you can't find the library in the manual you are probably not searching in the newest version (3.0.0). — Qrrbrbirlbel, Apr 29 '15 at 22:58
@Qrrbrbirlbel Ok now I'm understanding it better, but there's one thing I can't seem to do properly. Is there a every edge/.style={} kind of command I can apply? I tried this and every path in the \tikzset but nothing works, or it affects the wrong paths (i.e. the tree branches). And in \begin{tikzpicture}[...], I don't know how to properly set the arrow tips. Plus being 1:30 AM does not help. :D Thanks for your help though! — Alenanno, Apr 29 '15 at 23:27
(+1) just for the arrow on the curly bracket. (I thought that wouldn't work for some reason.) You might want to use font=\sffamily to match the style in the OP's image. — cfr, Apr 29 '15 at 23:53
@Alenanno (Sorry for the late response. Haven't seen your comment before.) You set the arrow tip just as before: -Latex, for the bended version you use -{Latex[bend]} (or >={Latex[bend]}. If you want to apply the option bend to all arrows in a scope you can to arrows={[bend]}. — Qrrbrbirlbel, May 04 '15 at 18:51
@Qrrbrbirlbel No worries! And thanks for the explanation! :D — Alenanno, May 04 '15 at 20:46

cfr · Answer 2 · 2015-04-30T00:10:09.293

Here's a solution using forest. Note that this takes the 'like this' of the target image extremely seriously. This means that the actual specification of the main tree is very, very compact:

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

Obviously if you want something rather less generic, you can specify the contents of the nodes by hand.

Note also that there is really no reason for me to specify the labels of nodes 4-13 in the way I do. In particular, the specification of nodes numbered 10-13 is really just because I wanted to experiment a bit with node walks.

\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}

node walk tree

Creating dots/lines brackets in tree with Tikz

2 Answers2

Output

Code

Linked