使用 tikz 为二叉树绘制两个对称的伪根节点

Question

我需要绘制一棵二叉树（实际上是 Stern-Brocot 树），其中两个伪节点作为根的父节点，如第一张图所示。

目前，我正在使用 tikz 来绘制它，但两个伪节点都在左侧。（见第二张图片）我该如何对齐它们，或者还有其他完全不同、更好的方法吗？

我正在使用的代码：

\begin{figure}
    \centering
        \begin{tikzpicture}
            \tikzset{
                level 1/.style={level distance=15mm,sibling distance=65mm},
                level 2/.style={level distance=15mm,sibling distance=30mm},
                level 3/.style={level distance=15mm,sibling distance=15mm},
                level 4/.style={level distance=15mm,sibling distance=10mm},
            }
            \node {$\frac{1}{1}$}
            child[grow=up, left] {node {$\frac{0}{1}$} edge from parent[dashed]} 
            child[grow=up, right] {node {$\frac{1}{0}$} edge from parent[dashed]} 
            child {node {$\frac{1}{2}$}
                child {node {$\frac{1}{3}$}
                    child {node {$\frac{1}{4}$}}
                    child {node {$\frac{2}{5}$}}
                }
                child {node {$\frac{2}{3}$}
                    child {node {$\frac{3}{5}$}}
                    child {node {$\frac{3}{4}$}}
                }
            }
            child {node {$\frac{2}{1}$}
                child {node {$\frac{3}{2}$}
                    child {node {$\frac{4}{3}$}}
                    child {node {$\frac{5}{3}$}}
                }
                child {node {$\frac{3}{1}$}
                    child {node {$\frac{5}{2}$}}
                    child {node {$\frac{4}{1}$}}
                }
            };
        \end{tikzpicture}
    \caption{...}
\end{figure}

Answer 1

我不知道自己在做什么，但我玩了一下......

\documentclass[11pt]{article}
\usepackage{tikz}
\begin{document}
\centering
        \begin{tikzpicture}
            \tikzset{
                level 1/.style={level distance=15mm,sibling distance=65mm},
                level 2/.style={level distance=15mm,sibling distance=30mm},
                level 3/.style={level distance=15mm,sibling distance=15mm},
                level 4/.style={level distance=15mm,sibling distance=10mm},
            }
            \node {$\frac{1}{1}$}
            child[grow=up, left=7cm] {node {$\frac{0}{1}$} edge from parent[dashed]} 
            child[grow=up, right=7cm] {node {$\frac{1}{0}$} edge from parent[dashed]} 
            child [left=6cm] {node {$\frac{1}{2}$}
                child [right=-.5cm] {node {$\frac{1}{3}$}
                    child {node {$\frac{1}{4}$}}
                    child {node {$\frac{2}{5}$}}
                }
                child [left=-.5cm] {node {$\frac{2}{3}$}
                    child {node {$\frac{3}{5}$}}
                    child {node {$\frac{3}{4}$}}
                }
            }
            child [left=6cm]  {node {$\frac{2}{1}$}
                child [right=-.5cm] {node {$\frac{3}{2}$}
                    child {node {$\frac{4}{3}$}}
                    child {node {$\frac{5}{3}$}}
                }
                child [left=-.5cm] {node {$\frac{3}{1}$}
                    child {node {$\frac{5}{2}$}}
                    child {node {$\frac{4}{1}$}}
                }
            };
        \end{tikzpicture}

\end{document}