使用 Tikz 将树置于中心

Question

\documentclass{article}
\usepackage{tikz}

\begin{document}
\usetikzlibrary{positioning,trees}
\begin{tikzpicture}[level/.style={sibling distance=85mm/#1}]
\node {T(n)}
    child {node {$T\left(\left(\frac{1}{3}\right)^{1}\cdot\left(\frac{2}{3}\right)^{0}\cdot n\right)$}
        child {node {$T\left(\left(\frac{1}{3}\right)^{2}\cdot\left(\frac{2}{3}\right)^{0}\cdot n\right)$}
            child {node {$T\left(\left(\frac{1}{3}\right)^{2}\cdot\left(\frac{2}{3}\right)^{0}\cdot n\right)$}}
            child {node {$T\left(\left(\frac{1}{3}\right)^{1}\cdot\left(\frac{2}{3}\right)^{1}\cdot n\right)$}}}
        child {node {$T\left(\left(\frac{1}{3}\right)^{1}\cdot\left(\frac{2}{3}\right)^{1}\cdot n\right)$}}
    }
    child {node {$T\left(\left(\frac{1}{3}\right)^{0}\cdot\left(\frac{2}{3}\right)^{1}\cdot n\right)$}
        child {node {$T\left(\left(\frac{1}{3}\right)^{2}\cdot\left(\frac{2}{3}\right)^{0}\cdot n\right)$}}
        child {node {$T\left(\left(\frac{1}{3}\right)^{1}\cdot\left(\frac{2}{3}\right)^{1}\cdot n\right)$}}
};

\end{tikzpicture}
\end{document}

我正在尝试使用 tree 绘制简单的递归树，但节点超出了页面边界。我已经尝试过 \begin{center}/\centering

Answer 1

您可以设置scale和transform shape选项来调整整个tikzpicture环境内容的大小：

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{positioning,trees}

\begin{document}

\begin{tikzpicture}[level/.style={sibling distance=85mm/#1}, scale=0.6, transform shape]
    \node {T(n)}
        child {node {$T\left(\left(\frac{1}{3}\right)^{1}\cdot\left(\frac{2}{3}\right)^{0}\cdot n\right)$}
            child {node {$T\left(\left(\frac{1}{3}\right)^{2}\cdot\left(\frac{2}{3}\right)^{0}\cdot n\right)$}
                child {node {$T\left(\left(\frac{1}{3}\right)^{2}\cdot\left(\frac{2}{3}\right)^{0}\cdot n\right)$}}
                child {node {$T\left(\left(\frac{1}{3}\right)^{1}\cdot\left(\frac{2}{3}\right)^{1}\cdot n\right)$}}}
            child {node {$T\left(\left(\frac{1}{3}\right)^{1}\cdot\left(\frac{2}{3}\right)^{1}\cdot n\right)$}}
        }
        child {node {$T\left(\left(\frac{1}{3}\right)^{0}\cdot\left(\frac{2}{3}\right)^{1}\cdot n\right)$}
            child {node {$T\left(\left(\frac{1}{3}\right)^{2}\cdot\left(\frac{2}{3}\right)^{0}\cdot n\right)$}}
            child {node {$T\left(\left(\frac{1}{3}\right)^{1}\cdot\left(\frac{2}{3}\right)^{1}\cdot n\right)$}}
    };
\end{tikzpicture}

\end{document}

Answer 2

我会使用forest。不仅因为它更节省空间，还因为您可以以编程方式创建树。（全部功劳归功于 Sašo Zivanović 和 cfr 为我们提供包和许多此类示例。）

\documentclass{article}
\usepackage{geometry}
\usepackage[edges]{forest}
\begin{document}

\begin{forest}
for tree={edge={semithick,draw},
l sep+=1ex,s sep+=-1ex,
if level=0{}{delay={%
content/.wrap 2 pgfmath
args={$\pgfmathtruncatemacro{\myn}{min(2,#1)+1-#2}
\pgfmathtruncatemacro{\mym}{#2-1}
T\left(\left(\frac{1}{3}\right)^{\myn}\left(\frac{2}{3}\right)^{\mym}n\right)$}{level}{n}}}}
[$T(n)$
 [
  [
   []
   []
  ]
  [
  ]
 ]
 [
  [
  ]
  [
  ]
 ]
]
\end{forest}
\end{document}

如您所见，您不必输入公式。如果您有另一个递归，您只需更改公式即可。