绘制 5 周期二项树

Question 1

这是使用强大forest包的开始。此编辑版本通过定义一个样式来自动化树的生成，bag该样式采用 2 个参数，分别为的数量W和的数量B，自动创建边缘标签并将计算中使用的分数附加到终端节点。

\documentclass[tikz,border=5pt,10pt]{standalone}
\usepackage{forest}
\usetikzlibrary{arrows.meta}

\begin{document}

\newcounter{bag}
\forestset{
  bag/.style 2 args= {
    text width=4em,
    text centered,
    if n=1{
      content = {$\frac{#1}{\pgfmathsetmacro\totalinbag{int(#1+#2)}\totalinbag}$},
    }{
      content = {$\frac{#2}{\pgfmathsetmacro\totalinbag{int(#1+#2)}\totalinbag}$},
    },
    before typesetting nodes={
      content/.wrap pgfmath arg = {Bag ##1 $#1W, #2B$}{int(level()+1)},
    },
    for children={
      if n=1{
        branch label={W}{#1}{\pgfmathsetmacro\totalinbag{int(#1+#2)}\totalinbag},
      }{
        branch label={B}{#2}{\pgfmathsetmacro\totalinbag{int(#1+#2)}\totalinbag},
      }
    },
  },
  terminus/.style = {
    align=left,
    child anchor=west,
    for parent={s sep=10mm},
    edge path={
      \noexpand\path [draw, -{Circle[]}, \forestoption{edge}] (!u.parent anchor) -- (.child anchor)\forestoption{edge label};
    },
    delay={
      content/.wrap 6 pgfmath args = {$P(##6)=$##5$\cdot$##4$\cdot$##3$\cdot$##2$\cdot$##1}{content("!u")}{content("!uu")}{content("!uuu")}{content("!uuuu")}{content("!uuuuu")}{content()}
    },
  },
  branch label/.style n args = 3{
    edge label={node [above, midway, sloped] {$#1$} node [below, midway, sloped] {$\frac{#2}{#3}$}},
  },
}

  \begin{forest}
    for tree={
      if n children=0{terminus}{},
      grow=0,
      l sep=15mm,
    }
    [,bag={4}{3}
      [,bag={4}{5}
        [,bag={1}{3}
          [,bag={2}{3}
            [,bag={2}{4}
              [{W_1\cap W_2\cap W_3\cap W_4}
              ]
              [{W_1\cap W_2\cap W_3\cap B_4}
              ]
            ]
            [,bag={2}{4}
              [{W_1\cap W_2\cap W_3\cap W_4}
              ]
              [{W_1\cap W_2\cap W_3\cap B_4}
              ]
            ]
          ]
          [,bag={2}{3}
            [,bag={2}{4}
              [{W_1\cap W_2\cap B_3\cap W_4}
              ]
              [{W_1\cap W_2\cap B_3\cap B_4}
              ]
            ]
            [,bag={2}{4}
              [{W_1\cap W_2\cap B_3\cap W_4}
              ]
              [{W_1\cap W_2\cap B_3\cap B_4}
              ]
            ]
          ]
        ]
        [,bag={1}{3}
          [,bag={2}{3}
            [,bag={2}{4}
              [{W_1\cap B_2\cap W_3\cap W_4}
              ]
              [{W_1\cap B_2\cap W_3\cap B_4}
              ]
            ]
            [,bag={2}{4}
              [{W_1\cap B_2\cap W_3\cap W_4}
              ]
              [{W_1\cap B_2\cap W_3\cap B_4}
              ]
            ]
          ]
          [,bag={2}{3}
            [,bag={2}{4}
              [{W_1\cap B_2\cap B_3\cap W_4}
              ]
              [{W_1\cap B_2\cap B_3\cap B_4}
              ]
            ]
            [,bag={2}{4}
              [{W_1\cap B_2\cap B_3\cap W_4}
              ]
              [{W_1\cap B_2\cap B_3\cap B_4}
              ]
            ]
          ]
        ]
      ]
      [,bag={3}{6}
        [,bag={1}{3}
          [,bag={6}{7}
            [,bag={1}{2}
              [{B_1\cap W_2\cap W_3}
              ]
              [{B_1\cap W_2\cap W_3}
              ]
            ]
            [,bag={1}{2}
              [{B_1\cap W_2\cap W_3}
              ]
              [{B_1\cap W_2\cap W_3}
              ]
            ]
          ]
          [,bag={6}{7}
            [,bag={4}{8}
              [{B_1\cap W_2\cap B_3}
              ]
              [{B_1\cap W_2\cap B_3}
              ]
            ]
            [,bag={4}{8}
              [{B_1\cap W_2\cap B_3}
              ]
              [{B_1\cap W_2\cap B_3}
              ]
            ]
          ]
        ]
        [,bag={1}{3}
          [,bag={4}{6}
            [,bag={3}{6}
              [{B_1\cap B_2\cap W_3}
              ]
              [{B_1\cap B_2\cap W_3}
              ]
            ]
            [,bag={3}{6}
              [{B_1\cap B_2\cap W_3}
              ]
              [{B_1\cap B_2\cap W_3}
              ]
            ]
          ]
          [,bag={4}{6}
            [,bag={3}{6}
              [{B_1\cap B_2\cap W_3}
              ]
              [{B_1\cap B_2\cap W_3}
              ]
            ]
            [,bag={3}{6}
              [{B_1\cap B_2\cap W_3}
              ]
              [{B_1\cap B_2\cap W_3}
              ]
            ]
          ]
        ]
      ]
    ]
  \end{forest}

\end{document}

森林二项式

Answer

这是使用强大forest包的开始。此编辑版本通过定义一个样式来自动化树的生成，bag该样式采用 2 个参数，分别为的数量W和的数量B，自动创建边缘标签并将计算中使用的分数附加到终端节点。

\documentclass[tikz,border=5pt,10pt]{standalone}
\usepackage{forest}
\usetikzlibrary{arrows.meta}

\begin{document}

\newcounter{bag}
\forestset{
  bag/.style 2 args= {
    text width=4em,
    text centered,
    if n=1{
      content = {$\frac{#1}{\pgfmathsetmacro\totalinbag{int(#1+#2)}\totalinbag}$},
    }{
      content = {$\frac{#2}{\pgfmathsetmacro\totalinbag{int(#1+#2)}\totalinbag}$},
    },
    before typesetting nodes={
      content/.wrap pgfmath arg = {Bag ##1 $#1W, #2B$}{int(level()+1)},
    },
    for children={
      if n=1{
        branch label={W}{#1}{\pgfmathsetmacro\totalinbag{int(#1+#2)}\totalinbag},
      }{
        branch label={B}{#2}{\pgfmathsetmacro\totalinbag{int(#1+#2)}\totalinbag},
      }
    },
  },
  terminus/.style = {
    align=left,
    child anchor=west,
    for parent={s sep=10mm},
    edge path={
      \noexpand\path [draw, -{Circle[]}, \forestoption{edge}] (!u.parent anchor) -- (.child anchor)\forestoption{edge label};
    },
    delay={
      content/.wrap 6 pgfmath args = {$P(##6)=$##5$\cdot$##4$\cdot$##3$\cdot$##2$\cdot$##1}{content("!u")}{content("!uu")}{content("!uuu")}{content("!uuuu")}{content("!uuuuu")}{content()}
    },
  },
  branch label/.style n args = 3{
    edge label={node [above, midway, sloped] {$#1$} node [below, midway, sloped] {$\frac{#2}{#3}$}},
  },
}

  \begin{forest}
    for tree={
      if n children=0{terminus}{},
      grow=0,
      l sep=15mm,
    }
    [,bag={4}{3}
      [,bag={4}{5}
        [,bag={1}{3}
          [,bag={2}{3}
            [,bag={2}{4}
              [{W_1\cap W_2\cap W_3\cap W_4}
              ]
              [{W_1\cap W_2\cap W_3\cap B_4}
              ]
            ]
            [,bag={2}{4}
              [{W_1\cap W_2\cap W_3\cap W_4}
              ]
              [{W_1\cap W_2\cap W_3\cap B_4}
              ]
            ]
          ]
          [,bag={2}{3}
            [,bag={2}{4}
              [{W_1\cap W_2\cap B_3\cap W_4}
              ]
              [{W_1\cap W_2\cap B_3\cap B_4}
              ]
            ]
            [,bag={2}{4}
              [{W_1\cap W_2\cap B_3\cap W_4}
              ]
              [{W_1\cap W_2\cap B_3\cap B_4}
              ]
            ]
          ]
        ]
        [,bag={1}{3}
          [,bag={2}{3}
            [,bag={2}{4}
              [{W_1\cap B_2\cap W_3\cap W_4}
              ]
              [{W_1\cap B_2\cap W_3\cap B_4}
              ]
            ]
            [,bag={2}{4}
              [{W_1\cap B_2\cap W_3\cap W_4}
              ]
              [{W_1\cap B_2\cap W_3\cap B_4}
              ]
            ]
          ]
          [,bag={2}{3}
            [,bag={2}{4}
              [{W_1\cap B_2\cap B_3\cap W_4}
              ]
              [{W_1\cap B_2\cap B_3\cap B_4}
              ]
            ]
            [,bag={2}{4}
              [{W_1\cap B_2\cap B_3\cap W_4}
              ]
              [{W_1\cap B_2\cap B_3\cap B_4}
              ]
            ]
          ]
        ]
      ]
      [,bag={3}{6}
        [,bag={1}{3}
          [,bag={6}{7}
            [,bag={1}{2}
              [{B_1\cap W_2\cap W_3}
              ]
              [{B_1\cap W_2\cap W_3}
              ]
            ]
            [,bag={1}{2}
              [{B_1\cap W_2\cap W_3}
              ]
              [{B_1\cap W_2\cap W_3}
              ]
            ]
          ]
          [,bag={6}{7}
            [,bag={4}{8}
              [{B_1\cap W_2\cap B_3}
              ]
              [{B_1\cap W_2\cap B_3}
              ]
            ]
            [,bag={4}{8}
              [{B_1\cap W_2\cap B_3}
              ]
              [{B_1\cap W_2\cap B_3}
              ]
            ]
          ]
        ]
        [,bag={1}{3}
          [,bag={4}{6}
            [,bag={3}{6}
              [{B_1\cap B_2\cap W_3}
              ]
              [{B_1\cap B_2\cap W_3}
              ]
            ]
            [,bag={3}{6}
              [{B_1\cap B_2\cap W_3}
              ]
              [{B_1\cap B_2\cap W_3}
              ]
            ]
          ]
          [,bag={4}{6}
            [,bag={3}{6}
              [{B_1\cap B_2\cap W_3}
              ]
              [{B_1\cap B_2\cap W_3}
              ]
            ]
            [,bag={3}{6}
              [{B_1\cap B_2\cap W_3}
              ]
              [{B_1\cap B_2\cap W_3}
              ]
            ]
          ]
        ]
      ]
    ]
  \end{forest}

\end{document}

森林二项式

Question 2

forest下面是用于自动构建树的动态代码：

\documentclass[]{standalone}
\usepackage{forest}
\bracketset{action character=@}

\def\pexp#1#2{\pgfmathsetmacro{\x}{int(#1)}\pgfmathparse{\x>0?(\x>1?"#2^{\x}":"#2"):""}\pgfmathresult}%
\def\btreelabel#1#2{node[midway,sloped,font=\scriptsize,/forest,if n=1{/tikz/below}{/tikz/above}]{$\pexp{#1}{p}\pexp{#2}{(1-p)}$}}%
\def\btree#1#2#3{,grow=east,l*=2,edge label=\btreelabel{#1}{#2},if={#3>0}{append=[@\btree{#1}{#2+1}{#3-1}],append=[@\btree{#1+1}{#2}{#3-1}]}{}}%

\begin{document}
\begin{forest}
    before typesetting nodes={for descendants={content/.pgfmath={int(content("!u")*2-int(n)+2)}}}
    [1@\btree{0}{0}{5}]% Set tree depth here
    % \btree#1#2#3 builds a subtree starting with probability p^#1,(1-p)^#2, and depth #3
\end{forest}
\end{document}

它并不完整，但可以向您展示如何使用forest包构建动态树。

Answer

forest下面是用于自动构建树的动态代码：

\documentclass[]{standalone}
\usepackage{forest}
\bracketset{action character=@}

\def\pexp#1#2{\pgfmathsetmacro{\x}{int(#1)}\pgfmathparse{\x>0?(\x>1?"#2^{\x}":"#2"):""}\pgfmathresult}%
\def\btreelabel#1#2{node[midway,sloped,font=\scriptsize,/forest,if n=1{/tikz/below}{/tikz/above}]{$\pexp{#1}{p}\pexp{#2}{(1-p)}$}}%
\def\btree#1#2#3{,grow=east,l*=2,edge label=\btreelabel{#1}{#2},if={#3>0}{append=[@\btree{#1}{#2+1}{#3-1}],append=[@\btree{#1+1}{#2}{#3-1}]}{}}%

\begin{document}
\begin{forest}
    before typesetting nodes={for descendants={content/.pgfmath={int(content("!u")*2-int(n)+2)}}}
    [1@\btree{0}{0}{5}]% Set tree depth here
    % \btree#1#2#3 builds a subtree starting with probability p^#1,(1-p)^#2, and depth #3
\end{forest}
\end{document}

它并不完整，但可以向您展示如何使用forest包构建动态树。

绘制 5 周期二项树

答案1

答案2

相关内容