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画出有不同高度叶子的树

tag-icon • tag-icon forest
画出有不同高度叶子的树

我正在尝试绘制一棵类似于下图的树（节点内容不同）。我的叶子非常宽，我需要通过“抬起”其他叶子来将它们紧密地靠在一起。

Tree with elevated leaves

是否可以调整下面的代码，让我的叶子处于不同的层次上，从而更靠近彼此，如上图所示？

\documentclass{standalone}
\usepackage{forest}    

\begin{document}
\begin{forest}
[{$r_{1,8} = p \bmod a_{1,8}$}
    [{$r_{1,4} = r_{1,8} \bmod a_{1,4}$} 
        [{$r_{1,2} = r_{1,4} \bmod a_{1,2}$} 
            [{$r_{1,1} = r_{1,2} \bmod (x-1)$}
                [{$v_1$} ]
            ]
            [{$r_{2,2} = r_{1,2} \bmod (x-2)$}
                [{$v_2$} ]
            ]
        ]
        [{$r_{3,4} = r_{1,4} \bmod a_{3,4}$} 
            [{$r_{3,3} = r_{3,4} \bmod (x-3)$}
                [{$v_3$} ]
            ]
            [{$r_{4,4} = r_{3,4} \bmod (x-4)$}
                [{$v_4$} ]
            ]
        ]
    ]
    [{$r_{5,8} = r_{1,8} \bmod a_{5,8}$} 
        [{$r_{5,6} = r_{5,8} \bmod a_{5,6}$} 
            [{$r_{5,5} = r_{5,6} \bmod (x-5)$}
                [{$v_5$} ]
            ]
            [{$r_{6,6} = r_{5,6} \bmod (x-6)$}
                [{$v_6$} ]
            ]
        ]
        [{$r_{7,8} = r_{5,8} \bmod a_{7,8}$} 
            [{$r_{7,7} = r_{7,8} \bmod (x-7)$}
                [{$v_7$} ]
            ]
            [{$r_{8,8} = r_{7,8} \bmod (x-8)$}
                [{$v_8$} ]
            ]
        ]
    ]
]
\end{forest}
\end{document}

稍后编辑：我已尝试以下操作。

首先，奇数和偶数的r_{i,i}分层不同。

\documentclass{standalone}
\usepackage{forest}

\begin{document}
\begin{forest}
[{$r_{1,8} = p \bmod a_{1,8}$}
    [{$r_{1,4} = r_{1,8} \bmod a_{1,4}$}
        [{$r_{1,2} = r_{1,4} \bmod a_{1,2}$}
            [{$r_{1,1} = r_{1,2} \bmod (x-1)$},tier=odd
                [{$v_1$} ]
            ]
            [{$r_{2,2} = r_{1,2} \bmod (x-2)$},tier=even
                [{$v_2$} ]
            ]
        ]
        [{$r_{3,4} = r_{1,4} \bmod a_{3,4}$}
            [{$r_{3,3} = r_{3,4} \bmod (x-3)$},tier=odd
                [{$v_3$}  ]
            ]
            [{$r_{4,4} = r_{3,4} \bmod (x-4)$},tier=even
                [{$v_4$} ]
            ]
        ]
    ]
    [{$r_{5,8} = r_{1,8} \bmod a_{5,8}$}
        [{$r_{5,6} = r_{5,8} \bmod a_{5,6}$}
            [{$r_{5,5} = r_{5,6} \bmod (x-5)$},tier=odd
                [{$v_5$}  ]
            ]
            [{$r_{6,6} = r_{5,6} \bmod (x-6)$},tier=even
                [{$v_6$} ]
            ]
        ]
        [{$r_{7,8} = r_{5,8} \bmod a_{7,8}$}
            [{$r_{7,7} = r_{7,8} \bmod (x-7)$},tier=odd
                [{$v_7$} ]
            ]
            [{$r_{8,8} = r_{7,8} \bmod (x-8)$},tier=even
                [{$v_8$} ]
            ]
        ]
    ]
]
\end{forest}
\end{document}

其次，对偶数r_{i,i}的和v_i的分层也不同。

\documentclass{standalone}
\usepackage{forest}

\begin{document}
\begin{forest}
[{$r_{1,8} = p \bmod a_{1,8}$}
    [{$r_{1,4} = r_{1,8} \bmod a_{1,4}$}
        [{$r_{1,2} = r_{1,4} \bmod a_{1,2}$}
            [{$r_{1,1} = r_{1,2} \bmod (x-1)$},tier=odd
                [{$v_1$},tier=last ]
            ]
            [{$r_{2,2} = r_{1,2} \bmod (x-2)$}
                [{$v_2$},tier=last ]
            ]
        ]
        [{$r_{3,4} = r_{1,4} \bmod a_{3,4}$}
            [{$r_{3,3} = r_{3,4} \bmod (x-3)$},tier=odd
                [{$v_3$},tier=last  ]
            ]
            [{$r_{4,4} = r_{3,4} \bmod (x-4)$}
                [{$v_4$},tier=last ]
            ]
        ]
    ]
    [{$r_{5,8} = r_{1,8} \bmod a_{5,8}$}
        [{$r_{5,6} = r_{5,8} \bmod a_{5,6}$}
            [{$r_{5,5} = r_{5,6} \bmod (x-5)$},tier=odd
                [{$v_5$},tier=last  ]
            ]
            [{$r_{6,6} = r_{5,6} \bmod (x-6)$}
                [{$v_6$},tier=last ]
            ]
        ]
        [{$r_{7,8} = r_{5,8} \bmod a_{7,8}$}
            [{$r_{7,7} = r_{7,8} \bmod (x-7)$},tier=odd
                [{$v_7$},tier=last ]
            ]
            [{$r_{8,8} = r_{7,8} \bmod (x-8)$}
                [{$v_8$},tier=last ]
            ]
        ]
    ]
]
\end{forest}
\end{document}

答案1

是的。就是这样tiers 的用途。（如果你懂德语，你就会明白为什么我有选择murmel。;-)

\documentclass{standalone}
\usepackage{forest}    

\begin{document}
\begin{forest}
[{$r_{1,8} = p \bmod a_{1,8}$}
    [{$r_{1,4} = r_{1,8} \bmod a_{1,4}$} 
        [{$r_{1,2} = r_{1,4} \bmod a_{1,2}$} 
            [{$r_{1,1} = r_{1,2} \bmod (x-1)$}
                [{$v_1$},tier=murmel ]
            ]
            [{$r_{2,2} = r_{1,2} \bmod (x-2)$},tier=murmel 
                [{$v_2$} ]
            ]
        ]
        [{$r_{3,4} = r_{1,4} \bmod a_{3,4}$} 
            [{$r_{3,3} = r_{3,4} \bmod (x-3)$}
                [{$v_3$},tier=murmel  ]
            ]
            [{$r_{4,4} = r_{3,4} \bmod (x-4)$},tier=murmel 
                [{$v_4$} ]
            ]
        ]
    ]
    [{$r_{5,8} = r_{1,8} \bmod a_{5,8}$} 
        [{$r_{5,6} = r_{5,8} \bmod a_{5,6}$} 
            [{$r_{5,5} = r_{5,6} \bmod (x-5)$}
                [{$v_5$},tier=murmel  ]
            ]
            [{$r_{6,6} = r_{5,6} \bmod (x-6)$},tier=murmel 
                [{$v_6$} ]
            ]
        ]
        [{$r_{7,8} = r_{5,8} \bmod a_{7,8}$} 
            [{$r_{7,7} = r_{7,8} \bmod (x-7)$}
                [{$v_7$},tier=murmel  ]
            ]
            [{$r_{8,8} = r_{7,8} \bmod (x-8)$},tier=murmel 
                [{$v_8$} ]
            ]
        ]
    ]
]
\end{forest}
\end{document}

enter image description here

v_i附录：所有的都处于同一级别，但上方节点的级别交替的版本。

\documentclass{standalone}
\usepackage{forest}    
\tikzset{bullet/.style={circle,fill,inner sep=0.2pt,outer sep=0pt}}
\begin{document}
\begin{forest}
[{$r_{1,8} = p \bmod a_{1,8}$}
    [{$r_{1,4} = r_{1,8} \bmod a_{1,4}$} 
        [{$r_{1,2} = r_{1,4} \bmod a_{1,2}$} 
            [{$r_{1,1} = r_{1,2} \bmod (x-1)$},tier=faul
                [{$v_1$},tier=murmel ]
            ]
            [,bullet,tier=faul
               [{$r_{2,2} = r_{1,2} \bmod (x-2)$},tier=schnabel
                   [{$v_2$},tier=murmel ]
               ]
            ]
        ]
        [{$r_{3,4} = r_{1,4} \bmod a_{3,4}$} 
            [{$r_{3,3} = r_{3,4} \bmod (x-3)$},tier=faul
                [{$v_3$},tier=murmel  ]
            ]
            [,bullet,tier=faul
               [{$r_{4,4} = r_{3,4} \bmod (x-4)$},tier=schnabel 
                   [{$v_4$},tier=murmel ]
               ]
            ]
        ]
    ]
    [{$r_{5,8} = r_{1,8} \bmod a_{5,8}$} 
        [{$r_{5,6} = r_{5,8} \bmod a_{5,6}$} 
            [{$r_{5,5} = r_{5,6} \bmod (x-5)$},tier=faul
                [{$v_5$},tier=murmel  ]
            ]
            [,bullet,tier=faul
               [{$r_{6,6} = r_{5,6} \bmod (x-6)$},tier=schnabel 
                   [{$v_6$},tier=murmel ]
               ]
            ]
        ]
        [{$r_{7,8} = r_{5,8} \bmod a_{7,8}$} 
            [{$r_{7,7} = r_{7,8} \bmod (x-7)$},tier=faul
                [{$v_7$},tier=murmel  ]
            ]
            [,bullet,tier=faul
               [{$r_{8,8} = r_{7,8} \bmod (x-8)$},tier=schnabel 
                   [{$v_8$},tier=murmel ]
               ]
            ]
        ]
    ]
]
\end{forest}
\end{document}

enter image description here

答案2

我认为您可以稍微调整一下子l叶子的规范。例如，此代码不会生成最“美观”的树，但它似乎朝着您需要的方向迈进了一步。有关叶子放置的更多详细信息，请参阅文档（例如第 10 页）

\documentclass{standalone}
\usepackage{forest}

\begin{document}
\begin{forest}
    [{$r_{1,8} = p \bmod a_{1,8}$}
    [{$r_{1,4} = r_{1,8} \bmod a_{1,4}$} 
    [{$r_{1,2} = r_{1,4} \bmod a_{1,2}$} 
    [{$r_{1,1} = r_{1,2} \bmod (x-1)$}, l = 22mm,
    [{$v_1$} ]
    ]
    [{$r_{2,2} = r_{1,2} \bmod (x-2)$}, l = 12mm,
    [{$v_2$}, l = 15mm ]
    ]
    ]
    [{$r_{3,4} = r_{1,4} \bmod a_{3,4}$} 
    [{$r_{3,3} = r_{3,4} \bmod (x-3)$}, l = 22mm,
    [{$v_3$} ]
    ]
    [{$r_{4,4} = r_{3,4} \bmod (x-4)$}, l = 12mm,
    [{$v_4$}, l = 15mm ]
    ]
    ]
    ]
    [{$r_{5,8} = r_{1,8} \bmod a_{5,8}$} 
    [{$r_{5,6} = r_{5,8} \bmod a_{5,6}$} 
    [{$r_{5,5} = r_{5,6} \bmod (x-5)$}, l = 22mm,
    [{$v_5$} ]
    ]
    [{$r_{6,6} = r_{5,6} \bmod (x-6)$}, l = 12mm,
    [{$v_6$}, l = 15mm ]
    ]
    ]
    [{$r_{7,8} = r_{5,8} \bmod a_{7,8}$} 
    [{$r_{7,7} = r_{7,8} \bmod (x-7)$}, l = 22mm,
    [{$v_7$} ]
    ]
    [{$r_{8,8} = r_{7,8} \bmod (x-8)$}, l = 12mm,
    [{$v_8$}, l = 15mm ]
    ]
    ]
    ]
    ]
\end{forest}
\end{document}

enter image description here

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