Draw recursion tree

Question

Suppose we want to draw recursion tree of T(n)=T(n/4)+T(n/2)+n^2 using Justtree package that introduced here (justtree.sty).

I try as follows:

    \begin{justtree}
    {
        declare count={tree n}{1},
        just format={xshift=1.5em},
        annotate/.style={% style should be applied to the rightmost node at each level for which an arrow and annotation is required
            if n children=0{}{
                right just=$n^2$,
            },
        },
        where n children=0{
            edge={dotted},
        }{},
        for tree={
            math content,
            if level=0{}{%
                if level=1{%
                    tree n'=1,
                }{%
                    if n=1{%
                        tree n/.wrap pgfmath arg={#1}{tree_n("!u")},
                    }{%
                        tree n/.wrap pgfmath arg={#1}{int((tree_n("!u"))},
                    },
                },
            },
            delay={
                if level=1{
                    content=n^2,
                    tikz+={
                        \draw [<->] (!F.south west) +(-2.5em,0) coordinate (c) -- (.north -| c) node [midway, anchor=south, sloped] {$\log_{\frac{4}{3}}n$};
                    }
                    ,
                }{
                    if n children=0{%
                    }{
                        if level=0{}{
                            content/.wrap 2 pgfmath args={(\frac{#1n}{#2})^2}{(tree_n()==1) ? "" : (tree_n())}{int(4^(level("!u")))},
                        }
                    }
                }
            },
        },
    }
    [, annotate
    [
    [
    [[][]]
    [[][]]
    ]
    [
    [[][]]
    [[][]]
    ]
    ]
    [, annotate
    [
    [[][]]
    [[][]]
    ]
    [, annotate
    [, annotate[][]]
    [[][]]
    ]
    ]
    ]
\end{justtree}

Unfortunately, above code draws a recursion tree for T(n)=T(n/4)+T(3n/4)+n^2 Could someone help me to modify the above code to achieve my goal?

Answer 1

Note 1: I don't really think I should answer this question. It provides a fragment of copied code without link or attribution, makes no effort to adapt that code and doesn't even bother to explain what the new tree should look like. I'm answering because I like doing things with Forest. If someone finds it useful, well and good.

Note 2: I consider justtrees inherently flawed and abandoned work on it several years ago. Unlike prooftrees, justtrees died an early death and never made it to CTAN. I have no plans to resurrect it. I recommend using forest directly unless you are drawing tableaux, in which case I recommend prooftrees. If this answer is at odds with that position, so much the worse for this answer.

Caveat emptor ...

---

This case is significantly simpler than the earlier example because the numerator is always simply n. (But it took me some while to figure this out because I had to figure out what a recursion tree was first.)

\documentclass[border=10pt]{standalone}
\usepackage[linguistics]{forest}
\usepackage{justtrees}

\begin{document}
\begin{justtree}
  {% ateb cfr: https://tex.stackexchange.com/a/702157/
    declare count={tree n}{1},
    just format={xshift=1.5em},
    annotate/.style={% style should be applied to the rightmost node at each level for which an arrow and annotation is required
      if n children=0{}{
        right just=$#1$,
      },
    },
    where n children=0{
      edge={dotted},
    }{},
    for tree={
      math content,
      if level=0{}{%
        if level=1{%
          tree n'=1,
        }{%
          if n=1{%
            tree n/.process={ O+nw+P {!u.tree n} {int(4*#1)}},
          }{%
            tree n/.process={ O+nw+P {!u.tree n} {int(2*#1)}},
          },
        },
      },
      delay={
        if level=1{
          content=n^2,
          tikz+={
            \draw [<->] (!F.south west) +(-2.5em,0) coordinate (c) -- (.north -| c) ;
          }
          ,
        }{
          if n children=0{%
          }{
            if level=0{}{
              content/.process={%
                O  w
                {tree n}  {(\frac{n}{#1})^2}
              },
            }
          }
        }
      },
    },
  }
  [, annotate=n^2
    [
      [
        [[][]]
        [[][]]
      ]
      [
        [[][]]
        [[][]]
      ]
    ]
    [, annotate=\frac{5n^2}{16}
      [
        [[][]]
        [[][]]
      ]
      [
        [[][]]
        [[][]]
      ]
    ]
  ]
\end{justtree}

\end{document}