Copy the Merge sort recursion tree from tikz example with forest package

Question

I'm trying to explain the execution time of an algorithm and I'm using the forest as a package to drawing tree, and with this post, I'm asking if is possible to draw the same tree in the figure below with the package forest. Form the forest quick start I don't see an example like that.

Answer 1

% MergeSort-RecursionTree
% Manuel Kirsch
\documentclass[a4paper,landscape]{scrartcl}
\usepackage{fancybox}
\usepackage{tikz}
\title{MergeSort-RecursionTree}
\author{Manuel Kirsch}
\date{}
\begin{document}
\ovalbox{
\begin{tikzpicture}[level/.style={sibling distance=60mm/#1}]
\node [circle,draw] (z){$n$}
  child {node [circle,draw] (a) {$\frac{n}{2}$}
    child {node [circle,draw] (b) {$\frac{n}{2^2}$}
      child {node {$\vdots$}
        child {node [circle,draw] (d) {$\frac{n}{2^k}$}}
        child {node [circle,draw] (e) {$\frac{n}{2^k}$}}
      } 
      child {node {$\vdots$}}
    }
    child {node [circle,draw] (g) {$\frac{n}{2^2}$}
      child {node {$\vdots$}}
      child {node {$\vdots$}}
    }
  }
  child {node [circle,draw] (j) {$\frac{n}{2}$}
    child {node [circle,draw] (k) {$\frac{n}{2^2}$}
      child {node {$\vdots$}}
      child {node {$\vdots$}}
    }
  child {node [circle,draw] (l) {$\frac{n}{2^2}$}
    child {node {$\vdots$}}
    child {node (c){$\vdots$}
      child {node [circle,draw] (o) {$\frac{n}{2^k}$}}
      child {node [circle,draw] (p) {$\frac{n}{2^k}$}
        child [grow=right] {node (q) {$=$} edge from parent[draw=none]
          child [grow=right] {node (q) {$O_{k = \lg n}(n)$} edge from parent[draw=none]
            child [grow=up] {node (r) {$\vdots$} edge from parent[draw=none]
              child [grow=up] {node (s) {$O_2(n)$} edge from parent[draw=none]
                child [grow=up] {node (t) {$O_1(n)$} edge from parent[draw=none]
                  child [grow=up] {node (u) {$O_0(n)$} edge from parent[draw=none]}
                }
              }
            }
            child [grow=down] {node (v) {$O(n \cdot \lg n)$}edge from parent[draw=none]}
          }
        }
      }
    }
  }
};
\path (a) -- (j) node [midway] {+};
\path (b) -- (g) node [midway] {+};
\path (k) -- (l) node [midway] {+};
\path (k) -- (g) node [midway] {+};
\path (d) -- (e) node [midway] {+};
\path (o) -- (p) node [midway] {+};
\path (o) -- (e) node (x) [midway] {$\cdots$}
  child [grow=down] {
    node (y) {$O\left(\displaystyle\sum_{i = 0}^k 2^i \cdot \frac{n}{2^i}\right)$}
    edge from parent[draw=none]
  };
\path (q) -- (r) node [midway] {+};
\path (s) -- (r) node [midway] {+};
\path (s) -- (t) node [midway] {+};
\path (s) -- (l) node [midway] {=};
\path (t) -- (u) node [midway] {+};
\path (z) -- (u) node [midway] {=};
\path (j) -- (t) node [midway] {=};
\path (y) -- (x) node [midway] {$\Downarrow$};
\path (v) -- (y)
  node (w) [midway] {$O\left(\displaystyle\sum_{i = 0}^k n\right) = O(k \cdot n)$};
\path (q) -- (v) node [midway] {=};
\path (e) -- (x) node [midway] {+};
\path (o) -- (x) node [midway] {+};
\path (y) -- (w) node [midway] {$=$};
\path (v) -- (w) node [midway] {$\Leftrightarrow$};
\path (r) -- (c) node [midway] {$\cdots$};
\end{tikzpicture}}
\end{document}