How to draw a joining line between two picture tikz-pgf

Question

I'am having draw two tree using the tikz-pgf package

 \begin{frame}
\begin{columns}[c]
\begin{column}{2cm}
    \begin{tikzpicture}[scale=0.5] 
    \tikzstyle{level 1}=[sibling distance=10mm] 
    \node{f} 
    child{node{a}}
    child{node{f} child{node{b}} child{[red] node{f }   child{node{a}} child{node{f} child{node{b}}child{node{b}}}      }}
    ;
    \end{tikzpicture}
\end{column}

\begin{column}{2cm}
   \begin{tikzpicture}[scale=0.5] 
   \tikzstyle{level 1}=[sibling distance=10mm] 
   \node{f} 
    child{node{a}}
    child{node{f} child{node{b}} child{ node{f }   child{node{a}} child{node{g} child[missing] child{node{a}}}      }}
    ;
   \end{tikzpicture}
 \end{column}
 \end{columns}
\end{frame}

The result is :

Now i want to connect these two images by a curve line like this

i don't know how i will do it , any answer will be appreciates

Answer 1

You can name the nodes and, since the two nodes belong to different tikzpictures, you need to use the remember picture, overlay options to draw a line connecting them:

\documentclass{beamer}
\usepackage{tikz}

\begin{document}

 \begin{frame}

 \begin{columns}[c]
 \begin{column}{2cm}
    \begin{tikzpicture}[remember picture,overlay,scale=0.5] 
    \tikzstyle{level 1}=[sibling distance=10mm] 
    \node{f} 
    child{node{a}}
    child{node{f} child{node{b}} child{[red] node (f1) {f }   child{node{a}} child{node{f} child{node{b}}child{node{b}}}      }}
    ;
    \end{tikzpicture}
\end{column}    
\begin{column}{2cm}
   \begin{tikzpicture}[remember picture,overlay,scale=0.5] 
   \tikzstyle{level 1}=[sibling distance=10mm] 
   \node (f2) {f} 
    child{node{a}}
    child{node{f} child{node{b}} child{ node{f }   child{node{a}} child{node{g} child[missing] child{node{a}}}      }}
    ;
\draw (f1) .. controls (-3,3) .. (f2);
   \end{tikzpicture}
 \end{column}
 \end{columns}
\end{frame}

\end{document}

If both trees are part of the same tikzpicture, there's no need to use remember picture,overlay (but I don't know if using two environments is esential in your actual document).