Picture next to the table of contents (TOC) in Beamer correctly aligned vertically

Question

I want to place picture in Beamer presentation next to the table of contents (TOC), specifically on the right side of the TOC.

I know that there are several questions about similar or even identical problems, e.g.:

1. Beamer - Put a picture right of the table of contents
2. How to split a frame (of beamer) into 2 parts (minipage) side by side?
3. Displaying a new image for each new section with running table of contents

but the posted answers doesn't work well because as a result I get TOC lowered (see screenshots below).

This is answer from 1st linked question:

\documentclass{beamer}
\begin{document}

\begin{frame}
\begin{minipage}[t][0.6\textheight]{0.6\textwidth}
    \vspace{0pt}
    \tableofcontents
\end{minipage}
\begin{minipage}[t]{0.35\textwidth}
    \vspace{0pt}
    \includegraphics[width=.9\textwidth]{example-image-a}
\end{minipage}
\end{frame}

\section{A section with a name}
\begin{frame}
\end{frame}

\section{A longer section name, ....................}
\begin{frame}
\end{frame}

\section{another section}
\begin{frame}
\end{frame}

\section{a medium long section name}
\begin{frame}
\end{frame}

\end{document}

this is the result:

It seems to work well, but if you remove minipages like this:

\documentclass{beamer}
\begin{document}

\begin{frame}
\tableofcontents
\end{frame}

\section{A section with a name}
\begin{frame}
\end{frame}

\section{A longer section name, ....................}
\begin{frame}
\end{frame}

\section{another section}
\begin{frame}
\end{frame}

\section{a medium long section name}
\begin{frame}
\end{frame}

\end{document}

you get this:

If you put above screenshots side by side, like this:

you can clearly see that suggested solution lowers TOC. I want to place image next to TOC without lowering TOC and without absolute image positioning (because I want to be able to change aspectratio of the presentation without modifying hard coded image offsets).

How can I do this?

Answer 1

Here is a start.

It works as second section etc... is not too long else it would hit the picture. In that case you only need to use a suitable \rightskip setting (or whatever works with beamer class to temporarily set right margin; I suspect rightskip will not necessarily play well but I have not tested as the code works fine enough with given example) and push the picture by a \rlap into available space.

\documentclass{beamer}

\DeclareRobustCommand\PICINTOC{}%

\newcommand\MYPICINTOC
  {\hfill
   \smash{\raisebox{-\height}{\includegraphics[width=.3\textwidth]{example-image-a}}}}

\begin{document}

\begin{frame}
\addtocontents{toc}{\let\PICINTOC\string\MYPICINTOC}
\tableofcontents
\end{frame}

\section{A section with a name\PICINTOC}
\begin{frame}
\end{frame}

\section{A longer section name, ....................}
\begin{frame}
\end{frame}

\section{another section}
\begin{frame}
\end{frame}

\section{a medium long section name}
\begin{frame}
\end{frame}

\end{document}