\documentclass{article}


\newcommand{\dir}{../../latex}
\input{\dir/include.tex}
\load{recommended}

\setup{Algorithms and Probability}

\begin{document}
\startDocument
\usetcolorboxes
\setcounter{numberingConfig}{3}

\vspace{2cm}
\begin{Huge}
    \begin{align*}
          & \Pr[X|Y] \geq \Pr[X|\overline{Y}] \\
        X & := \text{I pass the exam}         \\
        Y & := \text{I read this summary}
    \end{align*}
\end{Huge}


\vspace{4cm}
\begin{center}
    \begin{Large}
        ``\textit{Dieses Algorithmus mapped $E$ nach $E$ Strich}''
    \end{Large}

    \hspace{3cm} - Rasmus Kyng, 2025
\end{center}

\vspace{3cm}
\begin{center}
    FS2025, ETHZ\\[0.2cm]
    \begin{Large}
        Summary of the Script and Lectures
    \end{Large}\\[0.2cm]
\end{center}




\newpage
\printtoc{ForestGreen}

% Graph algorithms
\input{parts/graphs/intro.tex}
\input{parts/graphs/connectivity.tex}
\input{parts/graphs/cycles.tex}
\input{parts/graphs/matchings.tex}
\input{parts/graphs/colourings.tex}


% Section on combinatorics
\input{parts/combinatorics.tex}


% Probability
\input{parts/probability/intro.tex}
\input{parts/probability/conditional-probability.tex}
\input{parts/probability/independence.tex}
\input{parts/probability/random-variable.tex}
\input{parts/probability/discrete-distribution.tex}
\input{parts/probability/multiple-random-variales.tex}
\input{parts/probability/approximating-probabilities.tex}
\input{parts/probability/algorithms.tex}


% Algorithms
\input{parts/algorithms/long-path.tex}
\input{parts/algorithms/flows/intro.tex}
\input{parts/algorithms/flows/max-flow-min-cut.tex}
\input{parts/algorithms/flows/algorithms.tex}
\input{parts/algorithms/flows/examples.tex}

\input{parts/coding.tex}


\end{document}