diff --git a/20210204/hp-20210204.pdf b/20210204/hp-20210204.pdf
index 12b377190ab0b04487433a8feba26b2c14f0f5e3..1906c32d866445597b7611b8a74ccda92b49806a 100644
Binary files a/20210204/hp-20210204.pdf and b/20210204/hp-20210204.pdf differ
diff --git a/20210204/hp-20210204.tex b/20210204/hp-20210204.tex
index dc4a31a69d54f224e4f274e0e09ba5489146d84a..037525827465f0a7f481dfd24dcfb969fed21905 100644
--- a/20210204/hp-20210204.tex
+++ b/20210204/hp-20210204.tex
@@ -699,413 +699,4 @@
\end{frame}
-\section{Datenstrukturen}
-\subsection{Stack und FIFO}
-
-\begin{frame}[fragile]
-
- \showsection
- \showsubsection
-
- \begin{minipage}{0.48\textwidth}
- Im letzten Praktikumsversuch:
- \begin{itemize}
- \item
- Array nur zum Teil benutzt
- \item
- Variable speichert genutzte Länge
- \item
- Elemente hinten anfügen\\
- oder entfernen
- \arrowitem
- Stack\\
- \strut
- \end{itemize}
- \bigskip
- \begin{itemize}
- \item
- hinten anfügen/entfernen: $\mathcal{O}(1)$\hspace*{-1cm}
- \item
- vorne oder in der Mitte einfügen/entfernen: $\mathcal{O}(n)$
- \end{itemize}
- \end{minipage}\hfill
- \begin{minipage}{0.52\textwidth}
- Auch möglich:
- \begin{itemize}
- \item
- Array nur zum Teil benutzt
- \item
- 2 Variable speichern\\genutzte Länge (ringförmig)
- \item
- Elemente hinten anfügen\\
- oder vorne entfernen
- \arrowitem
- FIFO
- \end{itemize}
- \bigskip
- \begin{itemize}
- \item
- vorne oder hinten\\
- anfügen oder entfernen: $\mathcal{O}(1)$
- \item
- in der Mitte einfügen/entfernen: $\mathcal{O}(n)$
- \end{itemize}
- \end{minipage}\hspace*{-1.5mm}
-
-\end{frame}
-
-\begin{frame}[fragile]
-
- \showsection
- \showsubsection
-
- \bigskip
-
- \begin{minipage}[b]{6cm}
- \begin{center}
- "`First In -- First Out"'
-
- \bigskip
-
- \begin{picture}(6,4)
- \thicklines
- \color{structure}
- \put(0.5,0){\line(1,0){5}}
-
- \put(3.5,0){\only<1-5>{\line(0,1){1}}}
- \put(4.5,0){\only<1-4>{\line(0,1){1}}}
- \put(3.5,1){\only<1-4>{\line(1,0){1}}}
- \put(4.0,0.5){\only<1-4>{\makebox(0,0){\lstinline{3}}}}
- \put(3.0,1.5){\only<1>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
- \put(3.0,1.5){\only<1>{\makebox(0,0)[b]{\lstinline{push (3)}}}}
-
- \put(2.5,0){\only<2-6>{\line(0,1){1}}}
- \put(2.5,1){\only<2-5>{\line(1,0){1}}}
- \put(3.0,0.5){\only<2-5>{\makebox(0,0){\lstinline{7}}}}
- \put(2.0,1.5){\only<2>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
- \put(2.0,1.5){\only<2>{\makebox(0,0)[b]{\lstinline{push (7)}}}}
-
- \put(1.5,0){\only<3-6>{\line(0,1){1}}}
- \put(1.5,1){\only<3-6>{\line(1,0){1}}}
- \put(2.0,0.5){\only<3-6>{\makebox(0,0){\lstinline{137}}}}
- \put(1.0,1.5){\only<3>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
- \put(1.0,1.5){\only<3>{\makebox(0,0)[b]{\lstinline{push (137)}}}}
-
- \put(4.55,1.05){\only<4>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
- \put(5.00,1.60){\only<4>{\makebox(0,0)[b]{\lstinline{pop ()}: 3}}}
-
- \put(3.55,1.05){\only<5>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
- \put(4.00,1.60){\only<5>{\makebox(0,0)[b]{\lstinline{pop ()}: 7}}}
-
- \put(2.55,1.05){\only<6>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
- \put(3.00,1.60){\only<6>{\makebox(0,0)[b]{\lstinline{pop ()}: 137}}}
- \end{picture}
-
- \bigskip
-
- FIFO = Queue = Reihe
- \end{center}
- \end{minipage}\hfill
- \begin{minipage}[b]{6cm}
- \begin{center}
- "`Last In -- First Out"'
-
- \bigskip
-
- \begin{picture}(6,4)
- \thicklines
- \color{structure}
- \put(1.5,0){\line(1,0){3}}
-
- \put(2.5,0){\line(0,1){1}}
- \put(3.5,0){\line(0,1){1}}
- \put(2.5,1){\line(1,0){1}}
- \put(3.0,0.5){\makebox(0,0){\lstinline{3}}}
- \put(2.0,1.5){\only<1>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
- \put(2.0,1.5){\only<1>{\makebox(0,0)[b]{\lstinline{push (3)}}}}
-
- \put(2.5,1){\only<2-5>{\line(0,1){1}}}
- \put(3.5,1){\only<2-5>{\line(0,1){1}}}
- \put(2.5,2){\only<2-5>{\line(1,0){1}}}
- \put(3.0,1.5){\only<2-5>{\makebox(0,0){\lstinline{7}}}}
- \put(2.0,2.5){\only<2>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
- \put(2.0,2.5){\only<2>{\makebox(0,0)[b]{\lstinline{push (7)}}}}
-
- \put(2.5,2){\only<3-4>{\line(0,1){1}}}
- \put(3.5,2){\only<3-4>{\line(0,1){1}}}
- \put(2.5,3){\only<3-4>{\line(1,0){1}}}
- \put(3.0,2.5){\only<3-4>{\makebox(0,0){\lstinline{137}}}}
- \put(2.0,3.5){\only<3>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
- \put(2.0,3.5){\only<3>{\makebox(0,0)[b]{\lstinline{push (137)}}}}
-
- \put(3.55,3.05){\only<4>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
- \put(4.00,3.60){\only<4>{\makebox(0,0)[b]{\lstinline{pop ()}: 137}}}
-
- \put(3.55,2.05){\only<5>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
- \put(4.00,2.60){\only<5>{\makebox(0,0)[b]{\lstinline{pop ()}: 7}}}
-
- \put(3.55,1.05){\only<6>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
- \put(4.00,1.60){\only<6>{\makebox(0,0)[b]{\lstinline{pop ()}: 3}}}
- \end{picture}
-
- \bigskip
-
- LIFO = Stack = Stapel
- \end{center}
- \end{minipage}
-
-%
-% \dots
-
-\end{frame}
-
-\begin{frame}
-
- \showsection
- \showsubsection
-
- \bigskip
-
- \begin{minipage}[t]{6cm}
- Array (Stack, FIFO):\\
- in der Mitte einfügen
- \begin{center}
- \begin{picture}(6,3.8)
- \thicklines
- \color{structure}
- \put(1.5,0){\line(1,0){3}}
-
- \put(2.5,0){\line(0,1){3}}
- \put(3.5,0){\line(0,1){3}}
- \put(2.5,1){\line(1,0){1}}
- \put(3.0,0.5){\makebox(0,0){\lstinline{3}}}
- \put(2.5,1){\line(1,0){1}}
- \put(3.0,1.5){\makebox(0,0){\lstinline{7}}}
- \put(2.5,2){\line(1,0){1}}
- \put(3.0,2.5){\makebox(0,0){\lstinline{137}}}
- \put(2.5,3){\line(1,0){1}}
-
- \put(1.5,1.5){\makebox(0,0)[b]{\lstinline{push (5)}}}
- \put(1.5,1.45){\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.95,-0.45);}}}
-
- \put(3.55,2.5){\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)..controls(0.5,0.45)..(0,0.9);}}}
- \put(3.55,1.5){\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)..controls(0.5,0.45)..(0,0.9);}}}
-
- \pause
- \color{red}
- \put(4.1,3.0){\makebox(0,0)[l]{\textbf{1.}}}
- \put(4.1,2.0){\makebox(0,0)[l]{\textbf{2.}}}
- \put(1.5,1.9){\makebox(0,0)[b]{\textbf{3.}}}
-
- \pause
- \put(6.0,1.5){\makebox(0,0)[tl]{$\mathcal{O}(n)$}}
- \put(5.95,1.45){\makebox(0,0)[br]{\tikz{\draw[-latex](0,0)--(-1.3,0.4);}}}
- \put(5.95,1.49){\makebox(0,0)[br]{\tikz{\draw[-latex](0,0)--(-1.3,1.1);}}}
- \end{picture}
- \end{center}
- \end{minipage}\pause\hfill
- \begin{minipage}[t]{5cm}
- In Array (Stack, FIFO) \dots
- \begin{itemize}
- \item
- einfügen: $\mathcal{O}(n)$
- \item
- suchen: $\mathcal{O}(n)$
- \item
- geschickt suchen: $\mathcal{O}(\log n)$
- \item
- beim Einfügen sortieren:\\
- $\mathcal{O}(n \log n)$ \hspace*{-1.8cm}\tikz{\draw[red](-1.8,0)--(0,0.2);\draw[red](-1.8,0.2)--(0,0);}
- $\mathcal{O}(n^2)$
- \end{itemize}
- \end{minipage}
-
-\end{frame}
-
-\subsection{Verkettete Listen}
-
-\begin{frame}
-
- \showsection
- \showsubsection
-
- \begin{tikzpicture}
- \color{structure}
- \node(first) at (0,0.5) {first};
- \node[shape=rectangle,draw,line width=1pt](3) at (1,2) {3};
- \node[shape=rectangle,draw,line width=1pt](5) at (2,1) {5};
- \node[shape=rectangle,draw,line width=1pt](7) at (3,2) {7};
- \node[shape=rectangle,draw,line width=1pt](137) at (5,2) {137};
- \node(NULL) at (7,2) {NULL};
- \draw[-latex](first)--(3);
- \only<1>{\draw[-latex](3)--(7);}
- \only<2>{\draw[-latex](3) to[out=0] (5);}
- \only<2>{\draw[-latex](5) to[in=180] (7);}
- \draw[-latex](7)--(137);
- \draw[-latex](137)--(NULL);
- \end{tikzpicture}
- \begin{itemize}
- \item
- Jeder Datensatz enthält einen Zeiger auf das nächste Element.
- \item
- Beim letzten Element zeigt der Zeiger auf \lstinline{NULL}.
- \item
- Eine Variable zeigt auf das erste Element.
- \item
- Wenn die Liste leer ist, zeigt die Variable auf \lstinline{NULL}.
- \arrowitem
- (einfach) \textbf{verkettete Liste}
- \end{itemize}
-
-\end{frame}
-
-\begin{frame}
-
- \showsection
- \showsubsection
-
- \begin{minipage}[t]{5cm}
- In Array (Stack, FIFO) \dots
- \begin{itemize}
- \item
- in der Mitte einfügen: $\mathcal{O}(n)$
- \item
- wahlfreier Zugriff: $\mathcal{O}(1)$
- \item
- suchen: $\mathcal{O}(n)$
- \item
- geschickt suchen: $\mathcal{O}(\log n)$
- \item
- beim Einfügen sortieren:\\
- $\mathcal{O}(n \log n)$ \hspace*{-1.8cm}\tikz{\draw[red](-1.8,0)--(0,0.2);\draw[red](-1.8,0.2)--(0,0);}
- $\mathcal{O}(n^2)$
- \end{itemize}
- \end{minipage}\hfill
- \begin{minipage}[t]{6cm}
- In (einfach) verkettete/r Liste \dots
- \begin{itemize}
- \item
- in der Mitte einfügen: $\mathcal{O}(1)$
- \item
- wahlfreier Zugriff: $\mathcal{O}(n)$
- \item
- suchen: $\mathcal{O}(n)$
- \item
- geschickt \hspace*{-1.7cm}\tikz{\draw[red](-1.7,0)--(0,0.2);\draw[red](-1.7,0.2)--(0,0);}
- suchen: {\color{red}$\mathcal{O}(n)$}
- \item
- beim Einfügen sortieren:
- $\mathcal{O}(n \log n)$ \hspace*{-1.8cm}\tikz{\draw[red](-1.8,0)--(0,0.2);\draw[red](-1.8,0.2)--(0,0);}
- $\mathcal{O}(n^2)$
- \end{itemize}
- \end{minipage}
- \pause
- \medskip
- \begin{center}
- \begin{minipage}[t]{6cm}
- In (ausbalancierten) Bäumen \dots
- \begin{itemize}
- \item
- in der Mitte einfügen: $\mathcal{O}(\log n)$
- \item
- wahlfreier Zugriff: $\mathcal{O}(\log n)$
- \item
- suchen: $\mathcal{O}(\log n)$
- \item
- beim Einfügen sortieren:
- $\mathcal{O}(n \log n)$
- \end{itemize}
- \end{minipage}
- \end{center}
- \vspace*{-1cm}
-
-\end{frame}
-
-\subsection{Bäume}
-
-\begin{frame}[fragile]
-
- \showsection
- \showsubsection
-
- \begin{minipage}[t]{5cm}
- \vspace*{-6cm}
- \begin{lstlisting}[gobble=6]
- ¡typedef struct node
- {
- int content;
- struct node *left, *right;
- } node;¿
- \end{lstlisting}
- \bigskip
- \bigskip
- \begin{onlyenv}<6->
- \begin{itemize}
- \item
- Einfügen: rekursiv, $\mathcal{O}(\log n)$
- \item
- Suchen: rekursiv, $\mathcal{O}(\log n)$
- \item
- beim Einfügen sortieren:\\
- rekursiv, $\mathcal{O}(n\log n)$
- \begin{onlyenv}<7->
- \smallskip
- \item
- {\color{red}
- \emph{Worst Case\/}: $\mathcal{O}(n^2)$\\
- vorher bereits sortiert}\\
- \textarrow\ balancierte Bäume\\
- \hspace*{2.15em}Anwendung: Datenbanken\hspace*{-2cm}
- \end{onlyenv}
- \end{itemize}
- \vspace*{-1cm}
- \end{onlyenv}
- \end{minipage}\hfill
- \begin{minipage}[t]{7cm}
- \begin{center}
- \begin{tikzpicture}
- \color{structure}
- \node(root) at (0,0) {\lstinline{node *root;}};
- \begin{onlyenv}<2>
- \node(3) at (-2,-3) {\lstinline{NULL}};
- \node(137) at (2,-3) {\lstinline{NULL}};
- \end{onlyenv}
- \begin{onlyenv}<2->
- \node[shape=rectangle,draw,line width=1pt](7) at (0,-1.5) {7};
- \draw[-latex](root)--(7);
- \draw[-latex](7)--(3);
- \draw[-latex](7)--(137);
- \end{onlyenv}
- \begin{onlyenv}<3>
- \node(3) at (-2,-3) {\lstinline{NULL}};
- \end{onlyenv}
- \begin{onlyenv}<3->
- \node[shape=rectangle,draw,line width=1pt](137) at (2,-3) {137};
- \node(137_left) at (1,-4.5) {\lstinline{NULL}};
- \node(137_right) at (3,-4.5) {\lstinline{NULL}};
- \draw[-latex](137)--(137_left);
- \draw[-latex](137)--(137_right);
- \end{onlyenv}
- \begin{onlyenv}<4>
- \node(5) at (-1,-4.5) {\lstinline{NULL}};
- \end{onlyenv}
- \begin{onlyenv}<4->
- \node[shape=rectangle,draw,line width=1pt](3) at (-2,-3) {3};
- \node(3_left) at (-3,-4.5) {\lstinline{NULL}};
- \draw[-latex](3)--(3_left);
- \draw[-latex](3)--(5);
- \end{onlyenv}
- \begin{onlyenv}<5->
- \node[shape=rectangle,draw,line width=1pt](5) at (-1,-4.5) {5};
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- \draw[-latex](5)--(5_left);
- \draw[-latex](5)--(5_right);
- \end{onlyenv}
- \end{tikzpicture}
- \end{center}
- \end{minipage}
-
-\end{frame}
-
\end{document}