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Commit b2b8c540 authored by Peter Gerwinski's avatar Peter Gerwinski
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Nachbereitung 4.2.2021

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...@@ -699,413 +699,4 @@ ...@@ -699,413 +699,4 @@
\end{frame} \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
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\thicklines
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\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}
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\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}}
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\put(1.5,1.45){\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.95,-0.45);}}}
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\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};
\node(5_left) at (-2,-6) {\lstinline{NULL}};
\node(5_right) at (0,-6) {\lstinline{NULL}};
\draw[-latex](5)--(5_left);
\draw[-latex](5)--(5_right);
\end{onlyenv}
\end{tikzpicture}
\end{center}
\end{minipage}
\end{frame}
\end{document} \end{document}
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