<?xml version="1.0"?>
<!DOCTYPE ipe SYSTEM "ipe.dtd">
<ipe version="70218" creator="Ipe 7.2.30">
<info created="D:20100422165822" modified="D:20251223164635" numberpages="yes"/>
<preamble>\usepackage[ngerman]{babel}
\usepackage{url}
%\usepackage{fix-cm}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage[utf8]{inputenc}
\usepackage{enumitem}
\usepackage{tabularx}
\usepackage{booktabs}

\newcommand{\es}{\operatorname{es}}	
\newcommand{\depth}{\operatorname{depth}}	


\newcommand{\bk}{\color{black}}
\newcommand{\rd}{\color{PK dark red}}
\newcommand{\bu}{\color{PK dark blue}}
\newcommand{\wt}{\color{white}}
\newcommand{\gn}{\color{PK dark green}}
\newcommand{\gy}{\color{PK dark gray}}
\newcommand{\yo}{\color{PK dark yellow}}
\newcommand{\og}{\color{PK dark orange}}

\usepackage{tikz}
\tikzset{
  circ/.style = {circle,draw,fill,inner sep=1pt},
  invisible/.style = {circle,draw=none,inner sep=0pt,font=\tiny}
}


\setlength{\itemsep}{0ex}
</preamble>
<bitmap id="1" width="2086" height="295" BitsPerComponent="8" ColorSpace="DeviceRGB" Filter="FlateDecode" length="125012" encoding="base64">
[encoded data, 168995 characters]
iZs=
</bitmap>
<ipestyle name="basic">
<symbol name="arrow/arc(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0 l
-1 0 l
h
</path>
</symbol>
<symbol name="arrow/farc(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0 l
-1 0 l
h
</path>
</symbol>
<symbol name="mark/circle(sx)" transformations="translations">
<path fill="sym-stroke">
0.6 0 0 0.6 0 0 e
0.4 0 0 0.4 0 0 e
</path>
</symbol>
<symbol name="mark/disk(sx)" transformations="translations">
<path fill="sym-stroke">
0.6 0 0 0.6 0 0 e
</path>
</symbol>
<symbol name="mark/fdisk(sfx)" transformations="translations">
<group>
<path fill="sym-fill">
0.5 0 0 0.5 0 0 e
</path>
<path fill="sym-stroke" fillrule="eofill">
0.6 0 0 0.6 0 0 e
0.4 0 0 0.4 0 0 e
</path>
</group>
</symbol>
<symbol name="mark/box(sx)" transformations="translations">
<path fill="sym-stroke" fillrule="eofill">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
-0.4 -0.4 m
0.4 -0.4 l
0.4 0.4 l
-0.4 0.4 l
h
</path>
</symbol>
<symbol name="mark/square(sx)" transformations="translations">
<path fill="sym-stroke">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
</path>
</symbol>
<symbol name="mark/fsquare(sfx)" transformations="translations">
<group>
<path fill="sym-fill">
-0.5 -0.5 m
0.5 -0.5 l
0.5 0.5 l
-0.5 0.5 l
h
</path>
<path fill="sym-stroke" fillrule="eofill">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
-0.4 -0.4 m
0.4 -0.4 l
0.4 0.4 l
-0.4 0.4 l
h
</path>
</group>
</symbol>
<symbol name="mark/cross(sx)" transformations="translations">
<group>
<path fill="sym-stroke">
-0.43 -0.57 m
0.57 0.43 l
0.43 0.57 l
-0.57 -0.43 l
h
</path>
<path fill="sym-stroke">
-0.43 0.57 m
0.57 -0.43 l
0.43 -0.57 l
-0.57 0.43 l
h
</path>
</group>
</symbol>
<symbol name="arrow/fnormal(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0 l
-1 0 l
h
</path>
</symbol>
<symbol name="arrow/pointed(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0 l
0 0 l
-1 0 l
h
</path>
</symbol>
<symbol name="arrow/fpointed(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0 l
0 0 l
-1 0 l
h
</path>
</symbol>
<symbol name="arrow/linear(spx)">
<path stroke="sym-stroke" pen="sym-pen">
-1 0 m
0 0 l
-1 0 l
</path>
</symbol>
<symbol name="arrow/fdouble(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0 l
-1 0 l
h
-1 0 m
-2 0 l
-2 0 l
h
</path>
</symbol>
<symbol name="arrow/double(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0 l
-1 0 l
h
-1 0 m
-2 0 l
-2 0 l
h
</path>
</symbol>
<anglesize name="22.5 deg" value="22.5"/>
<anglesize name="30 deg" value="30"/>
<anglesize name="45 deg" value="45"/>
<anglesize name="60 deg" value="60"/>
<anglesize name="90 deg" value="90"/>
<arrowsize name="large" value="10"/>
<arrowsize name="small" value="5"/>
<arrowsize name="tiny" value="3"/>
<color name="blue" value="0 0 1"/>
<color name="brown" value="0.647 0.165 0.165"/>
<color name="darkblue" value="0 0 0.545"/>
<color name="darkcyan" value="0 0.545 0.545"/>
<color name="darkgray" value="0.663"/>
<color name="darkgreen" value="0 0.392 0"/>
<color name="darkmagenta" value="0.545 0 0.545"/>
<color name="darkorange" value="1 0.549 0"/>
<color name="darkred" value="0.545 0 0"/>
<color name="gold" value="1 0.843 0"/>
<color name="gray" value="0.745"/>
<color name="green" value="0 1 0"/>
<color name="lightblue" value="0.678 0.847 0.902"/>
<color name="lightcyan" value="0.878 1 1"/>
<color name="lightgray" value="0.827"/>
<color name="lightgreen" value="0.565 0.933 0.565"/>
<color name="lightyellow" value="1 1 0.878"/>
<color name="navy" value="0 0 0.502"/>
<color name="orange" value="1 0.647 0"/>
<color name="pink" value="1 0.753 0.796"/>
<color name="purple" value="0.627 0.125 0.941"/>
<color name="red" value="1 0 0"/>
<color name="seagreen" value="0.18 0.545 0.341"/>
<color name="turquoise" value="0.251 0.878 0.816"/>
<color name="violet" value="0.933 0.51 0.933"/>
<color name="yellow" value="1 1 0"/>
<dashstyle name="dash dot dotted" value="[4 2 1 2 1 2] 0"/>
<dashstyle name="dash dotted" value="[4 2 1 2] 0"/>
<dashstyle name="dashed" value="[4] 0"/>
<dashstyle name="dotted" value="[1 3] 0"/>
<gridsize name="10 pts (~3.5 mm)" value="10"/>
<gridsize name="14 pts (~5 mm)" value="14"/>
<gridsize name="16 pts (~6 mm)" value="16"/>
<gridsize name="20 pts (~7 mm)" value="20"/>
<gridsize name="28 pts (~10 mm)" value="28"/>
<gridsize name="32 pts (~12 mm)" value="32"/>
<gridsize name="4 pts" value="4"/>
<gridsize name="56 pts (~20 mm)" value="56"/>
<gridsize name="8 pts (~3 mm)" value="8"/>
<pen name="fat" value="1.2"/>
<pen name="heavier" value="0.8"/>
<pen name="ultrafat" value="2"/>
<symbolsize name="large" value="5"/>
<symbolsize name="small" value="2"/>
<symbolsize name="tiny" value="1.1"/>
<textsize name="Huge" value="\Huge"/>
<textsize name="LARGE" value="\LARGE"/>
<textsize name="Large" value="\Large"/>
<textsize name="footnote" value="\footnotesize"/>
<textsize name="huge" value="\huge"/>
<textsize name="large" value="\large"/>
<textsize name="small" value="\small"/>
<textsize name="tiny" value="\tiny"/>
<textstyle name="center" begin="\begin{center}" end="\end{center}"/>
<textstyle name="item" begin="\begin{itemize}\item{}" end="\end{itemize}"/>
<textstyle name="itemize" begin="\begin{itemize}" end="\end{itemize}"/>
<tiling name="falling" angle="-60" step="4" width="1"/>
<tiling name="rising" angle="30" step="4" width="1"/>
</ipestyle>
<ipestyle name="pagenumbers-ur">
<pagenumberstyle pos="997 550" color="0.5" size="12" valign="baseline"></pagenumberstyle>
</ipestyle>
<ipestyle name="philipp-presentation">
<symbol name="arrow/arc(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/farc(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="mark/circle(sx)" transformations="translations">
<path fill="sym-stroke">
0.6 0 0 0.6 0 0 e
0.4 0 0 0.4 0 0 e
</path>
</symbol>
<symbol name="mark/disk(sx)" transformations="translations">
<path fill="sym-stroke">
0.6 0 0 0.6 0 0 e
</path>
</symbol>
<symbol name="mark/fdisk(sfx)" transformations="translations">
<group>
<path fill="sym-stroke" fillrule="eofill">
0.6 0 0 0.6 0 0 e
0.4 0 0 0.4 0 0 e
</path>
<path fill="sym-fill">
0.4 0 0 0.4 0 0 e
</path>
</group>
</symbol>
<symbol name="mark/box(sx)" transformations="translations">
<path fill="sym-stroke" fillrule="eofill">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
-0.4 -0.4 m
0.4 -0.4 l
0.4 0.4 l
-0.4 0.4 l
h
</path>
</symbol>
<symbol name="mark/square(sx)" transformations="translations">
<path fill="sym-stroke">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
</path>
</symbol>
<symbol name="mark/fsquare(sfx)" transformations="translations">
<group>
<path fill="sym-stroke" fillrule="eofill">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
-0.4 -0.4 m
0.4 -0.4 l
0.4 0.4 l
-0.4 0.4 l
h
</path>
<path fill="sym-fill">
-0.4 -0.4 m
0.4 -0.4 l
0.4 0.4 l
-0.4 0.4 l
h
</path>
</group>
</symbol>
<symbol name="mark/cross(sx)" transformations="translations">
<group>
<path fill="sym-stroke">
-0.43 -0.57 m
0.57 0.43 l
0.43 0.57 l
-0.57 -0.43 l
h
</path>
<path fill="sym-stroke">
-0.43 0.57 m
0.57 -0.43 l
0.43 -0.57 l
-0.57 0.43 l
h
</path>
</group>
</symbol>
<symbol name="arrow/fnormal(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/pointed(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0.333 l
-0.8 0 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/fpointed(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-0.8 0 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/linear(spx)">
<path stroke="sym-stroke" pen="sym-pen">
-1 0.333 m
0 0 l
-1 -0.333 l
</path>
</symbol>
<symbol name="arrow/fdouble(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
-1 0 m
-2 0.333 l
-2 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/double(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
-1 0 m
-2 0.333 l
-2 -0.333 l
h
</path>
</symbol>
<symbol name="sphere">
<path matrix="0.04 0 0 0.04 0 0" fill="blue" gradient="ball">
18 0 0 18 0 0 e
</path>
</symbol>
<symbol name="mark/sphere(sx)" transformations="translations">
<path matrix="0.04 0 0 0.04 0 0" fill="sym-stroke" gradient="ball">
18 0 0 18 0 0 e
</path>
</symbol>
<symbol name="mark/ftriang(sfx)" transformations="translations">
<path matrix="0.05 0 0 0.05 0 0" stroke="sym-stroke" fill="sym-fill">
-12 -7.3923 m
0 13.3923 l
12 -7.3923 l
h
</path>
</symbol>
<anglesize name="22.5 deg" value="22.5"/>
<anglesize name="30 deg" value="30"/>
<anglesize name="45 deg" value="45"/>
<anglesize name="60 deg" value="60"/>
<anglesize name="90 deg" value="90"/>
<arrowsize name="large" value="20"/>
<arrowsize name="normal" value="15"/>
<arrowsize name="small" value="10"/>
<arrowsize name="tiny" value="6"/>
<color name="blue" value="0 0 1"/>
<color name="brown" value="0.647 0.165 0.165"/>
<color name="darkblue" value="0 0 0.545"/>
<color name="darkcyan" value="0 0.545 0.545"/>
<color name="darkgray" value="0.5"/>
<color name="darkgreen" value="0 0.6 0"/>
<color name="darkmagenta" value="0.545 0 0.545"/>
<color name="darkorange" value="1 0.549 0"/>
<color name="darkred" value="0.545 0 0"/>
<color name="gold" value="1 0.843 0"/>
<color name="gray" value="0.625"/>
<color name="green" value="0 1 0"/>
<color name="lightblue" value="0.678 0.847 0.902"/>
<color name="lightcyan" value="0.878 1 1"/>
<color name="lightgray" value="0.75"/>
<color name="lightgreen" value="0.565 0.933 0.565"/>
<color name="lightred" value="1 0.608 0.537"/>
<color name="lightyellow" value="1 1 0.878"/>
<color name="navy" value="0 0 0.502"/>
<color name="olive" value="0.66 0.66 0"/>
<color name="orange" value="1 0.647 0"/>
<color name="pink" value="1 0.753 0.796"/>
<color name="purple" value="0.627 0.125 0.941"/>
<color name="red" value="1 0 0"/>
<color name="seagreen" value="0.18 0.545 0.341"/>
<color name="title" value="0.247 0.282 0.392"/>
<color name="turquoise" value="0.251 0.878 0.816"/>
<color name="violet" value="0.933 0.51 0.933"/>
<color name="yellow" value="1 1 0"/>
<dashstyle name="dash dot dotted" value="[4 2 1 2 1 2] 0"/>
<dashstyle name="dash dotted" value="[4 2 1 2] 0"/>
<dashstyle name="dashed" value="[4] 0"/>
<dashstyle name="dotted" value="[1 3] 0"/>
<dashstyle name="fine dotted" value="[0.5 1.5] 0"/>
<gridsize name="10 pts (~3.5 mm)" value="10"/>
<gridsize name="14 pts (~5 mm)" value="14"/>
<gridsize name="16 pts (~6 mm)" value="16"/>
<gridsize name="2 pts (~0.8 mm)" value="2"/>
<gridsize name="20 pts (~7 mm)" value="20"/>
<gridsize name="28 pts (~10 mm)" value="28"/>
<gridsize name="32 pts (~12 mm)" value="32"/>
<gridsize name="4 pts (~1.5 mm)" value="4"/>
<gridsize name="56 pts (~20 mm)" value="56"/>
<gridsize name="8 pts (~3 mm)" value="8"/>
<opacity name="10%" value="0.1"/>
<opacity name="25%" value="0.25"/>
<opacity name="33%" value="0.333"/>
<opacity name="50%" value="0.5"/>
<opacity name="66%" value="0.666"/>
<opacity name="75%" value="0.75"/>
<opacity name="90%" value="0.9"/>
<pen name="fat" value="3.6"/>
<pen name="heavier" value="2.4"/>
<pen name="normal" value="1.2"/>
<pen name="ultrafat" value="6"/>
<symbolsize name="large" value="15"/>
<symbolsize name="normal" value="9"/>
<symbolsize name="small" value="6"/>
<symbolsize name="tiny" value="3.3"/>
<textsize name="Huge" value="\Huge"/>
<textsize name="LARGE" value="\LARGE"/>
<textsize name="Large" value="\Large"/>
<textsize name="footnote" value="\footnotesize"/>
<textsize name="huge" value="\huge"/>
<textsize name="large" value="\large"/>
<textsize name="normal" value="\normalsize"/>
<textsize name="script" value="\scriptsize"/>
<textsize name="small" value="\small"/>
<textsize name="tiny" value="\tiny"/>
<textstretch name="Huge" value="2.8"/>
<textstretch name="LARGE" value="2.8"/>
<textstretch name="Large" value="2.8"/>
<textstretch name="footnote" value="2.8"/>
<textstretch name="huge" value="2.8"/>
<textstretch name="large" value="2.8"/>
<textstretch name="normal" value="2.8"/>
<textstretch name="script" value="2.8"/>
<textstretch name="small" value="2.8"/>
<textstretch name="tiny" value="2.8"/>
<textstyle name="center" begin="\begin{center}" end="\end{center}"/>
<textstyle name="item" begin="\begin{flushleft}\begin{itemize}\item{}" end="\end{itemize}\end{flushleft}"/>
<textstyle name="itemize" begin="\begin{flushleft}\begin{itemize}" end="\end{itemize}\end{flushleft}"/>
<textstyle name="normal" begin="\begin{flushleft}" end="\end{flushleft}"/>
<preamble>
\usepackage[ngerman]{babel}
\usepackage[utf8]{inputenc}
\usepackage[vlined]{algorithm2e}
\DontPrintSemicolon
\setlength{\algomargin}{2ex}
\SetArgSty{}
\SetKw{KwNot}{not}
\SetKw{KwAnd}{and}
\SetKw{KwOr}{or}
\SetKw{KwDownTo}{downto}
\SetKw{KwReturn}{return}
\SetKw{KwRequire}{Require:}
\SetKw{KwInvariant}{Invariant:}
\SetKwRepeat{KwRepeat}{repeat}{until}
\renewcommand\rmdefault{cmss}
\DeclareSymbolFont{operators}{OT1}{cmss}{m}{n}
\makeatletter
\leftmargini 1.5em
\leftmargin \leftmargini
\leftmarginii  1.2em
\leftmarginiii 1em
\def\@listI{\leftmargin\leftmargini
            \parsep \z@
	    \partopsep 3pt
	    \topsep \z@
            \itemsep \z@}
\@listI
\def\labelitemi{\raisebox{0.2ex}{\hbox to 0.3em{\ipesymbol{sphere}{}{}{}}}}
\def\@listii {\leftmargin\leftmarginii
              \labelwidth\leftmarginii
              \advance\labelwidth-\labelsep
              \topsep    \z@
              \parsep    \z@
              \itemsep   \parsep}
\def\@listiii{\leftmargin\leftmarginiii
              \labelwidth\leftmarginiii
              \advance\labelwidth-\labelsep
              \topsep    \z@
              \parsep    \z@
              \partopsep \z@
              \itemsep   \topsep}
\makeatother
\usepackage[sc]{mathpazo}
\usepackage{tabularx}
\usepackage{pifont}
\newcommand{\cmark}{\ding{51}}
\newcommand{\xmark}{\ding{55}}
\usepackage{amssymb}
\usepackage{amsmath}
\newcommand{\R}{\ensuremath{\mathbb{R}}}
</preamble>
<layout paper="1067 600" origin="32 32" frame="1003 472" skip="32" crop="no"/>
<titlestyle pos="0 512" size="Large" color="title"  valign="baseline"/>
<gradient name="ball" type="radial" coords="-4 10 2 0 0 18">
 <stop offset="0" color="1"/>
 <stop offset="1" color="0 0 1"/>
</gradient>
<tiling name="falling" angle="-60" step="12" width="3"/>
<tiling name="rising" angle="30" step="12" width="3"/>
</ipestyle>
<ipestyle name="philipp-colors">
<color name="PK dark blue" value="0.121 0.47 0.705"/>
<color name="PK dark brown" value="0.651 0.337 0.157"/>
<color name="PK dark cyan" value="0.106 0.62 0.467"/>
<color name="PK dark gray" value="0.5"/>
<color name="PK dark green" value="0.2 0.627 0.172"/>
<color name="PK dark orange" value="1 0.498 0"/>
<color name="PK dark pink" value="0.969 0.506 0.749"/>
<color name="PK dark purple" value="0.415 0.239 0.603"/>
<color name="PK dark red" value="0.89 0.102 0.109"/>
<color name="PK dark yellow" value="1 1 0.2"/>
<color name="PK light blue" value="0.651 0.807 0.89"/>
<color name="PK light brown" value="0.898 0.847 0.741"/>
<color name="PK light cyan" value="0.553 0.827 0.78"/>
<color name="PK light gray" value="0.8"/>
<color name="PK light green" value="0.698 0.874 0.541"/>
<color name="PK light orange" value="0.992 0.749 0.435"/>
<color name="PK light pink" value="0.992 0.855 0.925"/>
<color name="PK light purple" value="0.792 0.698 0.839"/>
<color name="PK light red" value="0.984 0.603 0.6"/>
<color name="PK light yellow" value="1 1 0.8"/>
<color name="print blue" value="0.169 0.514 0.729"/>
<color name="print green" value="0.671 0.867 0.643"/>
<color name="print orange" value="0.992 0.682 0.38"/>
<color name="print red" value="0.843 0.098 0.11"/>
<color name="print yellow" value="1 1 0.749"/>
</ipestyle>
<page section="Titelseite">
<layer name="alpha"/>
<view layers="alpha" active="alpha"/>
<text layer="alpha" matrix="1 0 0 1 128 -29.6832" transformations="translations" pos="0 194.196" stroke="PK dark blue" type="minipage" width="736" height="21.0756" depth="7.112" valign="top" style="center">Seminar Algorithmik</text>
<text matrix="1 0 0 1 41.6325 -111.006" transformations="translations" pos="0 160" stroke="black" type="minipage" width="908.735" height="17.3796" depth="3.388" valign="top">~~~~~~~~~~~~~Teilnehmerin 1 \hfill Teilnehmer 2~~~~~~~~~~~~~</text>
<text matrix="1 0 0 1 496 -67.2685" transformations="translations" pos="0 160" stroke="darkcyan" type="label" width="154.652" height="19.4964" depth="0.42" halign="center" valign="baseline">TT.MM.2024</text>
<text matrix="1 0 0 1 128 38.9533" transformations="translations" pos="0 328.943" stroke="title" type="minipage" width="736" height="71.9292" depth="58.1" valign="top" size="Large" style="center">\bf Titel \\
des Seminar-\\
themas</text>
<image matrix="1.47104 0 0 1.47104 -46.445 144.558" rect="117.679 200.609 618.321 271.391" bitmap="1"/>
<path fill="white">
984 568 m
984 536 l
1024 536 l
1024 568 l
h
</path>
</page>
<page title="Einführung">
<layer name="alpha"/>
<view layers="alpha" active="alpha"/>
</page>
</ipe>
