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Da wir nicht von $P = NP$ ausgehen, + haben, muss also \algt{Längster $s$-$t$-Weg} $\NPe$-schwer sein, denn + wenn es in $\Pe$ liegen würde, könnten wir auch Hamiltonweg in + polynomieller Zeit lösen. Da wir nicht von $\Pe = \NPe$ ausgehen, ist das nicht möglich. \points{2} diff --git a/übung_3/ngexrcs.cls b/übung_3/ngexrcs.cls index c7218dc..400ecbd 100644 --- a/übung_3/ngexrcs.cls +++ b/übung_3/ngexrcs.cls @@ -14,14 +14,10 @@ \KOMAoptions{mpinclude=true} \recalctypearea -\RequirePackage{enumitem} \RequirePackage{ngutils} % define fonts \RequirePackage{fontspec} -%\RequirePackage{tgpagella} -%\RequirePackage{tgheros} -%\RequirePackage{euler-math} \RequirePackage[math-style=upright]{unicode-math} \setmainfont{TeX Gyre Pagella} \setsansfont{TeX Gyre Heros} @@ -31,18 +27,6 @@ \setlength{\marginparwidth}{1.5\marginparwidth} \setlength{\fboxrule}{\heavyrulewidth} - -% -% \renewcommand\theenumi{\@alph\c@enumi} -% \renewcommand\theenumii{\@arabic\c@enumii} -%\renewcommand\theenumiii{\@roman\c@enumiii} -%\renewcommand\theenumiv{\@Alph\c@enumiv} - -% \renewcommand\labelenumi{\theenumi)} -% \renewcommand\labelenumii{\theenumii.} -%\renewcommand\labelenumiii{\theenumiii.} -%\renewcommand\labelenumiv{\theenumiv.} - % Use sansfont for all title elements \addtokomafont{titlehead}{\sffamily} \addtokomafont{subject}{\normalfont \sffamily \itshape} @@ -62,14 +46,26 @@ \newkomafont{points}{\sffamily} \newcommand\points[2][\quad]{\marginline{\framebox{{\usekomafont{points}#1 \textbf{/} #2}}}} -\newenvironment{tasks}[1][1em] +\newcounter{task} +\renewcommand{\thetask}{\@alph\c@task)} +\newenvironment{tasks} { -\setlist{leftmargin=*} -\renewcommand\theenumi{\@alph\c@enumi} -\renewcommand\theenumii{\@arabic\c@enumii} -\renewcommand\labelenumi{\theenumi)} -\renewcommand\labelenumii{\theenumii.} -\begin{enumerate} + \begin{list}{\thetask} + { + \usecounter{task} + \setlength{\leftmargin}{1.6em} + } }{% -\end{enumerate} + \end{list} } + +\DeclareNewTOC +[ + type=algorithm, + types=algorithms, + float, + floattype=4, + name=Algorithmus, + listname={Algorithmenverzeichnis} +] +{loa} diff --git a/übung_3/ngutils.sty b/übung_3/ngutils.sty index 986bd5c..7fb21db 100644 --- a/übung_3/ngutils.sty +++ b/übung_3/ngutils.sty @@ -7,7 +7,6 @@ \RequirePackage{booktabs} \RequirePackage{listings} - \lstnewenvironment{pseudocode}[1][] %defines the algorithm listing environment { \renewcommand{\lstlistingname}{Algorithmus} @@ -29,40 +28,44 @@ } {} -\newcommand{\seilpmi}{\ensuremath{\Longleftarrow}} +\newcommand{\seilpmi}{\Longleftarrow} -\newcommand\NN{\ensuremath{\mathbb{N}}} -\newcommand\ZZ{\ensuremath{\mathbb{Z}}} -\newcommand\QQ{\ensuremath{\mathbb{Q}}} -\newcommand\RR{\ensuremath{\mathbb{R}}} -\newcommand\CC{\ensuremath{\mathbb{C}}} -\newcommand\PP{\ensuremath{\mathbb{P}}} +\newcommand{\NN}{\mathbb{N}} +\newcommand{\ZZ}{\mathbb{Z}} +\newcommand{\QQ}{\mathbb{Q}} +\newcommand{\RR}{\mathbb{R}} +\newcommand{\CC}{\mathbb{C}} +\newcommand{\PP}{\mathbb{P}} -\newcommand\Oh{\ensuremath{\mathcal{O}}} -\newcommand\oh{\ensuremath{\scriptstyle{\mathcal{O}}}} -\newcommand\Eh{\ensuremath{\mathrm{E}}} -\newcommand\Var{\ensuremath{\mathrm{Var}}} -\newcommand\argmax{\ensuremath{\mathrm{arg\,max}}} -\newcommand\argmin{\ensuremath{\mathrm{arg\,min}}} +\newcommand{\Pe}{\mathrm{P}} +\newcommand{\NPe}{\mathrm{NP}} -\newcommand\parens[1]{\ensuremath{\left(#1\right)}} -\newcommand\brackets[1]{\ensuremath{\left[#1\right]}} -\newcommand\braces[1]{\ensuremath{\left\{#1\right\}}} -\newcommand\angled[1]{\ensuremath{\left\langle#1\right\rangle}} +\newcommand{\Oh}{\mathcal{O}} +\newcommand{\oh}{\scriptstyle{\mathcal{O}}} -\newcommand\tup[1]{\parens{#1}} -\newcommand\ivl[1]{\brackets{#1}} -\newcommand\set[1]{\braces{#1}} -\newcommand\arr[1]{\angled{#1}} -\newcommand\abs[1]{\ensuremath{\lvert#1\rvert}} -\newcommand\norm[1]{\ensuremath{\lVert#1\rVert}} -\newcommand\ceil[1]{\ensuremath{\lceil#1\rceil}} -\newcommand\floor[1]{\ensuremath{\lfloor#1\rfloor}} +\newcommand{\Eh}{\mathop{\mathrm{E}}} +\newcommand{\Var}{\mathop{\mathrm{Var}}} +\newcommand{\pot}{\mathop{\mathcal{P}}} +\newcommand{\argmax}{\mathop{\mathrm{arg\,max}}} +\newcommand{\argmin}{\mathop{\mathrm{arg\,min}}} -\newcommand\alg[2]{{\normalfont\scshape#1}{\normalfont(#2)}} -\newcommand\algt[1]{{\normalfont\scshape#1}} -\newcommand\com[1]{{\normalfont\itshape/\!\!/ #1}} +\newcommand{\parens}[1]{\left(#1\right)} +\newcommand{\brackets}[1]{\left[#1\right]} +\newcommand{\braces}[1]{\left\{#1\right\}} +\newcommand{\angled}[1]{\left\langle#1\right\rangle} +\newcommand{\tup}[1]{\parens{#1}} +\newcommand{\ivl}[1]{\brackets{#1}} +\newcommand{\set}[1]{\braces{#1}} +\newcommand{\arr}[1]{\angled{#1}} +\newcommand{\abs}[1]{\lvert#1\rvert} +\newcommand{\norm}[1]{\lVert#1\rVert} +\newcommand{\ceil}[1]{\lceil#1\rceil} +\newcommand{\floor}[1]{\lfloor#1\rfloor} + +\newcommand{\alg}[2]{{\normalfont\scshape#1}{\normalfont(#2)}} +\newcommand{\algt}[1]{{\normalfont\scshape#1}} +\newcommand{\com}[1]{{\normalfont\itshape/\!\!/ #1}} \newenvironment{algorithmic}[1][1em]{ \begin{minipage}[t]{\dimexpr\linewidth} @@ -74,38 +77,6 @@ \end{minipage} } -% \newenvironment{algorithm}[1][1em]{ -% \begin{center} -% \begin{minipage}[t]{\dimexpr\linewidth} -% \bfseries -% \begin{tabbing} -% \hspace{#1}\=\hspace{#1}\=\hspace{#1}\=\hspace{#1}\=\hspace{#1}\=\hspace{#1}\=\hspace{#1}\=\hspace{#1}\=\kill -% }{% -% \end{tabbing} -% \end{minipage} -% \end{center} -% } - -\makeatletter -\newcounter{algorithm}% the counter -\renewcommand*\thealgorithm{\arabic{algorithm}}% the default format for the counter -\newcommand*\fps@algorithm{tbp}% default floating options -\newcommand*\ftype@algorithm{4}% float type number, needs to be a power of 2; % \ftype@figure=1, \ftype@table=2 -\newcommand*\ext@algorithm{loa}% extension of file for the list of schemes -\newcommand*\fnum@algorithm{\algorithmname\nobreakspace\thealgorithm}% used in caption -\newcommand*\algorithmname{Algorithmus}% the name -\newcommand*\listalgorithmname{Algorithmenverzeichnis}% the name of the list -\newenvironment{algorithm}{\@float{algorithm}}{\end@float}% the environment -\newenvironment{algorithm*}{\@dblfloat{algorithm}}{\end@dblfloat}% the starred % version for twocolumn documents -\newcommand*\listofalgorithms{% the list of schemes - \section*{\listalgorithmname} - \@mkboth - {\MakeUppercase\listalgorithmname} - {\MakeUppercase\listalgorithmname} - \@starttoc{\ext@algorithm} } - \let\l@algorithm\l@figure % layout of list is the same as for figures -\makeatother - \newlength{\theoremskip} \setlength{\theoremskip}{6em}

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