commit b60d91b9ce27e641d3d238a7e9cefc25df8d2e0e Author: Never Gude Date: Wed Dec 24 05:06:10 2025 +0100 initial commit diff --git a/ads-exercise.aux b/ads-exercise.aux new file mode 100644 index 0000000..036996e --- /dev/null +++ b/ads-exercise.aux @@ -0,0 +1,19 @@ +\relax +\providecommand*\new@tpo@label[2]{} +\providecommand \babel@aux [2]{\global \let \babel@toc \@gobbletwo } +\@nameuse{bbl@beforestart} +\catcode `"\active +\providecommand\hyper@newdestlabel[2]{} +\providecommand\HyField@AuxAddToFields[1]{} +\providecommand\HyField@AuxAddToCoFields[2]{} +\providecommand\BKM@entry[2]{} +\BKM@entry{id=1,dest={73656374696F6E2E31},srcline={11},srcfile={2E2F6164732D65786572636973652E746578}}{5C3337365C3337375C303030475C303030725C303030755C3030306E5C303030645C3030306C5C303030615C303030675C303030655C3030306E} +\babel@aux{ngerman}{} +\@writefile{toc}{\contentsline {section}{\numberline {1}Grundlagen}{1}{section.1}\protected@file@percent } +\BKM@entry{id=2,dest={73656374696F6E2E32},srcline={50},srcfile={2E2F6164732D65786572636973652E746578}}{5C3337365C3337375C303030575C303030615C303030735C3030305C3034305C303030735C3030306F5C3030306E5C303030735C303030745C3030305C3034305C3030306E5C3030306F5C303030635C303030685C3030305C3034305C303030665C303030655C303030685C3030306C5C30303074} +\@writefile{toc}{\contentsline {section}{\numberline {2}Was sonst noch fehlt}{2}{section.2}\protected@file@percent } +\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Ein Graph. 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penalty, 16 gly +ph, 183 attribute, 60 glue_spec, 93 attribute_list, 1 write nodes + avail lists: 1:1,2:872,3:295,4:4,5:393,6:58,7:4088,8:18,9:749,10:4,11:292 + 49256 multiletter control sequences out of 65536+600000 + 120 fonts using 28861359 bytes + 122i,12n,114p,10945b,558s stack positions out of 10000i,1000n,20000p,200000b,200000s + +Output written on ads-exercise.pdf (3 pages, 48877 bytes). + +PDF statistics: 121 PDF objects out of 1000 (max. 8388607) + 81 compressed objects within 1 object stream + 14 named destinations out of 1000 (max. 131072) + 17 words of extra memory for PDF output out of 10000 (max. 100000000) + diff --git a/ads-exercise.pdf b/ads-exercise.pdf new file mode 100644 index 0000000..d6f4899 Binary files /dev/null and b/ads-exercise.pdf differ diff --git a/ads-exercise.tex b/ads-exercise.tex new file mode 100644 index 0000000..121e376 --- /dev/null +++ b/ads-exercise.tex @@ -0,0 +1,92 @@ +\documentclass{ngexrcs} +\title{Lösungen zum 42. Übungsblatt} +\subject{Algorithmen und Datenstrukturen} +\author{Malloc McSharkface \and Free Bluetooth \and Ada Finlace} +\date{\today} + +\begin{document} +\maketitle +\points[\qquad]{20} + +\section{Grundlagen} + +\begin{enumerate} + \item Mathematische Ausdrücke werden mit \$-Zeichen umschlossen um korrekt + gesetzt zu werden: + + \verb|$a = b \cdot c$| ergibt $a = b \cdot c$ + \points{1} + + \item Um Formeln außerhalb des Fließtextes darzustellen, kann \verb|\[...\]| oder die \verb|align*|-Umgebung verwendet werden. Letztere kann Einrückungen mit dem \&-Zeichen setzen: + \points{1} + \begin{align*} + \sum_{i=0}^n i & = 1 + 2 + \cdots + n-2 + n-1 + n \\ + & = \frac{n (n + 1)}{2} + \end{align*} + + \item Einige wichtige Symbole und Funktionen, sowie klammerartige Ausdrücke werden wie folgt gesetzt: + \begin{itemize} + \item $\Oh$, $\Omega$, $\Theta$, $\oh$, $\omega$ + \item $\NN$, $\ZZ$, $\QQ$, $\RR$, $\CC$, $\infty$ + \item $\implies$, $\iff$, $\to$, $\gets$, $\lor$, $\land$, $\neg$, $\exists$, $\forall$, $\checkmark$ + \item $<$, $\leq$, $\neq$, $>$, $\geq$ + \item $\in$, $\notin$, $\setminus$, $\subsetneq$, $\subseteq$, $\supsetneq$, $\supseteq$, $\cup$, $\cap$, $\emptyset$ + \item $\tup{x, y}$ $\set{x, y}$, $\abs{x}$, $\norm{x}$, $\ceil{x}$, $\floor{x}$, $\arr{a_1, a_2, a_2}$ + \item $\tup{\frac{x}{y}}$, $\log_a{b}$, $x\bmod y$, $\sum_a^b{c}$, $\prod_x^y{z}$, $\binom{a}{b}$ + \end{itemize} + \points{2} + + \item Pseudocode kann wie folgt gesetzt werden. Dabei werden Einrückungen mit \verb|\>| für eine Zeile gesetzt und mit \verb|\+| für alle folgenden Zeilen. Es existieren weitere Einrückungsbefehle, die denen der \verb|tabbing|-Umgebung entsprechen. + \begin{algorithm} + \+ \alg{Sum}$(a, b)$ \\ + \com{Berechne die Summe rekursiv} \\ + if $b = 0$ then\\ + \> return $a$ \\ + return \alg{Sum}$(a, b-1)+1$ + \end{algorithm} + \points{6} +\end{enumerate} + +\section{Was sonst noch fehlt} +\begin{enumerate} + \item + Abbildungen werden in einer \emph{floating}-Umgebung eingebunden. Diese verschiebt die Abbildung so, dass der umliegende Text so gut wie möglich fließt. + Soll die Abbildung möglichst an der relativen Position im Text bleiben, kann die Option \verb|!h| hinzugefügt werden. Um Verwirrung zu vermeiden, sollte auf die \autoref{fig:graph} verwiesen werden. + + \LaTeX\ unterstützt die Formate \emph{png, jpeg, pdf} und \emph{eps}. Zum Erstellen von Graphen kann \emph{Ipe} verwendet werden. + \begin{figure}[!h] + \centering + \includegraphics[width=0.5\textwidth]{graph.eps} + \caption{Ein Graph. Schön.} + \label{fig:graph} + \end{figure} + + Um die zu erreichenden Punkte zu setzen, kann folgender Befehl verwendet werden: + \points{4} + + \item + Tabellen werden, wie Abbildungen, in \emph{floating}-Umgebungen gesetzt. Die Bündigkeit + der Spalten kann mit den Optionen \verb|l| für eine linksbündige, \verb|c| für eine zentrierte und + \verb|r| für eine rechtsbündige Spalte. + Auch auf Tabellen sollte man Verweisen. Siehe \autoref{tab:recursion}. + \begin{table}[!hb] + \centering + \begin{tabular}{ccc} + \toprule + Iteration & Knoten & Beitrag \\ + \midrule + $0$ & $2^0 = 1$ & $2^0 \cdot 1$ \\ + $1$ & $2^1 = 2$ & $2^1 \cdot 1$ \\ + $\vdots$ & $\vdots$ & $\vdots$ \\ + $i$ & $2^i$ & $2^i \cdot 1$ \\ + $\vdots$ & $\vdots$ & $\vdots$ \\ + $\log_2 n$ & $2^{\log_2 n} = n$ & $n$ \\ + \bottomrule + \end{tabular} + \caption{Eine Tabelle mit \texttt{booktabs}} + \label{tab:recursion} + \end{table} + \points{6} + +\end{enumerate} +\end{document} diff --git a/adsslides.ipe b/adsslides.ipe new file mode 100644 index 0000000..8bc4198 --- /dev/null +++ b/adsslides.ipe @@ -0,0 +1,558 @@ + + + + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +0.6 0 0 0.6 0 0 e +0.4 0 0 0.4 0 0 e + + + + +0.6 0 0 0.6 0 0 e + + + + + +0.5 0 0 0.5 0 0 e + + +0.6 0 0 0.6 0 0 e +0.4 0 0 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\newcommand{\rd}{\color{NG dark red}} + \newcommand{\yo}{\color{NG dark yellow}} + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +703.316 368.059 m +704 336 l + + +704 336 m +832 288 l + + + + + +704 368 m +784 368 +784 320 +832 288 c + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +703.316 368.059 m +704 336 l + + +704 336 m +832 288 l + + + + + + +64 424 m +64 424 l +64 424 l +64 424 l +h + + +16 448 m +16 380 l +416 380 l +416 448 l +h + +Sei $A$ ein \textbf{\bu unsortiertes} Feld mit Elementen $a_i$ und $i \in [1; n]$. + + +4 0 0 4 756 368 e + + +4 0 0 4 756 368 e + + +727.867 401.022 m +776.709 370.273 l + + + +4 248 m +4 72 l +396 72 l +396 248 l +h + +\begin{algorithmic} + \+ \alg{Sum}$(a, b)$ \\ + if $b = 0$ then \\ + \> return $a$ \\ + else \\ + \> \com{Calculate sum and keep it to yourself} \\ + \> $result \gets a + b$ \\ + return \alg{Sum}$(a, b-1)+1$ +\end{algorithmic} 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+ + + \usepackage[ngerman]{babel} + \usepackage[sansdefault]{fontsetup} + \usepackage{enumitem} + \usepackage{ngutils} + + \setlist{leftmargin=*} + + \newcommand{\bk}{\color{black}} + \newcommand{\wt}{\color{white}} + \newcommand{\bu}{\color{NG dark blue}} + \newcommand{\bn}{\color{NG dark brown}} + \newcommand{\cn}{\color{NG dark cyan}} + \newcommand{\gy}{\color{NG dark gray}} + \newcommand{\gn}{\color{NG dark green}} + \newcommand{\og}{\color{NG dark orange}} + \newcommand{\pk}{\color{NG dark pink}} + \newcommand{\pl}{\color{NG dark purple}} + \newcommand{\rd}{\color{NG dark red}} + \newcommand{\yo}{\color{NG dark yellow}} + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +703.316 368.059 m +704 336 l + + +704 336 m +832 288 l + + + + + +704 368 m +784 368 +784 320 +832 288 c + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +703.316 368.059 m +704 336 l + + +704 336 m +832 288 l + + 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l +-0.8 0 l +-1 -0.333 l +h + + + + +-1 0.333 m +0 0 l +-1 -0.333 l + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h +-1 0 m +-2 0.333 l +-2 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h +-1 0 m +-2 0.333 l +-2 -0.333 l +h + + + + +18 0 0 18 0 0 e + + + + +18 0 0 18 0 0 e + + + + +-12 -7.3923 m +0 13.3923 l +12 -7.3923 l +h + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +\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}}} + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +Seminar Algorithmik +~~~~~~~~~~~~~Teilnehmerin 1 \hfill Teilnehmer 2~~~~~~~~~~~~~ +TT.MM.2024 +\bf Titel \\ +des Seminar-\\ +themas + + +984 568 m +984 536 l +1024 536 l +1024 568 l +h + + + + + + + diff --git a/ngexrcs.cls b/ngexrcs.cls new file mode 100644 index 0000000..4e38860 --- /dev/null +++ b/ngexrcs.cls @@ -0,0 +1,66 @@ +% vim: set filetype:tex + +% Identification % +\NeedsTeXFormat{LaTeX2e} +\ProvidesClass{ngexrcs}[2021/12/21 ADS Exercise class] + +% Handle options % +\DeclareOption*{\PassOptionsToClass{\CurrentOption}{scrartcl}} +\ProcessOptions\relax + +% More declarations % +\LoadClass{scrartcl} + +\KOMAoptions{mpinclude=true} +\recalctypearea + +\RequirePackage{ngutils} +\RequirePackage{enumitem} +\setlist{leftmargin=*} + + +% 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} +\setmonofont{TeX Gyre Cursor} +\setmathfont{Euler Math} + +\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} +\addtokomafont{title}{\sffamily} +\addtokomafont{subtitle}{\sffamily} +\addtokomafont{author}{\sffamily} +\addtokomafont{date}{\sffamily} +\addtokomafont{publishers}{\sffamily} + +% Use serif font for headings +\addtokomafont{disposition}{\rmfamily} + +% Let sections be formated as in: Aufgabe 1 -- Section title +\renewcommand*{\sectionformat}{Aufgabe \thesection\autodot\enskip--\enskip} + +% Let points of an exercise be printed as in: [__ / 2] +\newkomafont{points}{\sffamily} +\newcommand\points[2][\quad]{\marginline{\framebox{{\usekomafont{points}#1 \textbf{/} #2}}}} + diff --git a/ngslides.isy b/ngslides.isy new file mode 100644 index 0000000..0ca9e0a --- /dev/null +++ b/ngslides.isy @@ -0,0 +1,76 @@ + + + \usepackage[ngerman]{babel} + \usepackage[sansdefault]{fontsetup} + \usepackage{enumitem} + \usepackage{ngutils} + + \setlist{leftmargin=*} + + \newcommand{\bk}{\color{black}} + \newcommand{\wt}{\color{white}} + \newcommand{\bu}{\color{NG dark blue}} + \newcommand{\bn}{\color{NG dark brown}} + \newcommand{\cn}{\color{NG dark cyan}} + \newcommand{\gy}{\color{NG dark gray}} + \newcommand{\gn}{\color{NG dark green}} + \newcommand{\og}{\color{NG dark orange}} + \newcommand{\pk}{\color{NG dark pink}} + \newcommand{\pl}{\color{NG dark purple}} + \newcommand{\rd}{\color{NG dark red}} + \newcommand{\yo}{\color{NG dark yellow}} + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/ngutils.sty b/ngutils.sty new file mode 100644 index 0000000..b9000fb --- /dev/null +++ b/ngutils.sty @@ -0,0 +1,50 @@ +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{ngutils}[2025/12/24 Never's LaTeX utils] + +\RequirePackage[ngerman]{babel} +\RequirePackage{hyperref} +\RequirePackage{graphicx} +\RequirePackage{tabularx} +\RequirePackage{booktabs} + +\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\Oh{\ensuremath{\mathcal{O}}} +\newcommand\oh{\ensuremath{\scriptstyle{\mathcal{O}}}} + +\newcommand\tup[1]{\ensuremath{\left(#1\right)}} +\newcommand\set[1]{\ensuremath{\{#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\arr[1]{\ensuremath{\langle#1\rangle}} + +\newcommand\alg[1]{\normalfont \scshape #1} +\newcommand\com[1]{\normalfont \itshape /\!\!/ #1 } + +\newenvironment{algorithmic}[1][\quad]{ + \begin{minipage}[t]{\dimexpr\linewidth} + \bfseries + \begin{tabbing} + #1\=#1\=#1\=#1\=\kill + }{% + \end{tabbing} + \end{minipage} +} + +\newenvironment{algorithm}[1][\quad]{ + \begin{center} + \begin{minipage}[t]{\dimexpr\linewidth} + \bfseries + \begin{tabbing} + #1\=#1\=#1\=#1\=\kill + }{% + \end{tabbing} + \end{minipage} + \end{center} +}