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//////////////////// +\usepackage{amsmath} +% modifiziert amsmath +\usepackage{mathtools} +% mathematische Symbole, für \ceckmarks +\usepackage{amssymb} +% für proof +\usepackage{amsthm} +% für \mathscr +\usepackage{mathrsfs} +\usepackage{latexsym} +% für bessere Worttrennung +\usepackage{microtype} +% Spracheinstellung +\usepackage[ngerman]{babel} +% für Quellcode +\usepackage{verbatim} +\usepackage{listings} +% für Umlaute und Sonderzeichen in der Tex-Datei +\usepackage[utf8]{inputenc} +\usepackage{graphicx} +% für Tabellen mit gleicher Spaltenbreite und automatischen Umbrüchen +\usepackage{tabularx} +\usepackage{fullpage} +% für multirow in tabulars +\usepackage{multirow} +\usepackage{rotate} +% um Farben zu benutzen, kann mehr als das Paket color +\usepackage[cmyk,table]{xcolor} +% Verlinkungen +\usepackage[ +% farbige Schrift, statt farbiger Rahmen + colorlinks, +% verlinkt im Abb.Verzeichnis Seitenzahl statt Bildunterschrift + linktocpage, +% setzt Farbe der Links auf blau + linkcolor=blue +]{hyperref} +% nur für digitale Anwendungen, url = "http://www.example.com" +% für Webadressen wie e-mail usw.: "\url{http://www.example.com}" +\usepackage{url} +% für versch. Aufzählungezeichen wie z.B. a) +\usepackage{enumitem} +% folgt ein Leerzeichen nach einem \Befehl, wird es nicht verschluckt +\usepackage{xspace} +% für das Durchstreichen u.a. in Matheformeln mit \cancel +\usepackage{cancel} +% für \forloop und \whiledo +\usepackage{ifthen} + +% //////////////////// Syntaxhervorhebung //////////////////// +\lstloadlanguages{Python, Haskell, [LaTeX]TeX, Java} +\lstset{% +% \scriptsize: die Fontgröße für den Quelltext + basicstyle=\footnotesize\ttfamily, +% legt Farbe der Box fest + backgroundcolor = \color{bgcolour}, +% automatische Umbrüche nur nach Leerzeichen? + breakatwhitespace=false, +% automatische Zeilenumbrüche? + breaklines=true, +% die Überschrift steht oben, t = top + captionpos=t, +% Formatierung der Kommentare + commentstyle=\color{codeblue}\ttfamily, +% einfacher Rahmen um den Quelltext + frame=single, +% Behalte Leerzeichen im Quelltext. Nützlich, um +% Einrückungen zu erhalten (benötigt eventuell columns=flexible) + keepspaces=true, +% Formatierung der Schlüsselwörter + keywordstyle=\bfseries\ttfamily\color{codepurple}, +% Wohin mit den Zeilennummern? +% mögliche Werte sind: none, left, right + numbers=left, +% Formatierung der Zeilennummern + numberstyle=\tiny\color{codegreen}, +% Abstand zwischen Zeilennummern und Quelltext + numbersep=5pt, +% nummeriert nur jede i-te Zeile + stepnumber=1, +% Zeige alle Leerzeichen mit Hilfe von speziellen Unterstrichen; +% überschreibt 'showstringspaces' + showspaces=false, +% unterstreiche Leerzeichen nur in Zeichenketten + showstringspaces=false, +% Zeige Tabulatoren in Zeichenketten mit Hilfe von speziellen +% Unterstrichen + showtabs=false, + flexiblecolumns=false, +% Schrittweite zwischen Zeilennummern. +% Der Wert 1 bedeutet, dass jede Zeile nummeriert wird. + tabsize=1, +% Formatierung der Zeichenketten. + stringstyle=\color{orange}\ttfamily, +% leere Zeilen werden nicht nummeriert + numberblanklines=false, +% Abstand zum linken Seitenrand + xleftmargin=1.2em, +% Abstand zum rechten Seitenrand + xrightmargin=0.4em, + aboveskip=2ex, +} + +\lstdefinestyle{py}{% + language=Python, +} +\lstdefinestyle{hs}{% + language=Haskell, +} +\lstdefinestyle{tex}{% + language=[LaTeX]TeX, +% Um LaTex im Quelltext einzufügen + escapeinside={\%*}{*)}, +% Hervorhebung der TeX-Schlüsselwörter + texcsstyle=*\bfseries\color{blue}, + morekeywords={*,$,\{,\},\[,\],lstinputlisting,includegraphics, + rowcolor,columncolor,listoffigures,lstlistoflistings, + subsection,subsubsection,textcolor,tableofcontents,colorbox, + fcolorbox,definecolor,cellcolor,url,linktocpage,subtitle, + subject,maketitle,usetikzlibrary,node,path,addbibresource, + printbibliography}, + numbers=none, + numbersep=0pt, + xleftmargin=0.4em, +} + +\lstdefinestyle{java}{% + language=Java, + extendedchars=true, +} + +% füge einen x64-Assembler Dialekt hinzu +\lstdefinelanguage[x64]{Assembler} +% basiert auf dem "x86masm" Dialekt + [x86masm]{Assembler} + % zusätzliche Schlüsselwörter + {morekeywords={CDQE,CQO,CMPSQ,CMPXCHG16B,JRCXZ,LODSQ,MOVSXD, % + POPFQ,PUSHFQ,SCASQ,STOSQ,IRETQ,RDTSCP,SWAPGS, % + rax,rdx,rcx,rbx,rsi,rdi,rsp,rbp, % + r8,r8d,r8w,r8b,r9,r9d,r9w,r9b} +} + +\lstdefinestyle{c}{ + language=c, + extendedchars=true, +} + +% //////////////////// eigene Anweisungen //////////////////// +% benötigt package xspace +\newcommand\FU{Freie Universität Berlin\xspace} +\newcommand\gdw{g.\,d.\,w.\xspace} +\newcommand\oBdA{o.\,B.\,d.\,A.\xspace} +\newcommand\N{\mathbb{N}\xspace} +\newcommand\Q{\mathbb{Q}\xspace} +\newcommand\R{\mathbb{R}\xspace} +\newcommand\Z{\mathbb{Z}\xspace} +\newcommand\ohneNull{\ensuremath{\backslash\lbrace 0\rbrace}}% \{0} +% Schreibt Befehl \dh in \dhALT um +\let\dhALT\dh +%renew überschreibt command \dh +\renewcommand\dh{d.\,h.\xspace} +\newcommand{\from}{\ensuremath{\colon}} +\newcommand{\floor}[1]{\lfloor{#1}\rfloor} +\newcommand{\ceil}[1]{\lceil{#1}\rceil} +\newcommand{\abbrev}[2]{\expandafter\newcommand\csname + #1\endcsname{#2\xspace}} +\newcommand{\cclasss}[2]{\abbrev{#1}{\textsf{#2}}} +\newcommand{\cclass}[1]{\cclasss{#1}{#1}} +\cclasss{ccP}{P} +\cclass{NP} +\cclass{LOGSPACE} +\cclass{NL} + +% //////////////// mathematische Funktionen //////////////////// +\DeclareMathOperator{\True}{True} +\DeclareMathOperator{\False}{False} + +% //////////////////// eigene Theoreme //////////////////// +\newtheorem{theorem}{Satz} +\newtheorem{corollary}[theorem]{Korollar} +\newtheorem{lemma}[theorem]{Lemma} +\newtheorem{observation}[theorem]{Beobachtung} +\newtheorem{definition}[theorem]{Definition} +\newtheorem{Literatur}[theorem]{Literatur} + +% konfiguriert proof +\makeatletter +\newenvironment{Proof}[1][\proofname]{\par + \pushQED{\qed}% + \normalfont \topsep6\p@\@plus6\p@\relax + \trivlist + \item[\hskip\labelsep + \bfseries + #1\@addpunct{.}]\ignorespaces +}{% + \popQED\endtrivlist\@endpefalse +} +\makeatother + +% //////////////////// eigene Farben //////////////////// +\let\definecolor=\xdefinecolor +\definecolor{FUgreen}{RGB}{153,204,0} +\definecolor{FUblue}{RGB}{0,51,102} + +\definecolor{middlegray}{rgb}{0.5,0.5,0.5} +\definecolor{lightgray}{rgb}{0.8,0.8,0.8} +\definecolor{orange}{rgb}{0.8,0.3,0.3} +\definecolor{azur}{rgb}{0,0.7,1} +\definecolor{yac}{rgb}{0.6,0.6,0.1} +\definecolor{Pink}{rgb}{1,0,0.6} + +\definecolor{bgcolour}{rgb}{0.97,0.97,0.97} +\definecolor{codegreen}{rgb}{0,0.6,0} +\definecolor{codegray}{rgb}{0.35,0.35,0.35} +\definecolor{codepurple}{rgb}{0.58,0,0.82} +\definecolor{codeblue}{rgb}{0.4,0.5,1} + +% //////////////////// eigene Einstellungen //////////////////// + +% verhindert Einrückung der 1. Zeile eines Absatzes +\parindent 0pt +% <-- Nummer des Übungszettels +\newcommand{\ubungNo}{10} +% <-- Name der Lehrveranstaltung eintragen +\newcommand{\veranstaltung}{Funktionale Programmierung} +% <-- z.B. SoSo 17, WiSe 17/18 +\newcommand{\semester}{WiSe 23/24} +% % <-- Hier Anzahl der Aufgaben eintragen +\newcommand{\aufgNo}{3} + +% https://tex.stackexchange.com/a/117538 +\renewcommand\lstlistingname{Beispiel} + +\usepackage{tikz} + +% /////////////////////// BEGIN DOKUMENT ///////////////////////// +\begin{document} + +\setkomafont{section}{\large} + +% ////////////// Daten ////////////// +\begin{center} + +{\veranstaltung, \semester}\par +{\Large Tutoriumsaufgaben \ubungNo}\par +\end{center} +\vspace{-3ex} % Abstand +\rule{\linewidth}{0.8pt} % horizontale Linie +\vspace{-3ex} % Abstand + +% /////////////////////// Aufgabe 1 ///////////////////////// +%alter Zettel 8 Bäume zeichnen +%einfügen löschen, kleinstes Elem + +\section*{Aufgabe 1: Algorithmen per Hand durchführen} + +\begin{enumerate} + \item Schreiben Sie die folgenden Gleichungen in umgekehrte polnische Notation um und lösen Sie per Hand: + \begin{enumerate}[label=(\roman*)] + \item $(9-3) + \log (8)$ + \item $(10/4) - \sqrt{ 4 }$ + \end{enumerate} + \item Verwenden Sie den Algorithmus aus der Vorlesung um per Hand zu überprüfen, ob \texttt{[]([({}) []])} und \texttt{[][()){}]} gültige Klammerausdrücke sind. +\end{enumerate} + +\section*{Aufgabe 2: Module} + +\begin{enumerate} + \item Erstellen Sie ein Modul \lstinline{Queue}, das den algebraischen Datentyp \lstinline{Queue} und die Funktionen \lstinline{isEmpty}, \lstinline{dequeue} und \lstinline{enqueue} exportiert. \par + Die fraglichen Funktionen sind unten angefügt, ansonsten soll das Beispiel aus dem Live-Code der Vorlesung (\lstinline{FQueue}) verwendet werden.\par +Ergänzen Sie die Funktionen +\begin{enumerate}[label= (\roman*)] +\item \lstinline{hasElem :: Queuelike a => b -> a b -> Bool} (überprüft ob der übergebene Wert in der \lstinline{Queue} enthalten ist) +\item \lstinline{count :: Queuelike a => b -> a b -> Int} (zählt wie oft der übergebene Wert in der \lstinline{Queue} enthalten ist) +%\item \haskell{getPenultimate :: Queue a -> Maybe a} (gibt den vorletzten Wert aus der \haskell{Queue} zurück) +%\item \haskell{hasElem :: a -> Queue a -> Bool} (überprüft ob der übergebene Wert in der \haskell{Queue} enthalten ist) +%\item\haskell{getDistanceToFront :: a -> Queue a -> Maybe Int} (bekommt ein Element und eine \haskell{Queue} und gibt zurück wie viele Elemente vor dem Element stehen) +\end{enumerate} +hinzu und exportieren Sie diese. +\item Importieren Sie das Modul in eine neue Haskelldatei und schreiben Sie folgende Funktionen, die eine Kassenschlange eines Einkaufsladens simulieren. +In der Schlange stellen Sie Personen mit Einkaufswägen an. Jeder Einkaufswagen enthält verschiedene Produkte mit zugeordneten Preisen. + +\begin{enumerate}[label= (\roman*)] + \item Schreiben Sie passende Typsynonyme oder algebraische Datentypen, die einen Einkaufswagen und die Schlange von Einkaufswägen darstellen. + \item Schreiben Sie eine Funktion \lstinline{anstellen}, bei der ein Einkaufswagen in die Kassenschlange eingereiht wird. + \item Schreiben Sie eine Funktion \lstinline{kassieren}, bei der für den Einkaufswagen, der als erstes eingereiht wurde der Gesamtpreis der Waren bestimmt wird. + Die Rückgabe von \lstinline{kassieren} soll ein Tupel aus dem Gesamtpreis und der neuen Kassenschlange sein. +\end{enumerate} +\end{enumerate} + + +% /////////////////////// END DOKUMENT ///////////////////////// +\end{document} -- GitLab