From 480c39657e31d4366ceb6b954bce7b3ca0a724c6 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Jonah=20Br=C3=BCchert?= <jbb@kaidan.im> Date: Sun, 17 Dec 2023 21:21:34 +0100 Subject: [PATCH] 09: Prepare for english tutorial --- 09/tut09.md | 15 ++ 09/tut09.pdf | Bin 0 -> 102538 bytes 09/tut09_en.md | 15 ++ 09/tut09_en.pdf | Bin 0 -> 101537 bytes 09/{tut9.pdf => uebungen09.pdf} | Bin 152267 -> 152442 bytes 09/{tut9.tex => uebungen09.tex} | 34 +-- 09/uebungen09_en.pdf | Bin 0 -> 154025 bytes 09/uebungen09_en.tex | 373 ++++++++++++++++++++++++++++++++ 8 files changed, 420 insertions(+), 17 deletions(-) create mode 100644 09/tut09.md create mode 100644 09/tut09.pdf create mode 100644 09/tut09_en.md create mode 100644 09/tut09_en.pdf rename 09/{tut9.pdf => uebungen09.pdf} (79%) rename 09/{tut9.tex => uebungen09.tex} (92%) create mode 100644 09/uebungen09_en.pdf create mode 100644 09/uebungen09_en.tex diff --git a/09/tut09.md b/09/tut09.md new file mode 100644 index 0000000..86d4959 --- /dev/null +++ b/09/tut09.md @@ -0,0 +1,15 @@ +--- +theme: metropolis +aspectratio: 169 +--- + +# Tutorium 9 + +Bäume, Instanzen von Typklassen + +# Instanzen von Typklassen + +```Haskell +instance Show Datentyp where + show x = ... +``` diff --git a/09/tut09.pdf b/09/tut09.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9837480d63b4d48edbee1ea3ca6b7574e77caa5f GIT binary patch literal 102538 zcmY!laB<T$)HCH$y>R8|4K70y1p|frq%1BQ8!mmH)V%bP3<YB&Qw0d%(s#?uDM>9- z(09v8EJ<}qP0mkA<+8KmDlREXP0Z!0xb-%4w;!{iz?;9K(Z5t4RqU<1vu&aWi|h&6 z02f6^jv_^Ul^<1a?uc@Fv0G`}sdy{f|K{#Q+bBiW#}3-fdQTiQ8D}pyvF*O&*Yd9S zu;~+CO`juC85a^{HPbnJin%tnos|)LwCuRHsNX{ozvCC%a_>DfOyOX*ygc!o)82dM zq7Q36ZZ?(txV3EC(>bnPtNzcQe3zjw>E%iD$!}g?+3IkjY>s>KoK0IBZ+^P6FtYNK zz4437m-@mNYqTY|H>|j^biS${!)5Ppj69XC(-iFv&FvAD-g$qm)}^A)d*Z{GKgAV& z6<A-tw7CA_?}sxi#81!q7*OtEFL{{Z@{x`C-12uPZ~guBk5Z_Q%KBMv^KR9go4set zr`oGqenwnXvA-7=xBPZ4)9r0j+^^1`a?LS7=8L0ex0_+`q@d+XUM@MJ<b8Z+&m(TH 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> x = ( Node lt ( delete q rt ) ) | otherwise = delete' node - where - delete' (Node x Nil rt) = rt - delete' (Node x lt Nil) = lt - delete' (Node x lt rt) = Node maxE (delete maxE lt) rt - maxE = maxElem lt + where + delete' ( Node x Nil rt ) = rt + delete' ( Node x lt Nil ) = lt + delete' ( Node x lt rt ) = Node maxE ( delete maxE lt ) rt + maxE = maxElem lt \end{lstlisting} \begin{figure}[h] \centering @@ -302,8 +302,8 @@ delete q node@( Node x lt rt) child {node {5} child {node {2} } - child {node{6} - child {node {4}} + child {node{7} + child {node {6}} child [missing] } } @@ -326,7 +326,7 @@ Boolesche Ausdrücke können als Syntaxbaum dargestellt werden, in dem alle Oper \begin{enumerate}[label=\alph*)] \item Implementieren Sie einen Algebraischen Datentyp, der einen Booleschen Ausdruck speichern kann. Der Ausdruck soll mindestens die Verknüpfungen und, oder und die Negation enthalten können. \item Implementieren Sie eine Funktion, die einen Syntaxbaum zu einem Ergebnis vom Typ \texttt{Bool} auswertet. - \item Machen sie ihren Algebraischen Datentyp zu einer Instannz der Typklasse Show. + \item Machen sie ihren Algebraischen Datentyp zu einer Instanz der Typklasse Show. \end{enumerate} % ///////////////////// Aufgabe 2 /////////////////// @@ -339,10 +339,10 @@ data BHeightTree a = HNil | HNode a Int ( BHeightTree a ) ( BHeightTree a ) deriving Show \end{lstlisting} -Jeder Knoten, eines Baumes, ist die Wurzel eines Teilbaums. -Jeder Knoten, eines \texttt{BHeightTree}, speichert, die Höhe seines Teilbaums. +Jeder Knoten eines Baumes ist die Wurzel eines Teilbaums. +Jeder Knoten eines \texttt{BHeightTree} speichert die Höhe seines Teilbaums. -\begin{lstlisting}[caption={\texttt{Beispiel Baum}}, language=Haskell] +\begin{lstlisting}[caption={\texttt{Beispielbaum}}, language=Haskell] 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und Katharina Klost + + % Dokumentenklasse +\documentclass[ +% globale Schriftgröße + 10pt, +% setzt Absatzabstand hoch + parskip=half-, +% Format + paper=a4, +% lädt Sprachpakete + english,ngerman, +]{scrartcl} + +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} + +% //////////////////// Pakete laden //////////////////// +\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}{9} +% <-- Name der Lehrveranstaltung eintragen +\newcommand{\veranstaltung}{Functional Programming} +% <-- 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{Example} + +\usepackage{tikz} + +% /////////////////////// BEGIN DOKUMENT ///////////////////////// +\begin{document} + +\setkomafont{section}{\large} + +% ////////////// Daten ////////////// +\begin{center} + +{\veranstaltung, \semester}\par +{\Large Tutorial Tasks \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*{Task 1: Binary Search Trees I} + +\begin{lstlisting}[caption={\texttt{BTree Operations}}, language=Haskell] +insert :: (Ord a) = > a -> BTree a -> BTree a +insert q Nil = Node q Nil Nil +insert q t@(Node x lt rt) + | q == x = t + | q < x = Node x (insert q lt) rt + | otherwise = Node x lt (insert q rt) + +delete ::( Ord a ) = > a -> BTree a -> BTree a +delete q Nil = Nil +delete q node@ ( Node x lt rt ) + | q < x = ( Node ( delete q lt ) rt ) + | q > x = ( Node lt ( delete q rt ) ) + | otherwise = delete' node + where + delete' ( Node x Nil rt ) = rt + delete' ( Node x lt Nil ) = lt + delete' ( Node x lt rt ) = Node maxE ( delete maxE lt ) rt + maxE = maxElem lt +\end{lstlisting} +\begin{figure}[h] + \centering + \begin{tikzpicture}[ + level distance=10mm, + level 1/.style={sibling distance=20mm}, + level 2/.style={sibling distance=10mm}, + level 3/.style={sibling distance=5mm}] + \node {8} + child {node {5} + child {node {2} + } + child {node{7} + child {node {6}} + child [missing] + } + } + child {node {20} + child {node {11} + } + child [missing] + }; + \end{tikzpicture} + \caption{BSearchTree Example} + \label{fig:figure2} +\end{figure} + +Do the following changes to the tree. Write down each step. + +\texttt{insert 7, insert 21, delete 2, delete 5, insert 12, insert 15, insert 14, delete 20} + +\section*{Task 2: Syntax Tree} + +Boolean expressions can be represented in a syntax tree. To create a syntax tree, add all possible parantheses to an expression without changing the meaning. Then, the operator that is applied last is the root, and its operands the subtrees. + +\begin{enumerate}[label=\alph*)] + \item Implement an algebraic datatype that can store a boolean expression. At least the operators ``and'', ``or'' and ``not'' should be representable. + \item Implement a function, that evaluates a syntax tree into a result of type \texttt{Bool}. + \item Make your data type an instance of the typeclass Show, without using \texttt{deriving}. +\end{enumerate} + +% ///////////////////// Aufgabe 2 /////////////////// +\section*{Task 3: Binary Search Trees II} +\begin{lstlisting}[caption={\texttt{algebraic data types}}, language=Haskell] +-- from lecture +data BTree a = Nil | Node a ( BTree a ) ( BTree a ) deriving Show +-- new +data BHeightTree a = HNil | HNode a Int + ( BHeightTree a ) ( BHeightTree a ) deriving Show +\end{lstlisting} + +Every node in a tree is the root of two subtrees. +Every node of a \texttt{BHeightTree} stores the height of its subtree + +\begin{lstlisting}[caption={\texttt{Example Tree}}, language=Haskell] +bHeightTreeBsp = + HNode 5 3 + (HNode 3 2 + (HNode 2 1 + HNil + HNil) + HNil) + (HNode 5 1 + HNil + HNil) +\end{lstlisting} + +\begin{enumerate} + \item + Write a function \texttt{heightTInsert :: a -> BHeightTree a -> BHeightTree a }. \\ + Input: an element x and a search tree t. \\ + Result: A search tree, with t's elements and x. + \item + Which subtree heights change when using \texttt{delete}? + \item + What is the difference in runtime complexity between a normal tree and a search tree? +\end{enumerate} + + +% /////////////////////// END DOKUMENT ///////////////////////// +\end{document} -- GitLab