From bd5c3b572027118d9e665432592b0656b855ed83 Mon Sep 17 00:00:00 2001
From: Peter Gerwinski <peter.gerwinski@hs-bochum.de>
Date: Thu, 4 Feb 2021 13:48:08 +0100
Subject: [PATCH] Vorbereitung 4.2.2021

---
 20210204/aufgabe-1a.c                         |   50 +
 20210204/aufgabe-1b.c                         |   50 +
 20210204/aufgabe-2.c                          |   22 +
 20210204/hello-gtk.png                        |    1 +
 20210204/hp-2020ws-p4.pdf                     |  Bin 0 -> 102871 bytes
 20210204/hp-2020ws-p4.tex                     |  193 +++
 20210204/hp-20210204.pdf                      |  Bin 0 -> 166909 bytes
 20210204/hp-20210204.tex                      | 1109 +++++++++++++++++
 20210204/hp-musterloesung-20210204.pdf        |  Bin 0 -> 81565 bytes
 20210204/hp-musterloesung-20210204.tex        |  629 ++++++++++
 20210204/hp-uebung-20210204.pdf               |  Bin 0 -> 61715 bytes
 20210204/hp-uebung-20210204.tex               |  303 +++++
 20210204/loesung-1d-0f.c                      |   54 +
 20210204/loesung-1d-1.c                       |   54 +
 20210204/loesung-1d-2.c                       |   54 +
 20210204/loesung-1e.c                         |   61 +
 20210204/loesung-1f.c                         |   69 +
 20210204/loesung-1g.c                         |   77 ++
 .../logo-hochschule-bochum-cvh-text-v2.pdf    |    1 +
 20210204/logo-hochschule-bochum.pdf           |    1 +
 20210204/pgscript.sty                         |    1 +
 20210204/pgslides.sty                         |    1 +
 README.md                                     |   12 +-
 hp-slides-2020ws.pdf                          |  Bin 2219771 -> 2764759 bytes
 hp-slides-2020ws.tex                          |    8 +-
 25 files changed, 2748 insertions(+), 2 deletions(-)
 create mode 100644 20210204/aufgabe-1a.c
 create mode 100644 20210204/aufgabe-1b.c
 create mode 100644 20210204/aufgabe-2.c
 create mode 120000 20210204/hello-gtk.png
 create mode 100644 20210204/hp-2020ws-p4.pdf
 create mode 100644 20210204/hp-2020ws-p4.tex
 create mode 100644 20210204/hp-20210204.pdf
 create mode 100644 20210204/hp-20210204.tex
 create mode 100644 20210204/hp-musterloesung-20210204.pdf
 create mode 100644 20210204/hp-musterloesung-20210204.tex
 create mode 100644 20210204/hp-uebung-20210204.pdf
 create mode 100644 20210204/hp-uebung-20210204.tex
 create mode 100644 20210204/loesung-1d-0f.c
 create mode 100644 20210204/loesung-1d-1.c
 create mode 100644 20210204/loesung-1d-2.c
 create mode 100644 20210204/loesung-1e.c
 create mode 100644 20210204/loesung-1f.c
 create mode 100644 20210204/loesung-1g.c
 create mode 120000 20210204/logo-hochschule-bochum-cvh-text-v2.pdf
 create mode 120000 20210204/logo-hochschule-bochum.pdf
 create mode 120000 20210204/pgscript.sty
 create mode 120000 20210204/pgslides.sty

diff --git a/20210204/aufgabe-1a.c b/20210204/aufgabe-1a.c
new file mode 100644
index 0000000..61b6e79
--- /dev/null
+++ b/20210204/aufgabe-1a.c
@@ -0,0 +1,50 @@
+#include <stdio.h>
+
+#define ANIMAL     0
+#define WITH_WINGS 1
+#define WITH_LEGS  2
+
+typedef struct animal
+{
+  int type;
+  char *name;
+} animal;
+
+typedef struct with_wings
+{
+  int wings;
+} with_wings;
+
+typedef struct with_legs
+{
+  int legs;
+} with_legs;
+
+int main (void)
+{
+  animal *a[2];
+
+  animal duck;
+  a[0] = &duck;
+  a[0]->type = WITH_WINGS;
+  a[0]->name = "duck";
+  a[0]->wings = 2;
+
+  animal cow;
+  a[1] = &cow;
+  a[1]->type = WITH_LEGS;
+  a[1]->name = "cow";
+  a[1]->legs = 4;
+
+  for (int i = 0; i < 2; i++)
+    if (a[i]->type == WITH_LEGS)
+      printf ("A %s has %d legs.\n", a[i]->name,
+              ((with_legs *) a[i])-> legs);
+    else if (a[i]->type == WITH_WINGS)
+      printf ("A %s has %d wings.\n", a[i]->name,
+              ((with_wings *) a[i])-> wings);
+    else
+      printf ("Error in animal: %s\n", a[i]->name);
+
+  return 0;
+}
diff --git a/20210204/aufgabe-1b.c b/20210204/aufgabe-1b.c
new file mode 100644
index 0000000..2cf3b56
--- /dev/null
+++ b/20210204/aufgabe-1b.c
@@ -0,0 +1,50 @@
+#include <stdio.h>
+
+#define ANIMAL     0
+#define WITH_WINGS 1
+#define WITH_LEGS  2
+
+typedef struct animal
+{
+  int type;
+  char *name;
+} animal;
+
+typedef struct with_wings
+{
+  int wings;
+} with_wings;
+
+typedef struct with_legs
+{
+  int legs;
+} with_legs;
+
+int main (void)
+{
+  animal *a[2];
+
+  animal duck;
+  a[0] = &duck;
+  a[0]->type = WITH_WINGS;
+  a[0]->name = "duck";
+  ((with_wings *) a[0])->wings = 2;
+
+  animal cow;
+  a[1] = &cow;
+  a[1]->type = WITH_LEGS;
+  a[1]->name = "cow";
+  ((with_legs *) a[1])->legs = 4;
+
+  for (int i = 0; i < 2; i++)
+    if (a[i]->type == WITH_LEGS)
+      printf ("A %s has %d legs.\n", a[i]->name,
+              ((with_legs *) a[i])-> legs);
+    else if (a[i]->type == WITH_WINGS)
+      printf ("A %s has %d wings.\n", a[i]->name,
+              ((with_wings *) a[i])-> wings);
+    else
+      printf ("Error in animal: %s\n", a[i]->name);
+
+  return 0;
+}
diff --git a/20210204/aufgabe-2.c b/20210204/aufgabe-2.c
new file mode 100644
index 0000000..a1054f2
--- /dev/null
+++ b/20210204/aufgabe-2.c
@@ -0,0 +1,22 @@
+#include <stdio.h>
+
+void foreach (int *a, void (*fun) (int x))
+{
+  for (int *p = a; *p >= 0; p++)
+    fun (*p);
+}
+
+void even_or_odd (int x)
+{
+  if (x % 2)
+    printf ("%d ist ungerade.\n", x);
+  else
+    printf ("%d ist gerade.\n", x);
+}
+
+int main (void)
+{
+  int numbers[] = { 12, 17, 32, 1, 3, 16, 19, 18, -1 };
+  foreach (numbers, even_or_odd);
+  return 0;
+}
diff --git a/20210204/hello-gtk.png b/20210204/hello-gtk.png
new file mode 120000
index 0000000..cca9920
--- /dev/null
+++ b/20210204/hello-gtk.png
@@ -0,0 +1 @@
+../common/hello-gtk.png
\ No newline at end of file
diff --git a/20210204/hp-2020ws-p4.pdf b/20210204/hp-2020ws-p4.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..21bff505fd5fa6ca5d8913a694261a19ac6f55fd
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diff --git a/20210204/hp-2020ws-p4.tex b/20210204/hp-2020ws-p4.tex
new file mode 100644
index 0000000..c5eb30c
--- /dev/null
+++ b/20210204/hp-2020ws-p4.tex
@@ -0,0 +1,193 @@
+% hp-2020ws-p4.pdf - Labor Notes on Low-Level Programming
+% Copyright (C) 2014, 2015, 2016, 2018, 2019, 2020, 2021  Peter Gerwinski
+%
+% This document is free software: you can redistribute it and/or
+% modify it either under the terms of the Creative Commons
+% Attribution-ShareAlike 3.0 License, or under the terms of the
+% GNU General Public License as published by the Free Software
+% Foundation, either version 3 of the License, or (at your option)
+% any later version.
+%
+% This document is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this document.  If not, see <http://www.gnu.org/licenses/>.
+%
+% You should have received a copy of the Creative Commons
+% Attribution-ShareAlike 3.0 Unported License along with this
+% document.  If not, see <http://creativecommons.org/licenses/>.
+
+% README: Versuch 4: Objektorientiertes Grafik-Programm
+
+\documentclass[a4paper]{article}
+
+\usepackage{pgscript}
+\usepackage{multicol}
+\usepackage{amsmath}
+\usepackage{sfmath}
+
+\sloppy
+%\pagestyle{empty}
+\newcommand{\sep}{~$\cdot$~}
+\newcommand{\mylicense}{CC-by-sa (Version 3.0) oder GNU GPL (Version 3 oder höher)}
+
+\begin{document}
+
+  \makebox(0,0.005)[tl]{\includegraphics[scale=0.72]{logo-hochschule-bochum-cvh-text-v2.pdf}}\hfill
+  \makebox(0,0)[tr]{\includegraphics[scale=0.5]{logo-hochschule-bochum.pdf}}
+  \par\bigskip\bigskip
+  \begin{center}
+    \Large\textbf{Praktikumsversuch 4: Objektorientiertes Grafik-Programm}
+    \par\medskip
+    \normalsize Hardwarenahe Programmierung\sep
+    Wintersemester 2020/21\sep
+    Prof.~Dr.~Peter Gerwinski
+  \end{center}
+
+  Aufgabe: Schreiben Sie ein GTK+-Programm,
+  mit dem man verschiedene Objekte (z.\,B.\ Rechtecke, Kreise, Dreiecke)
+  in eine Grafik einfügen und nachträglich verändern kann
+  (z.\,B.\ Position, Größe, Farbe).
+
+  (Beispiel: Ich füge zunächst zwei Rechtecke und einen Kreis in eine Grafik ein,
+  wähle anschließend das erste Rechteck aus und ändere dessen Farbe.)
+
+  \bigskip
+
+  Hinweise:
+  \vspace*{-\medskipamount}
+
+  \begin{itemize}
+    \item
+      Das Beispielprogramm \gitfile{hp}{2020ws/20210128}{objects-9.c} zeigt,
+      wie man in C verschiedenartige Objekte
+      in einem Array von Zeigern verwaltet.
+    \item
+      Das Beispielprogramm \gitfile{hp}{2020ws/script}{gtk-6.c} zeigt,
+      wie man mit Hilfe der GUI-Bibliothek GTK+
+      verschiedene Objekte in ein Fenster zeichnet.
+    \item
+      Das Beispielprogramm \gitfile{hp}{2020ws/script}{gtk-7.c} zeigt,
+      wie man in der GUI-Bibliothek GTK+
+      Tastatur- und Maus-Eingaben entgegennimmt und verarbeitet.
+    \item
+      Das Auswählen eines bereits vorhandenen Objekts geht am einfachsten
+      mittels Tastatur-Eingaben (z.\,B.\ Ziffer 1 für das erste Objekt usw.).
+      Auswahl mit der Maus ist auch möglich, aber schwieriger.
+    \item
+      Mit Hilfe der Funktion \lstinline{gtk_widget_queue_draw()}
+      teilen Sie GTK+ mit, daß Sie ein \lstinline{GtkWidget}
+      neu zeichnen lassen möchten.
+    \item
+      Das Compilieren eines GTK+-Programms
+      (z.\,B.\ \gitfile{hp}{2020ws/script}{gtk-7.c}) geschieht wie folgt:
+      \begin{lstlisting}[style=cmd,gobble=8]
+        gcc $(pkg-config --cflags gtk+-3.0) -Wall -O gtk-7.c \
+            $(pkg-config --libs gtk+-3.0) -o gtk-7
+      \end{lstlisting}
+      (Den Backslash am Ende der ersten Zeile entfällt,
+      wenn Sie den ganzen Befehl in eine einzige Zeile schreiben.)
+  \end{itemize}
+
+  \bigskip
+  \textbf{GTK+ unter GNU/Linux}
+  \begin{itemize}
+    \item
+      Installieren Sie das Entwickler-Paket für GTK+-3,\\
+      z.\,B.\ unter Debian GNU/Linux und darauf basierenden Systemen:
+      \begin{lstlisting}[style=cmd,gobble=8]
+        apt-get install libgtk-3-dev
+      \end{lstlisting}
+  \end{itemize}
+
+  \bigskip
+  \goodbreak
+  \textbf{GTK+ unter MacOS X}
+  \begin{itemize}
+    \item
+      Zuerst den Paketmanager "`Homebrew"' installieren:
+      \begin{lstlisting}[style=cmd,gobble=8]
+        ruby -e "$(curl -fsSL https://raw.githubusercontent.com/
+                              Homebrew/install/2020ws/install)"
+      \end{lstlisting}
+      (Die URL nicht trennen, sondern in einer Zeile schreiben.)
+    \item
+      Danach mit Hilfe von \lstinline[style=cmd]{brew} GTK+ installieren:
+      \begin{lstlisting}[style=cmd,gobble=8]
+        brew install gtk+3
+      \end{lstlisting}
+  \end{itemize}
+
+  \bigskip
+  \goodbreak
+  \textbf{GTK+ unter Microsoft Windows: Cygwin}
+  \begin{itemize}
+    \item
+      Im Cygwin-Setup-Programm die Pakete \file{libgtk3-devel},
+      \file{xorg-server} und \file{dbus-x11} installieren.
+    \item
+      Bevor Sie GTK+-Programme starten können,
+      müssen Sie einmalig den X-Server starten:
+      \begin{lstlisting}[style=cmd,gobble=8]
+        XWin -multiwindow &
+      \end{lstlisting}
+    \item
+      Bevor Sie GTK+-Programme starten können,
+      müssen Sie einmalig pro Shell-Sitzung\\
+      die \lstinline[style=cmd]{DISPLAY}-Variable setzen:
+      \begin{lstlisting}[style=cmd,gobble=8]
+        export DISPLAY=:0.0
+      \end{lstlisting}
+  \end{itemize}
+
+  \bigskip
+  \goodbreak
+  \textbf{GTK+ unter Microsoft Windows: MinGW}
+  \begin{itemize}
+    \item
+      Installieren Sie \file{MSYS2} (Installer).
+    \item
+      Installieren Sie von der MinGW-Shell aus GTK+
+      und weitere Entwicklungswerkzeuge:
+      \begin{lstlisting}[style=cmd,gobble=8]
+        pacman -S mingw-w64-x86_64-gcc
+        pacman -S mingw-w64-x86_64-gtk3
+        pacman -S mingw-w64-x86_64-pkg-config
+      \end{lstlisting}
+    \item
+      Falls nötig, ergänzen Sie in der MinGW-Shell
+      den Pfad zu den neu installierten Programmen:
+      \begin{lstlisting}[style=cmd,gobble=8]
+        export PATH=$PATH:/mingw64/bin
+      \end{lstlisting}
+  \end{itemize}
+
+  \bigskip
+
+  \strut\hfill\emph{Viel Erfolg!}
+
+  \vfill
+
+  \begingroup
+
+    \small
+
+    \setlength{\leftskip}{3cm}
+
+    Stand: 4.\ Februar 2021
+
+%    Soweit nicht anders angegeben:\\
+    Copyright \copyright\ 2014, 2015, 2016, 2018, 2019, 2020, 2021\quad Peter Gerwinski\\
+    Lizenz: \mylicense
+
+    Sie können diese Praktikumsunterlagen einschließlich \LaTeX-Quelltext
+%    und Beispielprogramme\\
+    herunterladen unter:\\
+    \url{https://gitlab.cvh-server.de/pgerwinski/hp}
+
+  \endgroup
+
+\end{document}
diff --git a/20210204/hp-20210204.pdf b/20210204/hp-20210204.pdf
new file mode 100644
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diff --git a/20210204/hp-20210204.tex b/20210204/hp-20210204.tex
new file mode 100644
index 0000000..ecfb230
--- /dev/null
+++ b/20210204/hp-20210204.tex
@@ -0,0 +1,1109 @@
+% hp-20210204.pdf - Lecture Slides on Low-Level Programming
+% Copyright (C) 2012, 2013, 2015, 2016, 2017, 2018, 2019, 2020, 2021  Peter Gerwinski
+%
+% This document is free software: you can redistribute it and/or
+% modify it either under the terms of the Creative Commons
+% Attribution-ShareAlike 3.0 License, or under the terms of the
+% GNU General Public License as published by the Free Software
+% Foundation, either version 3 of the License, or (at your option)
+% any later version.
+%
+% This document is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this document.  If not, see <http://www.gnu.org/licenses/>.
+%
+% You should have received a copy of the Creative Commons
+% Attribution-ShareAlike 3.0 Unported License along with this
+% document.  If not, see <http://creativecommons.org/licenses/>.
+
+% README: Objektorientierte Programmierung: virtuelle Methoden
+
+\documentclass[10pt,t]{beamer}
+
+\usepackage{pgslides}
+\usepackage{rotating}
+\usepackage{tikz}
+
+\title{Hardwarenahe Programmierung}
+\author{Prof.\ Dr.\ rer.\ nat.\ Peter Gerwinski}
+\date{4.\ Februar 2021}
+
+\begin{document}
+
+\maketitleframe
+
+\nosectionnonumber{\inserttitle}
+
+\begin{frame}
+
+  \shownosectionnonumber
+
+  \begin{itemize}
+    \item[\textbf{1}] \textbf{Einführung}
+      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/hp}}}
+    \item[\textbf{2}] \textbf{Einführung in C}
+    \item[\textbf{3}] \textbf{Bibliotheken}
+    \item[\textbf{4}] \textbf{Algorithmen}
+    \item[\textbf{5}] \textbf{Hardwarenahe Programmierung}
+    \item[\textbf{6}] \textbf{Objektorientierte Programmierung}
+      \begin{itemize}
+        \color{medgreen}
+        \item[6.0] Dynamische Speicherverwaltung
+        \item[6.1] Konzepte und Ziele
+        \item[6.2] Beispiel: Zahlen und Buchstaben
+        \item[6.3] Unions
+        \color{red}
+        \item[6.4] Virtuelle Methoden
+        \item[6.5] Beispiel: Graphische Benutzeroberfläche (GUI)
+        \item[6.6] Ausblick: C++
+      \end{itemize}
+    \item[\textbf{7}] \textbf{Datenstrukturen}
+    \vspace*{-1cm}
+  \end{itemize}
+
+\end{frame}
+
+\setcounter{section}{5}
+\section{Objektorientierte Programmierung}
+
+\addtocounter{subsection}{-1}
+\subsection{Dynamische Speicherverwaltung}
+
+\begin{frame}[fragile]
+
+  \showsection
+  \showsubsection
+
+  \begin{itemize}
+    \item
+      Array: feste Anzahl von Elementen desselben Typs (z.\,B.\ 3 ganze Zahlen)
+    \item
+      Dynamisches Array: variable Anzahl von Elementen desselben Typs
+  \end{itemize}
+
+  \bigskip
+
+  \begin{lstlisting}
+    char *name[] = { "Anna", "Berthold", "Caesar" };
+
+    ...
+
+     name[3] = "Dieter";
+  \end{lstlisting}
+
+  \begin{picture}(0,0)
+    \color{red}
+    \put(0,0){\line(3,1){3.5}}
+    \put(0,1){\line(3,-1){3.5}}
+  \end{picture}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsection
+  \showsubsection
+
+  \bigskip
+
+  \begin{lstlisting}
+    #include <stdlib.h>
+
+    ...
+
+      char **name = malloc (3 * sizeof (char *));
+        /* Speicherplatz für 3 Zeiger anfordern */
+
+    ...
+
+      free (name);
+        /* Speicherplatz freigeben */
+
+  \end{lstlisting}
+
+\end{frame}
+
+\subsection{Konzepte und Ziele}
+
+\begin{frame}
+
+  \showsection
+  \showsubsection
+
+  \begin{itemize}
+    \item
+%      Array: feste Anzahl von Elementen desselben Typs (z.\,B.\ 3 ganze Zahlen)
+      Array: Elemente desselben Typs (z.\,B.\ 3 ganze Zahlen)
+%    \item
+%      Dynamisches Array: variable Anzahl von Elementen desselben Typs
+    \item
+      Problem: Elemente unterschiedlichen Typs
+    \item
+      Lösung: den Typ des Elements zusätzlich speichern \textarrow\ \newterm{Objekt}
+    \item
+      Problem: Die Elemente sind unterschiedlich groß (Speicherplatz).
+    \item
+      Lösung: Im Array nicht die Objekte selbst speichern, sondern Zeiger darauf.
+  \end{itemize}
+  \begin{itemize}
+    \item
+      Funktionen, die mit dem Objekt arbeiten: \newterm{Methoden}
+    \begin{onlyenv}<1>
+      \item
+        Was die Funktion bewirkt,\\
+        hängt vom Typ des Objekts ab
+      \item
+        Realisierung über endlose \lstinline{if}-Ketten
+    \end{onlyenv}
+    \begin{onlyenv}<2>
+      \item
+        Was die Funktion bewirkt
+        \begin{picture}(0,0)
+          \color{red}
+          \put(-4.00,-0.05){\tikz{\draw[thick](0,0.25)--(3.75,-0.05);%
+                                  \draw[thick](-0.1,-0.05)--(3.75,0.3);}}
+        \end{picture}%
+        Welche Funktion aufgerufen wird,\\
+        hängt vom Typ des Objekts ab: \newterm{virtuelle Methode}
+      \item
+        Realisierung über endlose \lstinline{if}-Ketten%
+        \begin{picture}(0,0)
+          \color{red}
+          \put(-2.75,-0.05){\tikz{\draw[thick](0,0.25)--(2.5,-0.05);%
+                                  \draw[thick](-0.1,-0.05)--(2.5,0.3);}}
+          \put(1.5,-1.1){\begin{rotate}{7}\large\bf\textarrow\
+                           kommt gleich
+%                           nächste Woche
+                         \end{rotate}}
+        \end{picture}
+        Zeiger, die im Objekt gespeichert sind\\
+        (Genaugenommen: Tabelle von Zeigern)
+    \end{onlyenv}
+  \end{itemize}
+
+\end{frame}
+
+\begin{frame}
+
+  \showsection
+  \showsubsection
+
+  \begin{itemize}
+    \item
+      Problem: Elemente unterschiedlichen Typs
+    \item
+      Lösung: den Typ des Elements zusätzlich speichern \textarrow\ \newterm{Objekt}
+    \item
+      \newterm{Methoden\/} und \newterm{virtuelle Methoden}
+  \end{itemize}
+
+  \begin{itemize}
+    \item
+      Zeiger auf verschiedene Strukturen\\
+      mit einem gemeinsamen Anteil von Datenfeldern\\
+      \textarrow\ "`verwandte"' \newterm{Objekte}, \newterm{Klassenhierarchie} von Objekten
+    \item
+      Struktur, die \emph{nur\/} den gemeinsamen Anteil enthält\\
+      \textarrow\ "`Vorfahr"', \newterm{Basisklasse}, \newterm{Vererbung}
+    \item
+%      Explizite Typumwandlung eines Zeigers auf die Basisklasse\\
+%      in einen Zeiger auf die \newterm{abgeleitete Klasse}\\
+%      \textarrow\ Man kann ein Array unterschiedlicher Objekte\\
+%      \strut\phantom{\textarrow} in einer Schleife abarbeiten.\\
+      Zeiger auf die Basisklasse dürfen auf Objekte\\
+      der \newterm{abgeleiteten Klasse} zeigen\\
+      \textarrow\ \newterm{Polymorphie}
+  \end{itemize}
+
+\end{frame}
+
+\subsection{Beispiel: Zahlen und Buchstaben}
+
+\begin{frame}[fragile]
+
+  \showsection
+  \showsubsection
+
+  \begin{center}
+    \begin{minipage}{5cm}
+      \begin{lstlisting}[gobble=8]
+        ¡typedef struct
+        {
+          int type;
+        } t_base;¿
+      \end{lstlisting}
+    \end{minipage}\\[0.5cm]
+    \begin{minipage}{5cm}
+      \begin{lstlisting}[gobble=8]
+        ¡typedef struct
+        {
+          int type;
+          int content;
+        } t_integer;¿
+      \end{lstlisting}
+    \end{minipage}
+    \begin{minipage}{5cm}
+      \begin{lstlisting}[gobble=8]
+        ¡typedef struct
+        {
+          int type;
+          char *content;
+        } t_string;¿
+      \end{lstlisting}
+    \end{minipage}
+  \end{center}
+  
+\end{frame}
+
+\begin{frame}[fragile]
+  \begin{center}
+    \begin{minipage}{5cm}
+      \begin{lstlisting}[gobble=8]
+        ¡typedef struct
+        {
+          int type;
+        } t_base;¿
+      \end{lstlisting}
+    \end{minipage}\\[0.5cm]
+    \begin{minipage}{5cm}
+      \begin{lstlisting}[gobble=8]
+        ¡typedef struct
+        {
+          int type;
+          int content;
+        } t_integer;¿
+      \end{lstlisting}
+    \end{minipage}
+    \begin{minipage}{5cm}
+      \begin{lstlisting}[gobble=8]
+        ¡typedef struct
+        {
+          int type;
+          char *content;
+        } t_string;¿
+      \end{lstlisting}
+    \end{minipage}\\[0.7cm]
+    \begin{onlyenv}<1>
+      \begin{minipage}{8cm}
+        \begin{lstlisting}[gobble=10]
+          ¡t_integer i = { 1, 42 };
+          t_string s = { 2, "Hello, world!" };
+
+          t_base *object[] = { (t_base *) &i, (t_base *) &s };¿
+        \end{lstlisting}
+      \end{minipage}%
+      \begin{picture}(0,0)
+        \color{red}
+        \put(-5.4,-0.8){\mbox{$\underbrace{\rule{1.45cm}{0pt}}_{\shortstack{\strut explizite\\Typumwandlung}}$}}
+      \end{picture}
+    \end{onlyenv}
+%    \begin{onlyenv}<2>
+%      \begin{minipage}{5cm}
+%        \begin{lstlisting}[gobble=10]
+%          ¡typedef union
+%          {
+%            t_base base;
+%            t_integer integer;
+%            t_string string;
+%          } t_object;¿
+%        \end{lstlisting}
+%      \end{minipage}
+%    \end{onlyenv}
+  \end{center}
+  
+\end{frame}
+
+\subsection{Unions}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  Variable teilen sich denselben Speicherplatz.
+
+  \medskip
+
+  \begin{minipage}[t]{3.7cm}
+    \begin{lstlisting}[gobble=6]
+      ¡typedef union
+      {
+        int8_t i;
+        uint8_t u;
+      } num8_t;¿
+    \end{lstlisting}
+  \end{minipage}%
+  \begin{minipage}[t]{4.5cm}
+    \begin{lstlisting}[gobble=6]
+      ¡int main (void)
+      {
+        num8_t test;
+        test.i = -1;
+        printf ("%d\n", test.u);
+        return 0;
+      }¿
+    \end{lstlisting}
+  \end{minipage}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  Variable teilen sich denselben Speicherplatz.
+
+  \medskip
+
+  \begin{minipage}[t]{3.7cm}
+    \begin{lstlisting}[gobble=6]
+      ¡typedef union
+      {
+        char s[8];
+        uint64_t x;
+      } num_char_t;¿
+    \end{lstlisting}
+  \end{minipage}%
+  \begin{minipage}[t]{4.5cm}
+    \begin{lstlisting}[gobble=6]
+      ¡int main (void)
+      {
+        num_char_t test = { "Hello!" };
+        printf ("%lx\n", test.x);
+        return 0;
+      }¿
+    \end{lstlisting}
+  \end{minipage}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  Variable teilen sich denselben Speicherplatz.
+
+  \medskip
+
+  \begin{minipage}[t]{3.7cm}
+    \begin{lstlisting}[gobble=6]
+      ¡typedef union
+      {
+        t_base base;
+        t_integer integer;
+        t_string string;
+      } t_object;¿
+    \end{lstlisting}
+  \end{minipage}%
+  \begin{minipage}[t]{3.0cm}
+    \begin{lstlisting}[gobble=6]
+
+      ¡typedef struct
+      {
+        int type;
+      } t_base;¿
+    \end{lstlisting}
+  \end{minipage}%
+  \begin{minipage}[t]{3.0cm}
+    \begin{lstlisting}[gobble=6]
+
+      ¡typedef struct
+      {
+        int type;
+        int content;
+      } t_integer;¿
+    \end{lstlisting}
+  \end{minipage}%
+  \begin{minipage}[t]{3.0cm}
+    \begin{lstlisting}[gobble=6]
+
+      ¡typedef struct
+      {
+        int type;
+        char *content;
+      } t_string;¿
+    \end{lstlisting}
+  \end{minipage}
+
+  \bigskip
+
+  \begin{center}
+    \begin{minipage}{8.5cm}
+      \begin{lstlisting}[gobble=8]
+        ¡if (this->base.type == T_INTEGER)
+          printf ("Integer: %d\n", this->integer.content);
+        else if (this->base.type == T_STRING)
+          printf ("String: \"%s\"\n", this->string.content);¿
+      \end{lstlisting}
+    \end{minipage}
+  \end{center}
+
+\end{frame}
+
+\subsection{Virtuelle Methoden}
+
+\begin{frame}[fragile]
+  \showsubsection
+
+  \begin{lstlisting}
+    void print_object (t_object *this)
+    {
+      if (this->base.type == T_INTEGER)
+        printf ("Integer: %d\n", this->integer.content);
+      else if (this->base.type == T_STRING)
+        printf ("String: \"%s\"\n", this->string.content);
+    }
+  \end{lstlisting}
+
+  \begin{picture}(0,0)
+    \color{red}
+    \put(9,1.7){\shortstack[l]{if-Kette:\\\strut wird unübersichtlich}}
+    \put(1,-2){\mbox{\textarrow}}
+    \put(0,-3){\mbox{Zeiger auf Funktionen}}
+  \end{picture}
+
+  \begin{lstlisting}[xleftmargin=4cm]
+    void print_integer (t_object *this)
+    {
+      printf ("Integer: %d\n", this->integer.content);
+    }
+
+    void print_string (t_object *this)
+    {
+      printf ("String: \"%s\"\n", this->string.content);
+    }
+  \end{lstlisting}
+
+\end{frame}
+
+\begin{frame}[fragile]
+  \showsubsection
+
+  Zeiger auf Funktionen
+
+  \medskip
+
+  \begin{lstlisting}
+    void (* print) (t_object *this);
+  \end{lstlisting}
+  \begin{picture}(0,1.2)(0,-0.9)
+    \color{red}
+    \put(0.95,0.3){\mbox{$\underbrace{\rule{1cm}{0pt}}$}}
+    \put(0.2,-0.7){\shortstack{das, worauf print zeigt,\\ist eine Funktion}}
+  \end{picture}
+
+  \begin{itemize}
+    \item
+      Objekt enthält Zeiger auf Funktion
+      \begin{onlyenv}<1>
+        \medskip
+        \begin{lstlisting}[gobble=10]
+          typedef struct
+          {
+            void (* print) (union t_object *this);
+            int content;
+          } t_integer;
+        \end{lstlisting}
+      \end{onlyenv}
+      \begin{onlyenv}<2->
+        \vspace*{-3.5cm}  % Why doesn't a picture environment work here??? :-(
+        \begin{lstlisting}[gobble=10,xleftmargin=5.5cm]
+          typedef struct
+          {
+            void (* print) (union t_object *this);
+            int content;
+          } t_integer;
+        \end{lstlisting}
+        \vspace*{0.85cm}
+        \bigskip
+        \smallskip
+      \end{onlyenv}
+    \pause
+    \item
+      Konstruktor initialisiert diesen Zeiger
+      \begin{onlyenv}<2>
+        \medskip
+        \begin{lstlisting}[gobble=10]
+          t_object *new_integer (int i)
+          {
+            t_object *p = malloc (sizeof (t_integer));
+            p->integer.print = print_integer;
+            p->integer.content = i;
+            return p;
+          }
+        \end{lstlisting}
+        \vspace*{-2cm}
+      \end{onlyenv}
+    \pause
+    \item
+      Aufruf: "`automatisch"' die richtige Funktion
+      \begin{onlyenv}<3>
+        \medskip
+        \begin{lstlisting}[gobble=10]
+          for (int i = 0; object[i]; i++)
+            object[i]->base.print (object[i]);
+        \end{lstlisting}
+      \end{onlyenv}
+    \pause
+    \medskip
+    \item
+      in größeren Projekten:\\
+      Objekt enthält Zeiger auf Tabelle von Funktionen
+  \end{itemize}
+\end{frame}
+
+\subsection{Beispiel: Graphische Benutzeroberfläche (GUI)}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  \scriptsize
+  \begin{lstlisting}
+    #include <gtk/gtk.h>
+
+    int main (int argc, char **argv)
+    {
+      gtk_init (&argc, &argv);
+      GtkWidget *window = gtk_window_new (GTK_WINDOW_TOPLEVEL);
+      gtk_window_set_title (GTK_WINDOW (window), "Hello");
+      g_signal_connect (window, "destroy", G_CALLBACK (gtk_main_quit), NULL);
+      GtkWidget *vbox = gtk_box_new (GTK_ORIENTATION_VERTICAL, 5);
+      gtk_container_add (GTK_CONTAINER (window), vbox);
+      gtk_container_set_border_width (GTK_CONTAINER (vbox), 10);
+      GtkWidget *label = gtk_label_new ("Hello, world!");
+      gtk_container_add (GTK_CONTAINER (vbox), label);
+      GtkWidget *button = gtk_button_new_with_label ("Quit");
+      g_signal_connect (button, "clicked", G_CALLBACK (gtk_main_quit), NULL);
+      gtk_container_add (GTK_CONTAINER (vbox), button);
+      gtk_widget_show (button);
+      gtk_widget_show (label);
+      gtk_widget_show (vbox);
+      gtk_widget_show (window);
+      gtk_main ();
+      return 0;
+    }
+  \end{lstlisting}
+
+  \vspace*{-6cm}\strut\hfill
+  \includegraphics[scale=0.85]{hello-gtk.png}\\[2cm]
+  \begin{flushright}
+    \normalsize\bf Praktikumsversuch:\\
+    Objektorientiertes Zeichenprogramm
+  \end{flushright}
+  
+\end{frame}
+
+\subsection{Ausblick: C++}
+
+\begin{frame}[fragile]
+  \showsubsection
+
+  \begin{center}
+    \begin{minipage}{5cm}
+      \begin{lstlisting}[gobble=8]
+        ¡typedef struct
+        {
+          void (* print) (union t_object *this);
+        } t_base;¿
+      \end{lstlisting}
+    \end{minipage}\\[0.5cm]
+    \begin{minipage}{5.5cm}
+      \begin{lstlisting}[gobble=8]
+        ¡typedef struct
+        {
+          void (* print) (...);
+          int content;
+        } t_integer;¿
+      \end{lstlisting}
+    \end{minipage}
+    \begin{minipage}{5cm}
+      \begin{lstlisting}[gobble=8]
+        ¡typedef struct
+        {
+          void (* print) (union t_object *this);
+          char *content;
+        } t_string;¿
+      \end{lstlisting}
+    \end{minipage}
+  \end{center}
+  
+\end{frame}
+
+\begin{frame}[fragile]
+  \showsubsection
+
+  \begin{center}
+    \begin{minipage}{5cm}
+      \begin{lstlisting}[gobble=8]
+        ¡struct TBase
+        {
+          virtual void print (void);
+        };¿
+      \end{lstlisting}
+    \end{minipage}\\[0.5cm]
+    \begin{minipage}{5.5cm}
+      \begin{lstlisting}[gobble=8]
+        ¡struct TInteger: public TBase
+        {
+          virtual void print (void);
+          int content;
+        };¿
+      \end{lstlisting}
+    \end{minipage}
+    \begin{minipage}{5cm}
+      \begin{lstlisting}[gobble=8]
+        ¡struct TString: public TBase
+        {
+          virtual void print (void);
+          char *content;
+        };¿
+      \end{lstlisting}
+    \end{minipage}
+  \end{center}
+  
+\end{frame}
+
+\nosectionnonumber{\inserttitle}
+
+\begin{frame}
+
+  \shownosectionnonumber
+
+  \begin{itemize}
+    \item[\textbf{1}] \textbf{Einführung}
+      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/hp}}}
+    \item[\textbf{2}] \textbf{Einführung in C}
+    \item[\textbf{3}] \textbf{Bibliotheken}
+    \item[\textbf{4}] \textbf{Algorithmen}
+    \item[\textbf{5}] \textbf{Hardwarenahe Programmierung}
+    \item[\textbf{6}] \textbf{Objektorientierte Programmierung}
+      \begin{itemize}
+        \item[6.0] Dynamische Speicherverwaltung
+        \item[6.1] Konzepte und Ziele
+        \item[6.2] Beispiel: Zahlen und Buchstaben
+        \item[6.3] Unions
+        \color{medgreen}
+        \item[6.4] Virtuelle Methoden
+        \item[6.5] Beispiel: Graphische Benutzeroberfläche (GUI)
+        \item[6.6] Ausblick: C++
+      \end{itemize}
+    \item[\textbf{7}] \textbf{Datenstrukturen}
+    \vspace*{-1cm}
+  \end{itemize}
+
+\end{frame}
+
+\section{Datenstrukturen}
+\subsection{Stack und FIFO}
+
+\begin{frame}[fragile]
+
+  \showsection
+  \showsubsection
+
+  \begin{minipage}{0.48\textwidth}
+    Im letzten Praktikumsversuch:
+    \begin{itemize}
+      \item
+        Array nur zum Teil benutzt
+      \item
+        Variable speichert genutzte Länge
+      \item
+        Elemente hinten anfügen\\
+        oder entfernen
+      \arrowitem
+        Stack\\
+        \strut
+    \end{itemize}
+    \bigskip
+    \begin{itemize}
+      \item
+        hinten anfügen/entfernen: $\mathcal{O}(1)$\hspace*{-1cm}
+      \item
+        vorne oder in der Mitte einfügen/entfernen: $\mathcal{O}(n)$
+    \end{itemize}
+  \end{minipage}\hfill
+  \begin{minipage}{0.52\textwidth}
+    Auch möglich:
+    \begin{itemize}
+      \item
+        Array nur zum Teil benutzt
+      \item
+        2 Variable speichern\\genutzte Länge (ringförmig)
+      \item
+        Elemente hinten anfügen\\
+        oder vorne entfernen
+      \arrowitem
+        FIFO
+    \end{itemize}
+    \bigskip
+    \begin{itemize}
+      \item
+        vorne oder hinten\\
+        anfügen oder entfernen: $\mathcal{O}(1)$
+      \item
+        in der Mitte einfügen/entfernen: $\mathcal{O}(n)$
+    \end{itemize}
+  \end{minipage}\hspace*{-1.5mm}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsection
+  \showsubsection
+
+  \bigskip
+
+  \begin{minipage}[b]{6cm}
+    \begin{center}
+      "`First In -- First Out"'
+
+      \bigskip
+
+      \begin{picture}(6,4)
+        \thicklines
+        \color{structure}
+        \put(0.5,0){\line(1,0){5}}
+
+        \put(3.5,0){\only<1-5>{\line(0,1){1}}}
+        \put(4.5,0){\only<1-4>{\line(0,1){1}}}
+        \put(3.5,1){\only<1-4>{\line(1,0){1}}}
+        \put(4.0,0.5){\only<1-4>{\makebox(0,0){\lstinline{3}}}}
+        \put(3.0,1.5){\only<1>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
+        \put(3.0,1.5){\only<1>{\makebox(0,0)[b]{\lstinline{push (3)}}}}
+
+        \put(2.5,0){\only<2-6>{\line(0,1){1}}}
+        \put(2.5,1){\only<2-5>{\line(1,0){1}}}
+        \put(3.0,0.5){\only<2-5>{\makebox(0,0){\lstinline{7}}}}
+        \put(2.0,1.5){\only<2>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
+        \put(2.0,1.5){\only<2>{\makebox(0,0)[b]{\lstinline{push (7)}}}}
+
+        \put(1.5,0){\only<3-6>{\line(0,1){1}}}
+        \put(1.5,1){\only<3-6>{\line(1,0){1}}}
+        \put(2.0,0.5){\only<3-6>{\makebox(0,0){\lstinline{137}}}}
+        \put(1.0,1.5){\only<3>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
+        \put(1.0,1.5){\only<3>{\makebox(0,0)[b]{\lstinline{push (137)}}}}
+
+        \put(4.55,1.05){\only<4>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
+        \put(5.00,1.60){\only<4>{\makebox(0,0)[b]{\lstinline{pop ()}: 3}}}
+
+        \put(3.55,1.05){\only<5>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
+        \put(4.00,1.60){\only<5>{\makebox(0,0)[b]{\lstinline{pop ()}: 7}}}
+
+        \put(2.55,1.05){\only<6>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
+        \put(3.00,1.60){\only<6>{\makebox(0,0)[b]{\lstinline{pop ()}: 137}}}
+      \end{picture}
+
+      \bigskip
+
+      FIFO = Queue = Reihe
+    \end{center}
+  \end{minipage}\hfill
+  \begin{minipage}[b]{6cm}
+    \begin{center}
+      "`Last In -- First Out"'
+
+      \bigskip
+
+      \begin{picture}(6,4)
+        \thicklines
+        \color{structure}
+        \put(1.5,0){\line(1,0){3}}
+
+        \put(2.5,0){\line(0,1){1}}
+        \put(3.5,0){\line(0,1){1}}
+        \put(2.5,1){\line(1,0){1}}
+        \put(3.0,0.5){\makebox(0,0){\lstinline{3}}}
+        \put(2.0,1.5){\only<1>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
+        \put(2.0,1.5){\only<1>{\makebox(0,0)[b]{\lstinline{push (3)}}}}
+
+        \put(2.5,1){\only<2-5>{\line(0,1){1}}}
+        \put(3.5,1){\only<2-5>{\line(0,1){1}}}
+        \put(2.5,2){\only<2-5>{\line(1,0){1}}}
+        \put(3.0,1.5){\only<2-5>{\makebox(0,0){\lstinline{7}}}}
+        \put(2.0,2.5){\only<2>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
+        \put(2.0,2.5){\only<2>{\makebox(0,0)[b]{\lstinline{push (7)}}}}
+
+        \put(2.5,2){\only<3-4>{\line(0,1){1}}}
+        \put(3.5,2){\only<3-4>{\line(0,1){1}}}
+        \put(2.5,3){\only<3-4>{\line(1,0){1}}}
+        \put(3.0,2.5){\only<3-4>{\makebox(0,0){\lstinline{137}}}}
+        \put(2.0,3.5){\only<3>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
+        \put(2.0,3.5){\only<3>{\makebox(0,0)[b]{\lstinline{push (137)}}}}
+
+        \put(3.55,3.05){\only<4>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
+        \put(4.00,3.60){\only<4>{\makebox(0,0)[b]{\lstinline{pop ()}: 137}}}
+
+        \put(3.55,2.05){\only<5>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
+        \put(4.00,2.60){\only<5>{\makebox(0,0)[b]{\lstinline{pop ()}: 7}}}
+
+        \put(3.55,1.05){\only<6>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
+        \put(4.00,1.60){\only<6>{\makebox(0,0)[b]{\lstinline{pop ()}: 3}}}
+      \end{picture}
+
+      \bigskip
+
+      LIFO = Stack = Stapel
+    \end{center}
+  \end{minipage}
+
+%
+%  \dots
+
+\end{frame}
+
+\begin{frame}
+
+  \showsection
+  \showsubsection
+
+  \bigskip
+
+  \begin{minipage}[t]{6cm}
+    Array (Stack, FIFO):\\
+    in der Mitte einfügen
+    \begin{center}
+      \begin{picture}(6,3.8)
+        \thicklines
+        \color{structure}
+        \put(1.5,0){\line(1,0){3}}
+
+        \put(2.5,0){\line(0,1){3}}
+        \put(3.5,0){\line(0,1){3}}
+        \put(2.5,1){\line(1,0){1}}
+        \put(3.0,0.5){\makebox(0,0){\lstinline{3}}}
+        \put(2.5,1){\line(1,0){1}}
+        \put(3.0,1.5){\makebox(0,0){\lstinline{7}}}
+        \put(2.5,2){\line(1,0){1}}
+        \put(3.0,2.5){\makebox(0,0){\lstinline{137}}}
+        \put(2.5,3){\line(1,0){1}}
+
+        \put(1.5,1.5){\makebox(0,0)[b]{\lstinline{push (5)}}}
+        \put(1.5,1.45){\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.95,-0.45);}}}
+
+        \put(3.55,2.5){\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)..controls(0.5,0.45)..(0,0.9);}}}
+        \put(3.55,1.5){\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)..controls(0.5,0.45)..(0,0.9);}}}
+
+        \pause
+        \color{red}
+        \put(4.1,3.0){\makebox(0,0)[l]{\textbf{1.}}}
+        \put(4.1,2.0){\makebox(0,0)[l]{\textbf{2.}}}
+        \put(1.5,1.9){\makebox(0,0)[b]{\textbf{3.}}}
+
+        \pause
+        \put(6.0,1.5){\makebox(0,0)[tl]{$\mathcal{O}(n)$}}
+        \put(5.95,1.45){\makebox(0,0)[br]{\tikz{\draw[-latex](0,0)--(-1.3,0.4);}}}
+        \put(5.95,1.49){\makebox(0,0)[br]{\tikz{\draw[-latex](0,0)--(-1.3,1.1);}}}
+      \end{picture}
+    \end{center}
+  \end{minipage}\pause\hfill
+  \begin{minipage}[t]{5cm}
+    In Array (Stack, FIFO) \dots
+    \begin{itemize}
+      \item
+        einfügen: $\mathcal{O}(n)$
+      \item
+        suchen: $\mathcal{O}(n)$
+      \item
+        geschickt suchen: $\mathcal{O}(\log n)$
+      \item
+        beim Einfügen sortieren:\\
+        $\mathcal{O}(n \log n)$ \hspace*{-1.8cm}\tikz{\draw[red](-1.8,0)--(0,0.2);\draw[red](-1.8,0.2)--(0,0);}
+        $\mathcal{O}(n^2)$
+    \end{itemize}
+  \end{minipage}
+
+\end{frame}
+
+\subsection{Verkettete Listen}
+
+\begin{frame}
+
+  \showsection
+  \showsubsection
+
+  \begin{tikzpicture}
+    \color{structure}
+    \node(first) at (0,0.5) {first};
+    \node[shape=rectangle,draw,line width=1pt](3) at (1,2) {3};
+    \node[shape=rectangle,draw,line width=1pt](5) at (2,1) {5};
+    \node[shape=rectangle,draw,line width=1pt](7) at (3,2) {7};
+    \node[shape=rectangle,draw,line width=1pt](137) at (5,2) {137};
+    \node(NULL) at (7,2) {NULL};
+    \draw[-latex](first)--(3);
+    \only<1>{\draw[-latex](3)--(7);}
+    \only<2>{\draw[-latex](3) to[out=0] (5);}
+    \only<2>{\draw[-latex](5) to[in=180] (7);}
+    \draw[-latex](7)--(137);
+    \draw[-latex](137)--(NULL);
+  \end{tikzpicture}
+  \begin{itemize}
+    \item
+      Jeder Datensatz enthält einen Zeiger auf das nächste Element.
+    \item
+      Beim letzten Element zeigt der Zeiger auf \lstinline{NULL}.
+    \item
+      Eine Variable zeigt auf das erste Element.
+    \item
+      Wenn die Liste leer ist, zeigt die Variable auf \lstinline{NULL}.
+    \arrowitem
+      (einfach) \textbf{verkettete Liste}
+  \end{itemize}
+
+\end{frame}
+
+\begin{frame}
+
+  \showsection
+  \showsubsection
+
+  \begin{minipage}[t]{5cm}
+    In Array (Stack, FIFO) \dots
+    \begin{itemize}
+      \item
+        in der Mitte einfügen: $\mathcal{O}(n)$
+      \item
+        wahlfreier Zugriff: $\mathcal{O}(1)$
+      \item
+        suchen: $\mathcal{O}(n)$
+      \item
+        geschickt suchen: $\mathcal{O}(\log n)$
+      \item
+        beim Einfügen sortieren:\\
+        $\mathcal{O}(n \log n)$ \hspace*{-1.8cm}\tikz{\draw[red](-1.8,0)--(0,0.2);\draw[red](-1.8,0.2)--(0,0);}
+        $\mathcal{O}(n^2)$
+    \end{itemize}
+  \end{minipage}\hfill
+  \begin{minipage}[t]{6cm}
+    In (einfach) verkettete/r Liste \dots
+    \begin{itemize}
+      \item
+        in der Mitte einfügen: $\mathcal{O}(1)$
+      \item
+        wahlfreier Zugriff: $\mathcal{O}(n)$
+      \item
+        suchen: $\mathcal{O}(n)$
+      \item
+        geschickt \hspace*{-1.7cm}\tikz{\draw[red](-1.7,0)--(0,0.2);\draw[red](-1.7,0.2)--(0,0);}
+        suchen: {\color{red}$\mathcal{O}(n)$}
+      \item
+        beim Einfügen sortieren:
+        $\mathcal{O}(n \log n)$ \hspace*{-1.8cm}\tikz{\draw[red](-1.8,0)--(0,0.2);\draw[red](-1.8,0.2)--(0,0);}
+        $\mathcal{O}(n^2)$
+    \end{itemize}
+  \end{minipage}
+  \pause
+  \medskip
+  \begin{center}
+    \begin{minipage}[t]{6cm}
+      In (ausbalancierten) Bäumen \dots
+      \begin{itemize}
+        \item
+          in der Mitte einfügen: $\mathcal{O}(\log n)$
+        \item
+          wahlfreier Zugriff: $\mathcal{O}(\log n)$
+        \item
+          suchen: $\mathcal{O}(\log n)$
+        \item
+          beim Einfügen sortieren:
+          $\mathcal{O}(n \log n)$
+      \end{itemize}
+    \end{minipage}
+  \end{center}
+  \vspace*{-1cm}
+
+\end{frame}
+
+\subsection{Bäume}
+
+\begin{frame}[fragile]
+
+  \showsection
+  \showsubsection
+
+  \begin{minipage}[t]{5cm}
+    \vspace*{-6cm}
+    \begin{lstlisting}[gobble=6]
+      ¡typedef struct node
+      {
+        int content;
+        struct node *left, *right;
+      } node;¿
+    \end{lstlisting}
+    \bigskip
+    \bigskip
+    \begin{onlyenv}<6->
+      \begin{itemize}
+        \item
+          Einfügen: rekursiv, $\mathcal{O}(\log n)$
+        \item
+          Suchen: rekursiv, $\mathcal{O}(\log n)$
+        \item
+          beim Einfügen sortieren:\\
+          rekursiv, $\mathcal{O}(n\log n)$
+        \begin{onlyenv}<7->
+          \smallskip
+          \item
+            {\color{red}
+            \emph{Worst Case\/}: $\mathcal{O}(n^2)$\\
+            vorher bereits sortiert}\\
+            \textarrow\ balancierte Bäume\\
+            \hspace*{2.15em}Anwendung: Datenbanken\hspace*{-2cm}
+        \end{onlyenv}
+      \end{itemize}
+      \vspace*{-1cm}
+    \end{onlyenv}
+  \end{minipage}\hfill
+  \begin{minipage}[t]{7cm}
+    \begin{center}
+      \begin{tikzpicture}
+        \color{structure}
+        \node(root) at (0,0) {\lstinline{node *root;}};
+        \begin{onlyenv}<2>
+          \node(3) at (-2,-3) {\lstinline{NULL}};
+          \node(137) at (2,-3) {\lstinline{NULL}};
+        \end{onlyenv}
+        \begin{onlyenv}<2->
+          \node[shape=rectangle,draw,line width=1pt](7) at (0,-1.5) {7};
+          \draw[-latex](root)--(7);
+          \draw[-latex](7)--(3);
+          \draw[-latex](7)--(137);
+        \end{onlyenv}
+        \begin{onlyenv}<3>
+          \node(3) at (-2,-3) {\lstinline{NULL}};
+        \end{onlyenv}
+        \begin{onlyenv}<3->
+          \node[shape=rectangle,draw,line width=1pt](137) at (2,-3) {137};
+          \node(137_left) at (1,-4.5) {\lstinline{NULL}};
+          \node(137_right) at (3,-4.5) {\lstinline{NULL}};
+          \draw[-latex](137)--(137_left);
+          \draw[-latex](137)--(137_right);
+        \end{onlyenv}
+        \begin{onlyenv}<4>
+          \node(5) at (-1,-4.5) {\lstinline{NULL}};
+        \end{onlyenv}
+        \begin{onlyenv}<4->
+          \node[shape=rectangle,draw,line width=1pt](3) at (-2,-3) {3};
+          \node(3_left) at (-3,-4.5) {\lstinline{NULL}};
+          \draw[-latex](3)--(3_left);
+          \draw[-latex](3)--(5);
+        \end{onlyenv}
+        \begin{onlyenv}<5->
+          \node[shape=rectangle,draw,line width=1pt](5) at (-1,-4.5) {5};
+          \node(5_left) at (-2,-6) {\lstinline{NULL}};
+          \node(5_right) at (0,-6) {\lstinline{NULL}};
+          \draw[-latex](5)--(5_left);
+          \draw[-latex](5)--(5_right);
+        \end{onlyenv}
+      \end{tikzpicture}
+    \end{center}
+  \end{minipage}
+
+\end{frame}
+
+\end{document}
diff --git a/20210204/hp-musterloesung-20210204.pdf b/20210204/hp-musterloesung-20210204.pdf
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+% hp-musterloesung-20210204.pdf - Solutions to the Exercises on Low-Level Programming
+% Copyright (C) 2013, 2015, 2016, 2017, 2018, 2019, 2020, 2021  Peter Gerwinski
+%
+% This document is free software: you can redistribute it and/or
+% modify it either under the terms of the Creative Commons
+% Attribution-ShareAlike 3.0 License, or under the terms of the
+% GNU General Public License as published by the Free Software
+% Foundation, either version 3 of the License, or (at your option)
+% any later version.
+%
+% This document is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this document.  If not, see <http://www.gnu.org/licenses/>.
+%
+% You should have received a copy of the Creative Commons
+% Attribution-ShareAlike 3.0 Unported License along with this
+% document.  If not, see <http://creativecommons.org/licenses/>.
+
+% README: Objektorientierte Tier-Datenbank (Neuauflage), Iterationsfunktionen, dynamisches Bit-Array
+
+\documentclass[a4paper]{article}
+
+\usepackage{pgscript}
+
+\begin{document}
+
+  \section*{Hardwarenahe Programmierung\\
+            Musterlösung zu den Übungsaufgaben -- 4.\ Februar 2021}
+
+  \exercise{Objektorientierte Tier-Datenbank (Neuauflage)}
+
+  Diese Aufgabe ist eine Neuauflage von Aufgabe 3 der
+  Übung vom 28.\ Januar 2021,\\
+  ergänzt um die Teilaufgaben (e) bis (g).
+
+  \medskip
+
+  Das auf der nächsten Seite dargestellte Programm
+  (Datei: \gitfile{hp}{2020ws/20210204}{aufgabe-1a.c})
+  soll Daten von Tieren verwalten.
+
+  Beim Compilieren erscheinen die folgende Fehlermeldungen:
+  \begin{lstlisting}[style=terminal]
+    $ ¡gcc -std=c99 -Wall -O aufgabe-1a.c -o aufgabe-1a¿
+    aufgabe-1a.c: In function 'main':
+    aufgabe-1a.c:31: error: 'animal' has no member named 'wings'
+    aufgabe-1a.c:37: error: 'animal' has no member named 'legs'
+  \end{lstlisting}
+
+  Der Programmierer nimmt die auf der nächsten Seite in Rot dargestellten Ersetzungen vor\\
+  (Datei: \gitfile{hp}{2020ws/20210204}{aufgabe-1b.c}).
+  Daraufhin gelingt das Compilieren, und die Ausgabe des Programms lautet:
+  \begin{lstlisting}[style=terminal]
+    $ ¡gcc -std=c99 -Wall -O aufgabe-1b.c -o aufgabe-1b¿
+    $ ¡./aufgabe-1b¿
+    A duck has 2 legs.
+    Error in animal: cow
+  \end{lstlisting}
+
+  \begin{itemize}
+    \item[(a)]
+      Erklären Sie die o.\,a.\ Compiler-Fehlermeldungen.
+%      \points{2}
+    \item[(b)]
+      Wieso verschwinden die Fehlermeldungen nach den o.\,a.\ Ersetzungen?
+%      \points{3}
+    \item[(c)]
+      Erklären Sie die Ausgabe des Programms.
+%      \points{5}
+    \item[(d)]
+      Beschreiben Sie -- in Worten und/oder als C-Quelltext -- einen Weg,
+      das Programm so zu berichtigen, daß es die Eingabedaten
+      (``A duck has 2 wings. A cow has 4 legs.'') korrekt speichert und ausgibt. % \\
+%      \points{4}
+    \item[(e)]
+      Schreiben Sie das Programm so um,
+      daß es keine expliziten Typumwandlungen mehr benötigt.\par
+      Hinweis: Verwenden Sie \lstinline{union}.
+%      \points{4}
+    \item[(f)]
+      Schreiben Sie das Programm weiter um,
+      so daß es die Objektinstanzen \lstinline{duck} und \lstinline{cow}
+      dynamisch erzeugt.\par
+      Hinweis: Verwenden Sie \lstinline{malloc()} und schreiben Sie Konstruktoren.
+%      \points{4}
+    \item[(g)]
+      Schreiben Sie das Programm weiter um,
+      so daß die Ausgabe nicht mehr direkt im Hauptprogramm erfolgt,
+      sondern stattdessen eine virtuelle Methode \lstinline{print()}
+      aufgerufen wird.\par
+      Hinweis: Verwenden Sie in den Objekten Zeiger auf Funktionen,
+      und initialisieren Sie diese in den Konstruktoren.
+%      \points{4}
+  \end{itemize}
+
+  \begin{minipage}[t]{0.34\textwidth}
+    \begin{lstlisting}[gobble=6,xleftmargin=0pt]
+      #include <stdio.h>
+
+      #define ANIMAL     0
+      #define WITH_WINGS 1
+      #define WITH_LEGS  2
+
+      typedef struct animal
+      {
+        int type;
+        char *name;
+      } animal;
+
+      typedef struct with_wings
+      {
+        int wings;
+      } with_wings;
+
+      typedef struct with_legs
+      {
+        int legs;
+      } with_legs;
+    \end{lstlisting}
+  \end{minipage}\hfill
+  \begin{minipage}[t]{0.65\textwidth}
+    \begin{lstlisting}[gobble=6,xleftmargin=0pt]
+      int main (void)
+      {
+        animal *a[2];
+
+        animal duck;
+        a[0] = &duck;
+        a[0]->type = WITH_WINGS;
+        a[0]->name = "duck";
+        a[0]->wings = 2;
+
+        animal cow;
+        a[1] = &cow;
+        a[1]->type = WITH_LEGS;
+        a[1]->name = "cow";
+        a[1]->legs = 4;
+
+        for (int i = 0; i < 2; i++)
+          if (a[i]->type == WITH_LEGS)
+            printf ("A %s has %d legs.\n", a[i]->name,
+                    ((with_legs *) a[i])-> legs);
+          else if (a[i]->type == WITH_WINGS)
+            printf ("A %s has %d wings.\n", a[i]->name,
+                    ((with_wings *) a[i])-> wings);
+          else
+            printf ("Error in animal: %s\n", a[i]->name);
+
+        return 0;
+      }
+    \end{lstlisting}
+    \begin{picture}(0,0)
+      \color{red}
+      \put(3.7,6.207){\vector(-1,0){0.7}}
+      \put(3.8,6.207){\makebox(0,0)[l]{\lstinline[basicstyle=\color{red}]{((with_legs *) a[1])->legs = 4;}}}
+      \put(4.0,8.735){\vector(-1,0){0.7}}
+      \put(4.1,8.735){\makebox(0,0)[l]{\lstinline[basicstyle=\color{red}]{((with_wings *) a[0])->wings = 2;}}}
+    \end{picture}
+  \end{minipage}
+
+  \solution
+
+  \begin{itemize}
+    \item[(a)]
+      \textbf{Erklären Sie die o.\,a.\ Compiler-Fehlermeldungen.}
+
+      \lstinline{a[0]} und \lstinline{a[1]}
+      sind gemäß der Deklaration \lstinline{animal *a[2]}
+      Zeiger auf Variablen vom Typ \lstinline{animal} (ein \lstinline{struct}).
+      Wenn man diesen Zeiger dereferenziert (\lstinline{->}),
+      erhält man eine \lstinline{animal}-Variable.
+      Diese enthält keine Datenfelder \lstinline{wings} bzw.\ \lstinline{legs}.
+
+    \item[(b)]
+      \textbf{Wieso verschwinden die Fehlermeldungen nach den o.\,a.\ Ersetzungen?}
+
+      Durch die \emph{explizite Typumwandlung des Zeigers\/}
+      erhalten wir einen Zeiger auf eine \lstinline{with_wings}-
+      bzw.\ auf eine \lstinline{with_legs}-Variable.
+      Diese enthalten die Datenfelder \lstinline{wings} bzw.\ \lstinline{legs}.
+
+    \item[(c)]
+      \textbf{Erklären Sie die Ausgabe des Programms.}
+
+      Durch die explizite Typumwandlung des Zeigers
+      zeigt \lstinline{a[0]} auf eine \lstinline{with_wings}-Variable.
+      Diese enthält nur ein einziges Datenfeld \lstinline{wings},
+      das an genau derselben Stelle im Speicher liegt
+      wie \lstinline{a[0]->type}, also das Datenfeld \lstinline{type}
+      der \lstinline{animal}-Variable, auf die der Zeiger \lstinline{a[0]} zeigt.
+      Durch die Zuweisung der Zahl \lstinline{2}
+      an \lstinline{((with_wings *) a[0])->wings}
+      überschreiben wir also \lstinline{a[0]->type},
+      so daß das \lstinline{if} in der \lstinline{for}-Schleife
+      \lstinline{a[0]} als \lstinline{WITH_LEGS} erkennt.
+
+      Bei der Ausgabe \lstinline[style=terminal]{A duck has 2 legs.}
+      wird das Datenfeld \lstinline{((with_legs *)a[0])->legs} als Zahl ausgegeben.
+      Dieses Datenfeld befindet sich in denselben Speicherzellen wie
+      \lstinline{a[0]->type} und \lstinline{((with_wings *)} % :-(
+      \lstinline{a[0]->wings}
+      und hat daher ebenfalls den Wert 2.
+
+      Auf die gleiche Weise überschreiben wir durch die Zuweisung der Zahl 4
+      an \lstinline{((with_legs *) a[1])->legs}
+      das Datenfeld \lstinline{a[0]->type},
+      so daß das \lstinline{if} in der \lstinline{for}-Schleife
+      \lstinline{a[1]} als unbekanntes Tier (Nr.\ 4) erkennt und
+      \lstinline[style=terminal]{Error in animal: cow} ausgibt.
+
+    \item[(d)]
+      \textbf{Beschreiben Sie -- in Worten und/oder als C-Quelltext -- einen Weg,
+      das Programm so zu berichtigen, daß es die Eingabedaten
+      (``A duck has 2 wings. A cow has 4 legs.'') korrekt speichert und ausgibt.}
+
+      Damit die \emph{Vererbung\/} zwischen den Objekten
+      \lstinline{animal}, \lstinline{with_wings} und \lstinline{with_legs}
+      funktioniert, müssen die abgeleiteten Klassen \lstinline{with_wings} und \lstinline{with_legs}
+      alle Datenfelder der Basisklasse \lstinline{animal} erben.
+      In C geschieht dies explizit; die Datenfelder müssen in den
+      abgeleiteten Klassen neu angegeben werden
+      (siehe \gitfile{hp}{2020ws/20210204}{loesung-1d-1.c}):
+
+      \begin{lstlisting}[gobble=8]
+        typedef struct animal
+        {
+          int type;
+          char *name;
+        } animal;
+
+        typedef struct with_wings
+        {
+          int type;
+          char *name;
+          int wings;
+        } with_wings;
+
+        typedef struct with_legs
+        {
+          int type;
+          char *name;
+          int legs;
+        } with_legs;
+      \end{lstlisting}
+
+      Zusätzlich ist es notwendig,
+      die Instanzen \lstinline{duck} und \lstinline{cow}
+      der abgeleiteten Klassen \lstinline{with_wings} und \lstinline{with_legs}
+      auch als solche zu deklarieren,
+      damit für sie genügend Speicher reserviert wird:
+
+      \begin{lstlisting}[gobble=8]
+        animal *a[2];
+
+        with_wings duck;
+        a[0] = (animal *) &duck;
+        a[0]->type = WITH_WINGS;
+        a[0]->name = "duck";
+        ((with_wings *) a[0])->wings = 2;
+
+        with_legs cow;
+        a[1] = (animal *) &cow;
+        a[1]->type = WITH_LEGS;
+        a[1]->name = "cow";
+        ((with_legs *) a[1])->legs = 4;
+      \end{lstlisting}
+
+      Wenn man dies vergißt und sie nur als \lstinline{animal} deklariert,
+      wird auch nur Speicherplatz für (kleinere)
+      \lstinline{animal}-Variable angelegt.
+      Dadurch kommt es zu Speicherzugriffen außerhalb der
+      deklarierten Variablen, was letztlich zu einem Absturz führt
+      (siehe \gitfile{hp}{2020ws/20210204}{loesung-1d-0f.c}).
+
+      Für die Zuweisung eines Zeigers auf \lstinline{duck}
+      an \lstinline{a[0]}, also an einen Zeiger auf \lstinline{animal}
+      wird eine weitere explizite Typumwandlung notwendig.
+      Entsprechendes gilt für die Zuweisung eines Zeigers auf \lstinline{cow}
+      an \lstinline{a[1]}.
+
+      Es ist sinnvoll, explizite Typumwandlungen so weit wie möglich zu vermeiden.
+      Es ist einfacher und gleichzeitig sicherer,
+      direkt in die Variablen \lstinline{duck} und \lstinline{cow}
+      zu schreiben, anstatt dies über die Zeiger \lstinline{a[0]}
+      und \lstinline{a[1]} zu tun
+      (siehe \gitfile{hp}{2020ws/20210204}{loesung-1d-2.c}):
+
+      \begin{lstlisting}[gobble=8]
+        animal *a[2];
+
+        with_wings duck;
+        a[0] = (animal *) &duck;
+        duck.type = WITH_WINGS;
+        duck.name = "duck";
+        duck.wings = 2;
+
+        with_legs cow;
+        a[1] = (animal *) &cow;
+        cow.type = WITH_LEGS;
+        cow.name = "cow";
+        cow.legs = 4;
+      \end{lstlisting}
+
+    \item[(e)]
+      \textbf{Schreiben Sie das Programm so um,
+      daß es keine expliziten Typumwandlungen mehr benötigt.}\par
+      \textbf{Hinweis: Verwenden Sie \lstinline{union}.}
+
+      Siehe \gitfile{hp}{2020ws/20210204}{loesung-1e.c}.
+      
+      Diese Lösung basiert auf \gitfile{hp}{2020ws/20210204}{loesung-1d-2.c},
+      da diese bereits weniger explizite Typumwandlungen enthält
+      als \gitfile{hp}{2020ws/20210204}{loesung-1d-1.c}.
+
+      Arbeitsschritte:
+      \begin{itemize}
+        \item
+          Umbenennen des Basistyps \lstinline{animal} in \lstinline{base},
+          damit wir den Bezeichner \lstinline{animal}
+          für die \lstinline{union} verwenden können
+        \item
+          Schreiben einer \lstinline{union animal},
+          die die drei Klassen \lstinline{base},
+          \lstinline{with_wings} und \lstinline{with_legs}
+          als Datenfelder enthält
+        \item
+          Umschreiben der Initialisierungen:
+          Zugriff auf Datenfelder erfolgt nun durch
+          z.\,B.\ \lstinline{a[0]->b.name}.
+          Hierbei ist \lstinline{b} der Name des \lstinline{base}-Datenfelds
+          innerhalb der \lstinline{union animal}.
+        \item
+          Auf gleiche Weise schreiben wir die \lstinline{if}-Bedingungen
+          innerhalb der \lstinline{for}-Schleife
+          sowie die Parameter der \lstinline{printf()}-Aufrufe um.
+      \end{itemize}
+      Explizite Typumwandlungen sind nun nicht mehr nötig.
+
+      Nachteil dieser Lösung:
+      Jede Objekt-Variable belegt nun Speicherplatz
+      für die gesamte \lstinline{union animal},
+      anstatt nur für die benötigte Variable vom Typ
+      \lstinline{with_wings} oder \lstinline{with_legs}.
+      Dies kann zu einer Verschwendung von Speicherplatz führen,
+      auch wenn dies in diesem Beispielprogramm tatsächlich nicht der Fall ist.
+
+    \item[(f)]
+      \textbf{Schreiben Sie das Programm weiter um,
+      so daß es die Objektinstanzen \lstinline{duck} und \lstinline{cow}
+      dynamisch erzeugt.}\par
+      \textbf{Hinweis: Verwenden Sie \lstinline{malloc()} und schreiben Sie Konstruktoren.}
+
+      Siehe \gitfile{hp}{2020ws/20210204}{loesung-1f.c}.
+
+    \item[(g)]
+      \textbf{Schreiben Sie das Programm weiter um,
+      so daß die Ausgabe nicht mehr direkt im Hauptprogramm erfolgt,
+      sondern stattdessen eine virtuelle Methode \lstinline{print()}
+      aufgerufen wird.}\par
+      \textbf{Hinweis: Verwenden Sie in den Objekten Zeiger auf Funktionen,
+      und initialisieren Sie diese in den Konstruktoren.}
+
+      Siehe \gitfile{hp}{2020ws/20210204}{loesung-1g.c}.
+
+  \end{itemize}
+
+  \clearpage
+
+  \exercise{Iterationsfunktionen}
+
+  Wir betrachten das folgende Programm (\gitfile{hp}{2020ws/20210204}{loesung-1.c}):
+
+  \begin{minipage}[t]{0.4\textwidth}
+    \begin{lstlisting}[gobble=6]
+      #include <stdio.h>
+
+      void foreach (int *a, void (*fun) (int x))
+      {
+        for (int *p = a; *p >= 0; p++)
+          fun (*p);
+      }
+
+      void even_or_odd (int x)
+      {
+        if (x % 2)
+          printf ("%d ist ungerade.\n", x);
+        else
+          printf ("%d ist gerade.\n", x);
+      }
+    \end{lstlisting}
+  \end{minipage}\hfill
+  \begin{minipage}[t]{0.52\textwidth}
+    \begin{lstlisting}[gobble=6]
+      int main (void)
+      {
+        int numbers[] = { 12, 17, 32, 1, 3, 16, 19, 18, -1 };
+        foreach (numbers, even_or_odd);
+        return 0;
+      }
+    \end{lstlisting}
+    \begin{enumerate}[\quad(a)]
+      \item
+        Was bedeutet \lstinline{void (*fun) (int x)},
+        und welchen Sinn hat seine Verwendung in der Funktion \lstinline{foreach()}?
+%        \points{2}
+      \item
+        Schreiben Sie das Hauptprogramm \lstinline{main()} so um,
+        daß es unter Verwendung der Funktion \lstinline{foreach()}
+        die Summe aller positiven Zahlen in dem Array berechnet.
+        Sie dürfen dabei weitere Funktionen sowie globale Variable einführen.
+%        \points{4}
+    \end{enumerate}
+  \end{minipage}
+
+  \solution
+
+  \begin{enumerate}[\quad(a)]
+    \item
+      \textbf{Was bedeutet \lstinline{void (*fun) (int x)},
+      und welchen Sinn hat seine Verwendung in der Funktion \lstinline{foreach()}?}
+
+      \lstinline{void (*fun) (int x)} deklariert einen Zeiger \lstinline{fun},
+      der auf Funktionen zeigen kann, die einen Parameter \lstinline{x}
+      vom Typ \lstinline{int} erwarten und keinen Wert zurückgeben (\lstinline{void}).
+
+      Durch die Übergabe eines derartigen Parameters an die Funktion \lstinline{foreach()}
+      lassen wir dem Aufrufer die Wahl,
+      welche Aktion für alle Elemente des Arrays aufgerufen werden soll.
+
+    \item
+      \textbf{Schreiben Sie das Hauptprogramm \lstinline{main()} so um,
+      daß es unter Verwendung der Funktion \lstinline{foreach()}
+      die Summe aller positiven Zahlen in dem Array berechnet.
+      Sie dürfen dabei weitere Funktionen sowie globale Variable einführen.}
+
+      Siehe: \gitfile{hp}{2020ws/20210204}{loesung-1.c}
+
+      Damit die Funktion \lstinline{add_up()} Zugriff auf die Variable \lstinline{sum} hat,
+      muß diese global sein
+      und vor der Funktion \lstinline{add_up()} deklariert werden.
+
+      Die Bedingung, daß nur positive Zahlen summiert werden sollen,
+      ist durch die Arbeitsweise der Funktion \lstinline{foreach()}
+      bereits gewährleistet, da negative Zahlen als Ende-Markierungen dienen.
+
+      Wichtig ist, daß die Variable \lstinline{sum}
+      vor dem Aufruf der Funktion \lstinline{foreach()}
+      auf den Wert \lstinline{0} gesetzt wird.
+      In \gitfile{hp}{2020ws/20210204}{loesung-1.c} geschieht dies
+      durch die Initialisierung von \lstinline{sum}.
+      Wenn mehrere Summen berechnet werden sollen,
+      muß dies durch explizite Zuweisungen \lstinline{sum = 0}
+      vor den Aufrufen von \lstinline{foreach()} erfolgen.
+  \end{enumerate}
+
+  \exercise{Dynamisches Bit-Array}
+
+  Schreiben Sie die folgenden Funktionen zur Verwaltung eines dynamischen Bit-Arrays:
+  \begin{itemize}
+    \item
+      \lstinline{void bit_array_init (int n)}\\
+      Das Array initialisieren, so daß man \lstinline{n} Bits darin speichern kann.\\
+      Die Array-Größe \lstinline{n} ist keine Konstante, sondern erst im laufenden Programm bekannt.\\
+      Die Bits sollen auf den Anfangswert 0 initialisiert werden.
+    \item
+      \lstinline{void bit_array_set (int i, int value)}\\
+      Das Bit mit dem Index \lstinline{i} auf den Wert \lstinline{value} setzen.\\
+      Der Index \lstinline{i} darf von \lstinline{0} bis \lstinline{n - 1} gehen;
+      der Wert \lstinline{value} darf 1 oder 0 sein.
+    \item
+      \lstinline{void bit_array_flip (int i)}\\
+      Das Bit mit dem Index \lstinline{i} auf den entgegengesetzten Wert setzen,\\
+      also auf 1, wenn er vorher 0 ist, bzw.\ auf 0, wenn er vorher 1 ist.\\
+      Der Index \lstinline{i} darf von \lstinline{0} bis \lstinline{n - 1} gehen.
+    \item
+      \lstinline{int bit_array_get (int i)}\\
+      Den Wert des Bit mit dem Index \lstinline{i} zurückliefern.\\
+      Der Index \lstinline{i} darf von \lstinline{0} bis \lstinline{n - 1} gehen.
+    \item
+      \lstinline{void bit_array_resize (int new_n)}\\
+      Die Größe des Arrays auf \lstinline{new_n} Bits ändern.\\
+      Dabei soll der Inhalt des Arrays, soweit er in die neue Größe paßt, erhalten bleiben.\\
+      Neu hinzukommende Bits sollen auf 0 initialisiert werden.
+    \item
+      \lstinline{void bit_array_done (void)}\\
+      Den vom Array belegten Speicherplatz wieder freigeben.
+  \end{itemize}
+  Bei Bedarf dürfen Sie den Funktionen zusätzliche Parameter mitgeben,
+  beispielsweise um mehrere Arrays parallel verwalten zu können.
+  (In der objektorientierten Programmierung wäre dies der implizite Parameter \lstinline{this},
+  der auf die Objekt-Struktur zeigt.)
+
+  Die Bits sollen möglichst effizient gespeichert werden,
+  z.\,B.\ jeweils 8 Bits in einer \lstinline{uint8_t}-Variablen.
+
+  Die Funktionen sollen möglichst robust sein,
+  d.\,h.\ das Programm darf auch bei unsinnigen Parameterwerten nicht abstürzen,
+  sondern soll eine Fehlermeldung ausgeben.
+
+  \medskip
+
+  Die folgenden \textbf{Hinweise} beschreiben
+  einen möglichen Weg, die Aufgabe zu lösen.
+  Es seht Ihnen frei, die Aufgabe auch auf andere Weise zu lösen.
+  \begin{itemize}
+    \item
+      Setzen Sie zunächst voraus, daß das Array die konstante Länge 8 hat,
+      und schreiben Sie zunächst nur die Funktionen
+      \lstinline{bit_array_set()}, \lstinline{bit_array_flip()} und
+      \lstinline{bit_array_get()}.
+    \item
+      Verallgemeinern Sie nun auf eine konstante Länge,
+      bei der es sich um ein Vielfaches von 8 handelt.
+    \item
+      Implementieren Sie nun die Überprüfung auf unsinnige Parameterwerte.
+      Damit können Sie sich gleichzeitig von der Bedingung lösen,
+      daß die Länge des Arrays ein Vielfaches von 8 sein muß.
+    \item
+      Gehen Sie nun von einem statischen zu einem dynamischen Array über,
+      und implementieren sie die Funktionen \lstinline{bit_array_init()},
+      \lstinline{bit_array_done()} und \lstinline{bit_array_resize()}.
+  \end{itemize}
+
+%  \points{14}
+%
+%  \medskip
+%
+%  (Hinweis für die Klausur:
+%  Abgabe in digitaler Form ist erwünscht, aber nicht zwingend.)
+
+  \solution
+
+  Die hier vorgestellte Lösung folgt den Hinweisen.
+  \begin{itemize}
+    \item
+      \textbf{Setzen Sie zunächst voraus, daß das Array die konstante Länge 8 hat,
+      und schreiben Sie zunächst nur die Funktionen
+      \lstinline{bit_array_set()}, \lstinline{bit_array_flip()} und
+      \lstinline{bit_array_get()}.}
+
+      Siehe: \gitfile{hp}{2020ws/20210204}{loesung-3-1.c}
+
+      Wir speichern in jedem der acht Bit einer \lstinline{uint8_t}-Variablen
+      jeweils eine Zahl, die 0 oder 1 sein kann.
+      Dies geschieht durch Setzen bzw.\ Löschen bzw.\ Umklappen einzelner Bits
+      in der Variablen.
+
+      Das Programm enthält zusätzlich eine Funktion \lstinline{output()},
+      mit der man sich den Inhalt des Arrays anzeigen lassen kann,
+      sowie ein Hauptprogramm \lstinline{main()}, um die Funktionen zu testen.
+
+    \item
+      \textbf{Verallgemeinern Sie nun auf eine konstante Länge,
+      bei der es sich um ein Vielfaches von 8 handelt.}
+
+      Siehe: \gitfile{hp}{2020ws/20210204}{loesung-3-2.c}
+
+      In diesem Programm setzen wir die Länge auf konstant \lstinline{LENGTH} Bits,
+      wobei es sich um eine Präprozessor-Konstante mit dem Wert 32 handelt.
+
+      Um \lstinline{LENGTH} Bits zu speichern, benötigen wir ein Array
+      der Länge \lstinline{LENGTH / 8} Bytes.
+
+      Um auf ein einzelnes Bit zuzugreifen, müssen wir zunächst ermitteln,
+      in welchem der Bytes sich befindet. Außerdem interessieren wir uns
+      für die Nummer des Bits innerhalb des Bytes.
+      Den Array-Index des Bytes erhalten wir, indem wir den Index des Bits
+      durch 8 dividieren. Der bei dieser Division verbleibende Rest ist die
+      Nummer des Bits innerhalb des Bytes.
+
+      Diese Rechnungen führen wir in den drei Funktionen
+      \lstinline{bit_array_set()}, \lstinline{bit_array_flip()} und
+      \lstinline{bit_array_get()} durch.
+      (Diese ist eine eher unelegante Code-Verdopplung -- hier sogar eine Verdreifachung.
+      Für den Produktiveinsatz lohnt es sich, darüber nachzudenken,
+      wie man diese vermeiden kann, ohne gleichzeitig an Effizienz einzubüßen.
+      Hierfür käme z.\,B.\ ein Präprozessor-Makro in Frage.
+      Für die Lösung der Übungsaufgabe wird dies hingegen nicht verlangt.)
+
+    \item
+      \textbf{Implementieren Sie nun die Überprüfung auf unsinnige Parameterwerte.
+      Damit können Sie sich gleichzeitig von der Bedingung lösen,
+      daß die Länge des Arrays ein Vielfaches von 8 sein muß.}
+
+      Siehe: \gitfile{hp}{2020ws/20210204}{loesung-3-3.c}
+
+      Um weitere Code-Verdopplungen zu vermeiden,
+      führen wir eine Funktion \lstinline{check_index()} ein,
+      die alle Prüfungen durchführt.
+
+      Wenn die Länge des Arrays kein Vielfaches von 8 ist,
+      wird das letzte Byte nicht vollständig genutzt.
+      Die einzige Schwierigkeit besteht darin, die korrekte Anzahl von Bytes
+      zu ermitteln, nämlich die Länge dividiert durch 8, aber nicht ab-, sondern
+      aufgerundet. Am elegantesten geht dies durch vorherige Addition von 7:
+      \lstinline{#define BYTES ((LENGTH + 7) / 8)}.
+      Es ist aber auch zulässig, die Anzahl der Bytes mit Hilfe einer
+      \lstinline{if}-Anweisung zu ermitteln: Länge durch 8 teilen und abrunden;
+      falls die Division nicht glatt aufging, um 1 erhöhen.
+
+    \item
+      \textbf{Gehen Sie nun von einem statischen zu einem dynamischen Array über,
+      und implementieren sie die Funktionen \lstinline{bit_array_init()},
+      \lstinline{bit_array_done()} und \lstinline{bit_array_resize()}.}
+
+      Siehe: \gitfile{hp}{2020ws/20210204}{loesung-3-4.c}.
+      Damit ist die Aufgabe gelöst.
+
+      Aus den Präprozessor-Konstanten \lstinline{LENGTH} und \lstinline{BYTES}
+      werden nun globale \lstinline{int}-Variable.
+      Die Funktion \lstinline{bit_array_init()} berechnet die korrekten Werte
+      für diese Variablen und legt das Array mittels \lstinline{malloc()} dynamisch
+      an. Eine Größenänderung des Arrays erfolgt mittels \lstinline{realloc()},
+      das Freigeben mittels \lstinline{free()}.
+
+      Das Programm setzt Variable, die aktuell nicht verwendet werden,
+      auf den Wert \lstinline{0} bzw.\ \lstinline{NULL}.
+      Dies ermöglicht es der Funktion \lstinline{check_index()},
+      auch zu prüfen, ob das Array vorher korrekt mit \lstinline{bit_array_init()}
+      erzeugt wurde -- oder ob es vielleicht schon wieder mit
+      \lstinline{bit_array_done()} freigegeben wurde.
+
+  \end{itemize}
+
+\end{document}
diff --git a/20210204/hp-uebung-20210204.pdf b/20210204/hp-uebung-20210204.pdf
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diff --git a/20210204/hp-uebung-20210204.tex b/20210204/hp-uebung-20210204.tex
new file mode 100644
index 0000000..bef613f
--- /dev/null
+++ b/20210204/hp-uebung-20210204.tex
@@ -0,0 +1,303 @@
+% hp-uebung-20210204.pdf - Exercises on Low-Level Programming
+% Copyright (C) 2013, 2015, 2016, 2017, 2018, 2019, 2020, 2021  Peter Gerwinski
+%
+% This document is free software: you can redistribute it and/or
+% modify it either under the terms of the Creative Commons
+% Attribution-ShareAlike 3.0 License, or under the terms of the
+% GNU General Public License as published by the Free Software
+% Foundation, either version 3 of the License, or (at your option)
+% any later version.
+%
+% This document is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this document.  If not, see <http://www.gnu.org/licenses/>.
+%
+% You should have received a copy of the Creative Commons
+% Attribution-ShareAlike 3.0 Unported License along with this
+% document.  If not, see <http://creativecommons.org/licenses/>.
+
+% README: Objektorientierte Tier-Datenbank (Neuauflage), Iterationsfunktionen, dynamisches Bit-Array
+
+\documentclass[a4paper]{article}
+
+\usepackage{pgscript}
+
+\begin{document}
+
+%  \thispagestyle{empty}
+
+  \section*{Hardwarenahe Programmierung\\
+            Übungsaufgaben -- 4.\ Februar 2021}
+
+%  Diese Übung enthält Punkteangaben wie in einer Klausur.
+%  Um zu "`bestehen"', müssen Sie innerhalb von 100 Minuten
+%  unter Verwendung ausschließlich zugelassener Hilfsmittel
+%  17 Punkte (von insgesamt \totalpoints) erreichen.
+
+  \exercise{Objektorientierte Tier-Datenbank (Neuauflage)}
+
+  Diese Aufgabe ist eine Neuauflage von Aufgabe 3 der
+  Übung vom 28.\ Januar 2021,\\
+  ergänzt um die Teilaufgaben (e) bis (g).
+
+  \medskip
+
+  Das auf der nächsten Seite dargestellte Programm
+  (Datei: \gitfile{hp}{2020ws/20210204}{aufgabe-1a.c})
+  soll Daten von Tieren verwalten.
+
+  Beim Compilieren erscheinen die folgende Fehlermeldungen:
+  \begin{lstlisting}[style=terminal]
+    $ ¡gcc -std=c99 -Wall -O aufgabe-1a.c -o aufgabe-1a¿
+    aufgabe-1a.c: In function 'main':
+    aufgabe-1a.c:31: error: 'animal' has no member named 'wings'
+    aufgabe-1a.c:37: error: 'animal' has no member named 'legs'
+  \end{lstlisting}
+
+  Der Programmierer nimmt die auf der nächsten Seite in Rot dargestellten Ersetzungen vor\\
+  (Datei: \gitfile{hp}{2020ws/20210204}{aufgabe-1b.c}).
+  Daraufhin gelingt das Compilieren, und die Ausgabe des Programms lautet:
+  \begin{lstlisting}[style=terminal]
+    $ ¡gcc -std=c99 -Wall -O aufgabe-1b.c -o aufgabe-1b¿
+    $ ¡./aufgabe-1b¿
+    A duck has 2 legs.
+    Error in animal: cow
+  \end{lstlisting}
+
+  \begin{itemize}
+    \item[(a)]
+      Erklären Sie die o.\,a.\ Compiler-Fehlermeldungen.
+%      \points{2}
+    \item[(b)]
+      Wieso verschwinden die Fehlermeldungen nach den o.\,a.\ Ersetzungen?
+%      \points{3}
+    \item[(c)]
+      Erklären Sie die Ausgabe des Programms.
+%      \points{5}
+    \item[(d)]
+      Beschreiben Sie -- in Worten und/oder als C-Quelltext -- einen Weg,
+      das Programm so zu berichtigen, daß es die Eingabedaten
+      (``A duck has 2 wings. A cow has 4 legs.'') korrekt speichert und ausgibt. %\\
+%      \points{4}
+    \item[(e)]
+      Schreiben Sie das Programm so um,
+      daß es keine expliziten Typumwandlungen mehr benötigt.\par
+      Hinweis: Verwenden Sie \lstinline{union}.
+%      \points{4}
+    \item[(f)]
+      Schreiben Sie das Programm weiter um,
+      so daß es die Objektinstanzen \lstinline{duck} und \lstinline{cow}
+      dynamisch erzeugt.\par
+      Hinweis: Verwenden Sie \lstinline{malloc()} und schreiben Sie Konstruktoren.
+%      \points{4}
+    \item[(g)]
+      Schreiben Sie das Programm weiter um,
+      so daß die Ausgabe nicht mehr direkt im Hauptprogramm erfolgt,
+      sondern stattdessen eine virtuelle Methode \lstinline{print()}
+      aufgerufen wird.\par
+      Hinweis: Verwenden Sie in den Objekten Zeiger auf Funktionen,
+      und initialisieren Sie diese in den Konstruktoren.
+%      \points{4}
+  \end{itemize}
+
+  \begin{minipage}[t]{0.34\textwidth}
+    \begin{lstlisting}[gobble=6,xleftmargin=0pt]
+      #include <stdio.h>
+
+      #define ANIMAL     0
+      #define WITH_WINGS 1
+      #define WITH_LEGS  2
+
+      typedef struct animal
+      {
+        int type;
+        char *name;
+      } animal;
+
+      typedef struct with_wings
+      {
+        int wings;
+      } with_wings;
+
+      typedef struct with_legs
+      {
+        int legs;
+      } with_legs;
+    \end{lstlisting}
+  \end{minipage}\hfill
+  \begin{minipage}[t]{0.65\textwidth}
+    \begin{lstlisting}[gobble=6,xleftmargin=0pt]
+      int main (void)
+      {
+        animal *a[2];
+
+        animal duck;
+        a[0] = &duck;
+        a[0]->type = WITH_WINGS;
+        a[0]->name = "duck";
+        a[0]->wings = 2;
+
+        animal cow;
+        a[1] = &cow;
+        a[1]->type = WITH_LEGS;
+        a[1]->name = "cow";
+        a[1]->legs = 4;
+
+        for (int i = 0; i < 2; i++)
+          if (a[i]->type == WITH_LEGS)
+            printf ("A %s has %d legs.\n", a[i]->name,
+                    ((with_legs *) a[i])-> legs);
+          else if (a[i]->type == WITH_WINGS)
+            printf ("A %s has %d wings.\n", a[i]->name,
+                    ((with_wings *) a[i])-> wings);
+          else
+            printf ("Error in animal: %s\n", a[i]->name);
+
+        return 0;
+      }
+    \end{lstlisting}
+    \begin{picture}(0,0)
+      \color{red}
+      \put(3.7,6.207){\vector(-1,0){0.7}}
+      \put(3.8,6.207){\makebox(0,0)[l]{\lstinline[basicstyle=\color{red}]{((with_legs *) a[1])->legs = 4;}}}
+      \put(4.0,8.735){\vector(-1,0){0.7}}
+      \put(4.1,8.735){\makebox(0,0)[l]{\lstinline[basicstyle=\color{red}]{((with_wings *) a[0])->wings = 2;}}}
+    \end{picture}
+  \end{minipage}
+
+  \exercise{Iterationsfunktionen}
+
+  Wir betrachten das folgende Programm (\gitfile{hp}{2020ws/20210204}{aufgabe-2.c}):
+
+  \begin{minipage}[t]{0.4\textwidth}
+    \begin{lstlisting}[gobble=6]
+      #include <stdio.h>
+
+      void foreach (int *a, void (*fun) (int x))
+      {
+        for (int *p = a; *p >= 0; p++)
+          fun (*p);
+      }
+
+      void even_or_odd (int x)
+      {
+        if (x % 2)
+          printf ("%d ist ungerade.\n", x);
+        else
+          printf ("%d ist gerade.\n", x);
+      }
+    \end{lstlisting}
+  \end{minipage}\hfill
+  \begin{minipage}[t]{0.52\textwidth}
+    \begin{lstlisting}[gobble=6]
+      int main (void)
+      {
+        int numbers[] = { 12, 17, 32, 1, 3, 16, 19, 18, -1 };
+        foreach (numbers, even_or_odd);
+        return 0;
+      }
+    \end{lstlisting}
+    \begin{enumerate}[\quad(a)]
+      \item
+        Was bedeutet \lstinline{void (*fun) (int x)},
+        und welchen Sinn hat seine Verwendung in der Funktion \lstinline{foreach()}?
+%        \points{2}
+      \item
+        Schreiben Sie das Hauptprogramm \lstinline{main()} so um,
+        daß es unter Verwendung der Funktion \lstinline{foreach()}
+        die Summe aller positiven Zahlen in dem Array berechnet.
+        Sie dürfen dabei weitere Funktionen sowie globale Variable einführen.
+%        \points{4}
+    \end{enumerate}
+  \end{minipage}
+
+  \clearpage
+
+  \exercise{Dynamisches Bit-Array}
+
+  Schreiben Sie die folgenden Funktionen zur Verwaltung eines dynamischen Bit-Arrays:
+  \begin{itemize}
+    \item
+      \lstinline{void bit_array_init (int n)}\\
+      Das Array initialisieren, so daß man \lstinline{n} Bits darin speichern kann.\\
+      Die Array-Größe \lstinline{n} ist keine Konstante, sondern erst im laufenden Programm bekannt.\\
+      Die Bits sollen auf den Anfangswert 0 initialisiert werden.
+    \item
+      \lstinline{void bit_array_set (int i, int value)}\\
+      Das Bit mit dem Index \lstinline{i} auf den Wert \lstinline{value} setzen.\\
+      Der Index \lstinline{i} darf von \lstinline{0} bis \lstinline{n - 1} gehen;
+      der Wert \lstinline{value} darf 1 oder 0 sein.
+    \item
+      \lstinline{void bit_array_flip (int i)}\\
+      Das Bit mit dem Index \lstinline{i} auf den entgegengesetzten Wert setzen,\\
+      also auf 1, wenn er vorher 0 ist, bzw.\ auf 0, wenn er vorher 1 ist.\\
+      Der Index \lstinline{i} darf von \lstinline{0} bis \lstinline{n - 1} gehen.
+    \item
+      \lstinline{int bit_array_get (int i)}\\
+      Den Wert des Bit mit dem Index \lstinline{i} zurückliefern.\\
+      Der Index \lstinline{i} darf von \lstinline{0} bis \lstinline{n - 1} gehen.
+    \item
+      \lstinline{void bit_array_resize (int new_n)}\\
+      Die Größe des Arrays auf \lstinline{new_n} Bits ändern.\\
+      Dabei soll der Inhalt des Arrays, soweit er in die neue Größe paßt, erhalten bleiben.\\
+      Neu hinzukommende Bits sollen auf 0 initialisiert werden.
+    \item
+      \lstinline{void bit_array_done (void)}\\
+      Den vom Array belegten Speicherplatz wieder freigeben.
+  \end{itemize}
+  Bei Bedarf dürfen Sie den Funktionen zusätzliche Parameter mitgeben,
+  beispielsweise um mehrere Arrays parallel verwalten zu können.
+  (In der objektorientierten Programmierung wäre dies der implizite Parameter \lstinline{this},
+  der auf die Objekt-Struktur zeigt.)
+
+  Die Bits sollen möglichst effizient gespeichert werden,
+  z.\,B.\ jeweils 8 Bits in einer \lstinline{uint8_t}-Variablen.
+
+  Die Funktionen sollen möglichst robust sein,
+  d.\,h.\ das Programm darf auch bei unsinnigen Parameterwerten nicht abstürzen,
+  sondern soll eine Fehlermeldung ausgeben.
+
+  \medskip
+
+  Die folgenden \textbf{Hinweise} beschreiben
+  einen möglichen Weg, die Aufgabe zu lösen.
+  Es seht Ihnen frei, die Aufgabe auch auf andere Weise zu lösen.
+  \begin{itemize}
+    \item
+      Setzen Sie zunächst voraus, daß das Array die konstante Länge 8 hat,
+      und schreiben Sie zunächst nur die Funktionen
+      \lstinline{bit_array_set()}, \lstinline{bit_array_flip()} und
+      \lstinline{bit_array_get()}.
+    \item
+      Verallgemeinern Sie nun auf eine konstante Länge,
+      bei der es sich um ein Vielfaches von 8 handelt.
+    \item
+      Implementieren Sie nun die Überprüfung auf unsinnige Parameterwerte.
+      Damit können Sie sich gleichzeitig von der Bedingung lösen,
+      daß die Länge des Arrays ein Vielfaches von 8 sein muß.
+    \item
+      Gehen Sie nun von einem statischen zu einem dynamischen Array über,
+      und implementieren Sie die Funktionen \lstinline{bit_array_init()},
+      \lstinline{bit_array_done()} und \lstinline{bit_array_resize()}.
+  \end{itemize}
+
+%  \points{14}
+%
+%  \medskip
+%
+%  (Hinweis für die Klausur:
+%  Abgabe in digitaler Form ist erwünscht, aber nicht zwingend.)
+
+  \begin{flushright}
+    \textit{Viel Erfolg!}
+  \end{flushright}
+
+  \makeatletter
+    \immediate\write\@mainaux{\string\gdef\string\totalpoints{\arabic{points}}}
+  \makeatother
+
+\end{document}
diff --git a/20210204/loesung-1d-0f.c b/20210204/loesung-1d-0f.c
new file mode 100644
index 0000000..04b2d3e
--- /dev/null
+++ b/20210204/loesung-1d-0f.c
@@ -0,0 +1,54 @@
+#include <stdio.h>
+
+#define ANIMAL     0
+#define WITH_WINGS 1
+#define WITH_LEGS  2
+
+typedef struct animal
+{
+  int type;
+  char *name;
+} animal;
+
+typedef struct with_wings
+{
+  int type;
+  char *name;
+  int wings;
+} with_wings;
+
+typedef struct with_legs
+{
+  int type;
+  char *name;
+  int legs;
+} with_legs;
+
+int main (void)
+{
+  animal *a[2];
+
+  animal duck;
+  a[0] = &duck;
+  a[0]->type = WITH_WINGS;
+  a[0]->name = "duck";
+  ((with_wings *) a[0])->wings = 2;
+
+  animal cow;
+  a[1] = &cow;
+  a[1]->type = WITH_LEGS;
+  a[1]->name = "cow";
+  ((with_legs *) a[1])->legs = 4;
+
+  for (int i = 0; i < 2; i++)
+    if (a[i]->type == WITH_LEGS)
+      printf ("A %s has %d legs.\n", a[i]->name,
+              ((with_legs *) a[i])-> legs);
+    else if (a[i]->type == WITH_WINGS)
+      printf ("A %s has %d wings.\n", a[i]->name,
+              ((with_wings *) a[i])-> wings);
+    else
+      printf ("Error in animal: %s\n", a[i]->name);
+
+  return 0;
+}
diff --git a/20210204/loesung-1d-1.c b/20210204/loesung-1d-1.c
new file mode 100644
index 0000000..349523a
--- /dev/null
+++ b/20210204/loesung-1d-1.c
@@ -0,0 +1,54 @@
+#include <stdio.h>
+
+#define ANIMAL     0
+#define WITH_WINGS 1
+#define WITH_LEGS  2
+
+typedef struct animal
+{
+  int type;
+  char *name;
+} animal;
+
+typedef struct with_wings
+{
+  int type;
+  char *name;
+  int wings;
+} with_wings;
+
+typedef struct with_legs
+{
+  int type;
+  char *name;
+  int legs;
+} with_legs;
+
+int main (void)
+{
+  animal *a[2];
+
+  with_wings duck;
+  a[0] = (animal *) &duck;
+  a[0]->type = WITH_WINGS;
+  a[0]->name = "duck";
+  ((with_wings *) a[0])->wings = 2;
+
+  with_legs cow;
+  a[1] = (animal *) &cow;
+  a[1]->type = WITH_LEGS;
+  a[1]->name = "cow";
+  ((with_legs *) a[1])->legs = 4;
+
+  for (int i = 0; i < 2; i++)
+    if (a[i]->type == WITH_LEGS)
+      printf ("A %s has %d legs.\n", a[i]->name,
+              ((with_legs *) a[i])-> legs);
+    else if (a[i]->type == WITH_WINGS)
+      printf ("A %s has %d wings.\n", a[i]->name,
+              ((with_wings *) a[i])-> wings);
+    else
+      printf ("Error in animal: %s\n", a[i]->name);
+
+  return 0;
+}
diff --git a/20210204/loesung-1d-2.c b/20210204/loesung-1d-2.c
new file mode 100644
index 0000000..f831a75
--- /dev/null
+++ b/20210204/loesung-1d-2.c
@@ -0,0 +1,54 @@
+#include <stdio.h>
+
+#define ANIMAL     0
+#define WITH_WINGS 1
+#define WITH_LEGS  2
+
+typedef struct animal
+{
+  int type;
+  char *name;
+} animal;
+
+typedef struct with_wings
+{
+  int type;
+  char *name;
+  int wings;
+} with_wings;
+
+typedef struct with_legs
+{
+  int type;
+  char *name;
+  int legs;
+} with_legs;
+
+int main (void)
+{
+  animal *a[2];
+
+  with_wings duck;
+  a[0] = (animal *) &duck;
+  duck.type = WITH_WINGS;
+  duck.name = "duck";
+  duck.wings = 2;
+
+  with_legs cow;
+  a[1] = (animal *) &cow;
+  cow.type = WITH_LEGS;
+  cow.name = "cow";
+  cow.legs = 4;
+
+  for (int i = 0; i < 2; i++)
+    if (a[i]->type == WITH_LEGS)
+      printf ("A %s has %d legs.\n", a[i]->name,
+              ((with_legs *) a[i])-> legs);
+    else if (a[i]->type == WITH_WINGS)
+      printf ("A %s has %d wings.\n", a[i]->name,
+              ((with_wings *) a[i])-> wings);
+    else
+      printf ("Error in animal: %s\n", a[i]->name);
+
+  return 0;
+}
diff --git a/20210204/loesung-1e.c b/20210204/loesung-1e.c
new file mode 100644
index 0000000..b984d92
--- /dev/null
+++ b/20210204/loesung-1e.c
@@ -0,0 +1,61 @@
+#include <stdio.h>
+
+#define ANIMAL     0
+#define WITH_WINGS 1
+#define WITH_LEGS  2
+
+typedef struct
+{
+  int type;
+  char *name;
+} base;
+
+typedef struct
+{
+  int type;
+  char *name;
+  int wings;
+} with_wings;
+
+typedef struct
+{
+  int type;
+  char *name;
+  int legs;
+} with_legs;
+
+typedef union
+{
+  base b;
+  with_wings w;
+  with_legs l;
+} animal;
+
+int main (void)
+{
+  animal *a[2];
+
+  animal duck;
+  a[0] = &duck;
+  duck.b.type = WITH_WINGS;
+  duck.b.name = "duck";
+  duck.w.wings = 2;
+
+  animal cow;
+  a[1] = &cow;
+  cow.b.type = WITH_LEGS;
+  cow.b.name = "cow";
+  cow.l.legs = 4;
+
+  for (int i = 0; i < 2; i++)
+    if (a[i]->b.type == WITH_LEGS)
+      printf ("A %s has %d legs.\n", a[i]->b.name,
+              a[i]->l.legs);
+    else if (a[i]->b.type == WITH_WINGS)
+      printf ("A %s has %d wings.\n", a[i]->b.name,
+              a[i]->w.wings);
+    else
+      printf ("Error in animal: %s\n", a[i]->b.name);
+
+  return 0;
+}
diff --git a/20210204/loesung-1f.c b/20210204/loesung-1f.c
new file mode 100644
index 0000000..7b949e6
--- /dev/null
+++ b/20210204/loesung-1f.c
@@ -0,0 +1,69 @@
+#include <stdio.h>
+#include <stdlib.h>
+
+#define ANIMAL     0
+#define WITH_WINGS 1
+#define WITH_LEGS  2
+
+typedef struct
+{
+  int type;
+  char *name;
+} base;
+
+typedef struct
+{
+  int type;
+  char *name;
+  int wings;
+} with_wings;
+
+typedef struct
+{
+  int type;
+  char *name;
+  int legs;
+} with_legs;
+
+typedef union
+{
+  base b;
+  with_wings w;
+  with_legs l;
+} animal;
+
+animal *new_with_wings (char *name, int wings)
+{
+  animal *a = malloc (sizeof (with_wings));
+  a->b.type = WITH_WINGS;
+  a->b.name = name;
+  a->w.wings = wings;
+  return a;
+}
+
+animal *new_with_legs (char *name, int legs)
+{
+  animal *a = malloc (sizeof (with_legs));
+  a->b.type = WITH_LEGS;
+  a->b.name = name;
+  a->l.legs = legs;
+  return a;
+}
+
+int main (void)
+{
+  animal *a[2] = { new_with_wings ("duck", 2),
+                   new_with_legs ("cow", 4) };
+
+  for (int i = 0; i < 2; i++)
+    if (a[i]->b.type == WITH_LEGS)
+      printf ("A %s has %d legs.\n", a[i]->b.name,
+              a[i]->l.legs);
+    else if (a[i]->b.type == WITH_WINGS)
+      printf ("A %s has %d wings.\n", a[i]->b.name,
+              a[i]->w.wings);
+    else
+      printf ("Error in animal: %s\n", a[i]->b.name);
+
+  return 0;
+}
diff --git a/20210204/loesung-1g.c b/20210204/loesung-1g.c
new file mode 100644
index 0000000..b453a52
--- /dev/null
+++ b/20210204/loesung-1g.c
@@ -0,0 +1,77 @@
+#include <stdio.h>
+#include <stdlib.h>
+
+#define ANIMAL     0
+#define WITH_WINGS 1
+#define WITH_LEGS  2
+
+union animal;
+
+typedef struct
+{
+  int type;
+  char *name;
+  void (*print) (union animal *this);
+} base;
+
+typedef struct
+{
+  int type;
+  char *name;
+  void (*print) (union animal *this);
+  int wings;
+} with_wings;
+
+typedef struct
+{
+  int type;
+  char *name;
+  void (*print) (union animal *this);
+  int legs;
+} with_legs;
+
+typedef union animal
+{
+  base b;
+  with_wings w;
+  with_legs l;
+} animal;
+
+void print_with_wings (animal *this)
+{
+  printf ("A %s has %d wings.\n", this->b.name, this->w.wings);
+}
+
+void print_with_legs (animal *this)
+{
+  printf ("A %s has %d legs.\n", this->b.name, this->l.legs);
+}
+
+animal *new_with_wings (char *name, int wings)
+{
+  animal *a = malloc (sizeof (with_wings));
+  a->b.type = WITH_WINGS;
+  a->b.name = name;
+  a->b.print = print_with_wings;
+  a->w.wings = wings;
+  return a;
+}
+
+animal *new_with_legs (char *name, int legs)
+{
+  animal *a = malloc (sizeof (with_legs));
+  a->b.type = WITH_LEGS;
+  a->b.name = name;
+  a->b.print = print_with_legs;
+  a->l.legs = legs;
+  return a;
+}
+
+int main (void)
+{
+  animal *a[2] = { new_with_wings ("duck", 2),
+                   new_with_legs ("cow", 4) };
+  for (int i = 0; i < 2; i++)
+    a[i]->b.print (a[i]);
+  return 0;
+}
diff --git a/20210204/logo-hochschule-bochum-cvh-text-v2.pdf b/20210204/logo-hochschule-bochum-cvh-text-v2.pdf
new file mode 120000
index 0000000..4aa99b8
--- /dev/null
+++ b/20210204/logo-hochschule-bochum-cvh-text-v2.pdf
@@ -0,0 +1 @@
+../common/logo-hochschule-bochum-cvh-text-v2.pdf
\ No newline at end of file
diff --git a/20210204/logo-hochschule-bochum.pdf b/20210204/logo-hochschule-bochum.pdf
new file mode 120000
index 0000000..b6b9491
--- /dev/null
+++ b/20210204/logo-hochschule-bochum.pdf
@@ -0,0 +1 @@
+../common/logo-hochschule-bochum.pdf
\ No newline at end of file
diff --git a/20210204/pgscript.sty b/20210204/pgscript.sty
new file mode 120000
index 0000000..95c8884
--- /dev/null
+++ b/20210204/pgscript.sty
@@ -0,0 +1 @@
+../common/pgscript.sty
\ No newline at end of file
diff --git a/20210204/pgslides.sty b/20210204/pgslides.sty
new file mode 120000
index 0000000..5be1416
--- /dev/null
+++ b/20210204/pgslides.sty
@@ -0,0 +1 @@
+../common/pgslides.sty
\ No newline at end of file
diff --git a/README.md b/README.md
index e4029ae..9b2ab16 100644
--- a/README.md
+++ b/README.md
@@ -25,7 +25,10 @@ Vortragsfolien und Beispiele:
  * [10.12.2020: Präprozessor, Bibliotheken einbinden und verwenden](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20201210/hp-20201210.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2020ws/20201210/)
  * [17.12.2020: make, Differentialgleichungen](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20201217/hp-20201217.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2020ws/20201217/)
  * [07.01.2021: Rekursion, Aufwandsabschätzungen](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210107/hp-20210107.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2020ws/20210107/)
- * [14.01.2021: Hardwarenahe Programmierung](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210114/hp-20210114.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2020ws/20210114/)
+ * [14.01.2021: Hardwarenahe Programmierung: Bit-Operationen, I/O-Ports](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210114/hp-20210114.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2020ws/20210114/)
+ * [21.01.2021: Hardwarenahe Programmierung: Interrupts, volatile-Variable, Byte-Reihenfolge – Endianness, Binärdarstellung negativer Zahlen, Speicherausrichtung – Alignment](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210121/hp-20210121.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2020ws/20210121/)
+ * [28.01.2021: Objektorientierte Programmierung](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210128/hp-20210128.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2020ws/20210128/)
+ * [04.02.2021: Objektorientierte Programmierung: virtuelle Methoden](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210204/hp-20210204.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2020ws/20210204/)
  * [alle in 1 Datei](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/hp-slides-2020ws.pdf)
 
 Übungsaufgaben:
@@ -39,6 +42,9 @@ Vortragsfolien und Beispiele:
  * [17.12.2020: Kondensator, hüpfender Ball](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20201217/hp-uebung-20201217.pdf)
  * [07.01.2021: Fakultät, Länge von Strings (Neuauflage), Hexdumps](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210107/hp-uebung-20210107.pdf)
  * [14.01.2021: Zahlensysteme, Mikrocontroller, Einfügen in Strings (Ergänzung)](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210114/hp-uebung-20210114.pdf)
+ * [21.01.2021: Trickprogrammierung, Thermometer-Baustein an I²C-Bus, LED-Blinkmuster](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210121/hp-uebung-20210121.pdf)
+ * [28.01.2021: Speicherformate von Zahlen, Personen-Datenbank, objektorientierte Tier-Datenbank](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210128/hp-uebung-20210128.pdf)
+ * [04.02.2021: Objektorientierte Tier-Datenbank (Neuauflage), Iterationsfunktionen, dynamisches Bit-Array](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210204/hp-uebung-20210204.pdf)
 
 Musterlösungen:
 ---------------
@@ -50,6 +56,9 @@ Musterlösungen:
  * [17.12.2020: Kondensator, hüpfender Ball](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20201217/hp-musterloesung-20201217.pdf)
  * [07.01.2021: Fakultät, Länge von Strings (Neuauflage), Hexdumps](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210107/hp-musterloesung-20210107.pdf)
  * [14.01.2021: Zahlensysteme, Mikrocontroller](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210114/hp-musterloesung-20210114.pdf)
+ * [21.01.2021: Trickprogrammierung, Thermometer-Baustein an I²C-Bus, LED-Blinkmuster](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210121/hp-musterloesung-20210121.pdf)
+ * [28.01.2021: Speicherformate von Zahlen, Personen-Datenbank, objektorientierte Tier-Datenbank](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210128/hp-musterloesung-20210128.pdf)
+ * [04.02.2021: Objektorientierte Tier-Datenbank (Neuauflage), Iterationsfunktionen, dynamisches Bit-Array](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210204/hp-musterloesung-20210204.pdf)
 
 Tafelbilder:
 ------------
@@ -60,6 +69,7 @@ Praktikumsunterlagen:
  * [Versuch 1: RSA-Verschlüsselung](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20201112/hp-2020ws-p1.pdf)
  * [Versuch 2: Weltraum-Simulation](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20201217/hp-2020ws-p2.pdf)
  * [Versuch 3: Druckknopfampel](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210114/hp-2020ws-p3.pdf)
+ * [Versuch 4: Objektorientiertes Grafik-Programm](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210204/hp-2020ws-p4.pdf)
 
 Alte Klausuren:
 ---------------
diff --git a/hp-slides-2020ws.pdf b/hp-slides-2020ws.pdf
index 204153ff3843d9c96fb2acdd2c1cbe2b3bc62764..2a5d0ce9550c2e58f7edb021e84d836b00248e8c 100644
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diff --git a/hp-slides-2020ws.tex b/hp-slides-2020ws.tex
index 1bca6b8..551b589 100644
--- a/hp-slides-2020ws.tex
+++ b/hp-slides-2020ws.tex
@@ -26,6 +26,12 @@
   \includepdf[pages=-]{20201217/hp-20201217.pdf}
   \pdfbookmark[1]{07.01.2021: Rekursion, Aufwandsabschätzungen}{20210107}
   \includepdf[pages=-]{20210107/hp-20210107.pdf}
-  \pdfbookmark[1]{14.01.2021: Hardwarenahe Programmierung}{20210114}
+  \pdfbookmark[1]{14.01.2021: Hardwarenahe Programmierung: Bit-Operationen, I/O-Ports}{20210114}
   \includepdf[pages=-]{20210114/hp-20210114.pdf}
+  \pdfbookmark[1]{21.01.2021: Hardwarenahe Programmierung: Interrupts, volatile-Variable, Byte-Reihenfolge – Endianness, Binärdarstellung negativer Zahlen, Speicherausrichtung – Alignment}{20210121}
+  \includepdf[pages=-]{20210121/hp-20210121.pdf}
+  \pdfbookmark[1]{28.01.2021: Objektorientierte Programmierung}{20210128}
+  \includepdf[pages=-]{20210128/hp-20210128.pdf}
+  \pdfbookmark[1]{04.02.2021: Objektorientierte Programmierung: virtuelle Methoden}{20210204}
+  \includepdf[pages=-]{20210204/hp-20210204.pdf}
 \end{document}
-- 
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