From fd71d40213174f6156aa86bdffbaa7a9ee627a76 Mon Sep 17 00:00:00 2001
From: Peter Gerwinski <peter.gerwinski@hs-bochum.de>
Date: Wed, 6 Dec 2023 21:54:21 +0100
Subject: [PATCH] Vorbereitung 7.12.2023

---
 20231130/hp-uebung-20231130.tex               |   2 +-
 20231207/Tower_of_Hanoi.jpeg                  |   1 +
 20231207/aufgabe-1.c                          |  18 +
 20231207/aufgabe-2.c                          |  18 +
 20231207/hp-20231207.pdf                      | Bin 0 -> 382848 bytes
 20231207/hp-20231207.tex                      | 440 ++++++++++++++++++
 20231207/hp-musterloesung-20231207.pdf        | Bin 0 -> 99958 bytes
 20231207/hp-musterloesung-20231207.tex        | 378 +++++++++++++++
 20231207/hp-uebung-20231207.pdf               | Bin 0 -> 71767 bytes
 20231207/hp-uebung-20231207.tex               | 223 +++++++++
 20231207/landau-symbols-2.pdf                 |   1 +
 20231207/landau-symbols-3.pdf                 |   1 +
 20231207/landau-symbols.pdf                   |   1 +
 20231207/loesung-1-c-1.c                      |  15 +
 20231207/loesung-1-c-2.c                      |  15 +
 20231207/loesung-1-d-1.c                      |  34 ++
 20231207/loesung-1-d-2.c                      |  34 ++
 20231207/loesung-1-e-1.c                      |  15 +
 20231207/loesung-1-e-2.c                      |  15 +
 20231207/loesung-2e.c                         |  33 ++
 20231207/loesung-2g.c                         |  46 ++
 .../logo-hochschule-bochum-cvh-text-v2.pdf    |   1 +
 20231207/logo-hochschule-bochum.pdf           |   1 +
 20231207/pendulum.pdf                         |   1 +
 20231207/pgscript.sty                         |   1 +
 20231207/pgslides.sty                         |   1 +
 README.md                                     |   6 +
 hp-slides-2023ws.pdf                          | Bin 2020462 -> 2742679 bytes
 hp-slides-2023ws.tex                          |   6 +-
 29 files changed, 1305 insertions(+), 2 deletions(-)
 create mode 120000 20231207/Tower_of_Hanoi.jpeg
 create mode 100644 20231207/aufgabe-1.c
 create mode 100644 20231207/aufgabe-2.c
 create mode 100644 20231207/hp-20231207.pdf
 create mode 100644 20231207/hp-20231207.tex
 create mode 100644 20231207/hp-musterloesung-20231207.pdf
 create mode 100644 20231207/hp-musterloesung-20231207.tex
 create mode 100644 20231207/hp-uebung-20231207.pdf
 create mode 100644 20231207/hp-uebung-20231207.tex
 create mode 120000 20231207/landau-symbols-2.pdf
 create mode 120000 20231207/landau-symbols-3.pdf
 create mode 120000 20231207/landau-symbols.pdf
 create mode 100644 20231207/loesung-1-c-1.c
 create mode 100644 20231207/loesung-1-c-2.c
 create mode 100644 20231207/loesung-1-d-1.c
 create mode 100644 20231207/loesung-1-d-2.c
 create mode 100644 20231207/loesung-1-e-1.c
 create mode 100644 20231207/loesung-1-e-2.c
 create mode 100644 20231207/loesung-2e.c
 create mode 100644 20231207/loesung-2g.c
 create mode 120000 20231207/logo-hochschule-bochum-cvh-text-v2.pdf
 create mode 120000 20231207/logo-hochschule-bochum.pdf
 create mode 120000 20231207/pendulum.pdf
 create mode 120000 20231207/pgscript.sty
 create mode 120000 20231207/pgslides.sty

diff --git a/20231130/hp-uebung-20231130.tex b/20231130/hp-uebung-20231130.tex
index 59ac551..e107bad 100644
--- a/20231130/hp-uebung-20231130.tex
+++ b/20231130/hp-uebung-20231130.tex
@@ -164,7 +164,7 @@
   um die Teilaufgaben (e), (f) und (g). Für den "`Klausur-Modus"' können
   Sie die Teilaufgaben (a) bis (d) als "`bereits gelöst"' voraussetzen.
 
-  Wir betrachten das folgende Programm (\gitfile{hp}{2023ws/20231130}{aufgabe-1.c}):
+  Wir betrachten das folgende Programm (\gitfile{hp}{2023ws/20231130}{aufgabe-3.c}):
 %  \begin{lstlisting}[style=numbered]
   \begin{lstlisting}
     #include <stdio.h>
diff --git a/20231207/Tower_of_Hanoi.jpeg b/20231207/Tower_of_Hanoi.jpeg
new file mode 120000
index 0000000..a1a794a
--- /dev/null
+++ b/20231207/Tower_of_Hanoi.jpeg
@@ -0,0 +1 @@
+../common/Tower_of_Hanoi.jpeg
\ No newline at end of file
diff --git a/20231207/aufgabe-1.c b/20231207/aufgabe-1.c
new file mode 100644
index 0000000..d0b0659
--- /dev/null
+++ b/20231207/aufgabe-1.c
@@ -0,0 +1,18 @@
+#include <string.h>
+
+int fun_1 (char *s)
+{
+  int x = 0;
+  for (int i = 0; i < strlen (s); i++)
+    x += s[i];
+  return x;
+}
+
+int fun_2 (char *s)
+{
+  int i = 0, x = 0;
+  int len = strlen (s);
+  while (i < len)
+    x += s[i++];
+  return x;
+}
diff --git a/20231207/aufgabe-2.c b/20231207/aufgabe-2.c
new file mode 100644
index 0000000..15c9056
--- /dev/null
+++ b/20231207/aufgabe-2.c
@@ -0,0 +1,18 @@
+#include <stdio.h>
+#include <string.h>
+
+void insert_into_string (char src, char *target, int pos)
+{
+  int len = strlen (target);
+  for (int i = pos; i < len; i++)
+    target[i + 1] = target[i];
+  target[pos] = src;
+}
+
+int main (void)
+{
+  char test[100] = "Hochshule Bochum";
+  insert_into_string ('c', test, 5);
+  printf ("%s\n", test);
+  return 0;
+}
diff --git a/20231207/hp-20231207.pdf b/20231207/hp-20231207.pdf
new file mode 100644
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diff --git a/20231207/hp-20231207.tex b/20231207/hp-20231207.tex
new file mode 100644
index 0000000..4bf45fe
--- /dev/null
+++ b/20231207/hp-20231207.tex
@@ -0,0 +1,440 @@
+% hp-20231207.pdf - Lecture Slides on Low-Level Programming
+% Copyright (C) 2012, 2013, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023  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: Algorithmen: Aufwandsabschätzungen
+
+\documentclass[10pt,t]{beamer}
+
+\usepackage{pgslides}
+\usepackage{tikz}
+
+\newcommand{\redurl}[1]{\href{#1}{\color{red}\nolinkurl{#1}}}
+
+\title{Hardwarenahe Programmierung}
+\author{Prof.\ Dr.\ rer.\ nat.\ Peter Gerwinski}
+\date{7.\ Dezember 2023}
+
+\begin{document}
+
+\maketitleframe
+
+\title{Hardwarenahe Programmierung}
+
+\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{Hardwarenahe Programmierung}
+    \item[\textbf{5}] \textbf{Algorithmen}
+      \begin{itemize}
+        \color{medgreen}
+        \item[5.1] Differentialgleichungen
+        \item[5.2] Rekursion
+        \color{red}
+        \item[5.3] Aufwandsabschätzungen
+      \end{itemize}
+    \item[\textbf{6}] \textbf{Objektorientierte Programmierung}
+    \item[\textbf{7}] \textbf{Datenstrukturen}
+  \end{itemize}
+
+\end{frame}
+
+\setcounter{section}{4}
+\section{Algorithmen}
+\subsection{Differentialgleichungen}
+
+\begin{frame}[fragile]
+
+  \showsection
+  \showsubsection
+
+  \textbf{Beispiel 1: Gleichmäßig beschleunigte Bewegung}
+
+  \strut\hfill
+  \begin{minipage}{2.5cm}
+    \vspace*{0.6cm}
+    \begin{align*}
+      x'(t) &= v_x(t) \\[0.65cm]
+      y'(t) &= v_y(t) \\[0.75cm]
+      v_x'(t) &= 0 \\[0.65cm]
+      v_y'(t) &= -g
+    \end{align*}
+    \vspace*{0.0cm}
+  \end{minipage}%
+%  \only<1>{\hspace*{9.49cm}}\strut
+  \only<1>{\hfill$\Rightarrow$\hfill}%
+  \begin{onlyenv}<1>
+    \begin{minipage}{8.3cm}
+      \begin{align*}
+        x(t) &= \int v_x(t)\,dt
+          \visible<1->{= \int v_{0x}\,dt}
+          \visible<1->{= x_0 + v_{0x}\cdot t}\\[\medskipamount]
+        y(t) &= \int v_y(t)\,dt
+          \visible<1->{= \int v_{0y} - g\cdot t\,dt}
+          \visible<1->{= y_0 + v_{0y}\cdot t
+                         - {\textstyle\frac12}gt^2}\\[\bigskipamount]
+        v_x(t) &= \int 0\,dt
+          \visible<1->{= v_{0x}} \\[\medskipamount]
+        v_y(t) &= \int -g\,dt
+          \visible<1->{= v_{0y} - g\cdot t}
+      \end{align*}
+    \end{minipage}%
+  \end{onlyenv}%
+  \begin{onlyenv}<2>
+    \begin{minipage}{3.5cm}
+      \vspace*{0.5cm}
+      \begin{lstlisting}[gobble=8,xleftmargin=0.5em]
+        ¡x += vx * dt;¿
+      \end{lstlisting}
+      \vspace{0.75cm}
+      \begin{lstlisting}[gobble=8,xleftmargin=0.5em]
+        ¡y += vy * dt;¿
+      \end{lstlisting}
+      \vspace{0.90cm}
+      \begin{lstlisting}[gobble=8,xleftmargin=0.5em]
+        ¡vx += 0 * dt;¿
+      \end{lstlisting}
+      \vspace{0.75cm}
+      \begin{lstlisting}[gobble=8,xleftmargin=0.5em]
+        ¡vy += -g * dt;¿
+      \end{lstlisting}
+    \end{minipage}%
+    \begin{minipage}{5.13cm}
+%      Siehe: \file{gtk-13.c}
+      \strut
+    \end{minipage}
+  \end{onlyenv}%
+  \hfill\strut
+
+\end{frame}
+
+\begin{frame}[fragile]
+  \showsection
+  \showsubsection
+
+  \textbf{Beispiel 1: Gleichmäßig beschleunigte Bewegung}
+
+  \medskip
+
+  \textbf{Beispiel 2: Mathematisches Pendel}
+
+  \vspace*{-2\bigskipamount}
+
+  \begin{picture}(0,0)
+    \put(8,-6.5){\includegraphics{pendulum.pdf}}
+  \end{picture}
+
+  \begin{eqnarray*}
+    \varphi'(t) &=& \omega(t) \\[\smallskipamount]
+    \omega'(t) &=& -\frac{g}{l}\cdot\sin\varphi(t)\hspace*{7.1cm}
+  \end{eqnarray*}
+  \vspace*{-1.5\medskipamount}
+  \begin{itemize}
+    \item
+      Von Hand (analytisch):\\
+      Lösung raten (Ansatz), Parameter berechnen
+    \item
+      Mit Computer (numerisch):\\
+      Eulersches Polygonzugverfahren
+  \end{itemize}
+  \smallskip
+  \begin{lstlisting}[gobble=0]
+    phi += dt * omega;
+    omega += - dt * g / l * sin (phi);
+  \end{lstlisting}
+
+%  \pause
+  \bigskip
+
+  \textbf{Beispiel 3: Weltraum-Simulation}
+
+  Praktikumsaufgabe
+  \vspace*{-1cm}
+
+\end{frame}
+
+\subsection{Rekursion}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  Vollständige Induktion:
+  \vspace*{-0.725cm}
+  \begin{displaymath}
+    \hspace*{4cm}
+    \left.
+      \begin{array}{r}
+        \mbox{Aussage gilt für $n = 1$}\\[2pt]
+        \mbox{Schluß von $n - 1$ auf $n$}
+      \end{array}
+    \right\}
+    \mbox{Aussage gilt für alle $n\in\mathbb{N}$}
+  \end{displaymath}
+  \vspace*{-0.5cm}
+
+  \pause
+
+  Türme von Hanoi
+
+  \begin{onlyenv}<2>
+    \begin{center}
+      \includegraphics[width=12.2cm]{Tower_of_Hanoi.jpeg}
+    \end{center}
+  \end{onlyenv}
+
+  \begin{onlyenv}<3->
+    \begin{itemize}
+      \item
+        64 Scheiben, 3 Plätze,
+        \only<3-4>{\hfill\makebox(0,0)[rt]{\includegraphics[width=6cm]{Tower_of_Hanoi.jpeg}}}\\
+        immer 1 Scheibe verschieben
+      \item
+        Ziel: Turm verschieben
+      \item
+        Es dürfen nur kleinere Scheiben\\
+        auf größeren liegen.
+      \bigskip
+      \pause
+      \pause
+      \item
+        $n = 1$ Scheibe: fertig
+      \item
+        Wenn $n - 1$ Scheiben verschiebbar:\\
+        schiebe $n - 1$ Scheiben auf Hilfsplatz,\\
+        verschiebe die darunterliegende,\\
+        hole $n - 1$ Scheiben von Hilfsplatz
+    \end{itemize}
+    \begin{onlyenv}<5>
+      \vspace{-4.3cm}
+      \begin{lstlisting}[gobble=8,xleftmargin=6.4cm]
+        void move (int from, int to, int disks)
+        {
+          if (disks == 1)
+            move_one_disk (from, to);
+          else
+            {
+              int help = 0 + 1 + 2 - from - to;
+              move (from, help, disks - 1);
+              move (from, to, 1);
+              move (help, to, disks - 1);
+            }
+        }
+      \end{lstlisting}
+    \end{onlyenv}
+%     \begin{onlyenv}<6->
+%       \vspace{-5.0cm}
+%       \hspace*{7.4cm}\begin{minipage}[t]{5cm}
+%         32 Scheiben:
+%         \begin{lstlisting}[gobble=10,style=terminal]
+%           $ ¡time ./hanoi-9b¿
+%           ...
+%           real    0m30,672s
+%           user    0m30,662s
+%           sys     0m0,008s
+%         \end{lstlisting}
+%         \pause[7]
+%         \begin{itemize}
+%           \arrowitem
+%             etwas über 1 Minute\\
+%             für 64 Scheiben
+%         \end{itemize}
+%         \pause
+%         \vspace*{-0.5cm}
+%         \begin{picture}(0,0)
+%           \color{red}
+%           \put(0,0){\makebox(0,0)[bl]{\tikz[line width=1pt]{\draw(0,0)--(4,0.8);}}}
+%           \put(0,0.8){\makebox(0,0)[tl]{\tikz[line width=1pt]{\draw(0,0)--(4,-0.8);}}}
+%         \end{picture}
+% 
+%         Für jede zusätzliche Scheibe\\verdoppelt sich die Rechenzeit!
+%         % 30.672 * 2^32 / 3600 / 24 / 365.25 = 4174.43775518138261464750
+%         \begin{itemize}
+%           \arrowitem
+%             $\frac{30,672\,\text{s}\,\cdot\,2^{32}}{3600\,\cdot\,24\,\cdot\,365,25} \approx 4174$
+%             Jahre\\[\smallskipamount]
+%             für 64 Scheiben
+%         \end{itemize}
+%       \end{minipage}
+%     \end{onlyenv}
+  \end{onlyenv}
+
+\end{frame}
+
+\subsection{Aufwandsabschätzungen \protect\color{gray}-- Komplexitätsanalyse}
+
+\begin{frame}[fragile]
+
+%  \newcommand{\w}{\hspace*{0.75pt}}
+
+  \showsubsection
+
+  \begin{picture}(0,0)
+    \put(7.6,-0.5){%
+      \begin{minipage}[t]{5.3cm}
+%        \vspace*{-1.0cm}\includegraphics{landau-symbols.pdf}
+        \vspace*{-1.0cm}\alt<16->{\includegraphics{landau-symbols-3.pdf}}%
+                       {\alt<15->{\includegraphics{landau-symbols-2.pdf}}%
+                                 {\includegraphics{landau-symbols.pdf}}}
+        \small
+        \begin{description}\itemsep0pt\leftskip-0.5cm
+          \item[$n$:] Eingabedaten
+          \item[$g(n)$:] Rechenzeit
+        \end{description}
+      \end{minipage}}
+  \end{picture}
+
+  \vspace*{-\bigskipamount}
+
+  Wann ist ein Programm "`schnell"'?
+
+  \medskip
+
+  \begin{onlyenv}<1-2>
+      Türme von Hanoi: $\mathcal{O}(2^n)$
+      \par\medskip
+      Für jede zusätzliche Scheibe\\verdoppelt sich die Rechenzeit!
+      \begin{itemize}
+        \arrowitem
+          $\frac{30,672\,\text{s}\,\cdot\,2^{32}}{3600\,\cdot\,24\,\cdot\,365,25} \approx 4174$
+          Jahre\\[\smallskipamount]
+          für 64 Scheiben
+      \end{itemize}
+
+      \bigskip
+  \end{onlyenv}
+
+  \begin{onlyenv}<2->
+    Faustregel:\\Schachtelung der Schleifen zählen\\
+    $k$ Schleifen ineinander \textarrow\ $\mathcal{O}(n^k)$
+
+    \bigskip
+  \end{onlyenv}
+
+  \begin{onlyenv}<3-13>
+    \textbf{Beispiel: Sortieralgorithmen}
+
+    \smallskip
+
+    Anzahl der Vergleiche bei $n$ Strings
+    \begin{itemize}
+      \item
+        Maximum suchen \pause[4]mit Schummeln\pause: $\mathcal{O}(1)$
+      \pause
+      \item
+        Maximum suchen\pause: $\mathcal{O}(n)$
+      \pause
+      \item
+        Selection-Sort\pause: $\mathcal{O}(n^2)$
+      \pause
+      \item
+        Bubble-Sort\pause: $\mathcal{O}(n)$ bis $\mathcal{O}(n^2)$
+      \pause
+      \item
+        Quicksort\pause: $\mathcal{O}(n\log n)$ bis $\mathcal{O}(n^2)$
+    \end{itemize}
+
+  \end{onlyenv}
+
+  \begin{onlyenv}<14>
+    \textbf{Wie schnell ist RSA-Verschlüsselung?}
+
+    \smallskip
+
+    \begin{math}
+      c = m^e\,\%\,N
+    \end{math}
+    \quad
+    ("`$\%$"' = "`modulo"')
+
+    \medskip
+
+    \begin{lstlisting}[gobble=6,xleftmargin=2em]
+      int c = 1;
+      for (int i = 0; i < e; i++)
+        c = (c * m) % N;
+    \end{lstlisting}
+
+    \smallskip
+
+    \begin{itemize}
+      \item
+        $\mathcal{O}(e)$ Iterationen
+%      \item
+%        wenn $n$ die Anzahl der Binärziffern (Bits) von $e$ ist:
+%        $\mathcal{O}(2^n)$ Iterationen
+      \item
+        mit Trick:
+        $\mathcal{O}(\log e)$ Iterationen ($\log e$ = Anzahl der Ziffern von $e$)
+    \end{itemize}
+
+    \smallskip
+
+    Jede Iteration enthält eine Multiplikation und eine Division.\\
+    Aufwand dafür: $\mathcal{O}(\log e)$\\
+    \textarrow\ Gesamtaufwand: $\mathcal{O}\bigl((\log e)^2\bigr)$
+
+  \end{onlyenv}
+
+  \begin{onlyenv}<15->
+
+    \textbf{Wie schnell ist RSA?}\\
+
+    \smallskip
+
+    ($n$ = typische beteiligte Zahl, z.\,B. $e,p,q$)
+
+    \begin{itemize}
+      \item
+        Ver- und Entschlüsselung (Exponentiation):\\
+        \strut\hbox to 3.5cm{\color{red}$\mathcal{O}\!\left((\log n)^2\right)$\hss}
+        \only<16->{{\color{magenta}$\mathcal{O}(n^2)$}}
+      \item
+        Schlüsselerzeugung (Berechnung von $d$):\\
+        \strut\hbox to 3.5cm{\color{red}$\mathcal{O}\!\left((\log n)^2\right)$\hss}
+        \only<16->{{\color{magenta}$\mathcal{O}(n^2)$}}
+      \item
+        Verschlüsselung brechen (Primfaktorzerlegung):\\
+        \strut\hbox to 3.5cm{\color{red}$\mathcal{O}\bigl(2^{\sqrt{\log n\,\cdot\,\log\log n}}\bigr)$\hss}
+        \only<16->{{\color{magenta}$\mathcal{O}\bigl(2^{\sqrt{n\log n}}\bigr)$}}
+    \end{itemize}
+
+    \vspace{0cm plus 1filll}
+
+    \textbf{Die Sicherheit von RSA beruht darauf,
+    daß das Brechen der Verschlüsselung aufwendiger ist als
+    \boldmath$\mathcal{O}\bigl((\log n)^k\bigr)$ (für beliebiges $k$).}
+
+    \vspace*{0.65cm}
+
+  \end{onlyenv}
+
+\end{frame}
+
+\end{document}
diff --git a/20231207/hp-musterloesung-20231207.pdf b/20231207/hp-musterloesung-20231207.pdf
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diff --git a/20231207/hp-musterloesung-20231207.tex b/20231207/hp-musterloesung-20231207.tex
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+% hp-musterloesung-20231207.pdf - Solutions to the Exercises on Low-Level Programming / Applied Computer Sciences
+% Copyright (C) 2013, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023  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: Länge von Strings, Einfügen in Strings (Ergänzung)
+
+\documentclass[a4paper]{article}
+
+\usepackage{pgscript}
+\usepackage{gnuplot-lua-tikz}
+
+\begin{document}
+
+  \section*{Hardwarenahe Programmierung\\
+            Musterlösung zu den Übungsaufgaben -- 7.\ Dezember 2023}
+
+  \exercise{Länge von Strings}
+
+  Strings werden in der Programmiersprache C durch Zeiger auf \lstinline{char}-Variable realisiert.
+
+  Beispiel: \lstinline{char *hello_world = "Hello, world!\n"}
+
+  Die Systembibliothek stellt eine Funktion \lstinline{strlen()} zur Ermittlung der Länge von Strings\\
+  zur Verfügung (\lstinline{#include <string.h>}).
+
+  \begin{enumerate}[\quad(a)]
+    \item
+      Auf welche Weise ist die Länge eines Strings gekennzeichnet?
+      \points{1}
+    \item
+      Wie lang ist die Beispiel-String-Konstante \lstinline{"Hello, world!\n"},
+      und wieviel Speicherplatz belegt sie?\\
+      \points{2}
+    \item
+      Schreiben Sie eine eigene Funktion \lstinline{int strlen (char *s)},
+      die die Länge eines Strings zurückgibt.\\
+      \points{3}
+  \end{enumerate}
+
+  \goodbreak
+
+  Wir betrachten nun die folgenden Funktionen (Datei: \gitfile{hp}{2023ws/20231207}{aufgabe-1.c}):
+  \begin{center}
+    \begin{minipage}{8cm}
+      \begin{lstlisting}[gobble=8]
+        int fun_1 (char *s)
+        {
+          int x = 0;
+          for (int i = 0; i < strlen (s); i++)
+            x += s[i];
+          return x;
+        }
+      \end{lstlisting}
+    \end{minipage}%
+    \begin{minipage}{6cm}
+      \vspace*{-1cm}
+      \begin{lstlisting}[gobble=8]
+        int fun_2 (char *s)
+        {
+          int i = 0, x = 0;
+          int len = strlen (s);
+          while (i < len)
+            x += s[i++];
+          return x;
+        }
+      \end{lstlisting}
+      \vspace*{-1cm}
+    \end{minipage}
+  \end{center}
+  \begin{enumerate}[\quad(a)]\setcounter{enumi}{3}
+    \item
+      Was bewirken die beiden Funktionen?
+      \points{2}
+    \item
+      Schreiben Sie eine eigene Funktion,
+      die dieselbe Aufgabe erledigt wie \lstinline{fun_2()},\\
+      nur effizienter.
+      \points{4}
+    \item
+      Von welcher Ordnung (Landau-Symbol) sind die beiden Funktionen
+      hinsichtlich der Anzahl ihrer Zugriffe auf die Zeichen im String?
+      Begründen Sie Ihre Antwort.
+      Sie dürfen für \lstinline{strlen()} Ihre eigene Version der Funktion voraussetzen.
+       \points{3}
+    \item
+      Von welcher Ordnung (Landau-Symbol) ist Ihre effizientere Funktion?\\
+      Begründen Sie Ihre Antwort.
+      \points{1}
+  \end{enumerate}
+
+  \solution
+
+  \begin{itemize}
+    \item[(a)]
+      \textbf{Auf welche Weise ist die Länge eines Strings gekennzeichnet?}
+
+      Ein String ist ein Array von \lstinline{char}s.
+      Nach den eigentlichen Zeichen des Strings enthält das Array
+      \textbf{ein Null-Symbol} (Zeichen mit Zahlenwert 0,
+      nicht zu verwechseln mit der Ziffer \lstinline{'0'}) als Ende-Markierung.
+      Die Länge eines Strings ist die Anzahl der Zeichen
+      \emph{vor\/} diesem Symbol.
+
+    \item[(b)]
+      {\bf Wie lang ist die Beispiel-String-Konstante \lstinline{"Hello, world!\n"},
+      und wieviel Speicherplatz belegt sie?}
+
+      Sie ist 14 Zeichen lang (\lstinline{'\n'} ist nur 1 Zeichen;
+      das Null-Symbol, das das Ende markiert, zählt hier nicht mit)
+      und belegt Speicherplatz für 15 Zeichen
+      (15 Bytes -- einschließlich Null-Symbol / Ende-Markierung).
+
+    \item[(c)]
+      \textbf{Schreiben Sie eine eigene Funktion \lstinline{int strlen (char *s)},
+      die die Länge eines Strings zurückgibt.}
+
+      Siehe die Dateien \gitfile{hp}{2023ws/20231207}{loesung-1c-1.c} (mit Array-Index)
+      und \gitfile{hp}{2023ws/20231207}{loesung-1c-2.c} (mit Zeiger-Arithmetik).
+      Beide Lösungen sind korrekt und arbeiten gleich schnell.
+
+      Die Warnung \lstinline[style=terminal]{conflicting types for built-in function "strlen"}
+      kann normalerweise ignoriert werden;
+      auf manchen Systemen (z.\,B.\ MinGW) hat jedoch die eingebaute Funktion \lstinline{strlen()}
+      beim Linken Vorrang vor der selbstgeschriebenen,
+      so daß die selbstgeschriebene Funktion nie aufgerufen wird.
+      In solchen Fällen ist es zulässig, die selbstgeschriebene Funktion
+      anders zu nennen (z.\,B.\ \lstinline{my_strlen()}).
+
+    \item[(d)]
+      \textbf{Was bewirken die beiden Funktionen?}
+
+      Beide addieren die Zahlenwerte der im String enthaltenen Zeichen
+      und geben die Summe als Funktionsergebnis zurück.
+
+      Im Falle des Test-Strings \lstinline{"Hello, world!\n"}
+      lautet der Rückgabewert 1171 (siehe \gitfile{hp}{2023ws/20231207}{loesung-1d-1.c} und \gitfile{hp}{2023ws/20231207}{loesung-1d-2.c}).
+
+    \item[(e)]
+      \textbf{Schreiben Sie eine eigene Funktion,
+      die dieselbe Aufgabe erledigt wie \lstinline{fun_2()},
+      nur effizienter.}
+
+      Die Funktion wird effizienter,
+      wenn man auf den Aufruf von \lstinline{strlen()} verzichtet
+      und stattdessen die Ende-Prüfung in derselben Schleife vornimmt,
+      in der man auch die Zahlenwerte der Zeichen des Strings aufsummiert.
+
+      Die Funktion \lstinline{fun_3()} in der Datei \gitfile{hp}{2023ws/20231207}{loesung-1e-1.c}
+      realisiert dies mit einem Array-Index,
+      Die Funktion \lstinline{fun_4()} in der Datei \gitfile{hp}{2023ws/20231207}{loesung-1e-2.c}
+      mit Zeiger-Arithmetik.
+      Beide Lösungen sind korrekt und arbeiten gleich schnell.
+
+      \textbf{Bemerkung:} Die effizientere Version der Funktion
+      arbeitet doppelt so schnell wie die ursprüngliche,
+      hat aber ebenfalls die Ordnung $\mathcal{O}(n)$ -- siehe unten.
+
+    \item[(f)]
+      \textbf{Von welcher Ordnung (Landau-Symbol) sind die beiden Funktionen
+      hinsichtlich der Anzahl ihrer Zugriffe auf die Zeichen im String?
+      Begründen Sie Ihre Antwort.
+      Sie dürfen für \lstinline{strlen()} Ihre eigene Version der Funktion voraussetzen.}
+
+      Vorüberlegung: \lstinline{strlen()} greift in einer Schleife
+      auf alle Zeichen des Strings der Länge $n$ zu,
+      hat also $\mathcal{O}(n)$.
+
+      \lstinline{fun_1()} ruft in jedem Schleifendurchlauf
+      (zum Prüfen der \lstinline{while}-Bedingung) einmal \lstinline{strlen()} auf
+      und greift anschließend auf ein Zeichen des Strings zu,
+      hat also $\mathcal{O}\bigl(n\cdot(n+1)\bigr) = \mathcal{O}(n^2)$.
+
+      \lstinline{fun_2()} ruft einmalig \lstinline{strlen()} auf
+      und greift anschließend in einer Schleife auf alle Zeichen des Strings zu,
+      hat also $\mathcal{O}(n+n) = \mathcal{O}(n)$.
+
+    \item[(g)]
+      \textbf{Von welcher Ordnung (Landau-Symbol) ist Ihre effizientere Funktion?\\
+      Begründen Sie Ihre Antwort.}
+
+      In beiden o.\,a.\ Lösungsvarianten
+      -- \gitfile{hp}{2023ws/20231207}{loesung-1e-1.c}
+      und \gitfile{hp}{2023ws/20231207}{loesung-1e-2.c} --
+      arbeitet die Funktion mit einer einzigen Schleife,
+      die gleichzeitig die Zahlenwerte addiert und das Ende des Strings sucht.
+
+      Mit jeweils einer einzigen Schleife
+      haben beide Funktionen die Ordnung $\mathcal{O}(n)$.
+
+  \end{itemize}
+
+  \exercise{Einfügen in Strings (Ergänzung)}
+
+  Diese Aufgabe ist eine Ergänzung von Aufgabe 3 der Übung vom 31.\ Oktober
+  2022 um die Teilaufgaben (e), (f) und (g). Für den "`Klausur-Modus"' können
+  Sie die Teilaufgaben (a) bis (d) als "`bereits gelöst"' voraussetzen.
+
+  Wir betrachten das folgende Programm (\gitfile{hp}{2023ws/20231207}{aufgabe-2.c}):
+%  \begin{lstlisting}[style=numbered]
+  \begin{lstlisting}
+    #include <stdio.h>
+    #include <string.h>
+
+    void insert_into_string (char src, char *target, int pos)
+    {
+      int len = strlen (target);
+      for (int i = pos; i < len; i++)
+        target[i+1] = target[i];
+      target[pos] = src;
+    }
+
+    int main (void)
+    {
+      char test[100] = "Hochshule Bochum";
+      insert_into_string ('c', test, 5);
+      printf ("%s\n", test);
+      return 0;
+    }
+  \end{lstlisting}
+  Die Ausgabe des Programms lautet:
+  \lstinline[style=terminal]{Hochschhhhhhhhhhh}
+
+  \begin{enumerate}[\quad(a)]
+    \item
+      Erklären Sie, wie die Ausgabe zustandekommt.
+%      \points{3}
+%      \workspace{12}
+    \item
+      Schreiben Sie die Funktion \lstinline|insert_into_string()| so um,
+      daß sie den Buchstaben \lstinline{src} an der Stelle \lstinline{pos}
+      in den String \lstinline{target} einfügt.\par
+      Die Ausgabe des Programms müßte dann
+      \lstinline[style=terminal]{Hochschule Bochum} lauten.
+%      \points{2}
+%      \workspace{13}
+    \item
+      Was kann passieren, wenn Sie die Zeile
+      \lstinline{char test[100] = "Hochshule Bochum";}\\
+      durch
+      \lstinline{char test[] = "Hochshule Bochum";} ersetzen?
+      Begründen Sie Ihre Antwort.
+%      \points{2}
+%      \workspace{10}
+    \item
+      Was kann passieren, wenn Sie die Zeile
+      \lstinline{char test[100] = "Hochshule Bochum";}\\
+      durch
+      \lstinline{char *test = "Hochshule Bochum";} ersetzen?
+      Begründen Sie Ihre Antwort.
+%      \points{2}
+%      \workspace{10}
+    \item
+      Schreiben Sie eine Funktion
+      \lstinline{void insert_into_string_sorted (char src, char *target)},
+      die voraussetzt, daß der String \lstinline{target} alphabetisch sortiert ist
+      und den Buchstaben \lstinline{src} an der alphabetisch richtigen Stelle
+      einfügt. Diese Funktion darf die bereits vorhandene Funktion
+      \lstinline|insert_into_string()| aufrufen.\\
+      \points{4}\par
+      Zum Testen eignen sich die folgenden Zeilen im Hauptprogramm:
+      \begin{lstlisting}[gobble=8]
+        char test[100] = "";
+        insert_into_string_sorted ('c', test);
+        insert_into_string_sorted ('a', test);
+        insert_into_string_sorted ('d', test);
+        insert_into_string_sorted ('b', test);
+      \end{lstlisting}
+      Danach sollte \lstinline{test[]} die Zeichenfolge \lstinline{"abcd"} enthalten.
+%      \workspace{14}
+    \goodbreak
+    \item
+      Wie schnell (Landau-Symbol in Abhängigkeit von der Länge $n$ des Strings)
+      arbeitet Ihre Funktion
+      \lstinline{void insert_into_string_sorted (char src, char *target)}?
+      Begründen Sie Ihre Antwort.
+      \points{1}
+%      \workspace{10}
+    \item
+      Beschreiben Sie -- in Worten oder als C-Quelltext --, wie man die Funktion\\
+      \lstinline{void insert_into_string_sorted (char src, char *target)}
+      so gestalten kann,\\
+      daß sie in $\mathcal{O}(\log n)$ arbeitet.
+      \points{3}
+%      \workspace{35}
+  \end{enumerate}
+
+  \solution
+
+  \textbf{Bemerkung:} Die in dieser Aufgabe und ihrer Musterlösung vorkommenden
+  Funktionen prüfen nicht, ob durch das Einfügen eines Zeichens der für den
+  String reservierte Speicherplatz überläuft. Ein derartiges Verhalten wäre
+  in einem "`echten"' Programm ein \textbf{Fehler}, der katastrophale Folgen
+  haben kann. Wenn dergleichen hier nicht berücksichtigt wird, dann nur, um
+  in einer Klausur nicht den zeitlichen Rahmen zu sprengen.
+
+  \begin{enumerate}[\quad(a)]
+    \setcounter{enumi}{4}
+    \item
+      \textbf{Schreiben Sie eine Funktion
+      \lstinline{void insert_into_string_sorted (char src, char *target)},
+      die voraussetzt, daß der String \lstinline{target} alphabetisch sortiert ist
+      und den Buchstaben \lstinline{src} an der\break alphabetisch richtigen Stelle
+      einfügt. Diese Funktion darf die bereits vorhandene Funktion\break
+      \lstinline|insert_into_string()| aufrufen.}
+      \begin{lstlisting}{gobble=8}
+        void insert_into_string_sorted (char src, char *target)
+        {
+          int i = 0;
+          while (target[i] && target[i] < src)
+            i++;
+          insert_into_string (src, target, i);
+        }
+      \end{lstlisting}
+
+      Die Datei \gitfile{hp}{2023ws/20231207}{loesung-2e.c} enthält die o.\,a.\ Funktion
+      sowie zusätzliche Tests.
+
+    \item
+      \textbf{Wie schnell (Landau-Symbol in Abhängigkeit von der Länge $n$ des Strings)
+      arbeitet Ihre Funktion
+      \lstinline{void insert_into_string_sorted (char src, char *target)}?
+      Begründen Sie Ihre Antwort.}
+
+      Die Funktion sucht im Array \textbf{mittels einer Schleife}
+      nach der korrekten Position zum Einfügen des Zeichens
+      und hat daher von sich aus $\mathcal{O}(n)$.
+
+      Anschließend ruft sie die Funktion \lstinline{insert_into_string()} auf,
+      die ebenfalls eine Schleife verwendet, um im Array Platz zu Einfügen zu schaffen,
+      und daher ebenfalls $\mathcal{O}(n)$ hat.
+
+      Es bleibt daher bei $\mathcal{O}(n)$.
+
+    \item
+      \textbf{Beschreiben Sie -- in Worten oder als C-Quelltext --, wie man die Funktion\\
+      \lstinline{void insert_into_string_sorted (char src, char *target)}
+      so gestalten kann,\\
+      daß sie in $\mathcal{O}(\log n)$ arbeitet.}
+
+      In einem alphabetisch sortierten Array kann man die Suche in der Mitte beginnen
+      und sich durch Halbieren der Intervalle an die gesuchte Position herantasten.
+      Wegen des fortwährenden Halbierens geschieht dies in $\mathcal{O}(\log n)$.
+      (Für eine derartige Antwort gäbe es in der Klausur die volle Punktzahl.)
+
+      Wenn wir allerdings anschließend für das eigentliche Einfügen die Funktion
+      \lstinline{insert_into_string()} verwenden, die dafür $\mathcal{O}(n)$ benötigt,
+      kommen wir insgesamt auf $\mathcal{O}(n)$. Ein sortiertes Einfügen in ein Array
+      ist daher in $\mathcal{O}(\log n)$ nicht möglich.
+      (Wer dies bemerkt, kann zum einen während der Klausur nachfragen,
+      wie denn die Aufgabenstellung genau gemeint ist, und sich zum anderen
+      für die besondere Sorgfalt Zusatzpunkte verdienen.)
+
+      Die Datei \gitfile{hp}{2023ws/20231207}{loesung-2g.c} enthält einen C-Quelltext,
+      die den o.\,a.\ Algorithmus als Funktion implementiert.
+      Man beachte die Behandlung des Spezialfalls,
+      daß das einzufügende Zeichen am Ende angehängt werden muß.
+
+  \end{enumerate}
+
+\end{document}
diff --git a/20231207/hp-uebung-20231207.pdf b/20231207/hp-uebung-20231207.pdf
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diff --git a/20231207/hp-uebung-20231207.tex b/20231207/hp-uebung-20231207.tex
new file mode 100644
index 0000000..c7bcb4a
--- /dev/null
+++ b/20231207/hp-uebung-20231207.tex
@@ -0,0 +1,223 @@
+% hp-uebung-20231207.pdf - Exercises on Low-Level Programming / Applied Computer Sciences
+% Copyright (C) 2013, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023  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: Länge von Strings, Einfügen in Strings (Ergänzung)
+
+\documentclass[a4paper]{article}
+
+\usepackage{pgscript}
+\usepackage{gensymb}
+
+\newcommand{\ItwoC}{I\raisebox{0.5ex}{\footnotesize 2}C}
+\newcommand{\ITWOC}{I\raisebox{0.5ex}{\normalsize 2}C}
+
+\begin{document}
+
+  \thispagestyle{empty}
+
+  \section*{Hardwarenahe Programmierung\\
+            Übungsaufgaben -- 7.\ Dezember 2023}
+
+  Diese Übung enthält Punkteangaben wie in einer Klausur.
+  Um zu "`bestehen"', müssen Sie innerhalb von 70 Minuten
+  unter Verwendung ausschließlich zugelassener Hilfsmittel
+  12 Punkte (von insgesamt \totalpoints) erreichen.
+
+  \exercise{Länge von Strings}
+
+  Strings werden in der Programmiersprache C durch Zeiger auf \lstinline{char}-Variable realisiert.
+
+  Beispiel: \lstinline{char *hello_world = "Hello, world!\n"}
+
+  Die Systembibliothek stellt eine Funktion \lstinline{strlen()} zur Ermittlung der Länge von Strings\\
+  zur Verfügung (\lstinline{#include <string.h>}).
+
+  \begin{enumerate}[\quad(a)]
+    \item
+      Auf welche Weise ist die Länge eines Strings gekennzeichnet?
+      \points{1}
+    \item
+      Wie lang ist die Beispiel-String-Konstante \lstinline{"Hello, world!\n"},
+      und wieviel Speicherplatz belegt sie?\\
+      \points{2}
+    \item
+      Schreiben Sie eine eigene Funktion \lstinline{int strlen (char *s)},
+      die die Länge eines Strings zurückgibt.\\
+      \points{3}
+  \end{enumerate}
+
+  \goodbreak
+
+  Wir betrachten nun die folgenden Funktionen (Datei: \gitfile{hp}{2023ws/20231207}{aufgabe-1.c}):
+  \begin{center}
+    \begin{minipage}{8cm}
+      \begin{lstlisting}[gobble=8]
+        int fun_1 (char *s)
+        {
+          int x = 0;
+          for (int i = 0; i < strlen (s); i++)
+            x += s[i];
+          return x;
+        }
+      \end{lstlisting}
+    \end{minipage}%
+    \begin{minipage}{6cm}
+      \vspace*{-1cm}
+      \begin{lstlisting}[gobble=8]
+        int fun_2 (char *s)
+        {
+          int i = 0, x = 0;
+          int len = strlen (s);
+          while (i < len)
+            x += s[i++];
+          return x;
+        }
+      \end{lstlisting}
+      \vspace*{-1cm}
+    \end{minipage}
+  \end{center}
+  \begin{enumerate}[\quad(a)]\setcounter{enumi}{3}
+    \item
+      Was bewirken die beiden Funktionen?
+      \points{2}
+    \item
+      Schreiben Sie eine eigene Funktion,
+      die dieselbe Aufgabe erledigt wie \lstinline{fun_2()},\\
+      nur effizienter.
+      \points{4}
+    \item
+      Von welcher Ordnung (Landau-Symbol) sind die beiden Funktionen
+      hinsichtlich der Anzahl ihrer Zugriffe auf die Zeichen im String?
+      Begründen Sie Ihre Antwort.
+      Sie dürfen für \lstinline{strlen()} Ihre eigene Version der Funktion voraussetzen.
+       \points{3}
+    \item
+      Von welcher Ordnung (Landau-Symbol) ist Ihre effizientere Funktion?\\
+      Begründen Sie Ihre Antwort.
+      \points{1}
+  \end{enumerate}
+
+  \clearpage
+  \exercise{Einfügen in Strings (Ergänzung)}
+
+  Diese Aufgabe ist eine Ergänzung von Aufgabe 3 der Übung vom 2.\ November 2023
+  um die Teilaufgaben (e), (f) und (g). Für den "`Klausur-Modus"' können
+  Sie die Teilaufgaben (a) bis (d) als "`bereits gelöst"' voraussetzen.
+
+  Wir betrachten das folgende Programm (\gitfile{hp}{2023ws/20231207}{aufgabe-2.c}):
+%  \begin{lstlisting}[style=numbered]
+  \begin{lstlisting}
+    #include <stdio.h>
+    #include <string.h>
+
+    void insert_into_string (char src, char *target, int pos)
+    {
+      int len = strlen (target);
+      for (int i = pos; i < len; i++)
+        target[i+1] = target[i];
+      target[pos] = src;
+    }
+
+    int main (void)
+    {
+      char test[100] = "Hochshule Bochum";
+      insert_into_string ('c', test, 5);
+      printf ("%s\n", test);
+      return 0;
+    }
+  \end{lstlisting}
+  Die Ausgabe des Programms lautet:
+  \lstinline[style=terminal]{Hochschhhhhhhhhhh}
+
+  \begin{enumerate}[\quad(a)]
+    \item
+      Erklären Sie, wie die Ausgabe zustandekommt.
+%      \points{3}
+%      \workspace{12}
+    \item
+      Schreiben Sie die Funktion \lstinline|insert_into_string()| so um,
+      daß sie den Buchstaben \lstinline{src} an der Stelle \lstinline{pos}
+      in den String \lstinline{target} einfügt.\par
+      Die Ausgabe des Programms müßte dann
+      \lstinline[style=terminal]{Hochschule Bochum} lauten.
+%      \points{2}
+%      \workspace{13}
+    \item
+      Was kann passieren, wenn Sie die Zeile
+      \lstinline{char test[100] = "Hochshule Bochum";}\\
+      durch
+      \lstinline{char test[] = "Hochshule Bochum";} ersetzen?
+      Begründen Sie Ihre Antwort.
+%      \points{2}
+%      \workspace{10}
+    \item
+      Was kann passieren, wenn Sie die Zeile
+      \lstinline{char test[100] = "Hochshule Bochum";}\\
+      durch
+      \lstinline{char *test = "Hochshule Bochum";} ersetzen?
+      Begründen Sie Ihre Antwort.
+%      \points{2}
+%      \workspace{10}
+    \item
+      Schreiben Sie eine Funktion
+      \lstinline{void insert_into_string_sorted (char src, char *target)},
+      die voraussetzt, daß der String \lstinline{target} alphabetisch sortiert ist
+      und den Buchstaben \lstinline{src} an der alphabetisch richtigen Stelle
+      einfügt. Diese Funktion darf die bereits vorhandene Funktion
+      \lstinline|insert_into_string()| aufrufen.\\
+      \points{4}\par
+      Zum Testen eignen sich die folgenden Zeilen im Hauptprogramm:
+      \begin{lstlisting}[gobble=8]
+        char test[100] = "";
+        insert_into_string_sorted ('c', test);
+        insert_into_string_sorted ('a', test);
+        insert_into_string_sorted ('d', test);
+        insert_into_string_sorted ('b', test);
+      \end{lstlisting}
+      Danach sollte \lstinline{test[]} die Zeichenfolge \lstinline{"abcd"} enthalten.
+%      \workspace{14}
+    \goodbreak
+    \item
+      Wie schnell (Landau-Symbol in Abhängigkeit von der Länge $n$ des Strings)
+      arbeitet Ihre Funktion
+      \lstinline{void insert_into_string_sorted (char src, char *target)}?
+      Begründen Sie Ihre Antwort.
+      \points{1}
+%      \workspace{10}
+    \item
+      Beschreiben Sie -- in Worten oder als C-Quelltext --, wie man die Funktion\\
+      \lstinline{void insert_into_string_sorted (char src, char *target)}
+      so gestalten kann,\\
+      daß sie in $\mathcal{O}(\log n)$ arbeitet.
+      \points{3}
+%      \workspace{35}
+  \end{enumerate}
+
+  \begin{flushright}
+    \textit{Viel Erfolg!}
+  \end{flushright}
+
+  \makeatletter
+    \immediate\write\@mainaux{\string\gdef\string\totalpoints{\arabic{points}}}
+  \makeatother
+
+\end{document}
diff --git a/20231207/landau-symbols-2.pdf b/20231207/landau-symbols-2.pdf
new file mode 120000
index 0000000..6b458b6
--- /dev/null
+++ b/20231207/landau-symbols-2.pdf
@@ -0,0 +1 @@
+../common/landau-symbols-2.pdf
\ No newline at end of file
diff --git a/20231207/landau-symbols-3.pdf b/20231207/landau-symbols-3.pdf
new file mode 120000
index 0000000..46efa40
--- /dev/null
+++ b/20231207/landau-symbols-3.pdf
@@ -0,0 +1 @@
+../common/landau-symbols-3.pdf
\ No newline at end of file
diff --git a/20231207/landau-symbols.pdf b/20231207/landau-symbols.pdf
new file mode 120000
index 0000000..ca14542
--- /dev/null
+++ b/20231207/landau-symbols.pdf
@@ -0,0 +1 @@
+../common/landau-symbols.pdf
\ No newline at end of file
diff --git a/20231207/loesung-1-c-1.c b/20231207/loesung-1-c-1.c
new file mode 100644
index 0000000..69ddd0e
--- /dev/null
+++ b/20231207/loesung-1-c-1.c
@@ -0,0 +1,15 @@
+#include <stdio.h>
+
+int strlen (char *s)
+{
+  int l = 0;
+  while (s[l])
+    l++;
+  return l;
+}
+
+int main (void)
+{
+  printf ("%d\n", strlen ("Hello, world!\n"));
+  return 0;
+}
diff --git a/20231207/loesung-1-c-2.c b/20231207/loesung-1-c-2.c
new file mode 100644
index 0000000..e783c47
--- /dev/null
+++ b/20231207/loesung-1-c-2.c
@@ -0,0 +1,15 @@
+#include <stdio.h>
+
+int strlen (char *s)
+{
+  char *s0 = s;
+  while (*s)
+    s++;
+  return s - s0;
+}
+
+int main (void)
+{
+  printf ("%d\n", strlen ("Hello, world!\n"));
+  return 0;
+}
diff --git a/20231207/loesung-1-d-1.c b/20231207/loesung-1-d-1.c
new file mode 100644
index 0000000..5752138
--- /dev/null
+++ b/20231207/loesung-1-d-1.c
@@ -0,0 +1,34 @@
+
+#include <stdio.h>
+
+int strlen (char *s)
+{
+  int l = 0;
+  while (s[l])
+    l++;
+  return l;
+}
+
+int fun_1 (char *s)
+{
+  int x = 0;
+  for (int i = 0; i < strlen (s); i++)
+    x += s[i];
+  return x;
+}
+
+int fun_2 (char *s)
+{
+  int i = 0, x = 0;
+  int len = strlen (s);
+  while (i < len)
+    x += s[i++];
+  return x;
+}
+
+int main (void)
+{
+  printf ("%d\n", fun_1 ("Hello, world!\n"));
+  printf ("%d\n", fun_2 ("Hello, world!\n"));
+  return 0;
+}
diff --git a/20231207/loesung-1-d-2.c b/20231207/loesung-1-d-2.c
new file mode 100644
index 0000000..5f3f096
--- /dev/null
+++ b/20231207/loesung-1-d-2.c
@@ -0,0 +1,34 @@
+
+#include <stdio.h>
+
+int strlen (char *s)
+{
+  char *s0 = s;
+  while (*s)
+    s++;
+  return s - s0;
+}
+
+int fun_1 (char *s)
+{
+  int x = 0;
+  for (int i = 0; i < strlen (s); i++)
+    x += s[i];
+  return x;
+}
+
+int fun_2 (char *s)
+{
+  int i = 0, x = 0;
+  int len = strlen (s);
+  while (i < len)
+    x += s[i++];
+  return x;
+}
+
+int main (void)
+{
+  printf ("%d\n", fun_1 ("Hello, world!\n"));
+  printf ("%d\n", fun_2 ("Hello, world!\n"));
+  return 0;
+}
diff --git a/20231207/loesung-1-e-1.c b/20231207/loesung-1-e-1.c
new file mode 100644
index 0000000..74f5add
--- /dev/null
+++ b/20231207/loesung-1-e-1.c
@@ -0,0 +1,15 @@
+#include <stdio.h>
+
+int fun_3 (char *s)
+{
+  int i = 0, x = 0;
+  while (s[i])
+    x += s[i++];
+  return x;
+}
+
+int main (void)
+{
+  printf ("%d\n", fun_3 ("Hello, world!\n"));
+  return 0;
+}
diff --git a/20231207/loesung-1-e-2.c b/20231207/loesung-1-e-2.c
new file mode 100644
index 0000000..b223d2d
--- /dev/null
+++ b/20231207/loesung-1-e-2.c
@@ -0,0 +1,15 @@
+#include <stdio.h>
+
+int fun_4 (char *s)
+{
+  int x = 0;
+  while (*s)
+    x += *s++;
+  return x;
+}
+
+int main (void)
+{
+  printf ("%d\n", fun_4 ("Hello, world!\n"));
+  return 0;
+}
diff --git a/20231207/loesung-2e.c b/20231207/loesung-2e.c
new file mode 100644
index 0000000..bc41fb0
--- /dev/null
+++ b/20231207/loesung-2e.c
@@ -0,0 +1,33 @@
+#include <stdio.h>
+#include <string.h>
+
+void insert_into_string (char src, char *target, int pos)
+{
+  int len = strlen (target);
+  for (int i = len; i >= pos; i--)
+    target[i + 1] = target[i];
+  target[pos] = src;
+}
+
+void insert_into_string_sorted (char src, char *target)
+{
+  int i = 0;
+  while (target[i] && target[i] < src)
+    i++;
+  insert_into_string (src, target, i);
+}
+
+int main (void)
+{
+  char test[100] = "";
+  insert_into_string_sorted ('c', test);
+  insert_into_string_sorted ('a', test);
+  insert_into_string_sorted ('d', test);
+  insert_into_string_sorted ('b', test);
+  printf ("test = \"%s\"\n", test);
+  for (char ch = 'e'; ch < 'z'; ch += 2)
+    insert_into_string_sorted (ch, test);
+  insert_into_string_sorted ('n', test);
+  printf ("test = \"%s\"\n", test);
+  return 0;
+}
diff --git a/20231207/loesung-2g.c b/20231207/loesung-2g.c
new file mode 100644
index 0000000..4b0c29d
--- /dev/null
+++ b/20231207/loesung-2g.c
@@ -0,0 +1,46 @@
+#include <stdio.h>
+#include <string.h>
+
+void insert_into_string (char src, char *target, int pos)
+{
+  int len = strlen (target);
+  for (int i = len; i >= pos; i--)
+    target[i + 1] = target[i];
+  target[pos] = src;
+}
+
+void insert_into_string_sorted (char src, char *target)
+{
+  int l = 0;
+  int r = 0;
+  while (target[r])
+    r++;
+  int m = (l + r) / 2;
+  while (m > l)
+    {
+      if (src < target[m])
+        r = m;
+      else
+        l = m;
+      m = (l + r) / 2;
+    }
+  if (target[m] == 0 || src < target[m])
+    insert_into_string (src, target, m);
+  else
+    insert_into_string (src, target, m + 1);
+}
+
+int main (void)
+{
+  char test[100] = "";
+  insert_into_string_sorted ('c', test);
+  insert_into_string_sorted ('a', test);
+  insert_into_string_sorted ('d', test);
+  insert_into_string_sorted ('b', test);
+  printf ("test = \"%s\"\n", test);
+  for (char ch = 'e'; ch < 'z'; ch += 2)
+    insert_into_string_sorted (ch, test);
+  insert_into_string_sorted ('n', test);
+  printf ("test = \"%s\"\n", test);
+  return 0;
+}
diff --git a/20231207/logo-hochschule-bochum-cvh-text-v2.pdf b/20231207/logo-hochschule-bochum-cvh-text-v2.pdf
new file mode 120000
index 0000000..4aa99b8
--- /dev/null
+++ b/20231207/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/20231207/logo-hochschule-bochum.pdf b/20231207/logo-hochschule-bochum.pdf
new file mode 120000
index 0000000..b6b9491
--- /dev/null
+++ b/20231207/logo-hochschule-bochum.pdf
@@ -0,0 +1 @@
+../common/logo-hochschule-bochum.pdf
\ No newline at end of file
diff --git a/20231207/pendulum.pdf b/20231207/pendulum.pdf
new file mode 120000
index 0000000..7d1d873
--- /dev/null
+++ b/20231207/pendulum.pdf
@@ -0,0 +1 @@
+../common/pendulum.pdf
\ No newline at end of file
diff --git a/20231207/pgscript.sty b/20231207/pgscript.sty
new file mode 120000
index 0000000..95c8884
--- /dev/null
+++ b/20231207/pgscript.sty
@@ -0,0 +1 @@
+../common/pgscript.sty
\ No newline at end of file
diff --git a/20231207/pgslides.sty b/20231207/pgslides.sty
new file mode 120000
index 0000000..5be1416
--- /dev/null
+++ b/20231207/pgslides.sty
@@ -0,0 +1 @@
+../common/pgslides.sty
\ No newline at end of file
diff --git a/README.md b/README.md
index e381558..44ce3fc 100644
--- a/README.md
+++ b/README.md
@@ -25,6 +25,8 @@ Vortragsfolien und Beispiele:
  * [09.11.2023: Hardwarenahe Programmierung](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231109/hp-20231109.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2023ws/20231109/)
  * [16.11.2023: Byte-Reihenfolge, Darstellung negativer Zahlen, Darstellung von Gleitkommazahlen](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231116/hp-20231116.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2023ws/20231116/)
  * [23.11.2023: Speicherausrichtung, Algorithmen: Differentialgleichungen](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231123/hp-20231123.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2023ws/20231123/)
+ * [30.11.2023: Algorithmen: Rekursion](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231130/hp-20231130.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2023ws/20231130/)
+ * [07.12.2023: Algorithmen: Aufwandsabschätzungen](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231207/hp-20231207.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2023ws/20231207/)
  * [alle in 1 Datei](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/hp-slides-2023ws.pdf)
 
 Übungsaufgaben:
@@ -37,6 +39,8 @@ Vortragsfolien und Beispiele:
  * [09.11.2023: Text-Grafik-Bibliothek, Mikrocontroller, LED-Blinkmuster](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231109/hp-uebung-20231109.pdf)
  * [16.11.2023: Trickprogrammierung, Thermometer-Baustein an I²C-Bus, Speicherformate von Zahlen](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231116/hp-uebung-20231116.pdf)
  * [23.11.2023: Kondensator, Personen-Datenbank, Hexdumps](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231123/hp-uebung-20231123.pdf)
+ * [30.11.2023: PBM-Grafik, Fakultät](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231130/hp-uebung-20231130.pdf)
+ * [07.12.2023: Länge von Strings, Einfügen in Strings (Ergänzung)](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231207/hp-uebung-20231207.pdf)
 
 Musterlösungen:
 ---------------
@@ -47,6 +51,8 @@ Musterlösungen:
  * [09.11.2023: Text-Grafik-Bibliothek, Mikrocontroller, LED-Blinkmuster](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231109/hp-musterloesung-20231109.pdf)
  * [16.11.2023: Trickprogrammierung, Thermometer-Baustein an I²C-Bus, Speicherformate von Zahlen](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231116/hp-musterloesung-20231116.pdf)
  * [23.11.2023: Kondensator, Personen-Datenbank, Hexdumps](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231123/hp-musterloesung-20231123.pdf)
+ * [30.11.2023: PBM-Grafik, Fakultät](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231130/hp-musterloesung-20231130.pdf)
+ * [07.12.2023: Länge von Strings, Einfügen in Strings (Ergänzung)](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231207/hp-musterloesung-20231207.pdf)
 
 Praktikumsunterlagen:
 ---------------------
diff --git a/hp-slides-2023ws.pdf b/hp-slides-2023ws.pdf
index 4194a11bffce9b374c9a4ac056895cf9b987e760..474638caa45a31f260a04f713643fb47f4f44ce0 100644
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diff --git a/hp-slides-2023ws.tex b/hp-slides-2023ws.tex
index f577a24..56ca81f 100644
--- a/hp-slides-2023ws.tex
+++ b/hp-slides-2023ws.tex
@@ -25,6 +25,10 @@
   \includepdf[pages=-]{20231109/hp-20231109.pdf}
   \pdfbookmark[1]{16.11.2023: Byte-Reihenfolge, Darstellung negativer Zahlen, Darstellung von Gleitkommazahlen}{20231116}
   \includepdf[pages=-]{20231116/hp-20231116.pdf}
-  \pdfbookmark[1]{23.11.2023: Speicherausrichtung}{20231123}
+  \pdfbookmark[1]{23.11.2023: Speicherausrichtung, Algorithmen: Differentialgleichungen}{20231123}
   \includepdf[pages=-]{20231123/hp-20231123.pdf}
+  \pdfbookmark[1]{30.11.2023: Algorithmen: Rekursion}{20231130}
+  \includepdf[pages=-]{20231130/hp-20231130.pdf}
+  \pdfbookmark[1]{07.12.2023: Algorithmen: Aufwandsabschätzungen}{20231207}
+  \includepdf[pages=-]{20231207/hp-20231207.pdf}
 \end{document}
-- 
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