From 39a66b609d539957b88a7615c15985b07116c806 Mon Sep 17 00:00:00 2001
From: Peter Gerwinski <peter.gerwinski@hs-bochum.de>
Date: Thu, 28 Nov 2019 15:13:34 +0100
Subject: [PATCH] =?UTF-8?q?Musterl=C3=B6sung=2014.11.2019?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 20191114/hp-musterloesung-20191114.pdf | Bin 0 -> 79595 bytes
 20191114/hp-musterloesung-20191114.tex | 458 +++++++++++++++++++++++++
 20191114/loesung-1-1.c                 |  22 ++
 20191114/loesung-1-2.c                 |  26 ++
 20191114/loesung-1-3.c                 |  29 ++
 20191114/loesung-1-4.c                 |  31 ++
 20191114/loesung-1-5.c                 |  29 ++
 20191114/loesung-1-6.c                 |  23 ++
 20191114/loesung-2.c                   |  18 +
 20191114/loesung-3c-1.c                |  15 +
 20191114/loesung-3c-2.c                |  15 +
 20191114/loesung-3d-1.c                |  34 ++
 20191114/loesung-3d-2.c                |  34 ++
 20191114/loesung-3e-1.c                |  15 +
 20191114/loesung-3e-2.c                |  15 +
 15 files changed, 764 insertions(+)
 create mode 100644 20191114/hp-musterloesung-20191114.pdf
 create mode 100644 20191114/hp-musterloesung-20191114.tex
 create mode 100644 20191114/loesung-1-1.c
 create mode 100644 20191114/loesung-1-2.c
 create mode 100644 20191114/loesung-1-3.c
 create mode 100644 20191114/loesung-1-4.c
 create mode 100644 20191114/loesung-1-5.c
 create mode 100644 20191114/loesung-1-6.c
 create mode 100644 20191114/loesung-2.c
 create mode 100644 20191114/loesung-3c-1.c
 create mode 100644 20191114/loesung-3c-2.c
 create mode 100644 20191114/loesung-3d-1.c
 create mode 100644 20191114/loesung-3d-2.c
 create mode 100644 20191114/loesung-3e-1.c
 create mode 100644 20191114/loesung-3e-2.c

diff --git a/20191114/hp-musterloesung-20191114.pdf b/20191114/hp-musterloesung-20191114.pdf
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+% hp-musterloesung-20191114.pdf - Solutions to the Exercises on Low-Level Programming
+% Copyright (C) 2013, 2015, 2016, 2017, 2018, 2019  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: Ausgabe von Hexadezimalzahlen, Einfügen in Strings, Länge von Strings
+
+\documentclass[a4paper]{article}
+
+\usepackage{pgscript}
+
+\begin{document}
+
+  \section*{Hardwarenahe Programmierung\\
+            Musterlösung zu den Übungsaufgaben -- 14.\ November 2019}
+
+  \exercise{Ausgabe von Hexadezimalzahlen}
+
+  Schreiben Sie eine Funktion \lstinline{void print_hex (uint32_t x)},
+  die eine gegebene vorzeichenlose 32-Bit-Ganzzahl \lstinline{x}
+  als Hexadezimalzahl ausgibt.
+  (Der Datentyp \lstinline{uint32_t} ist mit \lstinline{#include <stdint.h>} verfügbar.)
+
+  Verwenden Sie dafür \emph{nicht\/} \lstinline{printf()} mit
+  der Formatspezifikation \lstinline{%x} als fertige Lösung,
+  sondern programmieren Sie die nötige Ausgabe selbst.
+  (Für Tests ist \lstinline{%x} hingegen erlaubt und sicherlich nützlich.)
+
+  Die Verwendung von \lstinline{printf()}
+  mit anderen Formatspezifikationen wie z.\,B.\ \lstinline{%d}
+  oder \lstinline{%c} oder \lstinline{%s} ist hingegen zulässig.
+
+  \points{8}
+
+  (Hinweis für die Klausur: Abgabe auf Datenträger ist erlaubt und erwünscht,
+  aber nicht zwingend.)
+
+  \solution
+
+  Um die Ziffern von \lstinline{x} zur Basis 16 zu isolieren,
+  berechnen wir \lstinline{x % 16} (modulo 16 = Rest bei Division durch 16)
+  und dividieren anschließend \lstinline{x} durch 16,
+  solange bis \lstinline{x} den Wert 0 erreicht.
+
+  Wenn wir die auf diese Weise ermittelten Ziffern direkt ausgeben,
+  sind sie \emph{Little-Endian}, erscheinen also in umgekehrter Reihenfolge.
+  Die Datei \gitfile{hp}{20191114}{loesung-1-1.c} setzt diesen Zwischenschritt um.
+
+  Die Ausgabe der Ziffern erfolgt in \gitfile{hp}{20191114}{loesung-1-1.c}
+  über \lstinline{printf ("%d")}
+  für die Ziffern 0 bis 9. Für die darüberliegenden Ziffern
+  wird der Buchstabe \lstinline{a} um die Ziffer abzüglich 10 inkrementiert
+  und der erhaltene Wert mit \lstinline{printf ("%c")} als Zeichen ausgegeben.
+
+  Um die umgekehrte Reihenfolge zu beheben,
+  speichern wir die Ziffern von \lstinline{x}
+  in einem Array \lstinline{digits[]} zwischen
+  und geben sie anschließend in einer zweiten Schleife
+  in umgekehrter Reihenfolge aus (siehe \gitfile{hp}{20191114}{loesung-1-2.c}).
+  Da wir wissen, daß \lstinline{x} eine 32-Bit-Zahl ist
+  und daher höchstens 8 Hexadezimalziffern haben kann,
+  ist 8 eine sinnvolle Länge für das Ziffern-Array \lstinline{digits[8]}.
+
+  Nun sind die Ziffern in der richtigen Reihenfolge,
+  aber wir erhalten zusätzlich zu den eigentlichen Ziffern führende Nullen.
+  Da in der Aufgabenstellung nicht von führenden Nullen die Rede war,
+  sind diese nicht verboten; \gitfile{hp}{20191114}{loesung-1-2.c} ist daher
+  eine richtige Lösung der Aufgabe.
+
+  \breath
+
+  Wenn wir die führenden Nullen vermeiden wollen,
+  können wir die \lstinline{for}-Schleifen durch \lstinline{while}-Schleifen ersetzen.
+  Die erste Schleife zählt hoch, solange \lstinline{x} ungleich 0 ist;
+  die zweite zählt von dem erreichten Wert aus wieder herunter
+  -- siehe \gitfile{hp}{20191114}{loesung-1-3.c}.
+  Da wir wissen, daß die Zahl \lstinline{x} höchstens 32 Bit,
+  also höchstens 8 Hexadezimalziffern hat,
+  wissen wir, daß \lstinline{i} höchstens den Wert 8 erreichen kann,
+  das Array also nicht überlaufen wird.
+
+  Man beachte, daß der Array-Index nach der ersten Schleife "`um einen zu hoch"' ist.
+  In der zweiten Schleife muß daher \emph{zuerst\/} der Index dekrementiert werden.
+  Erst danach darf ein Zugriff auf \lstinline{digit[i]} erfolgen.
+
+  \breath
+
+  Alternativ können wir auch mitschreiben,
+  ob bereits eine Ziffer ungleich Null ausgegeben wurde,
+  und andernfalls die Ausgabe von Null-Ziffern unterdrücken
+  -- siehe \gitfile{hp}{20191114}{loesung-1-4.c}.
+
+  \breath
+
+  Weitere Möglichkeiten ergeben sich, wenn man bedenkt,
+  daß eine Hexadezimalziffer genau einer Gruppe von vier Binärziffern entspricht.
+  Eine Bitverschiebung um 4 nach rechts
+  ist daher dasselbe wie eine Division durch 16,
+  und eine Und-Verknüpfung mit 15$_{10}$ = f$_{16}$ = 1111$_2$
+  ist dasselbe wie die Operation Modulo 16.
+  Die Datei \gitfile{hp}{20191114}{loesung-1-5.c} ist eine in dieser Weise abgewandelte Variante
+  von \gitfile{hp}{20191114}{loesung-1-3.c}.
+
+  Mit dieser Methode kann man nicht nur auf die jeweils unterste Ziffer,
+  sondern auf alle Ziffern direkt zugreifen.
+  Damit ist kein Array als zusätzlicher Speicher mehr nötig.
+  Die Datei \gitfile{hp}{20191114}{loesung-1-6.c} setzt dies auf einfache Weise um.
+  Sie gibt wieder führende Nullen mit aus,
+  ist aber trotzdem eine weitere richtige Lösung der Aufgabe.
+
+  Die führenden Nullen ließen sich auf die gleiche Weise vermeiden
+  wie in \gitfile{hp}{20191114}{loesung-1-4.c}.
+
+  Die Bitverschiebungsmethode hat den Vorteil,
+  daß kein zusätzliches Array benötigt wird.
+  Auch wird die als Parameter übergebene Zahl \lstinline{x} nicht verändert,
+  was bei größeren Zahlen, die über Zeiger übergeben werden, von Vorteil sein kann.
+  Demgegenüber steht der Nachteil,
+  daß diese Methode nur für eine ganze Anzahl von Bits funktioniert,
+  also für Basen, die Zweierpotenzen sind (z.\,B.\ 2, 8, 16, 256).
+  Für alle anderen Basen (z.\,B.\ 10) eignet sich nur die Methode
+  mit Division und Modulo-Operation.
+
+  \exercise{Einfügen in Strings}
+
+  Wir betrachten das folgende Programm (\gitfile{hp}{20191114}{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}
+%    \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)}
+%      und warum?
+%      \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
+
+  \begin{enumerate}[\quad(a)]
+    \item
+      \textbf{Erklären Sie, wie die Ausgabe zustandekommt.}
+
+      In der Schleife wird \emph{zuerst\/} der nächste Buchstabe \lstinline{target[i + 1]}
+      gleich dem aktuellen gesetzt
+      und \emph{danach\/} der Zähler \lstinline{i} erhöht.
+      Dadurch wird im nächsten Schleifendurchlauf der bereits verschobene Buchstabe
+      noch weiter geschoben und letztlich alle Buchstaben in \lstinline{target[]}
+      durch den an der Stelle \lstinline{pos} ersetzt.
+
+    \item
+      \textbf{Schreiben Sie die Funktion \lstinline|insert_into_string()| so um,
+      daß sie den Buchstben \lstinline{src} an der Stelle \lstinline{pos}
+      in den String \lstinline{target} einfügt.}\par
+      \textbf{Die Ausgabe des Programms müßte dann
+      \lstinline[style=terminal]{Hochschule Bochum} lauten.}
+
+      Um im String "`Platz zu schaffen"', muß man von hinten beginnen,
+      also die Schleife umdrehen\\
+      (siehe: \gitfile{hp}{20191114}{loesung-2.c}):
+      \begin{lstlisting}{gobble=8}
+        for (int i = len; i > pos; i++)
+          target[i] = target[i - 1];
+      \end{lstlisting}
+
+    \item
+      \textbf{Was kann passieren, wenn Sie die Zeile
+      \lstinline{char test[100] = "Hochshule Bochum";}\\
+      durch
+      \lstinline{char test[] = "Hochshule Bochum";}
+      ersetzen und warum?}
+
+      Die Schreibweise \lstinline{test[]} bedeutet,
+      daß der Compiler selbst zählt, wieviel Speicherplatz der String benötigt,
+      un dann genau die richtige Menge Speicher reserviert
+      (anstatt, wie wir es manuell getan haben, pauschal Platz für 100 Zeichen).
+
+      Wenn wir nun in den String ein zusätzliches Zeichen einfügen,
+      ist dafür kein Speicherplatz reserviert worden,
+      und wir \textbf{überschreiben} dann Speicher, an dem sich andere Variablen befinden,
+      was zu einem \textbf{Absturz} führen kann.
+
+      Da wir hier nur ein einziges Zeichen schreiben,
+      wird dieser Fehler nicht sofort auffallen.
+      Dies ist schlimmer, als wenn das Programm direkt beim ersten Test abstürzt,
+      denn dadurch entsteht bei uns der Eindruck, es sei in Ordnung.
+      Wenn danach der Fehler in einer Produktivumgebung auftritt,
+      kann dadurch Schaden entstehen -- je nach Einsatzgebiet der Software
+      u.\,U.\ erheblicher Vermögens-, Sach- und/oder Personenschaden
+      (z.\,B.\ Absturz eines Raumflugkörpers).
+
+    \item
+      \textbf{Was kann passieren, wenn Sie 
+      \lstinline{char test[100] = "Hochshule Bochum";}\\
+      durch
+      \lstinline{char *test = "Hochshule Bochum";}
+      ersetzen und warum?}
+
+      In diesem Fall wird der Speicher für den eigentlichen String
+      in einem unbenannten, \textbf{nicht schreibbaren} Teil des Speichers reserviert.
+      Unser Versuch, dorthin ein zusätzliches Zeichen zu schreiben,
+      fürt dann normalerweise zu einem \textbf{Absturz}.
+
+      In manchen Systemen (Betriebssystem, Compiler, \dots)
+      ist der Speicherbereich tatsächlich sehr wohl schreibbar.
+      In diesem Fall tritt der Absturz nicht immer und nicht immer sofort auf --
+      genau wie in Aufgabenteil (c).
+     
+  \end{enumerate}
+
+  \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{itemize}
+    \item[(a)]
+      Auf welche Weise ist die Länge eines Strings gekennzeichnet?
+      \points{1}
+    \item[(b)]
+      Wie lang ist die Beispiel-String-Konstante \lstinline{"Hello, world!\n"},
+      und wieviel Speicherplatz belegt sie?\\
+      \points{2}
+    \item[(c)]
+      Schreiben Sie eine eigene Funktion \lstinline{int strlen (char *s)},
+      die die Länge eines Strings zurückgibt.\\
+      \points{3}
+  \end{itemize}
+
+  Wir betrachten nun die folgenden Funktionen (Datei: \gitfile{hp}{20191114}{aufgabe-3.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{itemize}
+    \item[(d)]
+      Was bewirken die beiden Funktionen?
+      \points{2}
+    \item[(e)]
+%      Von welcher Ordnung (Landau-Symbol) sind die beiden Funktionen
+%      hinsichtlich der Anzahl ihrer Zugriffe auf die Zeichen im String -- und warum?
+%      Sie dürfen für \lstinline{strlen()} Ihre eigene Version der Funktion voraussetzen.
+%       \points 3
+%    \item[(f)]
+      Schreiben Sie eine eigene Funktion,
+      die dieselbe Aufgabe erledigt wie \lstinline{fun_2()},\\
+      nur effizienter.
+      \points{4}
+  \end{itemize}
+
+  \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}{20191114}{loesung-3c-1.c} (mit Array-Index)
+      und \gitfile{hp}{20191114}{loesung-3c-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}{20191114}{loesung-3d-1.c} und \gitfile{hp}{20191114}{loesung-3d-2.c}).
+
+    \item[(e)]
+%      \textbf{Von welcher Ordnung (Landau-Symbol) sind die beiden Funktionen
+%      hinsichtlich der Anzahl ihrer Zugriffe auf die Zeichen im String -- und warum?
+%      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[(f)]
+      \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}{20191114}{loesung-3e-1.c}
+      realisiert dies mit einem Array-Index,
+      Die Funktion \lstinline{fun_4()} in der Datei \gitfile{hp}{20191114}{loesung-3e-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 $\mathcal{O}(n)$.
+
+  \end{itemize}
+
+\end{document}
diff --git a/20191114/loesung-1-1.c b/20191114/loesung-1-1.c
new file mode 100644
index 0000000..98b2f03
--- /dev/null
+++ b/20191114/loesung-1-1.c
@@ -0,0 +1,22 @@
+#include <stdio.h>
+#include <stdint.h>
+
+void print_hex (uint32_t x)
+{
+  while (x)
+    {
+      int digit = x % 16;
+      if (digit < 10)
+        printf ("%d", digit);
+      else
+        printf ("%c", 'a' + digit - 10);
+      x /= 16;
+    }
+}
+
+int main (void)
+{
+  print_hex (0xcafe42);
+  printf ("\n");
+  return 0;
+}
diff --git a/20191114/loesung-1-2.c b/20191114/loesung-1-2.c
new file mode 100644
index 0000000..35aa3b3
--- /dev/null
+++ b/20191114/loesung-1-2.c
@@ -0,0 +1,26 @@
+#include <stdio.h>
+#include <stdint.h>
+
+void print_hex (uint32_t x)
+{
+  char digit[8];
+  for (int i = 0; i < 8; i++)
+    {
+      digit[i] = x % 16;
+      x /= 16;
+    }
+  for (int i = 7; i >= 0; i--)
+    {
+      if (digit[i] < 10)
+        printf ("%d", digit[i]);
+      else
+        printf ("%c", 'a' + digit[i] - 10);
+    }
+}
+
+int main (void)
+{
+  print_hex (0xcafe42);
+  printf ("\n");
+  return 0;
+}
diff --git a/20191114/loesung-1-3.c b/20191114/loesung-1-3.c
new file mode 100644
index 0000000..2462f2b
--- /dev/null
+++ b/20191114/loesung-1-3.c
@@ -0,0 +1,29 @@
+#include <stdio.h>
+#include <stdint.h>
+
+void print_hex (uint32_t x)
+{
+  char digit[8];
+  int i = 0;
+  while (x)
+    {
+      digit[i] = x % 16;
+      x /= 16;
+      i++;
+    }
+  while (i > 0)
+    {
+      i--;
+      if (digit[i] < 10)
+        printf ("%d", digit[i]);
+      else
+        printf ("%c", 'a' + digit[i] - 10);
+    }
+}
+
+int main (void)
+{
+  print_hex (0xcafe42);
+  printf ("\n");
+  return 0;
+}
diff --git a/20191114/loesung-1-4.c b/20191114/loesung-1-4.c
new file mode 100644
index 0000000..5083dcb
--- /dev/null
+++ b/20191114/loesung-1-4.c
@@ -0,0 +1,31 @@
+#include <stdio.h>
+#include <stdint.h>
+
+void print_hex (uint32_t x)
+{
+  char digit[8];
+  for (int i = 0; i < 8; i++)
+    {
+      digit[i] = x % 16;
+      x /= 16;
+    }
+  int printing = 0;
+  for (int i = 7; i >= 0; i--)
+    {
+      if (printing || digit[i] != 0)
+        {
+          printing = 1;
+          if (digit[i] < 10)
+            printf ("%d", digit[i]);
+          else
+            printf ("%c", 'a' + digit[i] - 10);
+        }
+    }
+}
+
+int main (void)
+{
+  print_hex (0xcafe42);
+  printf ("\n");
+  return 0;
+}
diff --git a/20191114/loesung-1-5.c b/20191114/loesung-1-5.c
new file mode 100644
index 0000000..e3446ed
--- /dev/null
+++ b/20191114/loesung-1-5.c
@@ -0,0 +1,29 @@
+#include <stdio.h>
+#include <stdint.h>
+
+void print_hex (uint32_t x)
+{
+  char digit[8];
+  int i = 0;
+  while (x)
+    {
+      digit[i] = x & 0x0000000f;
+      x >>= 4;
+      i++;
+    }
+  while (i > 0)
+    {
+      i--;
+      if (digit[i] < 10)
+        printf ("%d", digit[i]);
+      else
+        printf ("%c", 'a' + digit[i] - 10);
+    }
+}
+
+int main (void)
+{
+  print_hex (0xcafe42);
+  printf ("\n");
+  return 0;
+}
diff --git a/20191114/loesung-1-6.c b/20191114/loesung-1-6.c
new file mode 100644
index 0000000..7b8e8e1
--- /dev/null
+++ b/20191114/loesung-1-6.c
@@ -0,0 +1,23 @@
+#include <stdio.h>
+#include <stdint.h>
+
+void print_hex (uint32_t x)
+{
+  int i = 32;
+  while (i > 0)
+    {
+      i -= 4;
+      int digit = (x >> i) & 0x0000000f;
+      if (digit < 10)
+        printf ("%d", digit);
+      else
+        printf ("%c", 'a' + digit - 10);
+    }
+}
+
+int main (void)
+{
+  print_hex (0xcafe42);
+  printf ("\n");
+  return 0;
+}
diff --git a/20191114/loesung-2.c b/20191114/loesung-2.c
new file mode 100644
index 0000000..e415190
--- /dev/null
+++ b/20191114/loesung-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 = len; i > pos; i++)
+    target[i] = target[i - 1];
+  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/20191114/loesung-3c-1.c b/20191114/loesung-3c-1.c
new file mode 100644
index 0000000..69ddd0e
--- /dev/null
+++ b/20191114/loesung-3c-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/20191114/loesung-3c-2.c b/20191114/loesung-3c-2.c
new file mode 100644
index 0000000..e783c47
--- /dev/null
+++ b/20191114/loesung-3c-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/20191114/loesung-3d-1.c b/20191114/loesung-3d-1.c
new file mode 100644
index 0000000..5752138
--- /dev/null
+++ b/20191114/loesung-3d-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/20191114/loesung-3d-2.c b/20191114/loesung-3d-2.c
new file mode 100644
index 0000000..5f3f096
--- /dev/null
+++ b/20191114/loesung-3d-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/20191114/loesung-3e-1.c b/20191114/loesung-3e-1.c
new file mode 100644
index 0000000..74f5add
--- /dev/null
+++ b/20191114/loesung-3e-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/20191114/loesung-3e-2.c b/20191114/loesung-3e-2.c
new file mode 100644
index 0000000..b223d2d
--- /dev/null
+++ b/20191114/loesung-3e-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;
+}
-- 
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