From cd322723be1fd31baa5fdb2f985210eee4349a0d Mon Sep 17 00:00:00 2001
From: Peter Gerwinski <peter.gerwinski@hs-bochum.de>
Date: Thu, 24 Oct 2019 15:31:34 +0200
Subject: [PATCH] =?UTF-8?q?Musterl=C3=B6sung=2017.10.2019?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 20191017/hp-musterloesung-20191017.pdf | Bin 0 -> 64335 bytes
 20191017/hp-musterloesung-20191017.tex | 326 +++++++++++++++++++++++++
 20191017/hp-uebung-20191017.tex        |   2 -
 20191017/loesung-1-1.c                 |  29 +++
 20191017/loesung-1-2.c                 |  31 +++
 20191017/loesung-1-3.c                 |  21 ++
 20191017/loesung-1-4.c                 |  23 ++
 20191017/loesung-1-5.c                 |  13 +
 20191017/loesung-2-1.c                 |  13 +
 20191017/loesung-2-2.c                 |   9 +
 20191017/loesung-2-3.c                 |  21 ++
 20191017/loesung-2-f4.c                |   9 +
 20191017/loesung-3-1.c                 |  15 ++
 20191017/loesung-3-2.c                 |  13 +
 20191017/loesung-4.c                   |   8 +
 README.md                              |   2 +-
 16 files changed, 532 insertions(+), 3 deletions(-)
 create mode 100644 20191017/hp-musterloesung-20191017.pdf
 create mode 100644 20191017/hp-musterloesung-20191017.tex
 create mode 100644 20191017/loesung-1-1.c
 create mode 100644 20191017/loesung-1-2.c
 create mode 100644 20191017/loesung-1-3.c
 create mode 100644 20191017/loesung-1-4.c
 create mode 100644 20191017/loesung-1-5.c
 create mode 100644 20191017/loesung-2-1.c
 create mode 100644 20191017/loesung-2-2.c
 create mode 100644 20191017/loesung-2-3.c
 create mode 100644 20191017/loesung-2-f4.c
 create mode 100644 20191017/loesung-3-1.c
 create mode 100644 20191017/loesung-3-2.c
 create mode 100644 20191017/loesung-4.c

diff --git a/20191017/hp-musterloesung-20191017.pdf b/20191017/hp-musterloesung-20191017.pdf
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diff --git a/20191017/hp-musterloesung-20191017.tex b/20191017/hp-musterloesung-20191017.tex
new file mode 100644
index 0000000..dceca2f
--- /dev/null
+++ b/20191017/hp-musterloesung-20191017.tex
@@ -0,0 +1,326 @@
+% hp-musterloesung-20191017.pdf - Solutions to the Exercises on Low-Level Programming / Applied Computer Sciences
+% 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: Schaltjahr ermitteln, Multiplikationstabelle, Fibonacci-Zahlen, fehlerhaftes Programm
+
+\documentclass[a4paper]{article}
+
+\usepackage{pgscript}
+
+\begin{document}
+
+  \section*{Hardwarenahe Programmierung\\
+            Musterlösung zu den Übungsaufgaben -- 17.\ Oktober 2019}
+
+  \exercise{Schaltjahr ermitteln}
+
+  Schreiben Sie ein C-Programm, das eine Jahreszahl erfragt
+  und ausgibt, ob es sich um ein Schaltjahr handelt.
+  \begin{itemize}
+    \item Wenn die Jahreszahl durch 4 teilbar ist, ist das Jahr zunächst einmal ein Schaltjahr.
+    \item Ausnahme: Wenn die Jahreszahl durch 100 teilbar ist, ist das Jahr kein Schaltjahr.
+    \item Ausnahme von der Ausnahme: Wenn die Jahreszahl durch 400 teilbar ist,\\
+          ist das Jahr doch wieder ein Schaltjahr.
+  \end{itemize}
+
+  \solution
+
+  Am einfachsten ist es, die Aufgabenstellung in geschachtelte
+  \lstinline{if}-Verzweigungen zu übersetzen.
+  Im folgenden finden Sie eine Funktion \lstinline{is_leap_year()},
+  der man das Jahr übergibt und die für Schaltjahre \lstinline{1}
+  zurückgibt und für Nicht-Schaltjahre \lstinline{0}.
+  \begin{lstlisting}
+    #include <stdio.h>
+
+    int is_leap_year (int year)
+    {
+      int leap_year = 0;
+      if (year % 4 == 0)
+        {
+          leap_year = 1;
+          if (year % 100 == 0)
+            {
+              leap_year = 0;
+              if (year % 400 == 0)
+                leap_year = 1;
+            }
+        }
+      return leap_year;
+    }
+  \end{lstlisting}
+  (In C steht \lstinline{0} für den Wahrheitswert "`falsch"'
+  und jeder Wert ungleich \lstinline{0} für den Wahrheitswert "`wahr'";
+  die Zeile \lstinline{leap_year = 0} steht daher wörtlich und
+  selbsterklärend für "`ist kein Schaltjahr"'.)
+
+  Unter Verwendung von \lstinline{else} läßt sich dies verkürzen zu:
+  \begin{lstlisting}
+    #include <stdio.h>
+
+    int is_leap_year (int year)
+    {
+      if (year % 4 == 0)
+        {
+          if (year % 100 == 0)
+            {
+              if (year % 400 == 0)
+                return 1;
+              else
+                return 0;
+            }
+          else
+            return 1;
+        }
+      else
+        return 0;
+    }
+  \end{lstlisting}
+
+  Eine andere Möglichkeit ist es, die Schaltjahr-Bedingung in eine
+  Kette von "`und"'- und "`oder"'-Verknüpfungen
+  (C-Operatoren \lstinline{&&} und \lstinline{||}) zu übersetzen:
+  \begin{lstlisting}
+    int is_leap_year (int year)
+    {
+      if (year % 4 == 0 && (year % 100 != 0 || year % 400 == 0))
+        return 1;
+      else
+        return 0;
+    }
+  \end{lstlisting}
+  Dies ist zwar kürzer, aber nicht unbedingt übersichtlicher.
+  Der erzeugte Code ist übrigens \emph{nicht\/} kürzer und/oder
+  effizienter als bei der Verwendung mehrerer
+  \lstinline{if}-Verzweigungen.
+  Wir empfehlen, daß Sie immer so programmieren,
+  daß Sie selbst den maximalen Überblick über Ihr Programm behalten.
+
+  \goodbreak
+
+  Ein Hauptprogramm, das die o.\,a.\ Funktion aufruft,
+  könnte dann wie folgt aussehen:
+  \begin{lstlisting}
+    int main (void)
+    {
+      int year;
+      printf ("Bitte geben Sie eine Jahreszahl ein: ");
+      scanf ("%d", &year);
+      if (is_leap_year (year))
+        printf ("Das Jahr %d ist ein Schaltjahr.\n", year);
+      else
+        printf ("Das Jahr %d ist kein Schaltjahr.\n", year);
+      return 0;
+    }
+  \end{lstlisting}
+  In den Dateien \gitfile{hp}{20191017}{loesung-1-1.c} bis \gitfile{hp}{20191017}{loesung-1-3.c}
+  finden Sie lauffähige Programme, die die o.\,a.\ Funktionen aufrufen.
+  Beachten Sie, daß die Funktion \emph{vor\/} dem Hauptprogramm
+  deklariert werden muß, damit das Hauptprogramm sie kennt.
+  (Es gibt Tricks, mit denen es auch anders geht,
+  aber was hätten wir in diesem Zusammenhang davon?)
+
+  In \gitfile{hp}{20191017}{loesung-1-4.c} und \gitfile{hp}{20191017}{loesung-1-5.c}
+  findet die Schaltjahr-Prüfung direkt im Hauptprogramm statt.
+  Dies ist ebenfalls eine richtige Lösung der Aufgabe,
+  schränkt aber die Wiederverwertbarkeit des Codes ein.
+
+  Die Datei \gitfile{hp}{20191017}{loesung-1-4.c} enthält darüberhinaus Codeverdopplungen,
+  nämlich mehrere identische \lstinline{printf()}-Auf"-rufe
+  an unterschiedlichen Stellen.
+  Dies ist schlechter Programmierstil ("`Cut-and-paste-Programmierung"').
+
+  Die besten Lösungen sind \gitfile{hp}{20191017}{loesung-1-2.c}
+  und \gitfile{hp}{20191017}{loesung-1-3.c}.
+
+  \goodbreak
+
+  Zum Testen:\vspace*{-\medskipamount}
+  \begin{itemize}\itemsep0pt
+    \item 1900 ist kein Schaltjahr.
+    \item 1902 ist kein Schaltjahr.
+    \item 1904 ist ein Schaltjahr.
+    \item 1996 ist ein Schaltjahr.
+    \item 1998 ist kein Schaltjahr.
+    \item 2000 ist ein Schaltjahr.
+    \item 2002 ist kein Schaltjahr.
+    \item 2004 ist ein Schaltjahr.
+    \item 2016 ist ein Schaltjahr.
+    \item 2017 ist kein Schaltjahr.
+    \item 2018 ist kein Schaltjahr.
+    \item 2019 ist kein Schaltjahr.
+  \end{itemize}
+
+  \goodbreak
+
+  Hier noch ein Hinweis für Unix-Shell-Experten:
+  \begin{lstlisting}[style=cmd]
+    for y in 1 2 3 4 5; do
+      clear
+      for x in 1900 1902 1904 1996 1998 2000 2002 2004 2016 2017 2018 2019; do
+        echo $x | ./loesung-1-$y
+      done
+      sleep 2s
+    done
+  \end{lstlisting}
+
+  \exercise{Multiplikationstabelle}
+
+  Geben Sie mit Hilfe einer Schleife ein "`Einmaleins"' aus.\\
+  Dabei sollen die Faktoren und Ergebnisse rechtsbündig untereinander stehen:
+  \begin{lstlisting}[style=terminal]
+     1 * 7 =  7
+     2 * 7 = 14
+     ...
+    10 * 7 = 70
+  \end{lstlisting}
+  Hinweis: Verwenden Sie Formatspezifikationen wie z.\,B.\ \lstinline{%3d}\\
+  (siehe dazu die Dokumentation zu \lstinline{printf()},
+  z.\,B.\ \,\lstinline[style=cmd]{man 3 printf}\,)
+
+  \solution
+
+  Drei verschiedene richtige Lösungen finden Sie in den Dateien
+  \gitfile{hp}{20191017}{loesung-2-1.c}, \gitfile{hp}{20191017}{loesung-2-2.c} und \gitfile{hp}{20191017}{loesung-2-3.c}.
+  (Zum Compilieren von \gitfile{hp}{20191017}{loesung-2-2.c} und \gitfile{hp}{20191017}{loesung-2-3.c}
+  ist mindestens der C99-Standard erforderlich; bitte nötigenfalls
+  in \file{gcc} die Option \lstinline[style=cmd]{-std=c99} mit angeben.)
+
+  Die Lösung in \gitfile{hp}{20191017}{loesung-2-3.c} ist zwar richtig,
+  aber unnötig kompliziert und daher nicht empfohlen.
+
+  Eine \textbf{falsche} Lösung finden Sie in der Datei \gitfile{hp}{20191017}{loesung-2-f4.c}:
+  In der Ausgabe dieses Programms stehen die Faktoren und Ergebnisse
+  nicht rechtsbündig untereinander.
+
+  \exercise{Fibonacci-Zahlen}
+
+  Die Folge der Fibonacci-Zahlen ist definiert durch:
+  \begin{quote}
+    1.\ Zahl: 0\\
+    2.\ Zahl: 1\\
+    nächste Zahl = Summe der beiden vorherigen
+  \end{quote}
+  Schreiben Sie ein Programm, das die ersten 50 Fibonacci-Zahlen ausgibt.
+
+  Falls Ihnen dabei irgendwelche Besonderheiten auffallen
+  und/oder Sie irgendwelche besondere Maßnahmen treffen,
+  dokumentieren Sie diese.
+
+  (Wem dies zu einfach ist, kann auch gerne
+  die ersten 100 Fibonacci-Zahlen ausgeben.)
+
+  \solution
+
+  Zwei verschiedene richtige Lösungen finden Sie in den Dateien
+  \gitfile{hp}{20191017}{loesung-3-1.c} und \gitfile{hp}{20191017}{loesung-3-2.c}.
+
+  Die Lösung in \gitfile{hp}{20191017}{loesung-3-2.c}
+  speichert alle berechneten Zahlen in einem Array,
+  die in \gitfile{hp}{20191017}{loesung-3-1.c} hingegen
+  speichert immer nur maximal drei Zahlen gleichzeitig.
+  Sofern nicht alle berechneten Zahlen später noch benötigt werden,
+  ist daher \gitfile{hp}{20191017}{loesung-3-1.c} zu bevorzugen.
+
+  Wichtig in \gitfile{hp}{20191017}{loesung-3-1.c} ist, daß \lstinline{f0 + f1} berechnet wird,
+  \emph{bevor\/} \lstinline{f0} oder \lstinline{f1} ein neuer Wert zugewiesen wird.
+  Dies ist nur möglich, weil das Programm
+  eine zusätzliche Variable (hier: \lstinline{f2}) verwendet.
+
+  \emph{(Fortsetzung folgt.)}
+
+  \exercise{Fehlerhaftes Programm}
+
+  \begin{minipage}[t]{0.65\textwidth}
+    Wir betrachten das nebenstehende C-Programm
+    (Datei: \gitfile{hp}{20191017}{aufgabe-4.c}).
+    \begin{itemize}
+      \item[(a)]
+        Was bewirkt dieses Programm? Begründen Sie Ihre Antwort.
+
+        Schreiben Sie Ihre Begründung so auf,
+        daß man sie auch dann versteht,
+        wenn man gerade nicht die Möglichkeit hat,
+        bei Ihnen persönlich nachzufragen
+        (z.\,B.\ weil man gerade eine Klausur korrigiert).
+
+        Die Schwierigkeit dieser Aufgabe besteht
+        nicht allein darin, die Problematik zu verstehen,
+        sondern auch darin, dieses Verständnis für andere aufzuschreiben.
+      \item[(b)]
+        Ändern Sie das Programm so um,
+        daß es einen "`Countdown"' von 10 bis 0 ausgibt.
+    \end{itemize}
+  \end{minipage}\hfill
+  \begin{minipage}[t]{0.3\textwidth}
+    \begin{lstlisting}[gobble=6]
+      #include <stdio.h>
+
+      int main (void)
+      {
+        for (int i = 10; i = 0; i - 1)
+          printf ("%d\n", i);
+        return 0;
+      }
+    \end{lstlisting}
+  \end{minipage}
+
+  \solution
+
+  \begin{itemize}
+    \item[(a)]
+      \textbf{Was bewirkt dieses Programm und warum?}
+
+      Dieses Programm bewirkt nichts.
+      Die \lstinline{for}-Schleife wird nicht ausgeführt.
+
+      Begründung: Die \lstinline{for}-Bedingung ist eine Zuweisung
+      des Werts \lstinline{0} an die Variable \lstinline{i}.
+      Neben dem Seiteneffekt der Zuweisung liefert der Ausdruck
+      einen Wert zurück, nämlich den zugewiesenen Wert
+      \lstinline{0}. Dieser wird von \lstinline{for} als eine
+      Bedingung mit dem konstanten Wert "`falsch"' interpretiert.
+
+      (Hinweis: Ohne diese Begründung ist die Aufgabe nur zu einem
+      kleinen Teil gelöst.)
+
+      Darüberhinaus ist die Zähl-Anwendung unwirksam: Sie berechnet
+      den Wert \lstinline{i - 1} und vergißt ihn wieder, ohne ihn
+      einer Variablen (z.\,B.\ \lstinline{i}) zuzuweisen.
+
+    \item[(b)]
+      \textbf{Ändern Sie das Programm so, daß es einen "`Countdown"' von 10 bis 0 ausgibt.}
+
+      Datei \gitfile{hp}{20191017}{loesung-4.c}:
+      \begin{lstlisting}[gobble=8]
+        #include <stdio.h>
+
+        int main (void)
+        {
+          for (int i = 10; i >= 0; i--)
+            printf ("%d\n", i);
+          return 0;
+        }
+      \end{lstlisting}
+  \end{itemize}
+
+\end{document}
diff --git a/20191017/hp-uebung-20191017.tex b/20191017/hp-uebung-20191017.tex
index f8f7aa7..b12e973 100644
--- a/20191017/hp-uebung-20191017.tex
+++ b/20191017/hp-uebung-20191017.tex
@@ -26,8 +26,6 @@
 
 \usepackage{pgscript}
 
-\thispagestyle{empty}
-
 \begin{document}
 
   \thispagestyle{empty}
diff --git a/20191017/loesung-1-1.c b/20191017/loesung-1-1.c
new file mode 100644
index 0000000..ea41b8e
--- /dev/null
+++ b/20191017/loesung-1-1.c
@@ -0,0 +1,29 @@
+#include <stdio.h>
+
+int is_leap_year (int year)
+{
+  int leap_year = 0;
+  if (year % 4 == 0)
+    {
+      leap_year = 1;
+      if (year % 100 == 0)
+        {
+          leap_year = 0;
+          if (year % 400 == 0)
+            leap_year = 1;
+        }
+    }
+  return leap_year;
+}
+
+int main (void)
+{
+  int year;
+  printf ("Bitte geben Sie eine Jahreszahl ein: ");
+  scanf ("%d", &year);
+  if (is_leap_year (year))
+    printf ("Das Jahr %d ist ein Schaltjahr.\n", year);
+  else
+    printf ("Das Jahr %d ist kein Schaltjahr.\n", year);
+  return 0;
+}
diff --git a/20191017/loesung-1-2.c b/20191017/loesung-1-2.c
new file mode 100644
index 0000000..d9e4df8
--- /dev/null
+++ b/20191017/loesung-1-2.c
@@ -0,0 +1,31 @@
+#include <stdio.h>
+
+int is_leap_year (int year)
+{
+  if (year % 4 == 0)
+    {
+      if (year % 100 == 0)
+        {
+          if (year % 400 == 0)
+            return 1;
+          else
+            return 0;
+        }
+      else
+        return 1;
+    }
+  else
+    return 0;
+}
+
+int main (void)
+{
+  int year;
+  printf ("Bitte geben Sie eine Jahreszahl ein: ");
+  scanf ("%d", &year);
+  if (is_leap_year (year))
+    printf ("Das Jahr %d ist ein Schaltjahr.\n", year);
+  else
+    printf ("Das Jahr %d ist kein Schaltjahr.\n", year);
+  return 0;
+}
diff --git a/20191017/loesung-1-3.c b/20191017/loesung-1-3.c
new file mode 100644
index 0000000..97051b3
--- /dev/null
+++ b/20191017/loesung-1-3.c
@@ -0,0 +1,21 @@
+#include <stdio.h>
+
+int is_leap_year (int year)
+{
+  if (year % 4 == 0 && (year % 100 != 0 || year % 400 == 0))
+    return 1;
+  else
+    return 0;
+}
+
+int main (void)
+{
+  int year;
+  printf ("Bitte geben Sie eine Jahreszahl ein: ");
+  scanf ("%d", &year);
+  if (is_leap_year (year))
+    printf ("Das Jahr %d ist ein Schaltjahr.\n", year);
+  else
+    printf ("Das Jahr %d ist kein Schaltjahr.\n", year);
+  return 0;
+}
diff --git a/20191017/loesung-1-4.c b/20191017/loesung-1-4.c
new file mode 100644
index 0000000..3a0d218
--- /dev/null
+++ b/20191017/loesung-1-4.c
@@ -0,0 +1,23 @@
+#include <stdio.h>
+
+int main (void)
+{
+  int year;
+  printf ("Bitte geben Sie eine Jahreszahl ein: ");
+  scanf ("%d", &year);
+  if (year % 4 == 0)
+    {
+      if (year % 100 == 0)
+        {
+          if (year % 400 == 0)
+            printf ("Das Jahr %d ist ein Schaltjahr.\n", year);
+          else
+            printf ("Das Jahr %d ist kein Schaltjahr.\n", year);
+        }
+      else
+        printf ("Das Jahr %d ist ein Schaltjahr.\n", year);
+    }
+  else
+    printf ("Das Jahr %d ist kein Schaltjahr.\n", year);
+  return 0;
+}
diff --git a/20191017/loesung-1-5.c b/20191017/loesung-1-5.c
new file mode 100644
index 0000000..999d9f2
--- /dev/null
+++ b/20191017/loesung-1-5.c
@@ -0,0 +1,13 @@
+#include <stdio.h>
+
+int main (void)
+{
+  int year;
+  printf ("Bitte geben Sie eine Jahreszahl ein: ");
+  scanf ("%d", &year);
+  if (year % 4 == 0 && (year % 100 != 0 || year % 400 == 0))
+    printf ("Das Jahr %d ist ein Schaltjahr.\n", year);
+  else
+    printf ("Das Jahr %d ist kein Schaltjahr.\n", year);
+  return 0;
+}
diff --git a/20191017/loesung-2-1.c b/20191017/loesung-2-1.c
new file mode 100644
index 0000000..5ec9dd3
--- /dev/null
+++ b/20191017/loesung-2-1.c
@@ -0,0 +1,13 @@
+#include <stdio.h>
+
+int main (void)
+{
+  int a = 1;
+  int b = 7;
+  while (a <= 10)
+    {
+      printf ("%2d * %d = %2d\n", a, b, a * b);
+      a++;
+    }
+  return 0;
+}
diff --git a/20191017/loesung-2-2.c b/20191017/loesung-2-2.c
new file mode 100644
index 0000000..8f9319e
--- /dev/null
+++ b/20191017/loesung-2-2.c
@@ -0,0 +1,9 @@
+#include <stdio.h>
+
+int main (void)
+{
+  int x = 7;
+  for (int i = 1; i <= 10; i++)
+    printf ("%2d *%2d =%3d\n", i, x, i * x);
+  return 0;
+}
diff --git a/20191017/loesung-2-3.c b/20191017/loesung-2-3.c
new file mode 100644
index 0000000..71fca25
--- /dev/null
+++ b/20191017/loesung-2-3.c
@@ -0,0 +1,21 @@
+#include <stdio.h>
+
+int main (void)
+{
+  int x = 7;
+  for (int i = 1; i <= 10; i++)
+    {
+      if (i >= 10)
+        printf ("%d", i);
+      else
+        printf (" %d", i);
+      printf (" * %d = ", x);
+      int y = i * x;
+      if (y >= 10)
+        printf ("%d", y);
+      else
+        printf (" %d", y);
+      printf ("\n");
+    }
+  return 0;
+}
diff --git a/20191017/loesung-2-f4.c b/20191017/loesung-2-f4.c
new file mode 100644
index 0000000..8520d43
--- /dev/null
+++ b/20191017/loesung-2-f4.c
@@ -0,0 +1,9 @@
+#include <stdio.h>
+
+int main (void)
+{
+  int x = 7;
+  for (int i = 1; i <= 10; i++)
+    printf ("%d * %d = %d\n", i, x, i * x);
+  return 0;
+}
diff --git a/20191017/loesung-3-1.c b/20191017/loesung-3-1.c
new file mode 100644
index 0000000..ec5f4d9
--- /dev/null
+++ b/20191017/loesung-3-1.c
@@ -0,0 +1,15 @@
+#include <stdio.h>
+
+int main (void)
+{
+  int f0 = 0;
+  int f1 = 1;
+  for (int i = 0; i < 50; i++)
+    {
+      printf ("f[%d] = %d\n", i, f0);
+      int f2 = f0 + f1;
+      f0 = f1;
+      f1 = f2;
+    }
+  return 0;
+}
diff --git a/20191017/loesung-3-2.c b/20191017/loesung-3-2.c
new file mode 100644
index 0000000..7043f66
--- /dev/null
+++ b/20191017/loesung-3-2.c
@@ -0,0 +1,13 @@
+#include <stdio.h>
+
+int main (void)
+{
+  int f[50];
+  f[0] = 0;
+  f[1] = 1;
+  for (int i = 2; i < 50; i++)
+    f[i] = f[i - 2] + f[i - 1];
+  for (int i = 0; i < 50; i++)
+    printf ("f[%d] = %d\n", i, f[i]);
+  return 0;
+}
diff --git a/20191017/loesung-4.c b/20191017/loesung-4.c
new file mode 100644
index 0000000..f8481e9
--- /dev/null
+++ b/20191017/loesung-4.c
@@ -0,0 +1,8 @@
+#include <stdio.h>
+
+int main (void)
+{
+  for (int i = 10; i >= 0; i--)
+    printf ("%d\n", i);
+  return 0;
+}
diff --git a/README.md b/README.md
index 67a8fd2..b39e399 100644
--- a/README.md
+++ b/README.md
@@ -30,7 +30,7 @@ Vortragsfolien und Beispiele:
 
 Musterlösungen:
 ---------------
-(keine)
+ * [17.10.2019: Schaltjahr ermitteln, Multiplikationstabelle, Fibonacci-Zahlen, fehlerhaftes Programm](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20191017/hp-musterloesung-20191017.pdf)
 
 Tafelbilder:
 ------------
-- 
GitLab