From d2056dc36211febecada00dc562839fe32162d6a Mon Sep 17 00:00:00 2001
From: Thomas Ba <git@thomasba.de>
Date: Thu, 22 Dec 2011 23:55:40 +0100
Subject: [PATCH] =?UTF-8?q?AlgoDS2=20=C3=9Cbungsblatt=203=20hinzugef=C3=BC?=
 =?UTF-8?q?gt=20(L=C3=B6sung)?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 .../Uebung_3/Uebung_3.tex                     | 147 +++++
 .../Uebung_3/bilder/aufgabe_1.xml             | 399 ++++++++++++
 .../Uebung_3/bilder/aufgabe_2.xml             | 442 +++++++++++++
 .../Uebung_3/bilder/aufgabe_3a.xml            | 339 ++++++++++
 .../Uebung_3/bilder/aufgabe_3b.xml            | 591 ++++++++++++++++++
 .../Uebung_3/bilder/aufgabe_4.xml             | 434 +++++++++++++
 Sichere_Hardware/Sichere_Hardware.tex         |   8 +-
 7 files changed, 2356 insertions(+), 4 deletions(-)
 create mode 100644 Algorithmen_und_Datenstrukturen_2/Uebung_3/Uebung_3.tex
 create mode 100644 Algorithmen_und_Datenstrukturen_2/Uebung_3/bilder/aufgabe_1.xml
 create mode 100644 Algorithmen_und_Datenstrukturen_2/Uebung_3/bilder/aufgabe_2.xml
 create mode 100644 Algorithmen_und_Datenstrukturen_2/Uebung_3/bilder/aufgabe_3a.xml
 create mode 100644 Algorithmen_und_Datenstrukturen_2/Uebung_3/bilder/aufgabe_3b.xml
 create mode 100644 Algorithmen_und_Datenstrukturen_2/Uebung_3/bilder/aufgabe_4.xml

diff --git a/Algorithmen_und_Datenstrukturen_2/Uebung_3/Uebung_3.tex b/Algorithmen_und_Datenstrukturen_2/Uebung_3/Uebung_3.tex
new file mode 100644
index 0000000..3a38b70
--- /dev/null
+++ b/Algorithmen_und_Datenstrukturen_2/Uebung_3/Uebung_3.tex
@@ -0,0 +1,147 @@
+\documentclass[11pt]{scrartcl}
+\usepackage[utf8]{inputenc}
+\usepackage[ngerman]{babel}
+\usepackage{amsmath}
+%\usepackage{amssymb}
+\usepackage{multicol}
+%\usepackage{booktabs}
+%\usepackage{pstricks}
+%\usepackage{pst-node}
+\usepackage[paper=a4paper,left=30mm,right=20mm,top=20mm,bottom =25mm]{geometry}
+\usepackage[
+ pdftitle={Uebungsblatt 3: Programmiertechniken - AlgoDS2},
+ pdfsubject={Algorithmen und Datenstrukturen 2; Uebungsblatt 3: Programmiertechniken},
+ pdfauthor={Thomas Battermann},
+ pdfkeywords={Uebungsblatt 3: Programmiertechniken - AlgoDS2},
+ pdfborder={0 0 0}
+]{hyperref}
+\usepackage{tabularx}
+\usepackage{graphicx}
+\usepackage[usenames,dvipsnames]{color}
+\usepackage{lastpage}
+\usepackage{fancyhdr}
+\setlength{\parindent}{0ex}
+\setlength{\parskip}{2ex}
+\setcounter{secnumdepth}{4}
+\setcounter{tocdepth}{4}
+\definecolor{darkgreen}{rgb}{0,0.5,0}
+\definecolor{darkblue}{rgb}{0,0,0.5}
+
+\pagestyle{fancy} %eigener Seitenstil
+\fancyhf{} %alle Kopf- und Fußzeilenfelder bereinigen
+\fancyhead[L]{Übungsblatt 3\\Programmiertechniken} %Kopfzeile links
+\fancyhead[C]{} %zentrierte Kopfzeile
+\fancyhead[R]{\textsc{Algorithmen \& Datenstrukturen 2}\\22. Dezember 2011} %Kopfzeile rechts
+\renewcommand{\headrulewidth}{0.4pt} %obere Trennlinie
+\fancyfoot[C]{Seite \thepage\ von \pageref{LastPage}}
+\renewcommand{\footrulewidth}{0.4pt} %untere Trennlinie
+
+\newcommand{\spa}{\hspace*{4mm}}
+\newcommand{\defin}{\textcolor{darkgreen}{\textbf{Def.: }}}
+\newcommand{\rrfloor}{\right\rfloor}
+\newcommand{\llfloor}{\left\lfloor}
+
+
+\title{Übung Programmiertechniken -- AlgoDS2}
+\author{Thomas Battermann}
+\date{22. Dezember 2011}
+
+\begin{document}
+\pagestyle{fancy}
+
+\section*{Aufgabe 1}
+\addcontentsline{toc}{section}{Aufgabe 1}
+
+\includegraphics{bilder/aufgabe_1.eps}
+
+\begin{multicols}{2}
+	1. Sortieren nach aufsteigender Endzeit\\[3mm]
+	\begin{tabular}{c|c|c}
+		$i$ & $s_i$ & $f_i$\\
+		\hline
+		 3 &  2 &  3 \\
+		 2 &  4 &  5 \\
+		10 &  5 &  7 \\
+		 7 &  7 &  9 \\
+		 5 & 10 & 12 \\
+		 8 & 13 & 14
+	\end{tabular}
+	\columnbreak\\
+	2. Auswahl der Aktivitäten.\\[3mm]
+	\begin{tabular}{c|c|c}
+		$i$ & $s_i$ & $f_i$\\
+		\hline
+		  3 &  2 &  3\\
+		  2 &  4 &  5\\
+		 10 &  5 &  7\\
+		  7 &  7 &  9\\
+		  5 & 10 & 12\\
+		  8 & 13 & 14
+	\end{tabular}
+\end{multicols}
+
+\section*{Aufgabe 2}
+\addcontentsline{toc}{section}{Aufgabe 2}
+
+\includegraphics{bilder/aufgabe_2.eps}
+
+\begin{tabular}{c|c|c|c|c|c|c|c}
+	$A_{i}(j)$ &  1 &  2 &  3 &  4 &  5 &  6 & $E$ \\
+	\hline
+	1          & 10 & 13 & 18 & 22 & 25 & 33 &  37 \\
+	\hline
+	2          &  9 & 16 & 22 & 21 & 27 & 30 &  25
+\end{tabular}
+
+\begin{tabular}{c|c|c|c|c|c}
+	$j$   & 2 & 3 & 4 & 5 & 6 \\
+	\hline
+	$l_1$ & 1 & 1 & 1 & 1 & 1 \\
+	\hline
+	$l_2$ & 2 & 2 & 1 & 2 & 2
+\end{tabular}
+
+\section*{Aufgabe 3}
+\addcontentsline{toc}{section}{Aufgabe 3}
+
+\subsection*{a)}
+\addcontentsline{toc}{subsection}{a)}
+
+\includegraphics{bilder/aufgabe_3a.eps}\\
+\begin{align*}
+	  & 3 * ( 1000 + 700 + 2100 + 1500 + 1900 + 800 + 2000 )\\
+	=\, & 3 * 10000 = 30000
+\end{align*}
+
+\subsection*{b)}
+\addcontentsline{toc}{subsection}{b)}
+
+\includegraphics{bilder/aufgabe_3b.eps}\\
+\begin{align*}
+	   & ( 41 * 2 + 25*3+15*4+19*3)*100 = (82+75+60+57)*100\\
+	=\,& 274 * 100 = 27400 \Rightarrow \frac{27400}{30000} \approx 0.9133 = 91.22\%
+\end{align*}
+
+\section*{Aufgabe 4}
+\addcontentsline{toc}{section}{Aufgabe 4}
+
+\includegraphics{bilder/aufgabe_4.eps}
+
+\({\bf i=1;\,j=3}\)\\
+\begin{tabular}{l|lr}
+	1 & \(450\) & $*$\\
+	\hline
+	2 & \(1600\)\\
+\end{tabular}
+
+\({\bf i=1;\, j=4}\)\\
+\begin{tabular}{l|lr}
+	1 & \(0+525+10*5*15=1275\)\\
+	\hline
+	2 & \(1000+900+10*20*15=4900\)\\
+	\hline
+	3 & \(450+0+10*3*15=900\) & $*$
+\end{tabular}
+
+
+\end{document}
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+</path>
+<path stroke="gray">
+264 680 m
+268 684 l
+</path>
+<path stroke="gray">
+288 656 m
+292 660 l
+</path>
+<path stroke="gray">
+312 632 m
+316 636 l
+</path>
+<path stroke="gray">
+336 608 m
+340 612 l
+</path>
+</page>
+</ipe>
diff --git a/Sichere_Hardware/Sichere_Hardware.tex b/Sichere_Hardware/Sichere_Hardware.tex
index b6a1dc2..dcd7a4d 100644
--- a/Sichere_Hardware/Sichere_Hardware.tex
+++ b/Sichere_Hardware/Sichere_Hardware.tex
@@ -1,8 +1,8 @@
 \documentclass[11pt]{scrartcl}
 \usepackage[utf8]{inputenc}
 \usepackage[ngerman]{babel}
-%\usepackage{amsmath}
-%\usepackage{amssymb}
+\usepackage{amsmath}
+\usepackage{amssymb}
 %\usepackage{multicol}
 %\usepackage{booktabs}
 %\usepackage{pstricks}
@@ -223,9 +223,9 @@
 
 		\subsection{Digitale Signatur}
 
-		A \begin{tabular}{|c|c|} \hline \(pS(a) \) & \(öS(a) \) \\\hline \end{tabular} \\
+		A \begin{tabular}{|c|c|} \hline \(pS(a) \) & \(\mbox{ö}S(a) \) \\\hline \end{tabular} \\
 		A: Nachricht + \(pS(a) \to V_M \to B\) \\
-		B: \(V + öS(A) \to M\)
+		B: \(V + \mbox{ö}S(A) \to M\)
 
 		Authentizität, aber keine Vertraulichkeit!