From 49960e4154641780758a2414c2309b6142385766 Mon Sep 17 00:00:00 2001
From: Valentin Brandl <vbrandl@riseup.net>
Date: Tue, 27 Nov 2018 14:42:24 +0100
Subject: [PATCH] Add dima u06

---
 school/di-ma/uebung/06/06_1.tex | 67 +++++++++++++++++++++++
 school/di-ma/uebung/06/06_2.tex | 72 +++++++++++++++++++++++++
 school/di-ma/uebung/06/06_4.tex | 94 +++++++++++++++++++++++++++++++++
 3 files changed, 233 insertions(+)
 create mode 100644 school/di-ma/uebung/06/06_1.tex
 create mode 100644 school/di-ma/uebung/06/06_2.tex
 create mode 100644 school/di-ma/uebung/06/06_4.tex

diff --git a/school/di-ma/uebung/06/06_1.tex b/school/di-ma/uebung/06/06_1.tex
new file mode 100644
index 0000000..b59f574
--- /dev/null
+++ b/school/di-ma/uebung/06/06_1.tex
@@ -0,0 +1,67 @@
+\documentclass[12pt,a4paper,german]{article}
+\usepackage{url}
+%\usepackage{graphics}
+\usepackage{times}
+\usepackage[T1]{fontenc}
+\usepackage{ngerman}
+\usepackage{float}
+\usepackage{diagbox}
+\usepackage[utf8]{inputenc}
+\usepackage{geometry}
+\usepackage{amsfonts}
+\usepackage{amsmath}
+\usepackage{cancel}
+\usepackage{csquotes}
+\usepackage{graphicx}
+\usepackage{epsfig}
+\usepackage{paralist}
+\usepackage{tikz}
+\geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm}
+
+%%%%%%%%%% Fill out the the definitions %%%%%%%%%
+\def \name {Valentin Brandl}					%
+\def \matrikel {108018274494}				%
+\def \pname {Marvin Herrmann}				%
+\def \pmatrikel {108018265436}				%
+\def \gruppe {2 (Mi 10-12 Andre)}
+\def \qname {Pascal Brackmann}
+\def \qmatrikel {108017113834}				%
+\def \uebung {6}								%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+ % DO NOT MODIFY THIS HEADER
+\newcommand{\hwsol}{
+\vspace*{-2cm}
+\noindent \matrikel \quad \name \hfill \"Ubungsgruppe: \gruppe \\
+\noindent \pmatrikel \quad \pname \\
+\noindent \qmatrikel \quad \qname \\
+\begin{center}{\Large \bf L\"osung f\"ur \"Ubung \# \uebung}\end{center}
+}
+
+\begin{document}
+%Import header
+\hwsol
+
+\section*{Aufgabe 6.1}
+
+\begin{tabular}{|c|ccccccc|}
+    \hline
+    Stack & $pred[1]$ & $pred[2]$ & $pred[3]$ & $pred[4]$ & $pred[5]$ & $pred[6]$ & $pred[7]$ \\\hline
+    $\emptyset$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ \\\hline
+    \cancel{1} & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ \\\hline
+    1, \cancel{2} & $nil$ & $1$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ \\\hline
+    1, 2, \cancel{3} & $nil$ & $1$ & $2$ & $nil$ & $nil$ & $nil$ & $nil$ \\\hline
+    1, 2, 3, \cancel{4} & $nil$ & $1$ & $2$ & $3$ & $nil$ & $nil$ & $nil$ \\\hline
+    1, 2, \cancel{3} & $nil$ & $1$ & $2$ & $3$ & $nil$ & $nil$ & $nil$ \\\hline
+    1, \cancel{2} & $nil$ & $1$ & $2$ & $3$ & $nil$ & $nil$ & $nil$ \\\hline
+    1, 2, \cancel{6} & $nil$ & $1$ & $2$ & $3$ & $nil$ & $2$ & $nil$ \\\hline
+    1, 2, 6, \cancel{7} & $nil$ & $1$ & $2$ & $3$ & $nil$ & $2$ & $6$ \\\hline
+    1, 2, \cancel{6} & $nil$ & $1$ & $2$ & $3$ & $nil$ & $2$ & $6$ \\\hline
+    1, \cancel{2} & $nil$ & $1$ & $2$ & $3$ & $nil$ & $2$ & $6$ \\\hline
+    \cancel{1} & $nil$ & $1$ & $2$ & $3$ & $nil$ & $2$ & $6$ \\\hline
+    1, \cancel{5} & $nil$ & $1$ & $2$ & $3$ & $1$ & $2$ & $6$ \\\hline
+    \cancel{1} & $nil$ & $1$ & $2$ & $3$ & $1$ & $2$ & $6$ \\\hline
+    $\emptyset$ & $nil$ & $1$ & $2$ & $3$ & $1$ & $2$ & $6$ \\\hline
+\end{tabular}
+
+\end{document}
diff --git a/school/di-ma/uebung/06/06_2.tex b/school/di-ma/uebung/06/06_2.tex
new file mode 100644
index 0000000..ca8e003
--- /dev/null
+++ b/school/di-ma/uebung/06/06_2.tex
@@ -0,0 +1,72 @@
+\documentclass[12pt,a4paper,german]{article}
+\usepackage{url}
+%\usepackage{graphics}
+\usepackage{times}
+\usepackage[T1]{fontenc}
+\usepackage{ngerman}
+\usepackage{float}
+\usepackage{diagbox}
+\usepackage[utf8]{inputenc}
+\usepackage{geometry}
+\usepackage{amsfonts}
+\usepackage{amsmath}
+\usepackage{cancel}
+\usepackage{csquotes}
+\usepackage{graphicx}
+\usepackage{epsfig}
+\usepackage{paralist}
+\usepackage{tikz}
+\geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm}
+
+%%%%%%%%%% Fill out the the definitions %%%%%%%%%
+\def \name {Valentin Brandl}					%
+\def \matrikel {108018274494}				%
+\def \pname {Marvin Herrmann}				%
+\def \pmatrikel {108018265436}				%
+\def \gruppe {2 (Mi 10-12 Andre)}
+\def \qname {Pascal Brackmann}
+\def \qmatrikel {108017113834}				%
+\def \uebung {6}								%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+ % DO NOT MODIFY THIS HEADER
+\newcommand{\hwsol}{
+\vspace*{-2cm}
+\noindent \matrikel \quad \name \hfill \"Ubungsgruppe: \gruppe \\
+\noindent \pmatrikel \quad \pname \\
+\noindent \qmatrikel \quad \qname \\
+\begin{center}{\Large \bf L\"osung f\"ur \"Ubung \# \uebung}\end{center}
+}
+
+\begin{document}
+%Import header
+\hwsol
+
+\section*{Aufgabe 6.2}
+
+\begin{enumerate}[1.]
+
+    \item
+        \begin{tabular}{|c|ccccccc|}
+            \hline
+            Queue & $pred[1]$ & $pred[2]$ & $pred[3]$ & $pred[4]$ & $pred[5]$ & $pred[6]$ & $pred[7]$ \\\hline
+            $\emptyset$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ \\\hline
+            \cancel{1} & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ \\\hline
+            \cancel{2}, 5 & $nil$ & $1$ & $nil$ & $nil$ & $1$ & $nil$ & $nil$ \\\hline
+            \cancel{5}, 3, 6 & $nil$ & $1$ & $2$ & $nil$ & $1$ & $2$ & $nil$ \\\hline
+            \cancel{3}, 6 & $nil$ & $1$ & $2$ & $nil$ & $1$ & $2$ & $nil$ \\\hline
+            \cancel{6}, 4 & $nil$ & $1$ & $2$ & $3$ & $1$ & $2$ & $nil$ \\\hline
+            \cancel{4}, 7 & $nil$ & $1$ & $2$ & $3$ & $1$ & $2$ & $6$ \\\hline
+            \cancel{7} & $nil$ & $1$ & $2$ & $3$ & $1$ & $2$ & $6$ \\\hline
+            $\emptyset$ & $nil$ & $1$ & $2$ & $3$ & $1$ & $2$ & $6$ \\\hline
+        \end{tabular}
+
+    \item
+        Laufzeit Breitensuche mit Adjazenzmatrix: $O(|V|^2)$:
+
+        Jeder Knoten $v$ wird genau einmal besucht und die Bestimmung der Nachbarschaft $\Gamma(v)$ in einer
+        Adjazenzmatrix hat eine Laufzeit von $O(|V|)$
+
+\end{enumerate}
+
+\end{document}
diff --git a/school/di-ma/uebung/06/06_4.tex b/school/di-ma/uebung/06/06_4.tex
new file mode 100644
index 0000000..3f3781f
--- /dev/null
+++ b/school/di-ma/uebung/06/06_4.tex
@@ -0,0 +1,94 @@
+\documentclass[12pt,a4paper,german]{article}
+\usepackage{url}
+%\usepackage{graphics}
+\usepackage{times}
+\usepackage[T1]{fontenc}
+\usepackage{ngerman}
+\usepackage{float}
+\usepackage{diagbox}
+\usepackage[utf8]{inputenc}
+\usepackage{geometry}
+\usepackage{amsfonts}
+\usepackage{amsmath}
+\usepackage{cancel}
+\usepackage{csquotes}
+\usepackage{graphicx}
+\usepackage{epsfig}
+\usepackage{paralist}
+\usepackage{tikz}
+\geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm}
+
+%%%%%%%%%% Fill out the the definitions %%%%%%%%%
+\def \name {Valentin Brandl}					%
+\def \matrikel {108018274494}				%
+\def \pname {Marvin Herrmann}				%
+\def \pmatrikel {108018265436}				%
+\def \gruppe {2 (Mi 10-12 Andre)}
+\def \qname {Pascal Brackmann}
+\def \qmatrikel {108017113834}				%
+\def \uebung {6}								%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+ % DO NOT MODIFY THIS HEADER
+\newcommand{\hwsol}{
+\vspace*{-2cm}
+\noindent \matrikel \quad \name \hfill \"Ubungsgruppe: \gruppe \\
+\noindent \pmatrikel \quad \pname \\
+\noindent \qmatrikel \quad \qname \\
+\begin{center}{\Large \bf L\"osung f\"ur \"Ubung \# \uebung}\end{center}
+}
+
+\begin{document}
+%Import header
+\hwsol
+
+\section*{Aufgabe 6.4}
+
+\begin{tabular}{|c|c|}
+    \hline
+    Iteration & $T[i,j]$ \\\hline
+    0 & $\begin{pmatrix}
+        0 & 1 & 0 & 1 & 0 &  \\ 
+        0 & 0 & 1 & 0 & 1 &  \\
+        0 & 0 & 0 & 0 & 0 &  \\
+        0 & 1 & 0 & 0 & 0 &  \\
+        1 & 0 & 0 & 0 & 0 &  \\
+    \end{pmatrix}$ \\\hline
+    1 & $\begin{pmatrix}
+        0 & 1 & 0 & 1 & 0 &  \\
+        0 & 0 & 1 & 0 & 1 &  \\
+        0 & 0 & 0 & 0 & 0 &  \\
+        0 & 1 & 0 & 0 & 0 &  \\
+        1 & 1 & 0 & 1 & 0 &  \\
+    \end{pmatrix}$ \\\hline
+    2 & $\begin{pmatrix}
+        0 & 1 & 1 & 1 & 1 &  \\
+        0 & 0 & 1 & 0 & 1 &  \\
+        0 & 0 & 0 & 0 & 0 &  \\
+        0 & 1 & 1 & 0 & 1 &  \\
+        1 & 1 & 1 & 1 & 1 &  \\
+    \end{pmatrix}$ \\\hline
+    3 & $\begin{pmatrix}
+        0 & 1 & 1 & 1 & 1 &  \\
+        0 & 0 & 1 & 0 & 1 &  \\
+        0 & 0 & 0 & 0 & 0 &  \\
+        0 & 1 & 1 & 0 & 1 &  \\
+        1 & 1 & 1 & 1 & 1 &  \\
+    \end{pmatrix}$ \\\hline
+    4 & $\begin{pmatrix}
+        0 & 1 & 1 & 1 & 1 &  \\
+        0 & 0 & 1 & 0 & 1 &  \\
+        0 & 0 & 0 & 0 & 0 &  \\
+        0 & 1 & 1 & 0 & 1 &  \\
+        1 & 1 & 1 & 1 & 1 &  \\
+    \end{pmatrix}$ \\\hline
+    5 & $\begin{pmatrix}
+        1 & 1 & 1 & 1 & 1 &  \\
+        1 & 1 & 1 & 1 & 1 &  \\
+        0 & 0 & 0 & 0 & 0 &  \\
+        1 & 1 & 1 & 1 & 1 &  \\
+        1 & 1 & 1 & 1 & 1 &  \\
+    \end{pmatrix}$ \\\hline
+\end{tabular}
+
+\end{document}