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}