uni/ws2019/ipi/uebungen/ipi6.tex

\documentclass[uebung]{../../../lecture}

\usepackage{listings}
\usetikzlibrary{positioning}

\title{Übungsblatt 6}
\author{Samuel Weidemaier, Christian Merten}

\usepackage{xcolor}
 
\lstdefinestyle{mystyle}{
    commentstyle=\color{gray},
    keywordstyle=\color{blue},
    numberstyle=\tiny\color{gray},
    stringstyle=\color{black},
    basicstyle=\ttfamily\footnotesize,
    breakatwhitespace=false,         
    breaklines=true,                 
    captionpos=b,                    
    keepspaces=true,                 
    numbers=left,                    
    numbersep=5pt,                  
    showspaces=false,                
    showstringspaces=false,
    showtabs=false,                  
    tabsize=2
}
 
\lstset{style=mystyle}

\usepackage{tikz, wasysym} 
\usetikzlibrary{automata, positioning, arrows,shapes,shadows}

\tikzstyle{abstract}=[rectangle, draw=black,
    %text centered,
     anchor=north, text=black, text width=15cm, rounded corners]

\tikzstyle{subgroup}=[rectangle, draw=blue,
    %text centered,
     anchor=north, text=black, text width=3.5cm, rounded corners]
     
\tikzstyle{myarrow}=[->, >=stealth, thick]
\tikzstyle{gestrichen}=[->, >=stealth, dashed]

\begin{document}

\punkte

\begin{aufgabe}

    \vspace{5mm}
Marker 1:
    \vspace{-3mm}
\begin{center}
	\begin{tikzpicture}[shorten >= 1pt, node distance=2.5cm, on grid, auto]
	
	
		\node[abstract, rectangle split, rectangle split parts=2] (global) 	{
										Globale Umgebung
										\nodepart{second}$g$ int $1$
									};
								
								
								
		\node[subgroup, rectangle split, rectangle split parts=2, below left of=global, xshift=-3.3cm, yshift=-0.3cm] (main)		{ 
										main() \\
										\nodepart{second}
										$a$ int $2$ \\
										$b$ int $14$ 
									};
		
		\node[subgroup, rectangle split, rectangle split parts=2, below right of=main, yshift=-0.4cm] (block1)		{ 
										Block $1$ in main() \\
										\nodepart{second}
										$a$ int $7$ \\
										$g$ int $?$ 
									};
									
		\node[subgroup, rectangle split, rectangle split parts=2, right of=block1, , xshift=2.1cm, yshift=-0.32cm] (ggTab)		{ 
										ggT(b, a) \\
										\nodepart{second}
										$a$ int $14$ \\
										$b$ int $7$  \\
										Null int $0$ 
									};
									
	
				
		\node[subgroup, rectangle split, rectangle split parts=2, below right of=ggTab, yshift=-0.7cm] (amodb)		{ 
                                        $a \text{ mod } b(a,b)$ \\
										\nodepart{second}
										$a$ int $14$ \\
										$b$ int $7$ \\
										$m$ int $0$
									};
									
		
		\draw[myarrow] (main.west) -- ++(0,0) -| ([xshift=-7.2cm] global.south);
		
		\draw[myarrow] (block1.west) -- ++(0,0) -| ([xshift=-1cm] main.south);
		
		\draw[gestrichen] ([xshift=-1.4cm] ggTab.south) -- ++(0,-0.4) -| (block1.south);
		
		\draw[myarrow] (ggTab.west) -- ++(0,0) -| ([xshift=-1cm] global.south);
		
		
		\draw[gestrichen] (amodb.west) -- ++(0,0) -| ([xshift=-1.7cm] ggTab);
		
		\draw[myarrow] ([xshift=1cm] amodb.north) -- ++(0,0) -| ([xshift=4.1cm] global.south);
		
		
		
	\end{tikzpicture} 

    \vspace{-10mm}
    
\end{center}
	
	\nopagebreak
	
    Marker 2:
    \vspace{-2mm}
    \begin{center}
	\begin{tikzpicture}[shorten >= 1pt, node distance=2.5cm, on grid, auto]
	
	
		\node[abstract, rectangle split, rectangle split parts=2] (global) 	{
										Globale Umgebung
										\nodepart{second}$g$ int $2$
									};
								
								
								
		\node[subgroup, rectangle split, rectangle split parts=2, below left of=global, xshift=-3.3cm, yshift=-0.3cm] (main)		{ 
										main() \\
										\nodepart{second}
										$a$ int $2$ \\
										$b$ int $14$ 
									};
		
		\node[subgroup, rectangle split, rectangle split parts=2, below right of=main, yshift=-0.4cm] (block1)		{ 
										Block $1$ in main() \\
										\nodepart{second}
										$a$ int $7$ \\
										$g$ int $?$ 
									};
									
		\node[subgroup, rectangle split, rectangle split parts=2, right of=block1, , xshift=2.1cm, yshift=-0.32cm] (ggTab)		{ 
										ggT(b, a) \\
										\nodepart{second}
										$a$ int $14$ \\
										$b$ int $7$  \\
										Null int $0$ 
									};
									
		\node[subgroup, rectangle split, rectangle split parts=2, below right of=ggTab, , xshift=1cm, yshift=-0.7cm] (ggTmod)		{ 
                $ggT(b, a \text{ mod }b(a,b))$ \\
										\nodepart{second}
										$a$ int $7$ \\
										$b$ int $0$ \\
										Null int $0$
									};
				

		
		\draw[myarrow] (main.west) -- ++(0,0) -| ([xshift=-7.2cm] global.south);
		
		\draw[myarrow] (block1.west) -- ++(0,0) -| ([xshift=-1cm] main.south);
		
		\draw[gestrichen] ([xshift=-1.4cm] ggTab.south) -- ++(0,-0.4) -| (block1.south);
		
		\draw[myarrow] (ggTab.west) -- ++(0,0) -| ([xshift=-1cm] global.south);
		
		\draw[gestrichen] (ggTmod.west) -- ++(0,0) -| (ggTab.south);
		
		\draw[myarrow] (ggTmod.north) -- ++(0,0) -| ([xshift=4.1cm] global.south);
		
		
		
	\end{tikzpicture} 
        
    \end{center}
    Marker 3:
    \begin{center}

	\begin{tikzpicture}[shorten >= 1pt, node distance=2.5cm, on grid, auto]
	
	
		\node[abstract, rectangle split, rectangle split parts=2] (global) 	{
										Globale Umgebung
										\nodepart{second}$g$ int $2$
									};
								
								
								
		\node[subgroup, rectangle split, rectangle split parts=2, below left of=global, xshift=-3.3cm, yshift=-0.3cm] (main)		{ 
										main() \\
										\nodepart{second}
										$a$ int $2$ \\
										$b$ int $7$ 
									};
		 
		
		\draw[myarrow] (main.west) -- ++(0,0) -| ([xshift=-7.2cm] global.south);
		
		
		
	\end{tikzpicture} 
\end{center}

\end{aufgabe}

\newpage

\begin{aufgabe} Primfaktorzerlegung
    \begin{lstlisting}[language=C++, title=Primfaktorzerlegung, captionpos=b]
#include "cpp_headers/fcpp.hh"

int main() {
    int n = enter_int("Please enter a natural number: ");
    // search smallest factor, start with smallest possible: 2
    int k=2;
    // go until sqrt(n)
    while (k <= sqrt(n)) {
        // k is factor of n
        if (n % k == 0) {
            // print out the factor k
            print(k);
            // reset n to the quotient
            n = n / k;
            // restart at k=2
            k = 2;
        } else {
            // if k is not a factor, check next one
            k++;
        }
    }
    // n is the last prime factor of the original input number
    print(n);
}
    \end{lstlisting}

    Die algorithmische Komplexität des Programms für $n$ Primzahl ist $\sqrt{n}$, da die Schleife
    für Primzahlen bis $\sqrt{n} $ durchlaufen wird.
\end{aufgabe}

\begin{aufgabe}
    siehe \textit{taschenrechner.cpp}
    
\end{aufgabe}

\end{document}