1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/exercises/solutions/sol05.tex	Sat Jun 09 23:45:57 2012 +0200
     1.3 @@ -0,0 +1,85 @@
     1.4 +\documentclass[a4paper, 10pt, pagesize, smallheadings]{article}
     1.5 +\usepackage{graphicx}
     1.6 +%\usepackage[latin1]{inputenc}
     1.7 +\usepackage{amsmath, amsthm, amssymb}
     1.8 +\usepackage{typearea}
     1.9 +\usepackage{algorithm}
    1.10 +\usepackage{algorithmic}
    1.11 +\usepackage{fullpage}
    1.12 +\usepackage{mathtools}
    1.13 +\usepackage[all]{xy}
    1.14 +\usepackage{tikz}
    1.15 +\usepackage{tikz-qtree}
    1.16 +\usetikzlibrary{decorations.pathmorphing} % noisy shapes
    1.17 +\usetikzlibrary{fit}					% fitting shapes to coordinates
    1.18 +\usetikzlibrary{backgrounds}	% drawin
    1.19 +\usetikzlibrary{shapes,snakes}
    1.20 +\addtolength{\voffset}{-20pt}
    1.21 +\title{CSP Exercise 05 Solution}
    1.22 +\author{Eugen Sawin}
    1.23 +\renewcommand{\familydefault}{\sfdefault}
    1.24 +\newcommand{\R}{\mathcal{R}}
    1.25 +\newcommand{\N}{\mathbb{N}}
    1.26 +\newcommand{\C}{\mathcal{C}}
    1.27 +\newcommand{\bo}{\mathcal{O}}
    1.28 +
    1.29 +%\include{pythonlisting}
    1.30 +
    1.31 +\pagestyle{empty}
    1.32 +\begin{document}
    1.33 +\maketitle
    1.34 +%
    1.35 +\section*{Exercise 5.1}
    1.36 +(a) The following table shows the states during the iterations.\\\\
    1.37 +\begin{tabular}{r l l l}
    1.38 +Iteration & Queue & Revise & Domains\\\hline
    1.39 +      $0$ & $\{(v_1,v_2),(v_2,v_1),
    1.40 +               (v_2,v_3),(v_3,v_2),
    1.41 +               (v_1,v_3),(v_3,v_1)\}$
    1.42 +          & $$ 
    1.43 +          & $(\{1,2,3,4,5\},
    1.44 +              \{1,2,3,4,5\},
    1.45 +              \{1,2,3,4,5\})$\\
    1.46 +      $1$ & $\{(v_1,v_2),(v_2,v_1),
    1.47 +               (v_2,v_3),(v_3,v_2),
    1.48 +               (v_1,v_3)\}$
    1.49 +          & $(v_3,v_1)$
    1.50 +          & $(\{1,2,3,4,5\},
    1.51 +              \{1,2,3,4,5\},
    1.52 +              \{1,2,3,4,5\})$\\
    1.53 +      $2$ & $\{(v_1,v_2),(v_2,v_1),
    1.54 +               (v_2,v_3),(v_3,v_2)
    1.55 +               \}$
    1.56 +          & $(v_1,v_3)$
    1.57 +          & $(\{1,2,3,4,5\},
    1.58 +              \{1,2,3,4,5\},
    1.59 +              \{1,2,3,4,5\})$\\
    1.60 +      $3$ & $\{(v_1,v_2),(v_2,v_1),
    1.61 +            (v_2,v_3)\}\cup\{(v_1,v_3)\}$
    1.62 +          & $(v_3,v_2)$
    1.63 +          & $(\{1,2,3,4,5\},
    1.64 +              \{1,2,3,4,5\},
    1.65 +              \{1,2\})$\\
    1.66 +      $4$ & $\{(v_1,v_2),(v_2,v_1),
    1.67 +            (v_2,v_3)\}\cup\{\}$
    1.68 +          & $(v_1,v_3)$
    1.69 +          & $(\{1,2\},
    1.70 +              \{1,2,3,4,5\},
    1.71 +              \{1,2\})$\\
    1.72 +      $5$ & $\{(v_1,v_2),(v_2,v_1)\}$
    1.73 +          & $(v_2,v_3)$
    1.74 +          & $(\{1,2\},
    1.75 +              \{1,2\},
    1.76 +              \{1,2\})$\\
    1.77 +      $6$ & $\{(v_1,v_2)\}$
    1.78 +          & $(v_2,v_1)$
    1.79 +          & $(\{1,2\},
    1.80 +              \{1,2\},
    1.81 +              \{1,2\})$\\
    1.82 +      $7$ & $\{\}$
    1.83 +          & $(v_1,v_2)$
    1.84 +          & $(\{1,2\},
    1.85 +              \{1,2\},
    1.86 +              \{1,2\})$\\
    1.87 +\end{tabular}
    1.88 +\end{document}