Add exercices with graph examples
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ea4049863f
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3 changed files with 199 additions and 1 deletions
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filename=$(shell basename $(shell pwd))
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timestamp=$(shell date +%Y-%m-%d_%H:%M)
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all: snapshot
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all: snapshot exercice
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exercice: exercice.tex
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@latexmk -pdf exercice.tex
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@if ! cmp --silent build/exercice.pdf exercice_*.pdf; then \
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touch exercice_tmp.pdf; \
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rm exercice*.pdf; \
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cp build/main.pdf exercice_${timestamp}.pdf; \
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echo "Updated"; \
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fi
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snapshot: main.tex
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@latexmk -pdf main.tex
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95
theorie-graphes/exercice.tex
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95
theorie-graphes/exercice.tex
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\documentclass[a4paper,french,12pt]{article}
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\title{Théorie des graphes --- Exercices}
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\author{}
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\date{Dernière compilation~: \today{} à \currenttime}
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\usepackage{styles}
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\usepackage{tikz}
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\usetikzlibrary{shapes.multipart}
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\usetikzlibrary{automata, arrows.meta, positioning}
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\begin{document}
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\maketitle
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\section{Exercice 1}
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\paragraph{Graphe simple}
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\begin{tikzpicture}[auto,x=2cm,y=2cm]
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\node(a)[state] at (0,0) {};
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\node(b)[state] at (2,0) {};
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\path (a) edge (b);
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\end{tikzpicture}
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\paragraph{Graphe multigraphe}
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\begin{tikzpicture}[auto,x=2cm,y=2cm]
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\node(a)[state] at (0,0) {};
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\node(b)[state] at (2,0) {};
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\path
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(a) [bend left] edge (b)
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(b) [bend left] edge (a)
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;
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\end{tikzpicture}
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\paragraph{Graphe connexe}
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\begin{tikzpicture}[auto,x=2cm,y=2cm]
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\node(a)[state] at (0,0) {};
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\node(b)[state] at (1,1) {};
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\node(c)[state] at (2,0) {};
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\path
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(a) edge (b)
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(b) edge (c)
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(c) edge (a)
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;
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\end{tikzpicture}
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\paragraph{Graphe non connexe}
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\begin{tikzpicture}[auto,x=2cm,y=2cm]
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\node(a)[state] at (0,0) {};
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\node(b)[state] at (1,1) {};
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\node(c)[state] at (2,0) {};
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\path
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(a) edge (b)
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(b) edge (c)
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;
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\end{tikzpicture}
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\paragraph{Graphe complet}
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\begin{tikzpicture}[auto,x=2cm,y=2cm]
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\node(a)[state] at (0,0) {};
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\node(b)[state] at (1,0) {};
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\node(c)[state] at (0,1) {};
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\node(d)[state] at (1,1) {};
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\path
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(a) edge (b)
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(a) edge (c)
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(a) edge (d)
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(b) edge (c)
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(b) edge (d)
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(c) edge (d)
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;
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\end{tikzpicture}
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\paragraph{Graphe biparti}
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\begin{tikzpicture}[auto,x=2cm,y=2cm]
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\node(a)[state] at (0,0) {};
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\node(b)[state] at (1,0) {};
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\node(c)[state] at (0,1) {};
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\node(d)[state] at (1,1) {};
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\node(e)[state] at (2,0) {};
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\node(f)[state] at (2,1) {};
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\path
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(a) edge (b)
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(a) edge (c)
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(a) edge (d)
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(b) edge (c)
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(b) edge (d)
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(c) edge (d)
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(d) edge (e)
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(d) edge (f)
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(e) edge (f)
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;
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\end{tikzpicture}
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\end{document}
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94
theorie-graphes/styles.sty
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94
theorie-graphes/styles.sty
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\ProvidesPackage{styles}
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\usepackage[
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%showframe,
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a4paper,includeheadfoot,margin=2cm,top=1cm,bottom=1cm
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]{geometry}
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\setcounter{tocdepth}{2}
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\usepackage[utf8]{inputenc}
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\usepackage[T1]{fontenc}
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\usepackage{babel}
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\usepackage{datetime}
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\usepackage{color}
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\usepackage{amsmath}
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\usepackage{amsfonts}
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\everymath{\displaystyle}
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\newcommand*\dif{\mathop{}\!\mathrm{d}}
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\usepackage{booktabs}
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\usepackage{tabularx}
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\newcolumntype{Y}{>{\centering\arraybackslash}X}
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\usepackage{multicol}
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\usepackage{multirow}
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\usepackage{makecell}
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\usepackage{parskip}
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\usepackage{microtype}
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\usepackage{listingsutf8}
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\lstset{%
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inputencoding=utf8/latin1,
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basicstyle=\small\ttfamily,
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columns=flexible,
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breaklines=true,
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extendedchars=true,
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literate=
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{á}{{\'a}}1 {é}{{\'e}}1 {í}{{\'\i}}1 {ó}{{\'o}}1 {ú}{{\'u}}1
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{Á}{{\'A}}1 {É}{{\'E}}1 {Í}{{\'I}}1 {Ó}{{\'O}}1 {Ú}{{\'U}}1
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{à}{{\`a}}1 {è}{{\`e}}1 {ì}{{\`\i}}1 {ò}{{\`o}}1 {ù}{{\`u}}1
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{À}{{\`A}}1 {È}{{\`E}}1 {Ì}{{\`I}}1 {Ò}{{\`O}}1 {Ù}{{\`U}}1
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{ä}{{\"a}}1 {ë}{{\"e}}1 {ï}{{\"\i}}1 {ö}{{\"o}}1 {ü}{{\"u}}1
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{Ä}{{\"A}}1 {Ë}{{\"E}}1 {Ï}{{\"I}}1 {Ö}{{\"O}}1 {Ü}{{\"U}}1
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{â}{{\^a}}1 {ê}{{\^e}}1 {î}{{\^\i}}1 {ô}{{\^o}}1 {û}{{\^u}}1
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{Â}{{\^A}}1 {Ê}{{\^E}}1 {Î}{{\^I}}1 {Ô}{{\^O}}1 {Û}{{\^U}}1
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{Ã}{{\~A}}1 {ã}{{\~a}}1 {Õ}{{\~O}}1 {õ}{{\~o}}1 {œ}{{\oe}}1
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{Œ}{{\OE}}1 {æ}{{\ae}}1 {Æ}{{\AE}}1 {ß}{{\ss}}1 {ű}{{\H{u}}}1
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{Ű}{{\H{U}}}1 {ő}{{\H{o}}}1 {Ő}{{\H{O}}}1 {ç}{{\c c}}1
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{Ç}{{\c C}}1 {ø}{{\o}}1 {å}{{\r a}}1 {Å}{{\r A}}1
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{€}{{\euro}}1 {£}{{\pounds}}1 {«}{{\guillemotleft}}1
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{»}{{\guillemotright}}1 {ñ}{{\~n}}1 {Ñ}{{\~N}}1 {¿}{{?`}}1
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}
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\let\oldlstinputlisting\lstinputlisting
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% make \lstinputlisting always have frame
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\renewcommand{\lstinputlisting}[2][]{\oldlstinputlisting[frame=single,#1]{#2}}
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\lstnewenvironment{console}[1][]{%
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\lstset{%
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inputencoding=utf8/latin1,
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basicstyle=\small\ttfamily\color{white},
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columns=flexible,
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breaklines=true,
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extendedchars=true,
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literate=
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{á}{{\'a}}1 {é}{{\'e}}1 {í}{{\'\i}}1 {ó}{{\'o}}1 {ú}{{\'u}}1
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{Á}{{\'A}}1 {É}{{\'E}}1 {Í}{{\'I}}1 {Ó}{{\'O}}1 {Ú}{{\'U}}1
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{à}{{\`a}}1 {è}{{\`e}}1 {ì}{{\`\i}}1 {ò}{{\`o}}1 {ù}{{\`u}}1
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{À}{{\`A}}1 {È}{{\`E}}1 {Ì}{{\`I}}1 {Ò}{{\`O}}1 {Ù}{{\`U}}1
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{ä}{{\"a}}1 {ë}{{\"e}}1 {ï}{{\"\i}}1 {ö}{{\"o}}1 {ü}{{\"u}}1
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{Ä}{{\"A}}1 {Ë}{{\"E}}1 {Ï}{{\"I}}1 {Ö}{{\"O}}1 {Ü}{{\"U}}1
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{â}{{\^a}}1 {ê}{{\^e}}1 {î}{{\^\i}}1 {ô}{{\^o}}1 {û}{{\^u}}1
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{Â}{{\^A}}1 {Ê}{{\^E}}1 {Î}{{\^I}}1 {Ô}{{\^O}}1 {Û}{{\^U}}1
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{Ã}{{\~A}}1 {ã}{{\~a}}1 {Õ}{{\~O}}1 {õ}{{\~o}}1 {œ}{{\oe}}1
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{Œ}{{\OE}}1 {æ}{{\ae}}1 {Æ}{{\AE}}1 {ß}{{\ss}}1 {ű}{{\H{u}}}1
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{Ű}{{\H{U}}}1 {ő}{{\H{o}}}1 {Ő}{{\H{O}}}1 {ç}{{\c c}}1
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{Ç}{{\c C}}1 {ø}{{\o}}1 {å}{{\r a}}1 {Å}{{\r A}}1
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{€}{{\euro}}1 {£}{{\pounds}}1 {«}{{\guillemotleft}}1
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{»}{{\guillemotright}}1 {ñ}{{\~n}}1 {Ñ}{{\~N}}1 {¿}{{?`}}1,
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backgroundcolor=\color{black}, #1
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}%
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}{}
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\usepackage{graphicx}
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\usepackage[hyphens]{url}
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\usepackage[colorlinks,hidelinks]{hyperref}
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\usepackage{letltxmacro}
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\LetLtxMacro{\normalparagraph}{\paragraph}
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\renewcommand{\paragraph}[1]{\normalparagraph{#1}\mbox{}}
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\sloppy
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