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%%% decommenter si tikz necessaire
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%%% On charge le paquet ifthen pout faire des tests
\usepackage{ifthen}
%%% On définit un compteur numérique pour l'année
\newcounter{theyear}
\setcounter{theyear}{\number\year}
%%% Une macro pour écrire l'année académique automatiquement en
%%% fonction du mois en cours
\newcommand{\academicyear}[0]{
  \ifthenelse{\number\month<8}
  {\addtocounter{theyear}{-1}\arabic{theyear}\addtocounter{theyear}{-1999}\,-\arabic{theyear}}%
  {\arabic{theyear}\addtocounter{theyear}{-1999}\,-\arabic{theyear}}%
}%

%%% mettre les macros à la racine du cours et ajuster en conséquence
%%% pour éviter d'avoir plus d'une copie des macros par cours.
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%\input{SetColors.tex}

\newcommand{\mot}[1]{\textcolor{color2}{\textbf{#1}}}
\newcommand{\alert}[1]{\textcolor{color3}{\textbf{#1}}}
\newcommand{\JFLAP}[1]{\textcolor{color6}{\textbf{\texttt{#1}}}}

%%%%%%%%%%%%%%%%%%%%%%%% 
%%% Def d'environement de Math (Malika)
%%%%%%%%%%%%%%%%%%%%%%%%
\theoremstyle{plain}
\newtheorem*{theo}{Théorème}
\newtheorem*{cons}{Conséquence}
\newtheorem*{conss}{Conséquences}


\theoremstyle{definition}
\newtheorem{exo}{Exercice}
\newtheorem*{defi}{Définition}
\newtheorem*{probleme}{Problème}
\newtheorem*{reponse}{Réponse}


\theoremstyle{remark}
\newtheorem*{exemple}{Exemple}
\newtheorem*{remarque}{Remarque}
\newtheorem*{remarques}{Remarques}
\newtheorem*{prop}{Propriété}
\newtheorem*{props}{Propriétés}



%%%%%%%%%%%%%%%%%%%%%%%% 
%%% Macros diverses (Malika)
%%%%%%%%%%%%%%%%%%%%%%%%


\newcommand{\raus}[1]{}
\AtBeginDocument{
\renewcommand{\labelitemi}{\textbullet}
\renewcommand{\labelitemii}{$\circ$}
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%\pagestyle{fancy}
\fancyhf{}
\fancyhead{
\begin{minipage}{16cm}
\hspace{-2cm}
Nom : \fbox{\begin{minipage}{6cm}\hfill\vspace{.7cm}\end{minipage}}
\hfill
Pr\'enom : \fbox{\begin{minipage}{4cm}\hfill\vspace{.7cm}\end{minipage}}
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Groupe : \fbox{\begin{minipage}{.7cm}\hfill\vspace{.7cm}\end{minipage}}
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%%%%%%%%%%%%%%%%%%%%%%%% 
%%% Quelques paquets gérant la correction / espace pour la reponse
%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{comment}
%%% Pour afficher la correction et exclure les boites pour la reponse
\includecomment{correction}
\excludecomment{EspaceReponse}
%%% Pour version cachant la correction et incluant l'espace pour la reponse
%\excludecomment{correction}  
%\includecomment{EspaceReponse}




%%%
\begin{document}
\
\vspace{.2cm}

{\small
\noindent IUT Sénart-Fontainebleau, UPEC
\hfill
Florent Madelaine

\noindent Information Theory
\hfill
% intervenant 2

\noindent IUT Info 2A \hfill\noindent\academicyear{}

}
\vspace{.7cm}

\hrule
\vspace{.3cm}

\begin{center}

{\textbf{\Large
    Huffman Gruffalo Nightmare
}}
\vspace{.1cm}

\end{center}
\vspace{.3cm}

\hrule
\vspace{.3cm}


% %:-+-+-+- Engendré par : http://math.et.info.free.fr/TikZ/Arbre/
% \begin{center}
% % Racine à Gauche, développement vers la droite
% \begin{tikzpicture}[xscale=0.2,yscale=0.2]
% % Styles (MODIFIABLES)
% \tikzstyle{fleche}=[->,>=latex,thick]
% \tikzstyle{noeud}=[fill=yellow,circle,draw]
% \tikzstyle{feuille}=[fill=yellow,circle,draw]
% \tikzstyle{etiquette}=[midway,fill=white,draw]
% % Dimensions (MODIFIABLES)
% \def\DistanceInterNiveaux{3}
% \def\DistanceInterFeuilles{2}
% % Dimensions calculées (NON MODIFIABLES)
% \def\NiveauA{(0)*\DistanceInterNiveaux}
% \def\NiveauB{(1.875)*\DistanceInterNiveaux}
% \def\NiveauC{(3.625)*\DistanceInterNiveaux}
% \def\NiveauD{(5.25)*\DistanceInterNiveaux}
% \def\NiveauE{(6.75)*\DistanceInterNiveaux}
% \def\NiveauF{(8.125)*\DistanceInterNiveaux}
% \def\NiveauG{(9.375)*\DistanceInterNiveaux}
% \def\NiveauH{(10.5)*\DistanceInterNiveaux}
% \def\NiveauI{(11.5)*\DistanceInterNiveaux}
% \def\InterFeuilles{(-1)*\DistanceInterFeuilles}
% % Noeuds (MODIFIABLES : Styles et Coefficients d'InterFeuilles)
% \node[noeud] (R) at ({\NiveauA},{(13.5)*\InterFeuilles}) {\tiny $Tous$};
% \node[noeud] (Ra) at ({\NiveauB},{(3.5)*\InterFeuilles}) {$$};
% \node[noeud] (Raa) at ({\NiveauC},{(1)*\InterFeuilles}) {$$};
% \node[noeud] (Raaa) at ({\NiveauD},{(0.5)*\InterFeuilles}) {$$};
% \node[feuille] (Raaaa) at ({\NiveauE},{(0)*\InterFeuilles}) {\tiny $H$};
% \node[feuille] (Raaab) at ({\NiveauE},{(1)*\InterFeuilles}) {\tiny $T$};
% \node[feuille] (Raab) at ({\NiveauD},{(2)*\InterFeuilles}) {\tiny $E$};
% \node[noeud] (Rab) at ({\NiveauC},{(5)*\InterFeuilles}) {$$};
% \node[noeud] (Raba) at ({\NiveauD},{(4)*\InterFeuilles}) {$$};
% \node[feuille] (Rabaa) at ({\NiveauE},{(3)*\InterFeuilles}) {\tiny $A$};
% \node[noeud] (Rabab) at ({\NiveauE},{(4.5)*\InterFeuilles}) {$$};
% \node[feuille] (Rababa) at ({\NiveauF},{(4)*\InterFeuilles}) {\tiny $W$};
% \node[feuille] (Rababb) at ({\NiveauF},{(5)*\InterFeuilles}) {\tiny $G$};
% \node[noeud] (Rabb) at ({\NiveauD},{(6.5)*\InterFeuilles}) {$$};
% \node[feuille] (Rabba) at ({\NiveauE},{(6)*\InterFeuilles}) {\tiny $D$};
% \node[feuille] (Rabbb) at ({\NiveauE},{(7)*\InterFeuilles}) {\tiny $U$};
% \node[noeud] (Rb) at ({\NiveauB},{(17.5)*\InterFeuilles}) {$$};
% \node[noeud] (Rba) at ({\NiveauC},{(10.5)*\InterFeuilles}) {$$};
% \node[feuille] (Rbaa) at ({\NiveauD},{(8)*\InterFeuilles}) {\tiny $O$};
% \node[noeud] (Rbab) at ({\NiveauD},{(11)*\InterFeuilles}) {$$};
% \node[noeud] (Rbaba) at ({\NiveauE},{(10)*\InterFeuilles}) {$$};
% \node[noeud] (Rbabaa) at ({\NiveauF},{(9.5)*\InterFeuilles}) {$$};
% \node[feuille] (Rbabaaa) at ({\NiveauG},{(9)*\InterFeuilles}) {\tiny $.$};
% \node[feuille] (Rbabaab) at ({\NiveauG},{(10)*\InterFeuilles}) {\tiny $K$};
% \node[feuille] (Rbabab) at ({\NiveauF},{(11)*\InterFeuilles}) {\tiny $M$};
% \node[noeud] (Rbabb) at ({\NiveauE},{(12.5)*\InterFeuilles}) {$$};
% \node[feuille] (Rbabba) at ({\NiveauF},{(12)*\InterFeuilles}) {\tiny $L$};
% \node[feuille] (Rbabbb) at ({\NiveauF},{(13)*\InterFeuilles}) {\tiny $S$};
% \node[noeud] (Rbb) at ({\NiveauC},{(20.5)*\InterFeuilles}) {$$};
% \node[noeud] (Rbba) at ({\NiveauD},{(20)*\InterFeuilles}) {$$};
% \node[noeud] (Rbbaa) at ({\NiveauE},{(16.5)*\InterFeuilles}) {$$};
% \node[noeud] (Rbbaaa) at ({\NiveauF},{(16)*\InterFeuilles}) {$$};
% \node[noeud] (Rbbaaaa) at ({\NiveauG},{(14.5)*\InterFeuilles}) {$$};
% \node[feuille] (Rbbaaaaa) at ({\NiveauH},{(14)*\InterFeuilles}) {\tiny
%   $Y$};
% \node[feuille] (Rbbaaaab) at ({\NiveauH},{(15)*\InterFeuilles}) {\tiny
%   $"$};
% \node[noeud] (Rbbaaab) at ({\NiveauG},{(17)*\InterFeuilles}) {};
% \node[noeud] (Rbbaaaba) at ({\NiveauH},{(16.5)*\InterFeuilles}) {};
% \node[feuille] (Rbbaaabaa) at ({\NiveauI},{(16)*\InterFeuilles})
% {\tiny $F$};
% \node[feuille] (Rbbaaabab) at ({\NiveauI},{(17)*\InterFeuilles})
% {\tiny $X$};
% \node[feuille] (Rbbaaabb) at ({\NiveauH},{(18)*\InterFeuilles}) {\tiny
%   $B$};
% \node[feuille] (Rbbaab) at ({\NiveauF},{(19)*\InterFeuilles}) {\tiny $N$};
% \node[noeud] (Rbbab) at ({\NiveauE},{(23)*\InterFeuilles}) {$$};
% \node[feuille] (Rbbaba) at ({\NiveauF},{(20)*\InterFeuilles}) {\tiny $R$};
% \node[noeud] (Rbbabb) at ({\NiveauF},{(23.5)*\InterFeuilles}) {$$};
% \node[noeud] (Rbbabba) at ({\NiveauG},{(22.5)*\InterFeuilles}) {$$};
% \node[noeud] (Rbbabbaa) at ({\NiveauH},{(21.5)*\InterFeuilles}) {$$};
% \node[feuille] (Rbbabbaaa) at ({\NiveauI},{(21)*\InterFeuilles})
% {\tiny $P$};
% \node[feuille] (Rbbabbaab) at ({\NiveauI},{(22)*\InterFeuilles})
% {\tiny $V$};
% \node[noeud] (Rbbabbab) at ({\NiveauH},{(23.5)*\InterFeuilles}) {$$};
% \node[feuille] (Rbbabbaba) at ({\NiveauI},{(23)*\InterFeuilles})
% {\tiny $?$};
% \node[feuille] (Rbbabbabb) at ({\NiveauI},{(24)*\InterFeuilles})
% {\tiny $,$};
% \node[noeud] (Rbbabbb) at ({\NiveauG},{(25.5)*\InterFeuilles}) {$$};
% \node[feuille] (Rbbabbba) at ({\NiveauH},{(25)*\InterFeuilles}) {\tiny
%   $C$};
% \node[feuille] (Rbbabbbb) at ({\NiveauH},{(26)*\InterFeuilles}) {\tiny
%   $I$};
% \node[feuille] (Rbbb) at ({\NiveauD},{(27)*\InterFeuilles}) {\tiny $espace$};
% % Arcs (MODIFIABLES : Styles)
% \draw[fleche] (R)--(Ra) node[etiquette] {$0$};
% \draw[fleche] (Ra)--(Raa) node[etiquette] {$0$};
% \draw[fleche] (Raa)--(Raaa) node[etiquette] {$0$};
% \draw[fleche] (Raaa)--(Raaaa) node[etiquette] {$0$};
% \draw[fleche] (Raaa)--(Raaab) node[etiquette] {$1$};
% \draw[fleche] (Raa)--(Raab) node[etiquette] {$1$};
% \draw[fleche] (Ra)--(Rab) node[etiquette] {$1$};
% \draw[fleche] (Rab)--(Raba) node[etiquette] {$0$};
% \draw[fleche] (Raba)--(Rabaa) node[etiquette] {$0$};
% \draw[fleche] (Raba)--(Rabab) node[etiquette] {$1$};
% \draw[fleche] (Rabab)--(Rababa) node[etiquette] {$0$};
% \draw[fleche] (Rabab)--(Rababb) node[etiquette] {$1$};
% \draw[fleche] (Rab)--(Rabb) node[etiquette] {$1$};
% \draw[fleche] (Rabb)--(Rabba) node[etiquette] {$0$};
% \draw[fleche] (Rabb)--(Rabbb) node[etiquette] {$1$};
% \draw[fleche] (R)--(Rb) node[etiquette] {$1$};
% \draw[fleche] (Rb)--(Rba) node[etiquette] {$0$};
% \draw[fleche] (Rba)--(Rbaa) node[etiquette] {$0$};
% \draw[fleche] (Rba)--(Rbab) node[etiquette] {$1$};
% \draw[fleche] (Rbab)--(Rbaba) node[etiquette] {$0$};
% \draw[fleche] (Rbaba)--(Rbabaa) node[etiquette] {$0$};
% \draw[fleche] (Rbabaa)--(Rbabaaa) node[etiquette] {$0$};
% \draw[fleche] (Rbabaa)--(Rbabaab) node[etiquette] {$1$};
% \draw[fleche] (Rbaba)--(Rbabab) node[etiquette] {$1$};
% \draw[fleche] (Rbab)--(Rbabb) node[etiquette] {$1$};
% \draw[fleche] (Rbabb)--(Rbabba) node[etiquette] {$0$};
% \draw[fleche] (Rbabb)--(Rbabbb) node[etiquette] {$1$};
% \draw[fleche] (Rb)--(Rbb) node[etiquette] {$1$};
% \draw[fleche] (Rbb)--(Rbba) node[etiquette] {$0$};
% \draw[fleche] (Rbba)--(Rbbaa) node[etiquette] {$0$};
% \draw[fleche] (Rbbaa)--(Rbbaaa) node[etiquette] {$0$};
% \draw[fleche] (Rbbaaa)--(Rbbaaaa) node[etiquette] {$0$};
% \draw[fleche] (Rbbaaaa)--(Rbbaaaaa) node[etiquette] {$0$};
% \draw[fleche] (Rbbaaaa)--(Rbbaaaab) node[etiquette] {$1$};
% \draw[fleche] (Rbbaaa)--(Rbbaaab) node[etiquette] {$1$};
% \draw[fleche] (Rbbaaab)--(Rbbaaaba) node[etiquette] {$0$};
% \draw[fleche] (Rbbaaaba)--(Rbbaaabaa) node[etiquette] {$0$};
% \draw[fleche] (Rbbaaaba)--(Rbbaaabab) node[etiquette] {$1$};
% \draw[fleche] (Rbbaaab)--(Rbbaaabb) node[etiquette] {$1$};
% \draw[fleche] (Rbbaa)--(Rbbaab) node[etiquette] {$1$};
% \draw[fleche] (Rbba)--(Rbbab) node[etiquette] {$1$};
% \draw[fleche] (Rbbab)--(Rbbaba) node[etiquette] {$0$};
% \draw[fleche] (Rbbab)--(Rbbabb) node[etiquette] {$1$};
% \draw[fleche] (Rbbabb)--(Rbbabba) node[etiquette] {$0$};
% \draw[fleche] (Rbbabba)--(Rbbabbaa) node[etiquette] {$0$};
% \draw[fleche] (Rbbabbaa)--(Rbbabbaaa) node[etiquette] {$0$};
% \draw[fleche] (Rbbabbaa)--(Rbbabbaab) node[etiquette] {$1$};
% \draw[fleche] (Rbbabba)--(Rbbabbab) node[etiquette] {$1$};
% \draw[fleche] (Rbbabbab)--(Rbbabbaba) node[etiquette] {$0$};
% \draw[fleche] (Rbbabbab)--(Rbbabbabb) node[etiquette] {$1$};
% \draw[fleche] (Rbbabb)--(Rbbabbb) node[etiquette] {$1$};
% \draw[fleche] (Rbbabbb)--(Rbbabbba) node[etiquette] {$0$};
% \draw[fleche] (Rbbabbb)--(Rbbabbbb) node[etiquette] {$1$};
% \draw[fleche] (Rbb)--(Rbbb) node[etiquette] {$1$};
% \end{tikzpicture}
% \end{center}
% %:-+-+-+-+- Fin



\pagebreak

%:-+-+-+- Engendré par : http://math.et.info.free.fr/TikZ/Arbre/
\begin{center}
% Racine en Haut, développement vers le bas
\begin{tikzpicture}[xscale=0.4,yscale=0.45]
% Styles (MODIFIABLES)
\tikzstyle{fleche}=[->,>=latex,thick]
\tikzstyle{noeud}=[fill=yellow,circle,draw]
\tikzstyle{feuille}=[fill=yellow,circle,draw]
\tikzstyle{etiquette}=[midway,fill=white,draw]
% Dimensions (MODIFIABLES)
\def\DistanceInterNiveaux{3}
\def\DistanceInterFeuilles{2}
% Dimensions calculées (NON MODIFIABLES)
\def\NiveauA{(-0)*\DistanceInterNiveaux}
\def\NiveauB{(-1.875)*\DistanceInterNiveaux}
\def\NiveauC{(-3.625)*\DistanceInterNiveaux}
\def\NiveauD{(-5.25)*\DistanceInterNiveaux}
\def\NiveauE{(-6.75)*\DistanceInterNiveaux}
\def\NiveauF{(-8.125)*\DistanceInterNiveaux}
\def\NiveauG{(-9.375)*\DistanceInterNiveaux}
\def\NiveauH{(-10.5)*\DistanceInterNiveaux}
\def\NiveauI{(-11.5)*\DistanceInterNiveaux}
\def\InterFeuilles{(1)*\DistanceInterFeuilles}
% Noeuds (MODIFIABLES : Styles et Coefficients d'InterFeuilles)
\node[noeud] (R) at ({(13.5)*\InterFeuilles},{\NiveauA}) {\tiny Tous};
\node[noeud] (Ra) at ({(3.5)*\InterFeuilles},{\NiveauB}) {};
\node[noeud] (Raa) at ({(1)*\InterFeuilles},{\NiveauC}) {};
\node[noeud] (Raaa) at ({(0.5)*\InterFeuilles},{\NiveauD}) {};
\node[feuille] (Raaaa) at ({(0)*\InterFeuilles},{\NiveauE}) {\tiny H};
\node[feuille] (Raaab) at ({(1)*\InterFeuilles},{\NiveauE}) {\tiny T};
\node[feuille] (Raab) at ({(2)*\InterFeuilles},{\NiveauD}) {\tiny E};
\node[noeud] (Rab) at ({(5)*\InterFeuilles},{\NiveauC}) {};
\node[noeud] (Raba) at ({(4)*\InterFeuilles},{\NiveauD}) {};
\node[feuille] (Rabaa) at ({(3)*\InterFeuilles},{\NiveauE}) {\tiny A};
\node[noeud] (Rabab) at ({(4.5)*\InterFeuilles},{\NiveauE}) {};
\node[feuille] (Rababa) at ({(4)*\InterFeuilles},{\NiveauF}) {\tiny W};
\node[feuille] (Rababb) at ({(5)*\InterFeuilles},{\NiveauF}) {\tiny G};
\node[noeud] (Rabb) at ({(6.5)*\InterFeuilles},{\NiveauD}) {};
\node[feuille] (Rabba) at ({(6)*\InterFeuilles},{\NiveauE}) {\tiny D};
\node[feuille] (Rabbb) at ({(7)*\InterFeuilles},{\NiveauE}) {\tiny U};
\node[noeud] (Rb) at ({(17.5)*\InterFeuilles},{\NiveauB}) {};
\node[noeud] (Rba) at ({(10.5)*\InterFeuilles},{\NiveauC}) {};
\node[feuille] (Rbaa) at ({(8)*\InterFeuilles},{\NiveauD}) {\tiny O};
\node[noeud] (Rbab) at ({(11)*\InterFeuilles},{\NiveauD}) {};
\node[noeud] (Rbaba) at ({(10)*\InterFeuilles},{\NiveauE}) {};
\node[noeud] (Rbabaa) at ({(9.5)*\InterFeuilles},{\NiveauF}) {};
\node[feuille] (Rbabaaa) at ({(9)*\InterFeuilles},{\NiveauG}) {\tiny .};
\node[feuille] (Rbabaab) at ({(10)*\InterFeuilles},{\NiveauG}) {\tiny K};
\node[feuille] (Rbabab) at ({(11)*\InterFeuilles},{\NiveauF}) {\tiny M};
\node[noeud] (Rbabb) at ({(12.5)*\InterFeuilles},{\NiveauE}) {};
\node[feuille] (Rbabba) at ({(12)*\InterFeuilles},{\NiveauF}) {\tiny L};
\node[feuille] (Rbabbb) at ({(13)*\InterFeuilles},{\NiveauF}) {\tiny S};
\node[noeud] (Rbb) at ({(20.5)*\InterFeuilles},{\NiveauC}) {};
\node[noeud] (Rbba) at ({(20)*\InterFeuilles},{\NiveauD}) {};
\node[noeud] (Rbbaa) at ({(16.5)*\InterFeuilles},{\NiveauE}) {};
\node[noeud] (Rbbaaa) at ({(16)*\InterFeuilles},{\NiveauF}) {};
\node[noeud] (Rbbaaaa) at ({(14.5)*\InterFeuilles},{\NiveauG}) {};
\node[feuille] (Rbbaaaaa) at ({(14)*\InterFeuilles},{\NiveauH}) {\tiny
  Y};
\node[feuille] (Rbbaaaab) at ({(15)*\InterFeuilles},{\NiveauH}) {\tiny
  "};
\node[noeud] (Rbbaaab) at ({(17)*\InterFeuilles},{\NiveauG}) {};
\node[noeud] (Rbbaaaba) at ({(16.5)*\InterFeuilles},{\NiveauH}) {};
\node[feuille] (Rbbaaabaa) at ({(16)*\InterFeuilles},{\NiveauI})
{\tiny F};
\node[feuille] (Rbbaaabab) at ({(17)*\InterFeuilles},{\NiveauI})
{\tiny X};
\node[feuille] (Rbbaaabb) at ({(18)*\InterFeuilles},{\NiveauH}) {\tiny
  B};
\node[feuille] (Rbbaab) at ({(19)*\InterFeuilles},{\NiveauF}) {\tiny N};
\node[noeud] (Rbbab) at ({(23)*\InterFeuilles},{\NiveauE}) {};
\node[feuille] (Rbbaba) at ({(20)*\InterFeuilles},{\NiveauF}) {\tiny R};
\node[noeud] (Rbbabb) at ({(23.5)*\InterFeuilles},{\NiveauF}) {};
\node[noeud] (Rbbabba) at ({(22.5)*\InterFeuilles},{\NiveauG}) {};
\node[noeud] (Rbbabbaa) at ({(21.5)*\InterFeuilles},{\NiveauH}) {};
\node[feuille] (Rbbabbaaa) at ({(21)*\InterFeuilles},{\NiveauI})
{\tiny P};
\node[feuille] (Rbbabbaab) at ({(22)*\InterFeuilles},{\NiveauI})
{\tiny V};
\node[noeud] (Rbbabbab) at ({(23.5)*\InterFeuilles},{\NiveauH}) {};
\node[feuille] (Rbbabbaba) at ({(23)*\InterFeuilles},{\NiveauI})
{\tiny ?};
\node[feuille] (Rbbabbabb) at ({(24)*\InterFeuilles},{\NiveauI})
{\tiny ,};
\node[noeud] (Rbbabbb) at ({(25.5)*\InterFeuilles},{\NiveauG}) {};
\node[feuille] (Rbbabbba) at ({(25)*\InterFeuilles},{\NiveauH}) {\tiny
  C};
\node[feuille] (Rbbabbbb) at ({(26)*\InterFeuilles},{\NiveauH}) {\tiny
  I};
\node[feuille] (Rbbb) at ({(27)*\InterFeuilles},{\NiveauD}) {\tiny espace};
% Arcs (MODIFIABLES : Styles)
\draw[fleche] (R)--(Ra) node[etiquette] {\tiny 0};
\draw[fleche] (Ra)--(Raa) node[etiquette] {\tiny 0};
\draw[fleche] (Raa)--(Raaa) node[etiquette] {\tiny 0};
\draw[fleche] (Raaa)--(Raaaa) node[etiquette] {\tiny 0};
\draw[fleche] (Raaa)--(Raaab) node[etiquette] {\tiny 1};
\draw[fleche] (Raa)--(Raab) node[etiquette] {\tiny 1};
\draw[fleche] (Ra)--(Rab) node[etiquette] {\tiny 1};
\draw[fleche] (Rab)--(Raba) node[etiquette] {\tiny 0};
\draw[fleche] (Raba)--(Rabaa) node[etiquette] {\tiny 0};
\draw[fleche] (Raba)--(Rabab) node[etiquette] {\tiny 1};
\draw[fleche] (Rabab)--(Rababa) node[etiquette] {\tiny 0};
\draw[fleche] (Rabab)--(Rababb) node[etiquette] {\tiny 1};
\draw[fleche] (Rab)--(Rabb) node[etiquette] {\tiny 1};
\draw[fleche] (Rabb)--(Rabba) node[etiquette] {\tiny 0};
\draw[fleche] (Rabb)--(Rabbb) node[etiquette] {\tiny 1};
\draw[fleche] (R)--(Rb) node[etiquette] {\tiny 1};
\draw[fleche] (Rb)--(Rba) node[etiquette] {\tiny 0};
\draw[fleche] (Rba)--(Rbaa) node[etiquette] {\tiny 0};
\draw[fleche] (Rba)--(Rbab) node[etiquette] {\tiny 1};
\draw[fleche] (Rbab)--(Rbaba) node[etiquette] {\tiny 0};
\draw[fleche] (Rbaba)--(Rbabaa) node[etiquette] {\tiny 0};
\draw[fleche] (Rbabaa)--(Rbabaaa) node[etiquette] {\tiny 0};
\draw[fleche] (Rbabaa)--(Rbabaab) node[etiquette] {\tiny 1};
\draw[fleche] (Rbaba)--(Rbabab) node[etiquette] {\tiny 1};
\draw[fleche] (Rbab)--(Rbabb) node[etiquette] {\tiny 1};
\draw[fleche] (Rbabb)--(Rbabba) node[etiquette] {\tiny 0};
\draw[fleche] (Rbabb)--(Rbabbb) node[etiquette] {\tiny 1};
\draw[fleche] (Rb)--(Rbb) node[etiquette] {\tiny 1};
\draw[fleche] (Rbb)--(Rbba) node[etiquette] {\tiny 0};
\draw[fleche] (Rbba)--(Rbbaa) node[etiquette] {\tiny 0};
\draw[fleche] (Rbbaa)--(Rbbaaa) node[etiquette] {\tiny 0};
\draw[fleche] (Rbbaaa)--(Rbbaaaa) node[etiquette] {\tiny 0};
\draw[fleche] (Rbbaaaa)--(Rbbaaaaa) node[etiquette] {\tiny 0};
\draw[fleche] (Rbbaaaa)--(Rbbaaaab) node[etiquette] {\tiny 1};
\draw[fleche] (Rbbaaa)--(Rbbaaab) node[etiquette] {\tiny 1};
\draw[fleche] (Rbbaaab)--(Rbbaaaba) node[etiquette] {\tiny 0};
\draw[fleche] (Rbbaaaba)--(Rbbaaabaa) node[etiquette] {\tiny 0};
\draw[fleche] (Rbbaaaba)--(Rbbaaabab) node[etiquette] {\tiny 1};
\draw[fleche] (Rbbaaab)--(Rbbaaabb) node[etiquette] {\tiny 1};
\draw[fleche] (Rbbaa)--(Rbbaab) node[etiquette] {\tiny 1};
\draw[fleche] (Rbba)--(Rbbab) node[etiquette] {\tiny 1};
\draw[fleche] (Rbbab)--(Rbbaba) node[etiquette] {\tiny 0};
\draw[fleche] (Rbbab)--(Rbbabb) node[etiquette] {\tiny 1};
\draw[fleche] (Rbbabb)--(Rbbabba) node[etiquette] {\tiny 0};
\draw[fleche] (Rbbabba)--(Rbbabbaa) node[etiquette] {\tiny 0};
\draw[fleche] (Rbbabbaa)--(Rbbabbaaa) node[etiquette] {\tiny 0};
\draw[fleche] (Rbbabbaa)--(Rbbabbaab) node[etiquette] {\tiny 1};
\draw[fleche] (Rbbabba)--(Rbbabbab) node[etiquette] {\tiny 1};
\draw[fleche] (Rbbabbab)--(Rbbabbaba) node[etiquette] {\tiny 0};
\draw[fleche] (Rbbabbab)--(Rbbabbabb) node[etiquette] {\tiny 1};
\draw[fleche] (Rbbabb)--(Rbbabbb) node[etiquette] {\tiny 1};
\draw[fleche] (Rbbabbb)--(Rbbabbba) node[etiquette] {\tiny 0};
\draw[fleche] (Rbbabbb)--(Rbbabbbb) node[etiquette] {\tiny 1};
\draw[fleche] (Rbb)--(Rbbb) node[etiquette] {\tiny 1};
\end{tikzpicture}
\end{center}
%:-+-+-+-+- Fin


\end{document}






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%   un nouvel exo et sa correction       %%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%début-exo
\begin{exo}
  \begin{enumerate}
  \item %question 1

  \item %question 2

  \end{enumerate}
\end{exo}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%fin-exo

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%début-correction
\begin{correction}
  \begin{shaded}
    %%% \begin{minipage}{.9\linewidth}
    \begin{center}
      \textbf{solution.}
    \end{center}
    \begin{enumerate}
    \item %solution question 1

    \item %solution question 2

    \end{enumerate}
    %%%\end{minipage}
  \end{shaded}
  \medskip
\end{correction}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%fin-correction
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



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