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b/3InformationTheory/HuffmanGruffaloNightmare.out new file mode 100644 index 0000000..e69de29 diff --git a/3InformationTheory/HuffmanGruffaloNightmare.pdf b/3InformationTheory/HuffmanGruffaloNightmare.pdf new file mode 100644 index 0000000..d84dfbb Binary files /dev/null and b/3InformationTheory/HuffmanGruffaloNightmare.pdf differ diff --git a/3InformationTheory/HuffmanGruffaloNightmare.tex b/3InformationTheory/HuffmanGruffaloNightmare.tex new file mode 100644 index 0000000..8e005ee --- /dev/null +++ b/3InformationTheory/HuffmanGruffaloNightmare.tex @@ -0,0 +1,715 @@ +% -*- coding: utf-8; -*- +\documentclass[a4paper,6pt,landscape]{article} +%\usepackage{pdflscape} +%\usepackage{sagetex} + +\usepackage[francais]{babel} +%\usepackage[latin1]{inputenc} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{lmodern} +\usepackage{graphics,graphicx} +\usepackage{url} +\usepackage{hyperref} +\usepackage[pdftex,usenames,dvipsnames]{xcolor} +%%% decommenter si tikz necessaire +\usepackage{tikz} +\usetikzlibrary[decorations.pathmorphing] +\usetikzlibrary[decorations.pathreplacing] +\usetikzlibrary{backgrounds} +\usetikzlibrary{positioning} +\usetikzlibrary{arrows} +\usetikzlibrary[backgrounds] +\usetikzlibrary{automata,positioning,arrows.meta} +%%% +\usepackage{tcolorbox} +\tcbuselibrary{skins,breakable} +\tcbset{textmarker/.style={% + % skin=enhancedmiddlejigsaw, + breakable, + parbox=false, + boxrule=0mm,leftrule=5mm,rightrule=5mm,boxsep=0mm,arc=0mm,outer arc=0mm, + left=3mm,right=3mm,top=1mm,bottom=1mm,toptitle=1mm,bottomtitle=1mm,oversize}} +\newtcolorbox{yellow}{textmarker,colback=yellow!5!white,colframe=yellow} +\newtcolorbox{orange}{textmarker,colback=DarkOrange!5!white, + colframe=DarkOrange!75!yellow} +\newtcolorbox{red}{textmarker,colback=red!5!white,colframe=red} +\newtcolorbox{blue}{textmarker,colback=DeepSkyBlue!5!white,colframe=DeepSkyBlue} +\newtcolorbox{green}{textmarker,colback=Chartreuse!5!white,colframe=Chartreuse} +\newtcolorbox{rainbow}{textmarker,interior hidden, + frame style={top color=blue,bottom color=red,middle color=green}} +\newtcbox{\fluo}[1][yellow]{on line, +arc=7pt,colback=#1!10!white,colframe=#1!50!black, +before upper={\rule[-3pt]{0pt}{10pt}},boxrule=1pt, +boxsep=0pt,left=6pt,right=6pt,top=2pt,bottom=2pt} +%%% + +%\usepackage{tikz-uml} + +\usepackage[thicklines]{easytable} +\usepackage{framed} %%% boîtes permettant de gérer correctement le saut de page. +\usepackage{multicol} +\usepackage{savetrees} +%\usepackage[a4paper,width=17cm,height=23cm]{geometry} +\usepackage{a4wide} +\usepackage{paralist} +\usepackage{fancyhdr} +\usepackage{colortbl} +\usepackage{cancel} %%% +\usepackage{amssymb,amsmath,amsthm} + +%%% 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. +%\input{MyMacros.tex} +%\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}{$\circ$} +} + +%\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}} +\hfill +Groupe : \fbox{\begin{minipage}{.7cm}\hfill\vspace{.7cm}\end{minipage}} +\end{minipage} +} +\fancyfoot[C]{Page {\large\thepage}} + + +%%%%%%%%%%%%%%%%%%%%%%%% +%%% 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 MD1N \hfill\noindent\academicyear{} + +} +\vspace{.7cm} + +\hrule +\vspace{.3cm} + +\begin{center} + +{\textbf{\Large + Huffman Gruffalo Nightmare +}} +\vspace{.1cm} + +\end{center} +\vspace{.3cm} + +\hrule +\vspace{.3cm} + +\section*{Le texte qu'on souhaite compresser avec la méthode de Huffman} + +\begin{quotation} + A mouse took a stroll through the deep dark wood. A fox saw the + mouse and the mouse looked good. “Where are you going to, little + brown mouse? Come and have lunch in my underground house.” +\end{quotation} + +\section*{La méthode} +\paragraph{étape 1 (au tableau)} +On compte la fréquence des lettres. +Le moins fréquent est à traiter en premier. + +\paragraph{étape 2 (au tableau)} +On construit l'arbre de Huffman. +Les lettres les moins fréquentes se retrouvent en base de l'arbre, +donc avec un code plus long. + + +\paragraph{étape 3 : compression}. +On note les labels de la racine vers la feuille qui est le code de chaque lettre. + +\begin{verbatim} +A devient : 0100 +(j'écris _ pour l'espace) +_ devient : 111 +m devient : 10 101 +o devient : 100 +u devient : 0 111 +s devient : 10 111 +e devient : 001 +_ devient : 111 +t devient : 000 1 +o devient : 100 +o devient : 100 +k devient : 101 001 +_ devient : 111 +a devient : ???? +_ devient : 111 +\end{verbatim} + +% %:-+-+-+- Engendré par : http://math.et.info.free.fr/TikZ/Arbre/ +% \begin{center} +% % Racine à Gauche, développement vers la droite +% \begin{tikzpicture}[xscale=1,yscale=1] +% % 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}) {$Tous$}; +% \node[noeud] (Ra) at ({\NiveauB},{(3.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Raa) at ({\NiveauC},{(1)*\InterFeuilles}) {$$}; +% \node[noeud] (Raaa) at ({\NiveauD},{(0.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Raaaa) at ({\NiveauE},{(0)*\InterFeuilles}) {$H$}; +% \node[feuille] (Raaab) at ({\NiveauE},{(1)*\InterFeuilles}) {$T$}; +% \node[feuille] (Raab) at ({\NiveauD},{(2)*\InterFeuilles}) {$E$}; +% \node[noeud] (Rab) at ({\NiveauC},{(5)*\InterFeuilles}) {$$}; +% \node[noeud] (Raba) at ({\NiveauD},{(4)*\InterFeuilles}) {$$}; +% \node[feuille] (Rabaa) at ({\NiveauE},{(3)*\InterFeuilles}) {$A$}; +% \node[noeud] (Rabab) at ({\NiveauE},{(4.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rababa) at ({\NiveauF},{(4)*\InterFeuilles}) {$W$}; +% \node[feuille] (Rababb) at ({\NiveauF},{(5)*\InterFeuilles}) {$G$}; +% \node[noeud] (Rabb) at ({\NiveauD},{(6.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rabba) at ({\NiveauE},{(6)*\InterFeuilles}) {$D$}; +% \node[feuille] (Rabbb) at ({\NiveauE},{(7)*\InterFeuilles}) {$U$}; +% \node[noeud] (Rb) at ({\NiveauB},{(17.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Rba) at ({\NiveauC},{(10.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbaa) at ({\NiveauD},{(8)*\InterFeuilles}) {$O$}; +% \node[noeud] (Rbab) at ({\NiveauD},{(11)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbaba) at ({\NiveauE},{(10)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbabaa) at ({\NiveauF},{(9.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbabaaa) at ({\NiveauG},{(9)*\InterFeuilles}) {$.$}; +% \node[feuille] (Rbabaab) at ({\NiveauG},{(10)*\InterFeuilles}) {$K$}; +% \node[feuille] (Rbabab) at ({\NiveauF},{(11)*\InterFeuilles}) {$M$}; +% \node[noeud] (Rbabb) at ({\NiveauE},{(12.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbabba) at ({\NiveauF},{(12)*\InterFeuilles}) {$L$}; +% \node[feuille] (Rbabbb) at ({\NiveauF},{(13)*\InterFeuilles}) {$S$}; +% \node[noeud] (Rbb) at ({\NiveauC},{(20.5)*\InterFeuilles}) {$$}; +% \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}) {$Y$}; +% \node[feuille] (Rbbaaaab) at ({\NiveauH},{(15)*\InterFeuilles}) {$"$}; +% \node[noeud] (Rbbaaab) at ({\NiveauG},{(17)*\InterFeuilles}) {$Nœud36$}; +% \node[noeud] (Rbbaaaba) at ({\NiveauH},{(16.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbaaabaa) at ({\NiveauI},{(16)*\InterFeuilles}) {$F$}; +% \node[feuille] (Rbbaaabab) at ({\NiveauI},{(17)*\InterFeuilles}) {$X$}; +% \node[feuille] (Rbbaaabb) at ({\NiveauH},{(18)*\InterFeuilles}) {$B$}; +% \node[feuille] (Rbbaab) at ({\NiveauF},{(19)*\InterFeuilles}) {$N$}; +% \node[noeud] (Rbbab) at ({\NiveauE},{(23)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbaba) at ({\NiveauF},{(20)*\InterFeuilles}) {$R$}; +% \node[noeud] (Rbbabb) at ({\NiveauF},{(23.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbbabba) at ({\NiveauG},{(22.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbbabbaa) at ({\NiveauH},{(21.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbabbaaa) at ({\NiveauI},{(21)*\InterFeuilles}) {$P$}; +% \node[feuille] (Rbbabbaab) at ({\NiveauI},{(22)*\InterFeuilles}) {$V$}; +% \node[noeud] (Rbbabbab) at ({\NiveauH},{(23.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbabbaba) at ({\NiveauI},{(23)*\InterFeuilles}) {$?$}; +% \node[feuille] (Rbbabbabb) at ({\NiveauI},{(24)*\InterFeuilles}) {$,$}; +% \node[noeud] (Rbbabbb) at ({\NiveauG},{(25.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbabbba) at ({\NiveauH},{(25)*\InterFeuilles}) {$C$}; +% \node[feuille] (Rbbabbbb) at ({\NiveauH},{(26)*\InterFeuilles}) {$I$}; +% \node[feuille] (Rbbb) at ({\NiveauD},{(27)*\InterFeuilles}) {$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] {$A$}; +% \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 + + + +% %:-+-+-+- 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 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + +%%% LocalWords: +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: + diff --git a/3InformationTheory/file1.txt b/3InformationTheory/file1.txt new file mode 100644 index 0000000..cf8297e --- /dev/null +++ b/3InformationTheory/file1.txt @@ -0,0 +1,11 @@ +Ceci est un fichier texte pour tester la commande diff. + +Vous pouvez consulter le manuel de la commande diff en écrivant. + +man diff + +Ici j'ajoute une ligne qui sera absente du fichier file2.txt + +Pour faire la différence entre deux fichiers on peut faire : + +diff --color file1.txt file2.txt diff --git a/3InformationTheory/file2.txt b/3InformationTheory/file2.txt new file mode 100644 index 0000000..d862eef --- /dev/null +++ b/3InformationTheory/file2.txt @@ -0,0 +1,24 @@ +Ceci est un fichier texte pour tester la commande diff. + +Vous pouvez consulter le manuel de la commande diff en écrivant. + +man diff + +Je peux écrire le résultat (la page de manuel de diff) en écrivant + +man diff >> file2.txt + +Comme c'est un peu long, à la place j'ai utilisé + +man diff | head >> file2.txt + +GNU(1) User Commands GNU(1) + +NAME + GNU diff - compare files line by line + +SYNOPSIS + diff [OPTION]... FILES + +DESCRIPTION + Compare FILES line by line. diff --git a/3InformationTheory/gruffalo.txt b/3InformationTheory/gruffalo.txt new file mode 100644 index 0000000..eb37bb6 --- /dev/null +++ b/3InformationTheory/gruffalo.txt @@ -0,0 +1,168 @@ +A mouse took a stroll through the deep dark wood. A fox saw +the mouse and the mouse looked good. “Where are you going +to, little brown mouse? Come and have lunch in my +underground house.” + +étape 1 au tableau on compte la fréquence des lettres. +Le moins fréquent est à traiter en premier. + +étape 2 au tableau on construit l'arbre de Huffman. + +étape 3 : compression. +On note les labels de la racine vers la feuille qui est le code de chaque lettre. + +A devient : 0100 +(j'écris _ pour l'espace) +_ devient : 111 +m devient : 10 101 +o devient : 100 +u devient : 0 111 +s devient : 10 111 +e devient : 001 +_ devient : 111 +t devient : 000 1 +o devient : 100 +o devient : 100 +k devient : 101 001 +_ devient : 111 +a devient : ???? +_ devient : 111 + +%:-+-+-+- Engendré par : http://math.et.info.free.fr/TikZ/Arbre/ +\begin{center} +% Racine à Gauche, développement vers la droite +\begin{tikzpicture}[xscale=1,yscale=1] +% 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}) {$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}) {$H$}; +\node[feuille] (Raaab) at ({\NiveauE},{(1)*\InterFeuilles}) {$T$}; +\node[feuille] (Raab) at ({\NiveauD},{(2)*\InterFeuilles}) {$E$}; +\node[noeud] (Rab) at ({\NiveauC},{(5)*\InterFeuilles}) {$$}; +\node[noeud] (Raba) at ({\NiveauD},{(4)*\InterFeuilles}) {$$}; +\node[feuille] (Rabaa) at ({\NiveauE},{(3)*\InterFeuilles}) {$A$}; +\node[noeud] (Rabab) at ({\NiveauE},{(4.5)*\InterFeuilles}) {$$}; +\node[feuille] (Rababa) at ({\NiveauF},{(4)*\InterFeuilles}) {$W$}; +\node[feuille] (Rababb) at ({\NiveauF},{(5)*\InterFeuilles}) {$G$}; +\node[noeud] (Rabb) at ({\NiveauD},{(6.5)*\InterFeuilles}) {$$}; +\node[feuille] (Rabba) at ({\NiveauE},{(6)*\InterFeuilles}) {$D$}; +\node[feuille] (Rabbb) at ({\NiveauE},{(7)*\InterFeuilles}) {$U$}; +\node[noeud] (Rb) at ({\NiveauB},{(17.5)*\InterFeuilles}) {$$}; +\node[noeud] (Rba) at ({\NiveauC},{(10.5)*\InterFeuilles}) {$$}; +\node[feuille] (Rbaa) at ({\NiveauD},{(8)*\InterFeuilles}) {$O$}; +\node[noeud] (Rbab) at ({\NiveauD},{(11)*\InterFeuilles}) {$$}; +\node[noeud] (Rbaba) at ({\NiveauE},{(10)*\InterFeuilles}) {$$}; +\node[noeud] (Rbabaa) at ({\NiveauF},{(9.5)*\InterFeuilles}) {$$}; +\node[feuille] (Rbabaaa) at ({\NiveauG},{(9)*\InterFeuilles}) {$.$}; +\node[feuille] (Rbabaab) at ({\NiveauG},{(10)*\InterFeuilles}) {$K$}; +\node[feuille] (Rbabab) at ({\NiveauF},{(11)*\InterFeuilles}) {$M$}; +\node[noeud] (Rbabb) at ({\NiveauE},{(12.5)*\InterFeuilles}) {$$}; +\node[feuille] (Rbabba) at ({\NiveauF},{(12)*\InterFeuilles}) {$L$}; +\node[feuille] (Rbabbb) at ({\NiveauF},{(13)*\InterFeuilles}) {$S$}; +\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}) {$$}; +\node[feuille] (Rbbaaaaa) at ({\NiveauH},{(14)*\InterFeuilles}) {$Y$}; +\node[feuille] (Rbbaaaab) at ({\NiveauH},{(15)*\InterFeuilles}) {$"$}; +\node[noeud] (Rbbaaab) at ({\NiveauG},{(17)*\InterFeuilles}) {$Nœud36$}; +\node[noeud] (Rbbaaaba) at ({\NiveauH},{(16.5)*\InterFeuilles}) {$$}; +\node[feuille] (Rbbaaabaa) at ({\NiveauI},{(16)*\InterFeuilles}) {$F$}; +\node[feuille] (Rbbaaabab) at ({\NiveauI},{(17)*\InterFeuilles}) {$X$}; +\node[feuille] (Rbbaaabb) at ({\NiveauH},{(18)*\InterFeuilles}) {$B$}; +\node[feuille] (Rbbaab) at ({\NiveauF},{(19)*\InterFeuilles}) {$N$}; +\node[noeud] (Rbbab) at ({\NiveauE},{(23)*\InterFeuilles}) {$$}; +\node[feuille] (Rbbaba) at ({\NiveauF},{(20)*\InterFeuilles}) {$R$}; +\node[noeud] (Rbbabb) at ({\NiveauF},{(23.5)*\InterFeuilles}) {$$}; +\node[noeud] (Rbbabba) at ({\NiveauG},{(22.5)*\InterFeuilles}) {$$}; +\node[noeud] (Rbbabbaa) at ({\NiveauH},{(21.5)*\InterFeuilles}) {$$}; +\node[feuille] (Rbbabbaaa) at ({\NiveauI},{(21)*\InterFeuilles}) {$P$}; +\node[feuille] (Rbbabbaab) at ({\NiveauI},{(22)*\InterFeuilles}) {$V$}; +\node[noeud] (Rbbabbab) at ({\NiveauH},{(23.5)*\InterFeuilles}) {$$}; +\node[feuille] (Rbbabbaba) at ({\NiveauI},{(23)*\InterFeuilles}) {$?$}; +\node[feuille] (Rbbabbabb) at ({\NiveauI},{(24)*\InterFeuilles}) {$,$}; +\node[noeud] (Rbbabbb) at ({\NiveauG},{(25.5)*\InterFeuilles}) {$$}; +\node[feuille] (Rbbabbba) at ({\NiveauH},{(25)*\InterFeuilles}) {$C$}; +\node[feuille] (Rbbabbbb) at ({\NiveauH},{(26)*\InterFeuilles}) {$I$}; +\node[feuille] (Rbbb) at ({\NiveauD},{(27)*\InterFeuilles}) {$espace$}; +% 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] {$A$}; +\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 +