Ajoutd es fichiers

8 years ago · e7a9b1a7cf
28 changed files with 1610 additions and 0 deletions
--- a/.gitignore
+++ b/.gitignore
@ -0,0 +1,233 @@
+
+# Created by https://www.gitignore.io/api/latex
+
+### LaTeX ###
+## Core latex/pdflatex auxiliary files:
+*.aux
+*.lof
+*.log
+*.lot
+*.fls
+*.out
+*.toc
+*.fmt
+*.fot
+*.cb
+*.cb2
+
+## Intermediate documents:
+*.dvi
+*.xdv
+*-converted-to.*
+# these rules might exclude image files for figures etc.
+# *.ps
+# *.eps
+# *.pdf
+
+## Generated if empty string is given at "Please type another file name for output:"
+.pdf
+
+## Bibliography auxiliary files (bibtex/biblatex/biber):
+*.bbl
+*.bcf
+*.blg
+*-blx.aux
+*-blx.bib
+*.run.xml
+
+## Build tool auxiliary files:
+*.fdb_latexmk
+*.synctex
+*.synctex(busy)
+*.synctex.gz
+*.synctex.gz(busy)
+*.pdfsync
+*Notes.bib
+
+## Auxiliary and intermediate files from other packages:
+# algorithms
+*.alg
+*.loa
+
+# achemso
+acs-*.bib
+
+# amsthm
+*.thm
+
+# beamer
+*.nav
+*.pre
+*.snm
+*.vrb
+
+# changes
+*.soc
+
+# cprotect
+*.cpt
+
+# elsarticle (documentclass of Elsevier journals)
+*.spl
+
+# endnotes
+*.ent
+
+# fixme
+*.lox
+
+# feynmf/feynmp
+*.mf
+*.mp
+*.t[1-9]
+*.t[1-9][0-9]
+*.tfm
+
+#(r)(e)ledmac/(r)(e)ledpar
+*.end
+*.?end
+*.[1-9]
+*.[1-9][0-9]
+*.[1-9][0-9][0-9]
+*.[1-9]R
+*.[1-9][0-9]R
+*.[1-9][0-9][0-9]R
+*.eledsec[1-9]
+*.eledsec[1-9]R
+*.eledsec[1-9][0-9]
+*.eledsec[1-9][0-9]R
+*.eledsec[1-9][0-9][0-9]
+*.eledsec[1-9][0-9][0-9]R
+
+# glossaries
+*.acn
+*.acr
+*.glg
+*.glo
+*.gls
+*.glsdefs
+
+# gnuplottex
+*-gnuplottex-*
+
+# gregoriotex
+*.gaux
+*.gtex
+
+# hyperref
+*.brf
+
+# knitr
+*-concordance.tex
+# TODO Comment the next line if you want to keep your tikz graphics files
+*.tikz
+*-tikzDictionary
+
+# listings
+*.lol
+
+# makeidx
+*.idx
+*.ilg
+*.ind
+*.ist
+
+# minitoc
+*.maf
+*.mlf
+*.mlt
+*.mtc[0-9]*
+*.slf[0-9]*
+*.slt[0-9]*
+*.stc[0-9]*
+
+# minted
+_minted*
+*.pyg
+
+# morewrites
+*.mw
+
+# nomencl
+*.nlo
+
+# pax
+*.pax
+
+# pdfpcnotes
+*.pdfpc
+
+# sagetex
+*.sagetex.sage
+*.sagetex.py
+*.sagetex.scmd
+
+# scrwfile
+*.wrt
+
+# sympy
+*.sout
+*.sympy
+sympy-plots-for-*.tex/
+
+# pdfcomment
+*.upa
+*.upb
+
+# pythontex
+*.pytxcode
+pythontex-files-*/
+
+# thmtools
+*.loe
+
+# TikZ & PGF
+*.dpth
+*.md5
+*.auxlock
+
+# todonotes
+*.tdo
+
+# easy-todo
+*.lod
+
+# xindy
+*.xdy
+
+# xypic precompiled matrices
+*.xyc
+
+# endfloat
+*.ttt
+*.fff
+
+# Latexian
+TSWLatexianTemp*
+
+## Editors:
+# WinEdt
+*.bak
+*.sav
+
+# Texpad
+.texpadtmp
+
+# Kile
+*.backup
+
+# KBibTeX
+*~[0-9]*
+
+# auto folder when using emacs and auctex
+/auto/*
+
+# expex forward references with \gathertags
+*-tags.tex
+
+### LaTeX Patch ###
+# glossaries
+*.glstex
+
+
+# End of https://www.gitignore.io/api/latex
--- a/CSLogo.png
+++ b/CSLogo.png
--- a/MyPack2.sty
+++ b/MyPack2.sty
@ -0,0 +1,169 @@
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{MyPack2}
+
+%%%%%%%% INCLUSIONS GÉNÉRALES %%%%%%%%%
+\RequirePackage{babel}
+%\RequirePackage{titlesec}
+\RequirePackage{color}
+%\RequirePackage[a4paper]{geometry}
+\RequirePackage[font=small,format=plain,labelfont=bf,up,
+    textfont=normal,up,
+    justification=justified,
+    singlelinecheck=false]{caption}
+\RequirePackage[justification=centering]{caption}
+\RequirePackage{xcolor} % Required for specifying custom colours
+\definecolor{grey}{rgb}{0.9,0.9,0.9} % Colour of the box surrounding the title
+\RequirePackage[utf8]{inputenc} % Required for inputting international characters
+
+\RequirePackage[T1]{fontenc}
+% \RequirePackage[sfdefault]{ClearSans} % Use the Clear Sans font (sans serif)
+\RequirePackage{placeins}
+\RequirePackage{listings}
+\RequirePackage{graphicx}
+\RequirePackage{amsfonts}
+
+
+\definecolor{defaultColor}{RGB}{0,100,143}
+\definecolor{bleu}{RGB}{0,100,143}
+\definecolor{gris}{RGB}{130,130,140}
+\definecolor{grisBleu}{RGB}{65,115,141}
+
+
+
+%%%%%%%% MATH %%%%%%%%%
+\RequirePackage{stmaryrd}
+\newcommand*\intervalleEntier[2]{\intervalle{\llbracket}{#1}{#2}{\rrbracket}}
+\newcommand*\intervalle[4]{\left#1 #2 \, ; #3 \right#4}
+\newcommand*\intervalleOO[2]{\intervalle{]}{#1}{#2}{[}}
+\newcommand*\intervalleFF[2]{\intervalle{[}{#1}{#2}{]}}
+\newcommand*\intervalleOF[2]{\intervalle{]}{#1}{#2}{]}}
+\newcommand*\intervalleFO[2]{\intervalle{[}{#1}{#2}{[}}
+
+\let\ensembleNombre\mathbb
+\newcommand*\N{\ensembleNombre{N}}
+\newcommand*\Z{\ensembleNombre{Z}}
+\newcommand*\Q{\ensembleNombre{Q}}
+\newcommand*\R{\ensembleNombre{R}}
+\newcommand*\C{\ensembleNombre{C}}
+
+\newcommand*\enstq[2]{\left\{#1,\; #2\right\}}
+
+%\newcommand*\int[1]{\left\lfloor #1\right\rfloor}
+%\newcommand*\norme[1]{\left\lVert#1\right\rVert}
+%\newcommand*\abs[1]{\left\lvert#1\right\rvert}
+
+\let\vecteur\overrightarrow
+
+\newcommand*\Sys[1]{\left\{ \begin{aligned} #1 \end{aligned} \right. \kern-\nulldelimiterspace}
+
+\newcommand*\application[5]{
+	#1 \colon
+	\begin{alignedat}{2} &#2 &\to &#3\\
+	                     &#4 &\mapsto &#5
+	\end{alignedat}
+}
+\newcommand*\applicationSigne[3]{
+	#1 \colon #2 \to #3
+}
+
+\newtheorem{defi}{Définition}[section]
+\newtheorem{theo}{Théorème}[section]
+\newtheorem{prop}{Proposition}[section]
+\newtheorem{ex}{Exemple}[section]
+
+
+%%%%%%%% SECTIONNEMENT %%%%%%%%%
+
+%\renewcommand{\thesection}{\Roman{section}}
+%\renewcommand{\thesubsection}{\arabic{subsection}}
+
+%\renewcommand{\@seccntformat}[1]{
+%	\llap{
+%		\textcolor{defaultColor}{\csname the#1\endcsname}
+%		\hspace{1em}
+%	}
+%}
+%\renewcommand{\section}{
+%	\@startsection{section}{1}{0pt}
+%	{0pt}
+%	{0pt}
+%	{\normalfont\large\bfseries\llap}
+%}
+
+
+\newcommand*\emptyPage{\newpage\null\thispagestyle{empty}\addtocounter{page}{-1}\newpage}
+
+%%%%%%%% INTIALISATION DE LA PAGE %%%%%%%%%
+\RequirePackage{fancyhdr}
+\newcommand\initPage[3]{
+        \pagestyle{fancy}
+        \fancyhead{#1}
+        \lhead{#2}
+        \rhead{#3}
+        \rfoot{}
+        \lfoot{\includegraphics[scale=0.2]{CSLogo}}
+
+        %\titleformat*{\section}{\Large\bfseries\color{bleu}\Roman{section}}
+        %\titleformat*{\subsection}{\large\bfseries\color{grisBleu}}
+        %\titleformat*{\subsubsection}{\bfseries\color{gris}}
+        %\titlespacing*{\section}{-3em}{*1}{*1}
+        %\titlespacing*{\subsection}{-2em}{*1}{*1}
+        %\titlespacing*{\subsubsection}{-1em}{*1}{*1}
+
+}
+
+%%%%%%%% TITRE %%%%%%%%M
+\renewcommand{\maketitle}{
+\begin{titlepage} % Suppresses displaying the page number on the title page and the subsequent page counts as page 1
+	%------------------------------------------------
+	%	Grey title box
+	%------------------------------------------------
+  \topskip0pt
+  \vspace*{5cm}
+	\colorbox{grey}{
+		\parbox[t]{0.93\textwidth}{ % Outer full width box
+			\parbox[t]{0.91\textwidth}{ % Inner box for inner right text margin
+				\raggedleft % Right align the text
+				\fontsize{72pt}{80pt}\selectfont % Title font size, the first argument is the font size and the second is the line spacing, adjust depending on title length
+				\vspace{1cm} % Space between the start of the title and the top of the grey box
+
+				\@title
+
+				\vspace{1cm} % Space between the end of the title and the bottom of the grey box
+			}
+		}
+	}
+
+	\vfill % Space between the title box and author information
+
+	%------------------------------------------------
+	%	Author name and information
+	%------------------------------------------------
+
+	\parbox[t]{0.93\textwidth}{ % Box to inset this section slightly
+		\raggedleft % Right align the text
+		\large % Increase the font size
+		{\Large \@author}\\[4pt] % Extra space after name
+
+		\hfill\rule{0.2\linewidth}{1pt}\\% Horizontal line, first argument width, second thickness
+		\@date
+	}
+
+\end{titlepage}
+
+\emptyPage
+}
+
+
+
+%%%%%%%% FIN DU DOCUMENT %%%%%%%%%
+
+\newcommand{\roadMap}{
+	\clearpage
+	\listoffigures
+	\clearpage
+	\listoftables
+}
+
+% Fin du package
+\endinput
--- a/complementaire.pdf
+++ b/complementaire.pdf
--- a/complementaire.tex
+++ b/complementaire.tex
@ -0,0 +1,53 @@
+\include{macroTL}
+\title{Génie logiciel \\ -- \\TD4 - Questions complémentaires}
+\author{\bsc{Pietri} Yoann (A11)\\\bsc{Levy--Falk} Hugo (A11)}
+\date{Mars 2018}
+\usepackage{mathrsfs}
+\usepackage{MyPack2}
+\usepackage{pdftexcmds}
+\usepackage{minted}
+\begin{document}
+	\maketitle
+	\initPage{TL de Génie Logiciel}{\today}{\bsc{Pietri} Yoann, \bsc{Levy--Falk} Hugo}
+	\tableofcontents
+	\newpage
+	\section{lecture dans un fichier et transformation d'une chaîne de caractères}
+	Classe \mintinline{java}{Utilitaire} :
+	\inputminted{java}{questioncomplementaire/Utilitaire.java}
+	
+	\section{Codage complet des classes Morse et Cesar}
+	
+	\subsection{Classe \mintinline{java}{Cesar}}
+	\inputminted{java}{questioncomplementaire/Cesar.java}
+	
+	\subsection{Classe \mintinline{java}{Morse}}
+	\inputminted{java}{questioncomplementaire/Morse.java}
+	
+	
+	\section{Mesure des temps d'exécution}
+	
+	Classe \mintinline{java}{Comparateur} :
+	\inputminted{java}{questioncomplementaire/Comparateur.java}
+	
+	\section{Utilisation d'un patron pour ajouter un algorithme existant}
+	
+	Classe \mintinline{java}{CodageAClef} :
+	\inputminted{java}{questioncomplementaire/CodageAClef.java}
+	
+	\section{Codage d'Huffman}
+	
+	Classe \mintinline{java}{Huffman} :
+	\inputminted{java}{questioncomplementaire/Huffman.java}
+	
+	\section{Documentation}
+	\subsection{Classe \mintinline{java}{Noeud}}
+	\inputminted{java}{questioncomplementaire/Noeud.java}
+	\subsection{Classe \mintinline{java}{Arbre}}
+	\inputminted{java}{questioncomplementaire/Noeud.java}
+	\subsection{Classe \mintinline{java}{HuffmanCode}}
+	\inputminted{java}{questioncomplementaire/Noeud.java}
+	
+	\section{Sauvegarde des résultats}
+	Voir la classe \mintinline{java}{Comparateur} dans la section "Mesure des temps d'exécution".
+	
+\end{document}
--- a/compteRendu.pdf
+++ b/compteRendu.pdf
--- a/compteRendu.tex
+++ b/compteRendu.tex
@ -0,0 +1,60 @@
+\include{macroTL}
+\title{Génie logiciel \\ -- \\TD4}
+\author{\bsc{Pietri} Yoann (A11)\\\bsc{Levy--Falk} Hugo (A11)}
+\date{Mars 2018}
+\usepackage{mathrsfs}
+\usepackage{MyPack2}
+\usepackage{pdftexcmds}
+\usepackage{minted}
+\begin{document}
+	\maketitle
+	\initPage{TL de Génie Logiciel}{\today}{\bsc{Pietri} Yoann, \bsc{Levy--Falk} Hugo}
+	\tableofcontents
+	\newpage
+	\section{Lecture d'une chaîne de caractères dans un fichier}
+	Le mot clé \mintinline{java}{static} permet d'appeler la méthode \mintinline{java}{lireTexte} sans avoir besoin d'instancier d'objet de la classe \mintinline{java}{Utilitaire}.
+	
+	Code source de la classe Comparateur :
+	
+	\inputminted{java}{td4/question1/comparateur.java}
+	
+	\section{Implémentation de l'architecture logicielle}
+	
+	\subsection{Code source de la classe \mintinline{java}{Comparateur}}
+	\inputminted{java}{td4/question2/Comparateur.java}
+	
+	\subsection{Code source de la classe \mintinline{java}{AlgoCodage}}
+	\inputminted{java}{td4/question2/AlgoCodage.java}
+	
+	\subsection{Code source de la classe \mintinline{java}{Cesar}}
+	\inputminted{java}{td4/question2/Cesar.java}
+	
+	\section{Utilisation d'un patron pour ajouter un algorithme existant}
+	Les classe \mintinline{java}{EncodeurAClef} ne possède pas les méthodes \mintinline{java}{encode} et \mintinline{java}{décode}, mais possède des méthodes \mintinline{java}{chiffre} et \mintinline{java}{déchiffre}. De plus il n'hérite pas de \mintinline{java}{AlgoCodage}. La solution est d'utiliser le patron adaptateur.
+	
+	La figure \ref{fig:rationalrose} montre le diagramme \bsc{UML} de l'application.
+	
+	\begin{figure}[h!]
+		\centering
+		\includegraphics[width=0.7\linewidth]{td4/question3/rational_rose}
+		\caption{Diagramme UML}
+		\label{fig:rationalrose}
+	\end{figure}
+	
+	Le code à ajouter dans la classe comparateur est alors:
+	\begin{minted}{java}
+	algoAComparer.add(new AdapteEncodeurAClef("mon secret"));
+	algoAComparer.add(new AdapteEncodeurAClef(""));
+	\end{minted}
+	
+	\section{Tests unitaires pour codage d'Huffman}
+	Code source de la classe \mintinline{java}{ArbreTest} :
+	\inputminted{java}{td4/question4/ArbreTest.java}
+	
+	\section{Documentation}
+	Code source de la classe Feuille :
+	\inputminted{java}{td4/question5/Feuille.java}
+	
+	\clearpage
+	\listoffigures
+\end{document}
--- a/macroTL.tex
+++ b/macroTL.tex
@ -0,0 +1,40 @@
+%%% Macro TL
+%% Documentclass
+\documentclass[a4paper,titlepage]{article}
+
+%% Packages
+
+% Caractères et encodage
+\usepackage[utf8]{inputenc}
+\usepackage[francais]{babel}
+\usepackage{amsmath,amsfonts,amssymb}
+
+% Tikz
+\usepackage{tikz}
+%\usepackage{tkz-tab}
+
+% Pour les circuits électriques
+%\usepackage{circuitikz}
+
+% Pour les figures
+\usepackage{float}
+
+% Pour les tableaux
+\usepackage{tabularx}
+
+% Pour les unités
+\usepackage{siunitx}
+
+% Geometrie
+\usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
+
+% Pour le code
+\usepackage{moreverb}
+
+% Pour les couleurs
+\usepackage{colortbl}
+
+%% Commandes utiles
+\usepackage{fancyhdr}
+\pagestyle{fancy}
+
--- a/questioncomplementaire/AlgoCodage.java
+++ b/questioncomplementaire/AlgoCodage.java
@ -0,0 +1,19 @@
+package questioncomplementaire;
+
+public abstract class AlgoCodage {
+	
+	protected String nom;
+	
+	public abstract String encode(String s);
+	
+	public abstract String decode(String s);
+
+	public String getNom() {
+		return nom;
+	}
+	
+	@Override
+	public abstract String toString();
+	
+
+}
--- a/questioncomplementaire/Arbre.java
+++ b/questioncomplementaire/Arbre.java
@ -0,0 +1,82 @@
+package questioncomplementaire;
+
+import java.util.ArrayList;
+import java.util.PriorityQueue;
+
+public abstract class Arbre implements Comparable<Arbre> {
+	final int frequence;
+
+	/**
+	 * @param frequence fréquence cumulée des feuilles de l'arbre
+	 */
+	public Arbre(int frequence) {
+		this.frequence = frequence;
+	}
+
+	/**
+	 * @param s chaîne encodée dans l'arbre
+	 * @return un arbre des fréquences d'occurence des lettres de la chaîne
+	 */
+	public static Arbre buildTree(String s) {
+		// tableau de fréquence des caractères
+		// indexé par le code du caractère
+		// pour simplifier on fait l'hypothèse qu'aucun code n'est supérieur à 256
+		int[] frequenceCaracteres = new int[256];
+		
+		// parcourt la chaine génératrice et compte la fréquence de chaque caractère
+		for (char c : s.toCharArray())
+			frequenceCaracteres[c]++;
+
+		// liste des éléments 
+		PriorityQueue<Arbre> lesElements = new PriorityQueue<Arbre>();
+		
+		// au départ on a un ensemble d'arbres réduits chacun à feuille, une pour chaque caractère de la chaine génératrice, non reliés 
+		//for (int i = 0; i < frequenceCaracteres.length; i++)
+		for (int i = 0; i < frequenceCaracteres.length ; i++)
+			if (frequenceCaracteres[i] > 0)
+				lesElements.offer(new Feuille(frequenceCaracteres[i], (char) i));
+
+		// on assemble les arbres petit à petit
+		// on arrête d'itérer lorsqu'il n'y a plus d'une seule racine
+		while (lesElements.size() > 1) {
+			// sélectionne les 2 arbres avec la fréquence la plus basse et les retire de la liste
+			Arbre a = lesElements.poll();
+			Arbre b = lesElements.poll();
+			// assemble les 2 arbres retirés et place le nouvel arbre en queue
+			lesElements.offer(new Noeud(a, b));
+		}
+		return lesElements.poll();
+	}
+
+	// établit une relation d'ordre sur les arbres
+	public int compareTo(Arbre tree) {
+		return frequence - tree.frequence;
+	}
+
+	/**
+	 * @param prefixe chaîne constituant le préfixe des codes
+	 * @return la liste des codes de Huffman pour chacune des feuilles de l'arbre
+	 */
+	public ArrayList<HuffmanCode> collectCodes(StringBuffer prefixe) {
+		ArrayList<HuffmanCode> lesCodes = new ArrayList<HuffmanCode>();
+
+		if (this instanceof Feuille) {
+			Feuille leaf = (Feuille) this;
+			lesCodes.add(new HuffmanCode(leaf.lettre, prefixe.toString()));
+
+		} else if (this instanceof Noeud) {
+			Noeud node = (Noeud) this;
+
+			// traverse le fils gauche
+			prefixe.append('0');
+			lesCodes.addAll(node.filsGauche.collectCodes(prefixe));
+			prefixe.deleteCharAt(prefixe.length() - 1);
+			
+			// traverse le fils droit
+			prefixe.append('1');
+			lesCodes.addAll(node.filsDroit.collectCodes(prefixe));
+			prefixe.deleteCharAt(prefixe.length() - 1);
+		}
+		return lesCodes;
+	}
+}
--- a/questioncomplementaire/Cesar.java
+++ b/questioncomplementaire/Cesar.java
@ -0,0 +1,38 @@
+package questioncomplementaire;
+
+public class Cesar extends AlgoCodage{
+	private int decalage;
+	private String alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
+
+	public Cesar(int decalage){
+		this.nom = "César";
+		this.decalage = decalage;
+	}
+	
+	@Override
+	public String toString() {
+		return "codage de César (décalage=" + decalage + ")"; 
+	}
+
+	@Override
+	public String encode(String s) {
+		String encode = "";
+		for(int i=0;i<s.length();i++){
+			encode += alphabet.charAt((decalage +
+						alphabet.indexOf(s.charAt(i)))%alphabet.length());
+		}
+		return encode;
+	}
+
+	@Override
+	public String decode(String s) {
+		String decode = "";
+		int index;
+		for(int i=0; i<s.length(); i++) {
+			index = (alphabet.indexOf(s.charAt(i))-decalage) % alphabet.length();
+			index += (index<0)?alphabet.length():0;
+			decode += alphabet.charAt(index);
+		}
+		return decode;
+	}
+}
--- a/questioncomplementaire/CodageAClef.java
+++ b/questioncomplementaire/CodageAClef.java
@ -0,0 +1,39 @@
+package questioncomplementaire;
+
+import chiffrement.EncodeurAClef;
+
+public class CodageAClef extends AlgoCodage {
+	
+	EncodeurAClef encodeur;
+	String clef;
+	
+	public CodageAClef(String clef) {
+		if(clef.equals(""))
+			this.clef = "clef par défaut";
+		else
+			this.clef = clef;
+		
+		try {
+			encodeur = new EncodeurAClef(this.clef);
+		} catch (Exception e) {
+			System.out.println("Échec de la création de l'encodeur");
+			e.printStackTrace();
+		}
+	}
+	
+	@Override
+	public String encode(String s) {
+		return encodeur.chiffre(s);
+	}
+
+	@Override
+	public String decode(String s) {
+		return encodeur.dechiffre(s);
+	}
+
+	@Override
+	public String toString() {
+		return "codage à clef (clef = \"" + clef + "\")";
+	}
+
+}
--- a/questioncomplementaire/Comparateur.java
+++ b/questioncomplementaire/Comparateur.java
@ -0,0 +1,58 @@
+package questioncomplementaire;
+
+import java.io.FileNotFoundException;
+import java.io.PrintWriter;
+import java.util.ArrayList;
+
+public class Comparateur {
+
+	public static void main(String[] arg) {
+		PrintWriter out;
+		try {
+			out = new PrintWriter("resultats.txt");
+		} catch (FileNotFoundException e) {
+			System.out.println("Impossible d'ouvrpour les résultats.");
+			e.printStackTrace();
+			return;
+		}
+		int TAILLE_EXTRAIT = 50;
+		String texteClair = Utilitaire.lireTexte("texte1.txt");
+		out.println("début du texte original : "
+				+ texteClair.substring(0, Math.min(50, texteClair.length())));
+		texteClair = Utilitaire.getLettres(texteClair);
+		out.println("texte après `getLettres` : "
+				+ texteClair.substring(0, Math.min(50, texteClair.length())));
+
+		ArrayList<AlgoCodage> algoAComparer = new ArrayList<AlgoCodage>();
+		algoAComparer.add(new Cesar(3));
+		algoAComparer.add(new Morse());
+		algoAComparer.add(new Cesar(10));
+		algoAComparer.add(new CodageAClef("mon secret"));
+		algoAComparer.add(new CodageAClef(""));
+		algoAComparer.add(new Huffman(texteClair));
+
+		String encodee = "";
+		for (AlgoCodage algo : algoAComparer) {
+			out.println("algorithme : " + algo.toString());
+			long avant = System.currentTimeMillis();
+			encodee = algo.encode(texteClair);
+			long apres = System.currentTimeMillis();
+			long duree = apres - avant;
+			out.println("\tencodage : "
+				+ "\t durée : "
+				+ duree
+				+ "\t résultat : "
+				+ encodee.substring(0, Math.min(50, encodee.length())));
+			avant = System.currentTimeMillis();
+			String decodee = algo.decode(encodee);
+			apres = System.currentTimeMillis();
+			duree = apres - avant;
+			out.println("\tdécodage : "
+					+ "\t durée : "
+					+ duree
+				+ "\t résultat : "
+				+ decodee.substring(0, Math.min(50, decodee.length())));
+		}
+		out.close();
+	}
+}
--- a/questioncomplementaire/Feuille.java
+++ b/questioncomplementaire/Feuille.java
@ -0,0 +1,37 @@
+package questioncomplementaire;
+
+/**
+ * @author galtier
+ * 
+ *  Cette classe représente une feuille d'un arbre de Huffman.
+ *
+ */
+
+public class Feuille extends Arbre {
+	final char lettre;
+
+	/**
+	 * @param frequence nombre d'occurences de cette lettre dans le générateur
+	 * @param lettre caractère dont on compte le nombre d'occurences
+	 */
+	public Feuille(int frequence, char lettre) {
+		super(frequence);
+		this.lettre = lettre;
+	}
+
+	@Override
+	public boolean equals(Object obj) {
+		if (this == obj)
+			return true;
+		if (obj == null)
+			return false;
+		if (getClass() != obj.getClass())
+			return false;
+		Feuille other = (Feuille) obj;
+		if ((lettre != other.lettre) || (this.frequence != other.frequence))
+			return false;
+		return true;
+	}
+	
+	
+}
--- a/questioncomplementaire/Huffman.java
+++ b/questioncomplementaire/Huffman.java
@ -0,0 +1,54 @@
+package questioncomplementaire;
+
+import java.util.ArrayList;
+
+public class Huffman extends AlgoCodage {
+	private String generatrice;
+	private ArrayList<HuffmanCode> codes;
+	private Arbre arbre;
+
+	public Huffman(String generatrice) {
+		this.generatrice = generatrice;
+		arbre = Arbre.buildTree(generatrice);
+		codes = arbre.collectCodes(new StringBuffer(""));
+
+	}
+
+	@Override
+	public String encode(String s) {
+		String encode = s;
+		for (HuffmanCode huffmanCode : codes) {
+			encode = encode.replaceAll(
+					String.valueOf(huffmanCode.lettre), huffmanCode.code);
+		}
+		return encode;
+
+	}
+
+	@Override
+	public String decode(String s) {
+		String decode = "";
+		Arbre current = arbre;
+		for (int i=0; i<s.length(); i++) {
+			if(current instanceof Feuille) {
+				decode += ((Feuille) current).lettre;
+				current = arbre;
+			}
+			if(current instanceof Noeud) {
+				if(s.charAt(i) == '0')
+					current = ((Noeud)current).filsGauche;
+				else
+					current = ((Noeud)current).filsDroit;
+			}
+		}
+		return decode;
+	}
+
+	@Override
+	public String toString() {
+		return "Huffman (génératrice = "
+				+ generatrice.substring(0, Math.min(50, generatrice.length()))
+				+ ")";
+	}
+
+}
--- a/questioncomplementaire/HuffmanCode.java
+++ b/questioncomplementaire/HuffmanCode.java
@ -0,0 +1,24 @@
+package questioncomplementaire;
+
+/**
+ * @author galtier
+ * 
+ * cette classe représente un code de Huffman
+ */
+public class HuffmanCode {
+
+	char lettre;
+	String code;
+
+	/**
+	 * 
+	 * @param lettre caractère à encoder
+	 * @param code code représentant le caractère donné
+	 */
+	public HuffmanCode(char lettre, String code) {
+		super();
+		this.lettre = lettre;
+		this.code = code;
+	}
+
+}
--- a/questioncomplementaire/Morse.java
+++ b/questioncomplementaire/Morse.java
@ -0,0 +1,51 @@
+package questioncomplementaire;
+
+import java.util.HashMap;
+
+public class Morse extends AlgoCodage{
+
+	private String[] alphabet;
+	private HashMap<String, String> decoder;
+	
+	public Morse(){
+		this.nom = "Morse";
+		alphabet = new String[] {
+				".-", "-...", "-.-.", "-..", ".", "..-.",
+				"--.", "....", "..", ".---", "-.-", ".-..",
+				"--", "-.", "---", ".--.", "--.-", ".-.",
+				"...", "-", "..-", "...-", ".--", "-..-",
+				"-.--", "--.."
+		};
+		decoder = new HashMap<String, String>();
+		int a = 65;
+		for (int i = 0; i < alphabet.length; i++) {
+			decoder.put(alphabet[i], String.valueOf((char)(a+i)));
+		}
+	}
+	
+	@Override
+	public String toString() {
+		return "Morse"; 
+	}
+
+	@Override
+	public String encode(String s) {
+		String encode = "";
+		int a = 65; // Code ASCII de A
+		for (int i = 0; i < s.length(); i++) {
+			encode += alphabet[(int)s.charAt(i)-a] + "/";
+		}
+		return encode;
+	}
+
+	@Override
+	public String decode(String s) {
+		String decode = "";
+		int a = 65; // Code ASCII de A
+		String[] lettres = s.split("/");
+		for (int i = 0; i < lettres.length; i++) {
+			decode += decoder.get(lettres[i]);
+		}
+		return decode;
+	}
+}
--- a/questioncomplementaire/Noeud.java
+++ b/questioncomplementaire/Noeud.java
@ -0,0 +1,22 @@
+package questioncomplementaire;
+
+/**
+ * @author galtier
+ * 
+ * Cette classe représente un noeud d'un arbre de Huffman.
+ *
+ */
+public class Noeud extends Arbre {
+	final Arbre filsGauche, filsDroit;
+
+	/**
+	 * 
+	 * @param filsGauche fils gauche du noeud
+	 * @param filsDroit fils droit du noeud
+	 */
+	public Noeud(Arbre filsGauche, Arbre filsDroit) {
+		super(filsGauche.frequence + filsDroit.frequence);
+		this.filsGauche = filsGauche;
+		this.filsDroit = filsDroit;
+	}
+}
--- a/questioncomplementaire/Utilitaire.java
+++ b/questioncomplementaire/Utilitaire.java
@ -0,0 +1,46 @@
+package questioncomplementaire;
+
+import java.io.BufferedReader;
+import java.io.FileReader;
+
+/**
+ * @author galtier
+ *
+ */
+public class Utilitaire {
+
+	/**
+	 * Lit un fichier texte et place les caractères lus dans une chaîne de
+	 * caractères.
+	 * 
+	 * @param nomFichier
+	 *            le nom complet du fichier à lire
+	 * @return une chaine de caractères contenant le texte lu dans le fichier.
+	 *         Si le fichier n'existe pas ou ne peut pas être lu, retourne null.
+	 * 
+	 */
+	public static String lireTexte(String nomFichier) {
+		try {
+			String texte = "";
+			FileReader fr = new FileReader(nomFichier);
+			BufferedReader br = new BufferedReader(fr);
+			String ligne;
+			while ((ligne = br.readLine()) != null)
+				texte += ligne + "\n";
+			return texte;
+		} catch (Exception e) {
+			e.printStackTrace();
+			return null;
+		}
+	}
+	
+	/**
+	 * Supprime tous les caractères qui ne sont pas des lettres
+	 * et met les autres en majuscules.
+	 * @param input La chaîne à traîter.
+	 * @return La chaîne de caractères traîtée.
+	 */
+	public static String getLettres(String input) {
+		return input.replaceAll("[^a-zA-Z]*", "").toUpperCase();
+	}
+}
--- a/td4/question1/comparateur.java
+++ b/td4/question1/comparateur.java
@ -0,0 +1,10 @@
+package question1;
+
+public class Comparateur {
+
+	public static void main(String[] args) {
+		String nomFichier = "texte2.txt";
+		String txt = Utilitaire.lireTexte(nomFichier);
+		System.out.println(txt);
+	}
+}
--- a/td4/question2/AlgoCodage.java
+++ b/td4/question2/AlgoCodage.java
@ -0,0 +1,16 @@
+package question2;
+
+public abstract class AlgoCodage {
+	
+	protected String nom;
+	
+	public abstract String encode(String s);
+	
+	public abstract String decode(String s);
+
+	public String getNom() {
+		return nom;
+	}
+	
+
+}
--- a/td4/question2/Cesar.java
+++ b/td4/question2/Cesar.java
@ -0,0 +1,30 @@
+package question2;
+
+public class Cesar extends AlgoCodage{
+
+	private int decalage;
+	private String alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
+
+	public Cesar(int decalage){
+		this.nom = "César";
+		this.decalage = decalage;
+	}
+
+	@Override
+	public String encode(String s) {
+		String encode = "";
+		for(int i=0;i<s.length();i++){
+			encode += alphabet.charAt((decalage +
+						alphabet.indexOf(s.charAt(i)))%alphabet.length());
+		}
+		return encode;
+	}
+
+	@Override
+	public String decode(String s) {
+		return "Fonctionnalité décodage de César pas encore implémenté";
+	}
+
+
+
+}
--- a/td4/question2/Comparateur.java
+++ b/td4/question2/Comparateur.java
@ -0,0 +1,32 @@
+package question2;
+
+import java.util.ArrayList;
+
+public class Comparateur {
+
+	public static void main(String[] arg) {
+		int TAILLE_EXTRAIT = 50;
+		String texteClair = Utilitaire.lireTexte("texte2.txt");
+		System.out.println("début du texte original : "
+				+ texteClair.substring(0, Math.min(50, texteClair.length())));
+
+		ArrayList<AlgoCodage> algoAComparer = new ArrayList<AlgoCodage>();
+		algoAComparer.add(new Cesar(3));
+		algoAComparer.add(new Morse());
+		algoAComparer.add(new Cesar(10));
+
+		String encodee = "";
+		for (AlgoCodage algo : algoAComparer) {
+			System.out.println("algorithme : " + algo.getNom());
+			encodee = algo.encode(texteClair);
+			System.out.println("\tencodage : "
+				+ "\t résultat : "
+				+ encodee.substring(0, Math.min(50, encodee.length())));
+
+			String decodee = algo.decode(encodee);
+			System.out.println("\tdécodage : "
+				+ "\t résultat : "
+				+ decodee.substring(0, Math.min(50, decodee.length())));
+		}
+	}
+}
--- a/td4/question2/Morse.java
+++ b/td4/question2/Morse.java
@ -0,0 +1,19 @@
+package question2;
+
+public class Morse extends AlgoCodage{
+
+	public Morse(){
+		this.nom = "Morse";
+	}
+
+	@Override
+	public String encode(String s) {
+		return "Fonctionnalité encodage de Morse pas encore implémentée";
+	}
+
+	@Override
+	public String decode(String s) {
+		return "Fonctionnalité décodage de Morse pas encore implémentée";
+	}
+
+}
--- a/td4/question3/rational_rose.png
+++ b/td4/question3/rational_rose.png
--- a/td4/question4/ArbreTest.java
+++ b/td4/question4/ArbreTest.java
@ -0,0 +1,41 @@
+package question4;
+
+import static org.junit.Assert.*;
+
+import org.junit.Before;
+import org.junit.Test;
+
+public class ArbreTest {
+
+	Arbre arbre1;
+	Arbre arbre2;
+
+	@Before
+	public void setup() throws Exception{
+		arbre1 = Arbre.buildTree("a");
+
+		arbre2 = Arbre.buildTree("baob");
+	}
+
+	@Test
+	public void testBuildTree() {
+		assertEquals("La lettre n'est pas dans une feuille simple",
+				((Feuille)arbre1).lettre, 'a');
+		assertEquals("La fréquence est mauvaise dans une feuille simple",
+				((Feuille)arbre1).frequence, 1 );
+
+		assertEquals(arbre2.frequence, 4 );
+		Feuille feuilleB = (Feuille)((Noeud)arbre2).filsGauche;
+		assertEquals(feuilleB.frequence, 2);
+		assertEquals(feuilleB.lettre, 'b');
+		Noeud noeudDroit = (Noeud)((Noeud)arbre2).filsDroit;
+		assertEquals(noeudDroit.frequence, 2);
+		Feuille feuilleA = (Feuille)noeudDroit.filsGauche;
+		assertEquals(feuilleA.lettre, 'a');
+		assertEquals(feuilleA.frequence, 1);
+		Feuille feuilleO = (Feuille)noeudDroit.filsDroit;
+		assertEquals(feuilleO.lettre, 'o');
+		assertEquals(feuilleO.frequence, 1);
+	}
+
+}
--- a/td4/question5/Feuille.java
+++ b/td4/question5/Feuille.java
@ -0,0 +1,36 @@
+package question5;
+
+/**
+ * Cette classe représente une feuille d'un arbre de Huffman.
+ * @author galtier
+ *
+ */
+public class Feuille extends Arbre {
+	final char lettre;
+
+	/**
+	 *
+	 * @param frequence nombre d'occurrences de cette lettre dans le générateur
+	 * @param lettre caractère dont on compte le nombre d'occurences
+	 */
+	public Feuille(int frequence, char lettre) {
+		super(frequence);
+		this.lettre = lettre;
+	}
+
+	@Override
+	public boolean equals(Object obj) {
+		if (this == obj)
+			return true;
+		if (obj == null)
+			return false;
+		if (getClass() != obj.getClass())
+			return false;
+		Feuille other = (Feuille) obj;
+		if ((lettre != other.lettre) || (this.frequence != other.frequence))
+			return false;
+		return true;
+	}
+
+
+}
--- a/401
+++ b/401
@ -0,0 +1,401 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<XMI xmlns:UML="http://schema.omg.org/spec/UML/1.4" xmi.version="1.2" verified="false" timestamp="2018-03-27T16:38:32">
+ <XMI.header>
+  <XMI.documentation>
+   <XMI.exporter>umbrello uml modeller http://umbrello.kde.org</XMI.exporter>
+   <XMI.exporterVersion>1.6.12</XMI.exporterVersion>
+   <XMI.exporterEncoding>UnicodeUTF8</XMI.exporterEncoding>
+  </XMI.documentation>
+  <XMI.metamodel xmi.name="UML" xmi.version="1.4" href="UML.xml"/>
+ </XMI.header>
+ <XMI.content>
+  <UML:Model xmi.id="m1" name="UML Model" isAbstract="false" isRoot="false" isLeaf="false" isSpecification="false">
+   <UML:Namespace.ownedElement>
+    <UML:Stereotype xmi.id="folder" isAbstract="false" name="folder" isRoot="false" visibility="public" isLeaf="false" isSpecification="false" namespace="m1"/>
+    <UML:Model xmi.id="Logical_View" isAbstract="false" name="Logical View" isRoot="false" visibility="public" isLeaf="false" isSpecification="false" namespace="m1">
+     <UML:Namespace.ownedElement>
+      <UML:Package xmi.id="Datatypes" isAbstract="false" name="Datatypes" isRoot="false" visibility="public" isLeaf="false" isSpecification="false" stereotype="folder" namespace="Logical_View">
+       <UML:Namespace.ownedElement>
+        <UML:DataType xmi.id="uFoXLnwS24jDi" isAbstract="false" name="char" isRoot="false" visibility="public" isLeaf="false" isSpecification="false" namespace="Datatypes"/>
+        <UML:DataType xmi.id="uJF9r192gOBbm" isAbstract="false" name="int" isRoot="false" visibility="public" isLeaf="false" isSpecification="false" namespace="Datatypes"/>
+        <UML:DataType xmi.id="uQDSwZaqcgJwh" isAbstract="false" name="float" isRoot="false" visibility="public" isLeaf="false" isSpecification="false" namespace="Datatypes"/>
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+        <UML:DataType xmi.id="uI3kPavEUajOu" isAbstract="false" name="bool" isRoot="false" visibility="public" isLeaf="false" isSpecification="false" namespace="Datatypes"/>
+        <UML:DataType xmi.id="uTpOs9d4v6FCt" isAbstract="false" name="string" isRoot="false" visibility="public" isLeaf="false" isSpecification="false" namespace="Datatypes"/>
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+        <UML:DataType xmi.id="ucbRbdzzcIO8T" isAbstract="false" name="signed int" isRoot="false" visibility="public" isLeaf="false" isSpecification="false" namespace="Datatypes"/>
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+        <UML:DataType xmi.id="uZJHBCtkFabB5" isAbstract="false" name="long int" isRoot="false" visibility="public" isLeaf="false" isSpecification="false" namespace="Datatypes"/>
+        <UML:DataType xmi.id="u2oNEabiItOdr" isAbstract="false" name="signed long int" isRoot="false" visibility="public" isLeaf="false" isSpecification="false" namespace="Datatypes"/>
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+        <UML:DataType xmi.id="umuAnT8iCCVRd" isAbstract="false" name="long double" isRoot="false" visibility="public" isLeaf="false" isSpecification="false" namespace="Datatypes"/>
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+        <UML:DataType xmi.id="uOFZB3YNmvpiU" isAbstract="false" name="Vector&lt;ElementBase>" isRoot="false" visibility="public" elementReference="ukFumxgPIWZZS" isLeaf="false" isSpecification="false" namespace="Datatypes"/>
+       </UML:Namespace.ownedElement>
+      </UML:Package>
+      <UML:Class xmi.id="u0jMryxTfuAqC" isAbstract="false" name="LectureEcritureFichier" isRoot="false" visibility="public" isLeaf="false" isSpecification="false" namespace="Logical_View">
+       <UML:Classifier.feature>
+        <UML:Operation isQuery="false" xmi.id="uisqlAN2DLOp4" isAbstract="false" name="ouvrirFichierBmp" isRoot="false" visibility="public" isLeaf="false" isSpecification="false">
+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="u78YzdJCnsDYg" xmi.id="uEoZVIml3y3tt" name="nomFichier" value="" visibility="private" isSpecification="false"/>
+         </UML:BehavioralFeature.parameter>
+        </UML:Operation>
+        <UML:Operation isQuery="false" xmi.id="uPfh1wb9duVq9" isAbstract="false" name="enregistrerArbre" isRoot="false" visibility="public" isLeaf="false" isSpecification="false">
+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="uTwdPw0wW0NlV" xmi.id="uHsuuxCf083Ur" name="arbre" value="" visibility="private" isSpecification="false"/>
+          <UML:Parameter type="u78YzdJCnsDYg" xmi.id="uth4DEbMLodOt" name="nomFichier" value="" visibility="private" isSpecification="false"/>
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+          <UML:Parameter type="u78YzdJCnsDYg" xmi.id="uMduxhTnaWCSd" name="nomFichier" value="" visibility="private" isSpecification="false"/>
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+         </UML:BehavioralFeature.parameter>
+        </UML:Operation>
+       </UML:Classifier.feature>
+      </UML:Class>
+      <UML:Class xmi.id="uhjGdAaO97O7I" isAbstract="false" name="QuadTree" isRoot="false" visibility="public" isLeaf="false" isSpecification="false" namespace="Logical_View">
+       <UML:Classifier.feature>
+        <UML:Operation isQuery="false" xmi.id="uD20Jxn6U4MYO" ownerScope="classifier" isAbstract="false" name="main" isRoot="false" visibility="public" isLeaf="false" isSpecification="false">
+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="uy0q0G1pHWfPt" xmi.id="uNqpJMhM6gIZe" name="args" value="" visibility="private" isSpecification="false"/>
+         </UML:BehavioralFeature.parameter>
+        </UML:Operation>
+        <UML:Operation isQuery="false" xmi.id="uQ1uTFI0UxhQQ" isAbstract="false" name="calculInformationBloc" isRoot="false" visibility="public" isLeaf="false" isSpecification="false">
+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="uyI8NYpkKxiH3" xmi.id="uLpEo1KmY9b85" kind="return"/>
+          <UML:Parameter type="u5fiRB2ya1wTa" xmi.id="uvbHDGWK5n8Eg" name="img" value="" visibility="private" isSpecification="false"/>
+          <UML:Parameter type="uJF9r192gOBbm" xmi.id="uORXfQoEy6ncU" name="x0" value="" visibility="private" isSpecification="false"/>
+          <UML:Parameter type="uJF9r192gOBbm" xmi.id="uB07J4fKc1Teh" name="y0" value="" visibility="private" isSpecification="false"/>
+          <UML:Parameter type="uJF9r192gOBbm" xmi.id="uo3jTTDLLdAE7" name="x1" value="" visibility="private" isSpecification="false"/>
+          <UML:Parameter type="uJF9r192gOBbm" xmi.id="uXP1cR9rgZ8jU" name="y1" value="" visibility="private" isSpecification="false"/>
+         </UML:BehavioralFeature.parameter>
+        </UML:Operation>
+        <UML:Operation isQuery="false" xmi.id="uD6S6JIZLcvPC" isAbstract="false" name="construireArbreQuadTrees" isRoot="false" visibility="public" isLeaf="false" isSpecification="false">
+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="uTwdPw0wW0NlV" xmi.id="u6HNSNw2gKGiH" kind="return"/>
+          <UML:Parameter type="u5fiRB2ya1wTa" xmi.id="ueXJcmT5hQWd4" name="img" value="" visibility="private" isSpecification="false"/>
+          <UML:Parameter type="uJF9r192gOBbm" xmi.id="uBkTsrDiwGWkM" name="x0" value="" visibility="private" isSpecification="false"/>
+          <UML:Parameter type="uJF9r192gOBbm" xmi.id="uzvfSiXAHB5mr" name="y0" value="" visibility="private" isSpecification="false"/>
+          <UML:Parameter type="uJF9r192gOBbm" xmi.id="uTKCMTNHMAGwE" name="x1" value="" visibility="private" isSpecification="false"/>
+          <UML:Parameter type="uJF9r192gOBbm" xmi.id="u6ywldDLdHFoN" name="y1" value="" visibility="private" isSpecification="false"/>
+          <UML:Parameter type="uEAR962YASBC4" xmi.id="uZOoQwLr5KsOW" name="seuil" value="" visibility="private" isSpecification="false"/>
+         </UML:BehavioralFeature.parameter>
+        </UML:Operation>
+       </UML:Classifier.feature>
+      </UML:Class>
+      <UML:Class xmi.id="uyI8NYpkKxiH3" isAbstract="false" name="InformationBloc" isRoot="false" visibility="public" isLeaf="false" isSpecification="false" namespace="Logical_View">
+       <UML:Classifier.feature>
+        <UML:Attribute type="ufaU7RB2MERga" xmi.id="ugXBVAwyoOBHg" name="rouge" visibility="private" isSpecification="false"/>
+        <UML:Attribute type="ufaU7RB2MERga" xmi.id="uBOfcYe8EZfb3" name="vert" visibility="private" isSpecification="false"/>
+        <UML:Attribute type="ufaU7RB2MERga" xmi.id="uuRymoZ6rLvpZ" name="bleu" visibility="private" isSpecification="false"/>
+        <UML:Attribute type="uEAR962YASBC4" xmi.id="u81qkHZ47pjoR" name="dispersion" visibility="private" isSpecification="false"/>
+        <UML:Operation isQuery="false" xmi.id="ukjoy0OKVhSfg" isAbstract="false" name="InformationBloc" isRoot="false" visibility="public" isLeaf="false" isSpecification="false">
+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="ufaU7RB2MERga" xmi.id="uzwjPz12h5okj" name="rouge" value="" visibility="private" isSpecification="false"/>
+          <UML:Parameter type="ufaU7RB2MERga" xmi.id="ufGlq9LQSbEQg" name="vert" value="" visibility="private" isSpecification="false"/>
+          <UML:Parameter type="ufaU7RB2MERga" xmi.id="uYtZVLCx9xX85" name="bleu" value="" visibility="private" isSpecification="false"/>
+          <UML:Parameter type="uEAR962YASBC4" xmi.id="uYknjVHEDxX3b" name="dispersion" value="" visibility="private" isSpecification="false"/>
+         </UML:BehavioralFeature.parameter>
+        </UML:Operation>
+        <UML:Operation isQuery="false" xmi.id="u2le4H9usYi21" isAbstract="false" name="getRouge" isRoot="false" visibility="public" isLeaf="false" isSpecification="false">
+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="ufaU7RB2MERga" xmi.id="uIMiMcZH1IsIN" kind="return"/>
+         </UML:BehavioralFeature.parameter>
+        </UML:Operation>
+        <UML:Operation isQuery="false" xmi.id="ucQ0JLeYTRvox" isAbstract="false" name="getVert" isRoot="false" visibility="public" isLeaf="false" isSpecification="false">
+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="ufaU7RB2MERga" xmi.id="uM3BWvi7UP2Ge" kind="return"/>
+         </UML:BehavioralFeature.parameter>
+        </UML:Operation>
+        <UML:Operation isQuery="false" xmi.id="uePlQDhKFoU4h" isAbstract="false" name="getBleu" isRoot="false" visibility="public" isLeaf="false" isSpecification="false">
+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="ufaU7RB2MERga" xmi.id="u3xspVBvXCiGN" kind="return"/>
+         </UML:BehavioralFeature.parameter>
+        </UML:Operation>
+        <UML:Operation isQuery="false" xmi.id="uq6f266XdgDHl" isAbstract="false" name="getDispersion" isRoot="false" visibility="public" isLeaf="false" isSpecification="false">
+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="uEAR962YASBC4" xmi.id="uTMTC7lLrcJts" kind="return"/>
+         </UML:BehavioralFeature.parameter>
+        </UML:Operation>
+        <UML:Operation isQuery="false" xmi.id="uCUzJ2JG0C3OA" isAbstract="false" name="toString" isRoot="false" visibility="public" isLeaf="false" isSpecification="false">
+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="u78YzdJCnsDYg" xmi.id="uuPVHeWrYxQDE" kind="return"/>
+         </UML:BehavioralFeature.parameter>
+        </UML:Operation>
+       </UML:Classifier.feature>
+      </UML:Class>
+      <UML:Class xmi.id="uTwdPw0wW0NlV" isAbstract="true" name="ElementBase" isRoot="false" visibility="public" isLeaf="false" isSpecification="false" namespace="Logical_View">
+       <UML:Classifier.feature>
+        <UML:Operation isQuery="false" xmi.id="ukUBq4sQ09bxB" isAbstract="true" name="toString" isRoot="false" visibility="public" isLeaf="false" isSpecification="false">
+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="u78YzdJCnsDYg" xmi.id="uGyR0vsErmdv9" kind="return"/>
+         </UML:BehavioralFeature.parameter>
+        </UML:Operation>
+        <UML:Operation isQuery="false" xmi.id="uLDagKIKmbjPS" isAbstract="true" name="construireImage" isRoot="false" visibility="public" isLeaf="false" isSpecification="false">
+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="u5fiRB2ya1wTa" xmi.id="uVExJSI0eCCg2" name="img" value="" visibility="private" isSpecification="false"/>
+         </UML:BehavioralFeature.parameter>
+        </UML:Operation>
+        <UML:Operation isQuery="false" xmi.id="uanHayxjxsmRd" isAbstract="true" name="enregistrerElement" isRoot="false" visibility="public" isLeaf="false" isSpecification="false">
+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="udpxzEssyEMek" xmi.id="uUiiCV9NZxl68" name="flux" value="" visibility="private" isSpecification="false"/>
+         </UML:BehavioralFeature.parameter>
+        </UML:Operation>
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+      <UML:Class xmi.id="ukgKXvC3BIUbS" isAbstract="false" name="Noeud" isRoot="false" visibility="public" isLeaf="false" isSpecification="false" namespace="Logical_View">
+       <UML:GeneralizableElement.generalization>
+        <UML:Generalization xmi.idref="uguBegpzVc7Zc"/>
+        <UML:Generalization xmi.idref="uoWn0J5nHEdEk"/>
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+       <UML:Classifier.feature>
+        <UML:Operation isQuery="false" xmi.id="u8HZySGy9wr7a" isAbstract="false" name="Noeud" isRoot="false" visibility="public" isLeaf="false" isSpecification="false"/>
+        <UML:Operation isQuery="false" xmi.id="umcl4Sp7cImHi" isAbstract="false" name="ajouterNoeud" isRoot="false" visibility="public" isLeaf="false" isSpecification="false">
+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="uTwdPw0wW0NlV" xmi.id="uxY2SuWQ6TYFX" name="element" value="" visibility="private" isSpecification="false"/>
+         </UML:BehavioralFeature.parameter>
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+        <UML:Operation isQuery="false" xmi.id="uV5fYMHzF3vzD" isAbstract="false" name="toString" isRoot="false" visibility="public" isLeaf="false" isSpecification="false">
+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="u78YzdJCnsDYg" xmi.id="ux3zjgzVEqT7e" kind="return"/>
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+        <UML:Operation isQuery="false" xmi.id="u9c6JSpwIX9MM" isAbstract="false" name="construireImage" isRoot="false" visibility="public" isLeaf="false" isSpecification="false">
+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="u5fiRB2ya1wTa" xmi.id="uSGOTFzPk4h4j" name="img" value="" visibility="private" isSpecification="false"/>
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+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="udpxzEssyEMek" xmi.id="u6S9y3mHP6Onj" name="flux" value="" visibility="private" isSpecification="false"/>
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+       <UML:GeneralizableElement.generalization>
+        <UML:Generalization xmi.idref="uuIbOEuBwNqyk"/>
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+       <UML:Classifier.feature>
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+        <UML:Attribute type="uJF9r192gOBbm" xmi.id="uNbp5jyEIsomp" name="x1" visibility="private" isSpecification="false"/>
+        <UML:Attribute type="uJF9r192gOBbm" xmi.id="ueqMp8bS6o1Ag" name="y0" visibility="private" isSpecification="false"/>
+        <UML:Attribute type="uJF9r192gOBbm" xmi.id="uepK86uhVodiF" name="y1" visibility="private" isSpecification="false"/>
+        <UML:Attribute type="ufaU7RB2MERga" xmi.id="u8VMXfD7kLHh8" name="rouge" visibility="private" isSpecification="false"/>
+        <UML:Attribute type="ufaU7RB2MERga" xmi.id="u031vmesHJOdH" name="vert" visibility="private" isSpecification="false"/>
+        <UML:Attribute type="ufaU7RB2MERga" xmi.id="u5GvJWY5uTI4X" name="bleu" visibility="private" isSpecification="false"/>
+        <UML:Attribute type="uEAR962YASBC4" xmi.id="ufGPN5OEZh8YA" name="dispersion" visibility="private" isSpecification="false"/>
+        <UML:Operation isQuery="false" xmi.id="ua9KPyIlDq4La" isAbstract="false" name="Feuille" isRoot="false" visibility="public" isLeaf="false" isSpecification="false">
+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="uJF9r192gOBbm" xmi.id="uds0d8hkz61Sx" name="x0" value="" visibility="private" isSpecification="false"/>
+          <UML:Parameter type="uJF9r192gOBbm" xmi.id="uALgXjLlzeVZo" name="y0" value="" visibility="private" isSpecification="false"/>
+          <UML:Parameter type="uJF9r192gOBbm" xmi.id="uR7cicSdXI5gF" name="x1" value="" visibility="private" isSpecification="false"/>
+          <UML:Parameter type="uJF9r192gOBbm" xmi.id="uwP1aDVhBNq8o" name="y1" value="" visibility="private" isSpecification="false"/>
+          <UML:Parameter type="uyI8NYpkKxiH3" xmi.id="ulTbuzGdiSd8Q" name="bloc" value="" visibility="private" isSpecification="false"/>
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+         <UML:BehavioralFeature.parameter>
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+         <UML:BehavioralFeature.parameter>
+          <UML:Parameter type="u5fiRB2ya1wTa" xmi.id="uLmr5pMSPOnJn" name="img" value="" visibility="private" isSpecification="false"/>
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+         <UML:BehavioralFeature.parameter>
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+      <UML:Class xmi.id="udpxzEssyEMek" isAbstract="false" name="DataOutputStream" isRoot="false" visibility="public" isLeaf="false" isSpecification="false" namespace="Logical_View"/>
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