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Rentr\303\251e.typ" new file mode 100644 index 0000000..84c5d9d --- /dev/null +++ "b/semestre 4/algo/0- Rentr\303\251e.typ" @@ -0,0 +1,106 @@ +#import "@local/template:1.0.0": * +#import "@local/callout:1.0.0": * + +#show: doc.with( + authors: ( + (name: "William Hergès", affiliation: "Sorbonne Université", email: "william@herges.fr"), + ), + page_title: "Introduction", +) + += Introduction + +Un algorithme est un moyen de décomposer un problème en plein de petites tâches. +Une recette de cuisine est un algorithme. + +On cherche à trouver un moyen pour analyser les algorithmes et pour choisir le meilleur. + +Plan du semestre : +1. Théorie sur les algorithmes ; +2. Structure des données. + +Contrôle continu en TD, partiel et examen. +Utilise la règle du max. + +Les QCM sur Moodle ne sont pas notés. +Il y a souvent des QCM aux exams. + += Rappels mathématiques + +Raisonnements valides : +1. calculatoire +2. raisonnements logiques + - directe + - absurde + - contraposé +3. par récurrence + +C'est du blabla pour nous rappeler comment on fait des maths. + +Ne pas oublier que~: +$ sum^n_(i=1) i = (n(n-1))/2 $ +et que~: +$ forall x in RR, quad sum^n_(i=0) x^i = (x^(n+1)-1)/(x-1) $ + += Solution générale des suites + +== Suites récurrente linéaire homogène d'ordre 2 + +#defn[ + Une _suite récurrente linéaire homogène d'ordre 2_ est une suite définie par une relation de récurrence + $ u_n = a u_(n-1) + b u_(n-2) $ + avec des conditions initiales + $ u_0 = a_0 quad u_1 = a_1 $ + où $a$, $b$, $a_0$ et $a_1$ sont des nombres réels. +] + +#defn[ + On définit le _polynôme caractéristique_ associé à la suite récurrente précédente le polynôme~: + $ r^2 + a r - b $ +] + +Par exemple, le polynôme associé à la suite de Fibonacci est $ r^2-r-1 $ + +=== Méthode pour déterminer la solution + +On calcule les racines du _polynôme caractéristique_. + +*Si le polynôme possède deux racines* $r_1$, et $r_2$, alors la solution générale de la récurrence est de la forme~: +$ u_n = alpha r_1^n + beta r_2^n $ +On détermine ensuite $alpha$ et $beta$ à l'aide des conditions initiales~: +$ alpha + beta = a_0 \ +alpha r_1 + beta r_2 = a_1 $ + +*Si le polynôme possède une racine* $r$, alors la solution générale est de la forme~: +$ u_n = alpha r^n + beta n r^n $ +$alpha$ et $beta$ sont déterminés comme dans le cas précédent. + +== Autres cas + +Voir le diapo, car le prof n'a pas détaillé et est allé très vite. + += Notations de Landau + +#defn[ + Soient $f$ et $g$ deux fonctions de $NN$ dans $RR_+$. + + On écrit $f in O(g)$ si : + $ exists D > 0, exists n_0 >= 0, quad forall n > n_0, quad f(n) <= D g(n) $ + + On écrit $f in Omega (g)$ si : + $ exists C > 0, exists n_0 >= 0, quad forall n > n_0, quad C g(n) <= f(n) $ + + On écrit $f in Theta (g)$ si : + $ exists D >, exists C > 0, exists n_0 >= 0, quad forall n > n_0, quad C g(n) <= f(n) <= D g(n) $ +] +Autrement dit +- si $f in O(g)$, alors $f$ croit plus lentement que $g$~; +- si $f in Omega (g)$, alors $f$ croit plus vite que $g$, i.e. $g in O(f)$~; +- si $f in Theta (g)$, alors $f$ croit aussi vite que $g$, i.e. $f in O(g)$ et $f in Omega (g)$. + +#props[ + Dans le cas où $(f(n))/(g(n))$ adment une limite dans $n$ tend vers $+inf$, si~: + - $lim (f(n))/(g(n)) = 0$, alors $f in O(g)$~; + - $lim (f(n))/(g(n)) = +inf$, alors $f in Omega (g)$~; + - $lim (f(n))/(g(n)) = l$ (où $l in RR backslash {0}$), alors $f in Theta (g)$. +] diff --git "a/semestre 4/db/0- Rentr\303\251e.pdf" "b/semestre 4/db/0- Rentr\303\251e.pdf" new file mode 100644 index 0000000..f88f874 --- /dev/null +++ "b/semestre 4/db/0- Rentr\303\251e.pdf" @@ -0,0 +1,2864 @@ +%PDF-1.7 +% + +1 0 obj +<< + /Type /Pages + /Count 5 + /Kids [198 0 R 200 0 R 202 0 R 204 0 R 206 0 R] +>> +endobj + +2 0 obj +<< + /Type /Outlines + /First 3 0 R + /Last 8 0 R + /Count 4 +>> +endobj + +3 0 obj +<< + /Parent 2 0 R + /Next 4 0 R + /Title (1. 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"William Hergès", affiliation: "Sorbonne Université", email: "william@herges.fr"), + ), + page_title: "Introduction", +) + += Introduction + +Est un cours d'introduction aux bases de données. + +Il y a 3 interros comptant pour 50% de la note en TD. +Il n'y a pas de partiel. +On a le droit à une feuille A4 comme support (écrite à la main). +À l'examen, on a le droit aux documents. + +Le cours regardant le fonctionnement précis d'un DB est celui de L3. + += Pourquoi utiliser une base de données~? + +Une base de données sert à la gestion des données. +On cherche à~: +- accéder aux données, les modifier +- partager entre plusieurs applications +- éviter de stocker la même information plusieurs fois +- tout en évitant les erreurs +- en étant capable de gérer des grands volumes de données +- et d'une manière sécurisée + +Un système de fichiers ne répond pas à ces attentes~: +- accès séquentiel (en entier) +- accès simultané sans contrôle +- même information peut être répétée +- logiciel erroné peut facilement introduire des erreurs +- la gestion de grands fichiers est inefficace +- protection limitée + +Besoin de trouver une autre façon pour gérer les données. +Cette façon est le _système de gestion de bases de données_ (SGBD). +Ce système gère les données~: +- accès faisable via SQL par exemple +- contrôle centralisé des accès aux données +- gestion du stockage indépendante des applications +- gestion globale de la cohérence des données (schémas, pannes, concurrence...) +- optimisation d'accès aux données (indexation, cache...) +- protection fine des données sensibles + += Architecture + +== Architecture client/serveur + +#defn[ + Une _base de données_ (BD, BDD) est un ensemble structuré de données liées, représentant une réalité spécifique. +] + +#defn[ + Un _serveur_ est une instance d'un SGBD qui contrôle l'accès à la DB. + + Un _client_ est une application qui communique avec le serveur. + + La _communication_ est un échange de requêtes liés à des bases de données (via SQL, le protocol JDBC...). +] + +Le serveur SGBD reçoit les requêtes de tous les clients. +Il les ordonne, les optimise et exécute les requêtes. +(Missing part...) + +== Architecture des données + +Dans une base de données, il y a trois niveaux d'organisation. + +#defn[ + Niveau externe est celui accessible aux clients. + Il contient les vues. + + Niveau logique est celui accessible aux développeurs. + Il détermine comment les données sont organisées (via les tables par exemple). + + Niveau interne est celui accessible aux concepteurs et aux administrateurs. + Il définit comment les données sont stockées en physique (index, fichiers, matériel...). +] + +Ces couches sont indépendantes~: on peut modifier un niveau sans toucher les autres. + += Comment construire une base de données~? + +On a besoin de connaître les besoins, de modéliser les données et d'implanter tout cela. + +Pour modéliser les données, on traduit les besoins dans le *modèle Entité-Association*. diff --git 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"b/semestre 4/db/1- Mod\303\250le Entit\303\251-Association.typ" @@ -0,0 +1,138 @@ +#import "@local/template:1.0.0": * +#import "@local/callout:1.0.0": * + +#show: doc.with( + authors: ( + (name: "William Hergès", affiliation: "Sorbonne Université", email: "william@herges.fr"), + ), + page_title: "Modèle Entité-Association", +) + += Introduction + +Ici, on s'intéresse à une forme abstraite~: description de haut niveau. +Il s'agit d'une première description formelle des données dans une base de données. + +On va prendre comme exemple la création d'un DB d'un Université. + +Les besoins~: +- inscripitons des étudiants à un module +- affectation des tuteurs à des étudiants +- planning des salles + +Les objets à modéliser~: +- les étudiants +- les modules +- les tuteurs +- les salles + +Les liens entre les objets~: +- les étudiants s'inscrivent à un ou plusieurs modules pour une année universitaire +- le cours d'un module a lieu dans une salle donnée, il débute à une heure connue et se déroule pendant une durée connue + + += Définitions élémentaires + +Cherche à transcrire les besoins en terme de _classes_ d'_entités_ et de _classes_ d'_associations_. + +#defn[ + Une _entité_ est un objet du monde réel identifiable et pertinent pour l'application. +] + +Une salle 24-34-208 est une entité. +Le médecin John Doe est une entité. + +#defn[ + Un _attribut_ est une propriété/une caractéristique à une entitée. + Il possède un nom et un domaine de valeurs atomiques. +] + +Un prénom est un attribut pour une personne. + +#defn[ + Une _classe d'entités_ est un ensemble d'entités ayant les mêmes attributs. +] + +Les médecins sont une classe d'entité. +Les salles le sont aussi. + +#defn[ + Un _identifiant d'entité_ est un sous-ensemble d'attributs permettant de distinguer les entités de la même classe. + Il doit être unique et toute classe d'entités doit en posséder une. +] + +Un identifiant peut être naturel (construit à partir des propriétés des entités) ou artificiel (rajouté aux attributs de +la classe). + +#defn[ + Une _association_ est une relation entre plusieurs entités. +] + +«~L'enseignant John Doe gère le cours X~» est une association. + +#defn[ + Une _classe d'associations_ est un ensemble nommé de relations «~du même type~» entre des entités. +] + +Enseigner est une classe d'associations. + +Une association peut avoir des attributs, tout comme il peut avoir un identifiant. + +*Souvent, on oublie la distinction X et classe de X.* + +== Cardinalité d'une classe d'association + +#defn[ + La _cardinalité d'association_ pour une classe d'entité $E$ et une classe d'association $A$, le nombre minimum et le + maximum d'associations de $A$ qui peuvent exister pour une instance de $E$. + + La cardinalité est notée $min : max$. +] + +Valeurs communes~: $0$, $1$ et $N$ (n'importe quelle valeur). + +La cardinalité $1:N$ indique qu'il faut au moins une entité et qu'il n'y a pas de limites. + +== Type d'association + +#defn[ + Une association est dite _réflexive_, si elle relie des entités de la même classe. + + Elle peut être _symétrique_ si les cardinalités sont identiques des deux côtés. + Sinon, elle est _asymétrique_. +] + +La distance d'une ville à une autre est relation réflexive et symétrique. +La relation de subordination est aussi réflexive, mais elle est asymétrique. + +== Type d'entité + +#defn[ + Une entité est dite _faible_ si son identifiant dépend d'autres entités (dites fortes). + Elles possèdent un _identifiant partiel_ qui est unique dans le contexte de leur entité forte. +] + +La salle 24-25-103 est faible car elle dépend du bâtiment 24-25 (qui est fort). + += Exemples de schéma + +Code~: +- les entités sont des rectangles +- les attributs par des ronds +- les associations sont des losanges +- l'identifiant est souligné (s'il est faible, il est souligné avec des pointillés) + +#figure( + image("./1- entité et association.png"), + caption: [Deux entités liées par deux associations.], +) + +#figure( + image("./1- cardinalité.png"), + caption: [Représentation de la cardinalité d'une association.] +) + +#figure( + image("./1- généralisation.png"), + caption: [Représentation de la généralisation d'attributs. 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"@local/callout:1.0.0": * + +#show: doc.with( + authors: ( + (name: "William Hergès", affiliation: "Sorbonne Université", email: "william@herges.fr"), + ), + page_title: "Introduction", +) + += Introduction + +Partiel le lundi 9 mars. +TP solo durant la séance TP9. +Mini-projet, rendu & soutenance lors du dernier TP. +On a le droit à une feuille A4 écrite à la main lors des examens. + +== Programmation orientée objet + +Cherche à développer des systèmes complexes. +Divise le système en plusieurs objets tout en sécurisant les données sensibles. + +Permet de travailler à plusieurs~: toujours penser son programme pour les autres, donc on sécurise, on simplifie et on +compartimente. + +== Java + +Java est une application classique de l'OOP. +Langage moderne, robuste, sûre et fortement typée. + +Propose une architecture dynamique avec un compilateur pour créer des applications performantes. +Repose sur la JVM pour exécuter le code compilé~: permet de créer des applications indépendantes de la machine physique. + += Premier programme + +En Java, tout le code doit être écrit dans une classe. +```java +// contenu de MonPremierProgramme.java +public class MonPremierProgramme { + // code +} +``` + +Un fichier `.java` contient forcément un fichier. +Il doit avoir le même nom de la classe. + +Un programme est un ensemble de classes. +Le point d'entrée est la méthode `main`. + +La signature de la fonction `main` est~: +```java +public class MonPremierProgramme { + public static void main(String[] args) { + System.out.println("Hello world :D"); + } +} +``` + +Besoin du JDK pour développer en Java. +Pour compiler, on écrit dans le terminal~: +```bash +javac MonPremierProgramme.java +``` +Cela crée un fichier `MonPremierProgramme.class` qui contient du bytecode JVM. +Pour l'exécuter, on écrit +```bash +java MonPremierProgramme +``` + +Pour compiler plusieurs classes, on fait~: +```bash +javac *.java +``` + += Concept de base de l'OOP + +En OOP, tout est encapsulé dans un objet. +Un objet est autonome~: il est réutilisable partout. +Il est aussi sécurisé~: il garantie le bon usage. +Il intègre des données et des méthodes pour le manipuler proprement. + += Syntaxe de Java + +... + +Les objets sont représentés par deux valeurs en mémoire~: le type et ses attributs. -- cgit v1.2.3