From a4e7566e9b94924db960d3b6d7aaf258faaa8e56 Mon Sep 17 00:00:00 2001 From: Florian Mathieu Date: Mon, 6 Jan 2025 08:53:55 +0100 Subject: [PATCH] ajout dossier cours arbres --- arbres/ABR.md | 3 ++ arbres/README.md | 76 +++++++++++++++++++++++++++++++++++++++++ arbres/assets/bo.png | Bin 0 -> 87557 bytes arbres/assets/img1.png | Bin 0 -> 58193 bytes arbres/assets/img2.png | Bin 0 -> 4389 bytes arbres/assets/img3.png | Bin 0 -> 4090 bytes arbres/assets/img4.png | Bin 0 -> 5529 bytes arbres/assets/img5.png | Bin 0 -> 5471 bytes arbres/assets/img6.png | Bin 0 -> 21297 bytes arbres/assets/img7.png | Bin 0 -> 64629 bytes 10 files changed, 79 insertions(+) create mode 100644 arbres/ABR.md create mode 100644 arbres/README.md create mode 100644 arbres/assets/bo.png create mode 100644 arbres/assets/img1.png create mode 100644 arbres/assets/img2.png create mode 100644 arbres/assets/img3.png create mode 100644 arbres/assets/img4.png create mode 100644 arbres/assets/img5.png create mode 100644 arbres/assets/img6.png create mode 100644 arbres/assets/img7.png diff --git a/arbres/ABR.md b/arbres/ABR.md new file mode 100644 index 0000000..9080a47 --- /dev/null +++ b/arbres/ABR.md @@ -0,0 +1,3 @@ +## Arbres Binaires + +> Les arbres binaires sont utilisés pour les bases de données (indexation), les moteurs de recherche, et les compilateurs. \ No newline at end of file diff --git a/arbres/README.md b/arbres/README.md new file mode 100644 index 0000000..8edf8ad --- /dev/null +++ b/arbres/README.md @@ -0,0 +1,76 @@ +## Structures Arborescentes + +> Structure présente partout dans le monde numérique, des répertoires de fichiers sur un ordinateur aux bases de données et algorithmes de recherche, les abres sont un pan essentiel de l'informatique. Ils permettent de structurer efficacement des données hiérarchiques et d’optimiser certaines opérations comme la recherche ou le tri. En NSI, nous allons explorer une version particulière de ces structures : les arbres binaires. + +--------------------------------- + + + +### Le programme + + + +bo.png + + + + + +### Définition + +arbre_1 + + ***Attention, il y a quelques mots clés qui vont survenir dans les prochaines lignes !*** + + + +- Un arbre est une structure de données hiérarchique et récursive, composée d’éléments appelés des **noeuds**. + +- Chacun de ces **noeuds** peut être étiqueté pour représenter une information. + +- Les **nœuds** d’un arbre sont reliés entre eux par des liens que l’on appelle souvent **arêtes** lorsque l'on parle de graphes (que nous verrons prochainement), mais en contexte arborescent, on parle couramment de **fils** pour désigner les connexions hiérarchiques. + +- **Un nœud parent** est relié à ses **nœuds enfants** par ces fils. + + - Ces relations définissent la hiérarchie dans l’arbre. + +- Un lien “fils” est **orienté** : il part d’un parent vers un enfant. + + - Ce lien structure la hiérarchie descendante, qui est essentielle pour le parcours de l’arbre (comme un arbre généalogique). + + + +**Question** : *Pourquoi pensez-vous que cette structure est utilisée dans les systèmes informatiques ?* + +-------------- + +### Caractéristiques d'un arbre + +Un arbre possède donc un nombre de noeuds, qu'on appelle **taille d'un arbre**. + +**Question** : *Quelle est la taille de l'arbre représenté ci dessus ?* + + + +On parle également de **hauteur d'un arbre** : + +- Elle correspond à la **profondeur maximale** d’un nœud dans l’arbre, c’est-à-dire le **plus grand nombre d’arêtes** depuis la racine jusqu’à une feuille. +- La hauteur est le nombre maximum de niveaux dans l’arbre, en partant de la racine jusqu’à la feuille la plus profonde. +- Selon les points de vue, la hauteur est parfois définie différemment : + - On peut considérer la hauteur d'un arbre vide à 0, soit à 1. + +**Question** : *Quelle est la hauteur de l'arbre du dessus ?* + + + +### Conclusion + +Comprendre ces caractéristiques nous aidera à explorer comment manipuler efficacement ces structures pour chercher, insérer ou supprimer des données, et ce, très prochainement. + +---------------- + +Auteurs : Florian Mathieu, Timothée Decoster, Enzo Frémaux + +Licence CC BY NC + +Licence Creative Commons
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