From 503d3d37481bc18c1cc9b98667ad5098b976a0a7 Mon Sep 17 00:00:00 2001
From: Orestis <orestis.malaspinas@pm.me>
Date: Mon, 11 Apr 2022 17:58:26 +0200
Subject: [PATCH] ajout exemple insertion

---
 slides/cours_22.md        | 127 ++++++++++-
 slides/figs/barbres_1.svg |  99 +++++++++
 slides/figs/barbres_2.svg | 110 ++++++++++
 slides/figs/barbres_3.svg | 209 ++++++++++++++++++
 slides/figs/barbres_4.svg | 217 +++++++++++++++++++
 slides/figs/barbres_5.svg | 277 ++++++++++++++++++++++++
 slides/figs/barbres_6.svg | 285 +++++++++++++++++++++++++
 slides/figs/barbres_7.svg | 438 ++++++++++++++++++++++++++++++++++++++
 8 files changed, 1761 insertions(+), 1 deletion(-)
 create mode 100644 slides/figs/barbres_1.svg
 create mode 100644 slides/figs/barbres_2.svg
 create mode 100644 slides/figs/barbres_3.svg
 create mode 100644 slides/figs/barbres_4.svg
 create mode 100644 slides/figs/barbres_5.svg
 create mode 100644 slides/figs/barbres_6.svg
 create mode 100644 slides/figs/barbres_7.svg

diff --git a/slides/cours_22.md b/slides/cours_22.md
index 9b72500..d7ec0de 100644
--- a/slides/cours_22.md
+++ b/slides/cours_22.md
@@ -95,13 +95,138 @@ patat:
 
 ![B-arbre d'ordre 2.](figs/barbres_exemple.png)
  
-. . 
+. . .
 
 * Si `n` plus petit que la 1e clé ou plus grand que la dernière descendre.
 * Sinon parcourir séquentiellement jusqu'à trouver ou descendre entre 2 éléments.
 
 # Les B-arbres
 
+* Inspiration de <https://en.wikipedia.org/wiki/B-tree>
+
+## Exemples d'insertion: `1`
+
+![B-arbre d'ordre 1.](figs/barbres_1.svg)
+ 
+. . .
+
+* L'arbre est vide, on insère juste dans la première page.
+
+# Les B-arbres
+
+## Exemples d'insertion: `2`
+
+![B-arbre d'ordre 1, nb pages = 2.](figs/barbres_2.svg)
+ 
+. . .
+
+* La première page est pas pleine, on insère dans l'ordre (après 1).
+
+# Les B-arbres
+
+## Exemples d'insertion: `3`
+
+![B-arbre d'ordre 1, nb de pages max = 2.](figs/barbres_2.svg){width=50%}
+
+* Comment on insère (1min de réflexion avant de donner une réponse!)?
+
+# Les B-arbres
+
+## Exemples d'insertion: `3`
+
+![B-arbre d'ordre 1, nb de pages max = 2.](figs/barbres_3.svg){width=50%}
+ 
+. . .
+
+* La page est pleine, on crée deux enfants.
+* On choisit, `2`, la médiane de `1, 2, 3` et il est inséré à la racine.
+* `1` descend à gauche, `3` descend à droite.
+
+# Les B-arbres
+
+## Exemples d'insertion: `4`
+
+![B-arbre d'ordre 1.](figs/barbres_3.svg){width=50%}
+ 
+* Comment on insère (1min de réflexion avant de donner une réponse!)?
+
+# Les B-arbres
+
+## Exemples d'insertion: `4`
+
+![B-arbre d'ordre 1.](figs/barbres_4.svg){width=50%}
+ 
+. . .
+
+* On pourrait insérer à droite de `2`, mais... ça ferait 2 parents pour 2 enfants (mais `m` parents => `m+1` enfants ou `0`);
+* On descend à droite (`4 > 2`);
+* On insère à droite de `3`.
+
+# Les B-arbres
+
+## Exemples d'insertion: `5`
+
+![B-arbre d'ordre 1.](figs/barbres_4.svg){width=50%}
+ 
+* Comment on insère (1min de réflexion avant de donner une réponse!)?
+
+# Les B-arbres
+
+## Exemples d'insertion: `5`
+
+![B-arbre d'ordre 2.](figs/barbres_5.svg)
+ 
+. . .
+
+* On descend à droite (on peut pas insérer à la racine comme pour `4`);
+* On dépasse la capacité de l'enfant droite;
+* `4`, médiane de `3, 4, 5`, remonte à la racine;
+* On crée un nouveau noeud à droite de `4`;
+* La règle `m => m+1` est ok.
+
+# Les B-arbres
+
+## Exemples d'insertion: `6`
+
+![B-arbre d'ordre 1.](figs/barbres_5.svg){width=50%}
+ 
+* Comment on insère (1min de réflexion avant de donner une réponse!)?
+
+# Les B-arbres
+
+## Exemples d'insertion: `6`
+
+![B-arbre d'ordre 2.](figs/barbres_6.svg)
+ 
+. . .
+
+* `6 > 4` on descend à droite;
+* `6 > 5` et on a à la place à droite, on insère.
+
+# Les B-arbres
+
+## Exemples d'insertion: `7`
+
+![B-arbre d'ordre 1.](figs/barbres_6.svg){width=50%}
+ 
+* Comment on insère (1min de réflexion avant de donner une réponse!)?
+
+# Les B-arbres
+
+## Exemples d'insertion: `7`
+
+![B-arbre d'ordre 2.](figs/barbres_7.svg){width=50%}
+ 
+. . .
+
+* `7 > 4` on descend à droite;
+* `7 > 6` mais on a dépassé la capacité;
+* `6` est la médiane de `5, 6, 7`, remonte à la racine;
+* `5` reste à gauche, `7` à droite, mais `6` fait dépasser la capacité de la racine;
+* `4` est la médiane de `2, 4, 6`, `4` remonte, `2` reste à gauche, `6` à droite.
+
+# Les B-arbres
+
 ## Structure de données
 
 * Chaque page a une contrainte de remplissage, par rapport à l'ordre de l'arbre;
diff --git a/slides/figs/barbres_1.svg b/slides/figs/barbres_1.svg
new file mode 100644
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diff --git a/slides/figs/barbres_2.svg b/slides/figs/barbres_2.svg
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diff --git a/slides/figs/barbres_3.svg b/slides/figs/barbres_3.svg
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GitLab