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---
title: "B-Arbres"
date: "2022-04-13"
date: "2022-05-03"
patat:
eval:
tai:
......@@ -300,6 +300,111 @@ page ajouter_niveau(page, element)
![25 supprimé, on décale juste 27.](figs/barbres_ordre2_supp2.svg){width=80%}
# Les B-arbres: suppression
## Cas simple
![Suppression de 27.](figs/barbres_ordre2_supp2.svg){width=60%}
. . .
* On retire 27, mais....
* Chaque page doit avoir au moins 2 éléments.
* On doit déplacer des éléments dans une autre feuille! Mais comment?
. . .
![La médiane de la racine descend, fusion de 20 à gauche, et suppression à droite.](figs/barbres_ordre2_supp3.svg){width=60%}
# Les B-arbres: suppression
## Cas moins simple
![Suppression de 5.](figs/barbres_ordre2_supp4.svg){width=60%}
. . .
* Un élément à droite, comment on fait?
* Remonter `7`, serait ok si racine, mais... c'est pas forcément.
* On redistribue les feuilles.
. . .
![Descente de `3`, remontée médiane des feuilles `2`, .](figs/barbres_ordre2_supp5.svg){width=60%}
# Les B-arbres: suppression
## Cas ultra moins simple
![Suppression de 3.](figs/barbres_ordre2_supp6.svg){width=60%}
. . .
* `7` seul:
* Fusionner les feuilles et redistribuer, comment?
. . .
![Descendre `-1`, déplacer `7` à gauche, et décaler les éléments de droite au milieu.](figs/barbres_ordre2_supp7.svg){width=60%}
# Les B-arbres: suppression
## Cas ultra moins simple
![On a pas fini...](figs/barbres_ordre2_supp7.svg){width=60%}
. . .
* `8` est seul, c'est plus un B-arbre :
* Fusionner le niveau 2 et redistribuer, comment?
. . .
![Fusionner `8`, `17`, `22` et descendre `12`.](figs/barbres_ordre2_supp8.svg){width=40%}
. . .
* La profondeur a diminué de 1.
# Les B-arbres: suppression
## Algorithme pour les feuilles!
* Si la clé est supprimée d'une feuille:
* Si on a toujours `n` (ordre de l'arbre) clés dans la feuille on décale simplement les clés.
* Sinon on combine (récursivement) avec le noeud voisin et on descend la clé médiane.
# Les B-arbres: suppression
## Cas non-feuille!
![Suppression de 8.](figs/barbres_ordre2_supp9.svg){width=60%}
. . .
* On sait comment effacer une valeur d'une feuille, donc?
. . .
![Échanger le `8` avec le plus grand du sous-arbre de gauche.](figs/barbres_ordre2_supp10.svg){width=60%}
* Ensuite?
# Les B-arbres: suppression
## Cas non-feuille!
![Suppression de 8.](figs/barbres_ordre2_supp10.svg){width=60%}
. . .
* On sait comment effacer une valeur d'une feuille!
. . .
![Yaka enlever le 8.](figs/barbres_ordre2_supp11.svg){width=60%}
<!-- # Les B-arbres -->
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