diff --git a/slides/cours_19.md b/slides/cours_19.md
index 50e7459599ecde5f5ead47e94e36c533badcb908..c1b192b4456cff870a799625724e9dc48bb2e8ee 100644
--- a/slides/cours_19.md
+++ b/slides/cours_19.md
@@ -32,7 +32,7 @@ patat:
 
 # Encore un petit exercice
 
-* Insérer les noeuds suivants dans un arbre AVL
+* Insérer les nœuds suivants dans un arbre AVL
 
 ```
 25 | 60 | 35 | 10 | 5 | 20 | 65 | 45 | 70 | 40 | 50 | 55 | 30 | 15
@@ -323,15 +323,15 @@ graph TD;
 # Résumé de la suppression
 
 1. On supprime comme pour un arbre binaire de recherche.
-2. Si un noeud est déséquilibré, on le rééquilibre.
-    * Cette opération pour déséquilibrer un autre noeud.
-3. On continue à rééquilibrer tant qu'il y a des noeuds à équilibrer.
+2. Si un nœud est déséquilibré, on le rééquilibre.
+    * Cette opération pour déséquilibrer un autre nœud.
+3. On continue à rééquilibrer tant qu'il y a des nœuds à équilibrer.
 
 # Les arbres quaternaires
 
 ## Définition
 
-Arbre dont chaque noeud a 4 enfants ou aucun. 
+Arbre dont chaque nœud a 4 enfants ou aucun. 
 
 ![Un exemple de quadtree.](figs/quad_ex.svg)
 
@@ -341,7 +341,7 @@ Arbre dont chaque noeud a 4 enfants ou aucun.
 
 Typiquement utilisés pour représenter des données bidimensionnelles.
 
-Son équivalent tri-dimensionnel est l'octree (chaque noeud a 8 enfants ou aucun).
+Son équivalent tri-dimensionnel est l'octree (chaque nœud a 8 enfants ou aucun).
 
 ## Cas d'utilisation: images
 
@@ -402,7 +402,7 @@ struct node
         inf_gauche, inf_droit
 ```
 
-![Un noeud d'arbre quaternaire.](figs/quad_struct.svg)
+![Un nœud d'arbre quaternaire.](figs/quad_struct.svg)
 
 ::::
 
@@ -451,6 +451,7 @@ bool est_feuille(noeud)
 
 . . .
 
+* Inutile d'avoir 4 conditions (soit 4 enfants soit aucun!)
 * Facile d'en oublier un!
 * Comment changer la structure pour que ça soit moins terrible?
 
@@ -459,10 +460,10 @@ bool est_feuille(noeud)
 ```python
 struct node
     info
-    node sup_gauche[4]
+    node enfant[4]
 ```
 
-# Une fonctionnalité simple
+# Structure de données
 
 ## En C?
 
@@ -471,10 +472,206 @@ struct node
 ```C 
 typedef struct _node {
     int info;
-    struct _node *children;
+    struct _node *child[4];
 } node;
-typedef node *tree;
 ```
 
+## Fonction `is_leaf(node *tree)`?
+
+. . .
+
+```C 
+bool is_leaf(node *tree) {
+    return (NULL == tree->child[0]); // only first matters
+}
+```
+
+# Problème à résoudre
+
+* Construire un arbre quaternaire à partir d'une image:
+    * Créer l'arbre (allouer la mémoire pour tous les nœuds),
+    * Le remplir avec les valeurs des pixels.
+* Compression de l'image:
+    * Si les pixels sont les mêmes dans le quadrant on supprime le sous-arbre (sans perte)
+    * Si les pixels dévident pas trop on supprime le quadrant (avec perte)
+
+# Fonctions utiles (1/N)
+
+## Comment créer un arbre de profondeur `prof` (3min)?
+
+. . .
+
+```python
+arbre creer_arbre(prof)
+    n = nouveau_noeud() # alloue la mémoire
+    si prof > 0
+        pour i = 0 à 3
+            n.enfant[i] = creer_arbre(prof-1)
+    retourne n
+```
+
+## En `C` (3 min, matrix)?
+
+. . .
+
+```C
+node *qt_create(int depth) {
+    node *n = calloc(1, sizeof(*n));
+    if (depth > 0) {
+        for (int i = 0; i < 4; ++i) {
+            n->child[i] = qt_create(depth-1);
+        }
+    }
+    return n;
+}
+```
+
+# Fonctions utiles (2/N)
+
+## Comment remplir un arbre depuis une matrice?
+
+```
+   SG=0  |  SD=1
+ 21 | 12 | 4 |  4
+  9 |  7 | 4 |  4
+-----------------
+  1 |  1 | 0 | 31
+  1 |  1 | 3 | 27
+   IG=2  |  ID=3
+```
+
+## Quel arbre cela représente?
+
+. . .
+
+![L'arbre correspondant](figs/quad_img_simple.svg)
+
+# Fonctions utiles (3/N)
+
+* On veut transformer une ligne/colonne en feuille.
+* Comment?
+
+::: columns
+
+:::: {.column width=40%}
+
+## Soit `ligne=2`, `colonne=3`
+
+```
+   SG=0  |  SD=1
+ 21 | 12 | 4 |  4
+  9 |  7 | 4 |  4
+-----------------
+  1 |  1 | 0 | 31
+  1 |  1 | 3 | 27
+   IG=2  |  ID=3
+```
+
+::::
+
+:::: {.column width=70%}
+
+## Trouver un algorithme
+
+![Déterminer un algorithme.](figs/quad_img_simple.svg)
+
+* Quelle feuille?
+* Plus important: quel chemin?
+
+. . .
+
+* `co -> G/D`, `li -> S/I`,
+* `2 * (li / 2) + co / 2 -> 2 * 1 + 1 = 3`
+* `2 * ((li % 2) / 1) + (co % 2) / 1 -> 2 * 0 + 1 = 1`
+* Comment généraliser?
+
+::::
+
+:::
+
+# Fonctions utiles (4/N)
+
+::: columns
+
+:::: {.column width=40%}
+
+## Soit `ligne=2`, `colonne=3`
+
+```
+   SG=0  |  SD=1
+ 21 | 12 | 4 |  4
+  9 |  7 | 4 |  4
+-----------------
+  1 |  1 | 0 | 31
+  1 |  1 | 3 | 27
+   IG=2  |  ID=3
+```
+
+::::
+
+:::: {.column width=70%}
+
+## Trouver un algorithme
+
+![Déterminer un algorithme.](figs/quad_img_simple.svg)
+
+* Comment généraliser?
+
+. . .
+
+```C
+noeud position(li, co, arbre)
+    d = profondeur(arbre);
+    tant_que (d > 1)
+        index = 2 * ((li % 2^d) / 2^(d-1)) +
+            (col % 2^d) / 2^(d-1)
+        arbre = arbre.enfant[index]
+        d -= 1
+    retourn arbre
+```
+
+::::
+
+:::
+
+# Remplir l'arbre
+
+## A partir d'une matrice (pseudo-code, 5min, matrix)?
+
+. . .
+
+```C
+arbre matrice_à_arbre(matrice, arbre)
+    arbre = creer_arbre(profondeur)
+    pour li de 0 à nb_lignes(matrice)
+        pour co de 0 à nb_colonnes(matrice)
+            noeud = position(li, co, arbre)
+            noeud.info = matrice[co][li]
+    retourne arbre
+```
+
+. . .
+
+## A partir d'une matrice (C, 5min, matrix)?
+
+```C
+node *matrice_to_qt(int nb_li, int nb_co, int matrix[nb_li][nb_co], int depth)
+    node *qt = qt_create(depth);
+    for (int li = 0; li < nd_li; ++li) {
+        for (int co = 0; co < nd_co; ++co) {
+            node *current = position(li, co, qt);
+            current->info = matrix[li][co];
+        }
+    }
+    return qt;
+```
+
+
+# Interface
+
+## Quelles sont les fonctions à implémenter?
+
+
+
 
 # Implémentation
diff --git a/slides/figs/quad_img_simple.svg b/slides/figs/quad_img_simple.svg
new file mode 100644
index 0000000000000000000000000000000000000000..f9fea0d611cafcfc47bc0bdc6f3dd00f607c7f38
--- /dev/null
+++ b/slides/figs/quad_img_simple.svg
@@ -0,0 +1,257 @@
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+</g>
+<!-- 0&#45;&gt;sg1 -->
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+<title>0-&gt;id1</title>
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\ No newline at end of file