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+ d="m 113.77083,91.28125 c 0,0 -23.812497,21.16667 -43.656247,0"
+ id="path16437-9-1-6"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;marker-end:url(#Arrow2Lend-2)"
+ d="m 50.270836,50.270833 c 0,0 15.874997,-10.583333 31.749997,0"
+ id="path16437-7"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;marker-end:url(#Arrow2Lend-8-2)"
+ d="m 50.270836,50.270833 c 0,0 23.812497,-18.520833 47.624997,0"
+ id="path16437-9-5"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;marker-end:url(#Arrow2Lend-2-2)"
+ d="m 66.145833,50.270833 c 0,0 23.8125,-11.90625 47.624997,1.322917"
+ id="path16437-7-9"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;marker-end:url(#Arrow2Lend-8-2-9)"
+ d="m 66.145833,50.270833 c 0,0 31.75,-18.520833 62.177087,0"
+ id="path16437-9-5-7"
+ sodipodi:nodetypes="cc" />
+ </g>
+</svg>
diff --git a/slides/tri_par_tas.md b/slides/tri_par_tas.md
index 77c3d78f86f079e8469289f6fc9cf645a8fa5d85..4da67aa1fd0aac9d26720646ff92267a38af59a9 100644
--- a/slides/tri_par_tas.md
+++ b/slides/tri_par_tas.md
@@ -24,6 +24,387 @@ date: "2022-03-02"
# Visuellement
+::: columns
+:::: column
+* Où vont les indices correspondant du tableau?
+```{.mermaid format=pdf width=400 loc=figs/}
+graph TD;
+ id0(( ))-->id1(( ));
+ id0-->id2(( ));
+ id1-->id3(( ));
+ id1-->id4(( ));
+ id2-->id5(( ));
+ id2-->id6(( ));
+ id3-->id7(( ));
+ id3-->id8(( ));
+ id4-->id9(( ));
+ id4-->id10(( ));
+ style id10 fill:#fff,stroke:#fff
+```
+::::
+
+:::: column
+
+* Les flèche de gauche à droite, parent -> enfants.
+* Les flèche de droite à gauche, enfants -> parent.
+
+
+
+::::
+
+:::
+
+**Propriétés:**
+
+1. les feuilles sont toutes sur l'avant dernier ou dernier niveau.
+2. les feuilles de profondeur maximale sont "tassée" à gauche.
+
+# Le tas (ou heap)
+
+## Définition
+
+* Un arbre est un tas, si la valeur de chacun de ses descendants est inférieure
+ ou égale à sa propre valeur.
+
+## Exemples (ou pas)
+
+```
+16 8 14 6 2 10 12 4 5 # Tas
+16 14 8 6 2 10 12 4 5 # Non-tas, 10 > 8 et 12 > 8
+```
+
+## Exercices (ou pas)
+
+```
+19 18 12 12 17 1 13 4 5 # Tas ou pas tas?
+19 18 16 12 17 1 12 4 5 # Tas ou pas tas?
+```
+
+. . .
+
+```
+19 18 12 12 17 1 13 4 5 # Pas tas! 13 > 12
+19 18 16 12 17 1 12 4 5 # Tas!
+```
+
+# Exemple de tri par tas (1/N)
+
+```
+ | 1 | 16 | 5 | 12 | 4 | 2 | 8 | 10 | 6 | 7 |
+```
+
+::: columns
+
+:::: column
+
+* Quel est l'arbre que cela représente?
+
+. . .
+
+```{.mermaid format=pdf width=400 loc=figs/}
+graph TD;
+ id0((1))-->id1((16));
+ id0-->id2((5));
+ id1-->id3((12));
+ id1-->id4((4));
+ id2-->id5((2));
+ id2-->id6((8));
+ id3-->id7((10));
+ id3-->id8((6));
+ id4-->id9((7));
+ id4-->id10(( ));
+ style id10 fill:#fff,stroke:#fff
+```
+
+::::
+
+:::: column
+
+**But:** Transformer l'arbre en tas.
+
+* On commence à l'indice $N/2 = 5$: `7`.
+* `7 > 4` (enfant `>` parent).
+* intervertir `4` et `7`.
+
+```{.mermaid format=pdf width=400 loc=figs/}
+graph TD;
+ id0((1))-->id1((16));
+ id0-->id2((5));
+ id1-->id3((12));
+ id1-->id4((7));
+ id2-->id5((2));
+ id2-->id6((8));
+ id3-->id7((10));
+ id3-->id8((6));
+ id4-->id9((4));
+ id4-->id10(( ));
+ style id10 fill:#fff,stroke:#fff
+```
+
+::::
+
+:::
+
+. . .
+
+```
+ * *
+ | 1 | 16 | 5 | 12 | 7 | 2 | 8 | 10 | 6 | 4 |
+```
+
+# Exemple de tri par tas (2/N)
+
+```
+ | 1 | 16 | 5 | 12 | 7 | 2 | 8 | 10 | 6 | 4 |
+```
+
+::: columns
+
+:::: column
+
+**But:** Transformer l'arbre en tas.
+
+* On continue à l'indice $N/2-1 = 4$: `12`.
+* Déjà un tas, rien à faire.
+
+```{.mermaid format=pdf width=400 loc=figs/}
+graph TD;
+ id0((1))-->id1((16));
+ id0-->id2((5));
+ id1-->id3((12));
+ id1-->id4((7));
+ id2-->id5((2));
+ id2-->id6((8));
+ id3-->id7((10));
+ id3-->id8((6));
+ id4-->id9((4));
+ id4-->id10(( ));
+ style id10 fill:#fff,stroke:#fff
+```
+
+::::
+
+:::: column
+
+**But:** Transformer l'arbre en tas.
+
+* On continue à l'indice $N/2-2 = 3$: `5`.
+* `5 < 8`, échanger `8` et `5` (aka `max(2, 5, 8)`)
+
+```{.mermaid format=pdf width=400 loc=figs/}
+graph TD;
+ id0((1))-->id1((16));
+ id0-->id2((8));
+ id1-->id3((12));
+ id1-->id4((7));
+ id2-->id5((2));
+ id2-->id6((5));
+ id3-->id7((10));
+ id3-->id8((6));
+ id4-->id9((4));
+ id4-->id10(( ));
+ style id10 fill:#fff,stroke:#fff
+```
+
+::::
+
+:::
+
+. . .
+
+```
+ | 1 | 16 | 8 | 12 | 7 | 2 | 5 | 10 | 6 | 4 |
+```
+
+# Exemple de tri par tas (3/N)
+
+```
+ | 1 | 16 | 5 | 12 | 7 | 2 | 8 | 10 | 6 | 4 |
+```
+
+::: columns
+
+:::: column
+
+**But:** Transformer l'arbre en tas.
+
+* Indice $N/2-1 = 4$: `12`.
+* Déjà un tas, rien à faire.
+
+```{.mermaid format=pdf width=400 loc=figs/}
+graph TD;
+ id0((1))-->id1((16));
+ id0-->id2((5));
+ id1-->id3((12));
+ id1-->id4((7));
+ id2-->id5((2));
+ id2-->id6((8));
+ id3-->id7((10));
+ id3-->id8((6));
+ id4-->id9((4));
+ id4-->id10(( ));
+ style id10 fill:#fff,stroke:#fff
+```
+
+::::
+
+:::: column
+
+**But:** Transformer l'arbre en tas.
+
+* Indice $N/2-2 = 3$: `5`.
+* `5 < 8`, `5 <=> max(2, 5, 8)`
+
+```{.mermaid format=pdf width=400 loc=figs/}
+graph TD;
+ id0((1))-->id1((16));
+ id0-->id2((8));
+ id1-->id3((12));
+ id1-->id4((7));
+ id2-->id5((2));
+ id2-->id6((5));
+ id3-->id7((10));
+ id3-->id8((6));
+ id4-->id9((4));
+ id4-->id10(( ));
+ style id10 fill:#fff,stroke:#fff
+```
+
+::::
+
+:::
+
+```
+ * *
+ | 1 | 16 | 8 | 12 | 7 | 2 | 5 | 10 | 6 | 4 |
+```
+
+# Exemple de tri par tas (4/N)
+
+```
+ | 1 | 16 | 8 | 12 | 7 | 2 | 5 | 10 | 6 | 4 |
+```
+
+::: columns
+
+:::: column
+
+**But:** Transformer l'arbre en tas.
+
+* Indice $N/2-3 = 1$: `16`.
+* Déjà un tas, rien à faire.
+
+```{.mermaid format=pdf width=400 loc=figs/}
+graph TD;
+ id0((1))-->id1((16));
+ id0-->id2((5));
+ id1-->id3((12));
+ id1-->id4((7));
+ id2-->id5((2));
+ id2-->id6((8));
+ id3-->id7((10));
+ id3-->id8((6));
+ id4-->id9((4));
+ id4-->id10(( ));
+ style id10 fill:#fff,stroke:#fff
+```
+
+::::
+
+:::: column
+
+**But:** Transformer l'arbre en tas.
+
+* Indice $N/2-4 = 1$: `1`.
+* `1 < 16 && 1 < 8`, `1 <=> max(1, 16, 8)`
+
+```{.mermaid format=pdf width=400 loc=figs/}
+graph TD;
+ id0((16))-->id1((1));
+ id0-->id2((8));
+ id1-->id3((12));
+ id1-->id4((7));
+ id2-->id5((2));
+ id2-->id6((5));
+ id3-->id7((10));
+ id3-->id8((6));
+ id4-->id9((4));
+ id4-->id10(( ));
+ style id10 fill:#fff,stroke:#fff
+```
+
+::::
+
+:::
+
+```
+ * *
+ | 16 | 1 | 8 | 12 | 7 | 2 | 5 | 10 | 6 | 4 |
+```
+
+
+# Exemple de tri par tas (5/N)
+
+```
+ | 16 | 1 | 8 | 12 | 7 | 2 | 5 | 10 | 6 | 4 |
+```
+
+::: columns
+
+:::: column
+
+**But:** Transformer l'arbre en tas.
+
+* Recommencer avec `1`.
+* `1 <=> max(1, 12, 7)`.
+
+```{.mermaid format=pdf width=400 loc=figs/}
+graph TD;
+ id0((16))-->id1((12));
+ id0-->id2((5));
+ id1-->id3((1));
+ id1-->id4((7));
+ id2-->id5((2));
+ id2-->id6((8));
+ id3-->id7((10));
+ id3-->id8((6));
+ id4-->id9((4));
+ id4-->id10(( ));
+ style id10 fill:#fff,stroke:#fff
+```
+
+::::
+
+:::: column
+
+**But:** Transformer l'arbre en tas.
+
+* Recommencer avec `1`.
+* `1 <=> max(1, 10, 6)`.
+
+```{.mermaid format=pdf width=400 loc=figs/}
+graph TD;
+ id0((16))-->id1((12));
+ id0-->id2((8));
+ id1-->id3((10));
+ id1-->id4((7));
+ id2-->id5((2));
+ id2-->id6((5));
+ id3-->id7((1));
+ id3-->id8((6));
+ id4-->id9((4));
+ id4-->id10(( ));
+ style id10 fill:#fff,stroke:#fff
+```
+
+::::
+
+:::
+
+```
+ * * *
+ | 16 | 12 | 8 | 10 | 7 | 2 | 5 | 1 | 6 | 4 |
+```