diff --git a/slides/cours_9.md b/slides/cours_9.md
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+---
+title: "Piles et files d'attente"
+date: "2021-12-07"
+---
+
+# Les piles (1/5)
+
+## Qu'est-ce donc?
+
+* Structure de données abstraite...
+
+. . .
+
+* de type `LIFO` (*Last in first out*).
+
+](figs/Stack.svg){width=70%}
+
+## Des exemples de la vraie vie
+
+. . .
+
+* Pile d'assiettes, de livres, ...
+* Adresses visitées par un navigateur web.
+* Les calculatrices du passé (en polonaise inverse).
+* Les boutons *undo* de vos éditeurs de texte (aka *u* dans vim).
+
+# Les piles (2/5)
+
+## Fonctionnalités
+
+. . .
+
+1. Empiler (push): ajouter un élément sur la pile.
+2. Dépiler (pop): retirer l'élément du sommet de la pile et le retrouner.
+3. Liste vide? (is_empty?).
+
+. . .
+
+4. Jeter un oeil (peek): retourner l'élément du sommet de la pile (sans le dépiler).
+5. Nombre d'éléments (length).
+
+## Comment faire les 4,5 à partir de 1 à 3?
+
+. . .
+
+4. Dépiler l'élément, le copier, puis l'empiler à nouveau.
+5. Dépiler jusqu'à ce que la pile soit vide, puis empiler à nouveau.
+
+. . .
+
+## Existe en deux goûts
+
+* Pile avec ou sans limite de capacité (à concurrence de la taille de la
+mémoire).
+
+# Les piles (3/5)
+
+## Implémentation
+
+* Jusqu'ici on n'a pas du tout parlé d'implémentation (d'où le nom de structure
+ abstraite).
+* Pas de choix unique d'implémentation.
+
+## Quelle structure de données allons nous utiliser?
+
+. . .
+
+Et oui vous avez deviné: un tableau!
+
+## La structure: de quoi avons-nous besoin (pile de taille fixe)?
+
+. . .
+
+```C
+#define MAX_CAPACITY 500
+typedef struct _stack {
+ int data[MAX_CAPACITY]; // les données
+ int top; // indice du sommet
+} stack;
+```
+
+# Les piles (4/5)
+
+## Initialisation
+
+. . .
+
+```C
+void stack_init(stack *s) {
+ s->top = -1;
+}
+```
+
+## Est vide?
+
+. . .
+
+```C
+bool stack_is_empty(stack s) {
+ return s.top == -1;
+}
+```
+
+## Empiler (ajouter un élément au sommet)
+
+. . .
+
+```C
+void stack_push(stack *s, int val) {
+ s->top += 1;
+ s->data[s->top] = val;
+}
+```
+
+# Les piles (5/5)
+
+## Dépiler (enlever l'élément du sommet)
+
+. . .
+
+```C
+int stack_pop(stack *s) {
+ s->top -= 1;
+ return s->data[s->top+1];
+}
+```
+
+## Jeter un oeil (regarder le sommet)
+
+. . .
+
+```C
+int stack_peek(stack *s) {
+ return s->data[s->top];
+}
+```
+
+## Quelle est la complexité de ces opérations?
+
+. . .
+
+## Voyez-vous des problèmes potentiels avec cette implémentation?
+
+. . .
+
+* Empiler avec une pile pleine.
+* Dépiler avec une pile vide.
+* Jeter un oeil au sommet d'une pile vide.
+
+# Gestion d'erreur, level 0
+
+* Il y a plusieurs façon de traiter les erreur:
+ * Ne rien faire (laisser la responsabilité à l'utilisateur).
+ * Faire paniquer le programme (il plante plus ou moins violemment).
+ * Utiliser des codes d'erreurs.
+
+## La panique
+
+* En C, on a les `assert()` pour faire paniquer un programme.
+
+
+# Assertions (1/3)
+
+```C
+#include <assert.h>
+void assert(int expression);
+```
+
+## Qu'est-ce donc?
+
+- Macro permettant de tester une condition lors de l'exécution d'un programme:
+ - Si `expression == 0`{.C} (condition fausse), `assert()`{.C} affiche un message d'erreur sur `stderr`{.C} et termine l'exécution du programme.
+ - Sinon l'exécution se poursuit normalement.
+ - Peuvent être désactivés à la compilation avec `-DNDEBUG` (équivalent à `#define
+ NDEBUG`)
+
+## À quoi ça sert?
+
+- Permet de réaliser des tests unitaires.
+- Permet de tester des conditions catastrophiques d'un programme.
+- **Ne permet pas** de gérer les erreurs.
+
+# Assertions (2/3)
+
+<!-- \footnotesize -->
+
+## Exemple
+
+```C
+#include <assert.h>
+void stack_push(stack *s, int val) {
+ assert(s->top < MAX_CAPACITY-1);
+ s->top += 1;
+ s->data[s->top] = val;
+}
+int stack_pop(stack *s) {
+ assert(s->top >= 0);
+ s->top -= 1;
+ return s->data[s->top+1];
+}
+int stack_peek(stack *s) {
+ assert(s->top >= 0);
+ return s->data[s->top];
+}
+```
+
+# Assertions (3/3)
+
+## Cas typiques d'utilisation
+
+- Vérification de la validité des pointeurs (typiquement `!= NULL`{.C}).
+- Vérification du domaine des indices (dépassement de tableau).
+
+## Bug vs. erreur de *runtime*
+
+- Les assertions sont là pour détecter les bugs (erreurs d'implémentation).
+- Les assertions ne sont pas là pour gérer les problèmes externes au programme (allocation mémoire qui échoue, mauvais paramètre d'entrée passé par l'utilisateur, ...).
+
+. . .
+
+- Mais peuvent être pratiques quand même pour ça...
+- Typiquement désactivées dans le code de production.
+
+# La pile dynamique
+
+## Comment modifier le code précédent pour avoir une taille dynamique?
+
+. . .
+
+```C
+// alloue une zone mémoire de size octets
+void *malloc(size_t size);
+// change la taille allouée à size octets (contiguïté garantie)
+void *realloc(void *ptr, size_t size);
+```
+
+## Et maintenant?
+
+. . .
+
+```C
+stack_create(); // crée une pile avec une taille par défaut
+// vérifie si la pile est pleine et réalloue si besoin
+stack_push();
+// vérifie si la pile est vide/trop grande
+// et réalloue si besoin
+stack_pop();
+```
+
+## Exercice: ouvrir un repo/issues pour l'implémentation
+
+* Oui-oui cela est une introduction au développement collaboratif (et
+ hippie).
+
+# Le tri à deux piles (1/3)
+
+## Cas pratique
+
+{width=70%}
+
+# Le tri à deux piles (2/3)
+
+## Exercice: formaliser l'algorithme
+
+. . .
+
+## Algorithme de tri nécessitant 2 piles (G, D)
+
+Soit `tab` le tableau à trier:
+
+```C
+pour i de 0 à N-1
+ tant que (tab[i] > que le sommet de G)
+ dépiler G dans D
+ tant que (tab[i] < que le sommet de D)
+ dépiler de D dans G
+ empiler tab[i] sur G
+dépiler tout D dans G
+tab est trié dans G
+```
+
+# Le tri à deux piles (3/3)
+
+## Exercice: trier le tableau `[2, 10, 5, 20, 15]`
+
+```C
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+```
+
+# La calculatrice (1/8)
+
+## Vocabulaire
+
+```C
+2 + 3 = 2 3 +,
+```
+
+`2` et `3` sont les *opérandes*, `+` l'*opérateur*.
+
+. . .
+
+## La notation infixe
+
+```C
+2 * (3 + 2) - 4 = 6.
+```
+
+## La notation postfixe
+
+```C
+2 3 2 + * 4 - = 6.
+```
+
+## Exercice: écrire `2 * 3 * 4 + 2` en notation `postfixe`
+
+. . .
+
+```C
+2 3 4 * * 2 + = (2 * (3 * 4)) + 2.
+```
+
+# La calculatrice (2/8)
+
+## De infixe à post-fixe
+
+* Une *pile* est utilisée pour stocker *opérateurs* et *parenthèses*.
+* Les opérateurs on des *priorités* différentes.
+
+```C
+^ : priorité 3
+* / : priorité 2
++ - : priorité 1
+( ) : priorité 0 // pas un opérateur mais bon
+```
+
+
+# La calculatrice (3/8)
+
+## De infixe à post-fixe: algorithme
+
+* On lit l'expression infixe de gauche à droite.
+
+* On examine le prochain caractère de l'expression infixe.
+ * Si opérande, le placer dans l'expression du résultat.
+ * Si parenthèse le mettre dans la pile (priorité 0).
+ * Si opérateur, comparer sa priorité avec celui du sommet de la pile:
+ * Si sa priorité est plus élevée, empiler.
+ * Sinon dépiler l'opérateur de la pile dans l'expression du résultat et
+ recommencer jusqu'à apparition d'un opérateur de priorité plus faible
+ au sommet de la pile (ou pile vide).
+ * Si parenthèse fermée, dépiler les opérateurs du sommet de la pile et les
+ placer dans l'expression du résultat, jusqu'à ce qu'une parenthèse
+ ouverte apparaisse au sommet, dépiler également la parenthèse.
+ * Si il n'y a pas de caractère dans l'expression dépiler tous les
+ opérateurs dans le résultat.
+
+# La calculatrice (4/8)
+
+## De infixe à post-fixe: exemple
+
+```C
+Infixe Postfixe Pile Priorité
+((A*B)/D-F)/(G+H) Vide Vide Néant
+ (A*B)/D-F)/(G+H) Vide ( 0
+ A*B)/D-F)/(G+H) Vide (( 0
+ *B)/D-F)/(G+H) A (( 0
+ B)/D-F)/(G+H) A ((* 2
+ )/D-F)/(G+H) AB ((* 2
+ /D-F)/(G+H) AB* ( 0
+ D-F)/(G+H) AB* (/ 2
+ -F)/(G+H) AB*D (/ 2
+ F)/(G+H) AB*D/ (- 1
+ )/(G+H) AB*D/F (- 1
+ /(G+H) AB*D/F- Vide Néant
+```
+
+# La calculatrice (5/8)
+
+## De infixe à post-fixe: exemple
+
+```C
+Infixe Postfixe Pile Priorité
+((A*B)/D-F)/(G+H) Vide Vide Néant
+--------------------------------------------------------
+ /(G+H) AB*D/F- Vide Néant
+ (G+H) AB*D/F- / 2
+ G+H) AB*D/F- /( 0
+ +H) AB*D/F-G /( 0
+ H) AB*D/F-G /(+ 1
+ ) AB*D/F-GH /(+ 1
+ Vide AB*D/F-GH+ / 2
+ Vide AB*D/F-GH+/ Vide Néant
+```
+
+# La calculatrice (6/8)
+
+\footnotesize
+
+## Exercice: écrire le code et le poster sur matrix
+
+* Quelle est la signature de la fonction?
+
+. . .
+
+```C
+char *infix_to_postfix(char* infix) { // init and alloc stack and postfix
+ for (size_t i = 0; i < strlen(infix); ++i) {
+ if (is_operand(infix[i])) {
+ // we just add operands in the new postfix string
+ } else if (infix[i] == '(') {
+ // we push opening parenthesis into the stack
+ stack_push(&s, infix[i]);
+ } else if (infix[i] == ')') {
+ // we pop everything into the postfix
+ } else if (is_operator(infix[i])) {
+ // this is an operator. We add it to the postfix based
+ // on the priority of what is already in the stack and push it
+ }
+ }
+ // pop all the operators from the s at the end of postfix
+ // and end the postfix with `\0`
+ return postfix;
+}
+```
+
+
+# La calculatrice (7/8)
+
+## Évaluation d'expression postfixe: algorithme
+
+* Chaque *opérateur* porte sur les deux opérandes qui le précèdent.
+* Le *résultat d'une opération* est un nouvel *opérande* qui est remis au
+ sommet de la pile.
+
+## Exemple
+
+```C
+2 3 4 + * 5 - = ?
+```
+
+* On parcours de gauche à droite:
+
+```C
+Caractère lu Pile opérandes
+ 2 2
+ 3 2, 3
+ 4 2, 3, 4
+ + 2, (3 + 4)
+ * 2 * 7
+ 5 14, 5
+ - 14 - 5 = 9
+```
+
+# La calculatrice (8/8)
+
+## Évaluation d'expression postfixe: algorithme
+
+1. La valeur d'un opérande est *toujours* empilée.
+2. L'opérateur s'applique *toujours* au 2 opérandes au sommet.
+3. Le résultat est remis au sommet.
+
+## Exercice: écrire l'algorithme (et poster sur matrix)
+
+. . .
+
+```C
+bool evaluate(char *postfix, double *val) { // init stack
+ for (size_t i = 0; i < strlen(postfix); ++i) {
+ if (is_operand(postfix[i])) {
+ stack_push(&s, postfix[i]);
+ } else if (is_operator(postfix[i])) {
+ double rhs = stack_pop(&s);
+ double lhs = stack_pop(&s);
+ stack_push(&s, op(postfix[i], lhs, rhs);
+ } }
+ return stack_pop(&s);
+}
+```
+
diff --git a/slides/figs/tri_piles.svg b/slides/figs/tri_piles.svg
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