From 5f492594ff088989cc24d72b96992a8ebbacb889 Mon Sep 17 00:00:00 2001 From: "paul.albuquer" <paul.albuquerque@hesge.ch> Date: Sun, 14 Nov 2021 15:13:05 +0100 Subject: [PATCH] added source code and handout for sorted lists --- lessons/contenu_cours_struct_queue.md | 3 +- lessons/contenu_cours_struct_sorted_list.md | 206 ++++++++++++++++++ .../fig_1st_element_sorted_list_extract.png | Bin 0 -> 9227 bytes .../fig_1st_element_sorted_list_search.png | Bin 0 -> 44360 bytes .../fig_1st_position_sorted_list_insert.png | Bin 0 -> 20962 bytes .../figures/fig_empty_sorted_list_insert.png | Bin 0 -> 12996 bytes .../fig_free_element_sorted_list_extract.png | Bin 0 -> 112041 bytes .../fig_greater_value_sorted_list_extract.png | Bin 0 -> 6895 bytes .../fig_last_element_sorted_list_search.png | Bin 0 -> 31821 bytes .../fig_no_value_sorted_list_extract_1.png | Bin 0 -> 6593 bytes .../fig_no_value_sorted_list_extract_2.png | Bin 0 -> 7073 bytes ...ig_other_element_sorted_list_extract_1.png | Bin 0 -> 118416 bytes ...ig_other_element_sorted_list_extract_2.png | Bin 0 -> 115850 bytes .../fig_other_element_sorted_list_search.png | Bin 0 -> 39190 bytes .../fig_other_position_sorted_list_insert.png | Bin 0 -> 12293 bytes source_codes/sorted_lists/sorted_list_full.c | 110 ++++++++++ .../sorted_lists/sorted_list_partiel.c | 103 +++++++++ 17 files changed, 420 insertions(+), 2 deletions(-) create mode 100644 lessons/contenu_cours_struct_sorted_list.md create mode 100644 lessons/figures/fig_1st_element_sorted_list_extract.png create mode 100644 lessons/figures/fig_1st_element_sorted_list_search.png create mode 100644 lessons/figures/fig_1st_position_sorted_list_insert.png create mode 100644 lessons/figures/fig_empty_sorted_list_insert.png create mode 100644 lessons/figures/fig_free_element_sorted_list_extract.png create mode 100644 lessons/figures/fig_greater_value_sorted_list_extract.png create mode 100644 lessons/figures/fig_last_element_sorted_list_search.png create mode 100644 lessons/figures/fig_no_value_sorted_list_extract_1.png create mode 100644 lessons/figures/fig_no_value_sorted_list_extract_2.png create mode 100644 lessons/figures/fig_other_element_sorted_list_extract_1.png create mode 100644 lessons/figures/fig_other_element_sorted_list_extract_2.png create mode 100644 lessons/figures/fig_other_element_sorted_list_search.png create mode 100644 lessons/figures/fig_other_position_sorted_list_insert.png create mode 100644 source_codes/sorted_lists/sorted_list_full.c create mode 100644 source_codes/sorted_lists/sorted_list_partiel.c diff --git a/lessons/contenu_cours_struct_queue.md b/lessons/contenu_cours_struct_queue.md index 6c456fa..6d60b4b 100644 --- a/lessons/contenu_cours_struct_queue.md +++ b/lessons/contenu_cours_struct_queue.md @@ -94,8 +94,7 @@ Il faut considérer plusieurs cas: #### Extraction en tête de file d'attente -Voici l'entête de la procédure: -`int queue_extraire(queue* fa);` +Voici l'entête de la procédure: `int queue_extraire(queue* fa);` On commence par récupérer, la valeur en tête de file d'attente via l'appel `queue_tete(*fa);` diff --git a/lessons/contenu_cours_struct_sorted_list.md b/lessons/contenu_cours_struct_sorted_list.md new file mode 100644 index 0000000..fbe3f9d --- /dev/null +++ b/lessons/contenu_cours_struct_sorted_list.md @@ -0,0 +1,206 @@ +# Algorithmes et structures de données + +# Structure de liste triée + +***** + +## 1. Définition + +On considère une liste chaînée d'articles. Chaque article comportera un champ pour stocker les valeurs +dans la liste et un champ contenant une variable de type pointeur pour assurer le chaînage. +Schématiquement: + + + +La liste est triée pour autant que l'insertion de chaque nouvelle valeur dans la liste maintienne cette +propriété. +L'accès à la liste se fera uniquement par le pointeur lst qui référence le début de la liste. +Une telle liste chaînée sera déclarée par exemple sous la forme suivante: + +```C + typedef struct _element { // Elément de liste + int n; + struct _element* suivant; + } element; + + typedef element* liste; // Pointeur sur des éléments de liste +``` + +## 2. Insertion dans une liste triée + +Voici l'entête de la procédure : `liste inserer(liste lst,int val);` + +Il faut considérer plusieurs cas. + +### La liste est vide: `lst == NULL` + + + +### L'insertion se fait en 1ère position: `val <= lst->n` + +Par exemple, pour `val = 1` + + + +### Les positions autres que la 1ère position + +Par exemple, pour `val = 13` + + + +```C + (1) tmp = malloc(sizeof(element)); + tmp->n = 13; +``` + +On déplace un pointeur crt jusqu'à l'élément précédent la position d'insertion de sorte que +```C + crt->n < val <= crt->suivant->n +``` + +On utilise une boucle: +```C + (2) while (NULL != crt->suivant && val > crt->suivant->n) { + crt = crt->suivant; + } +``` + +Puis on raccroche l'élément pointé par tmp à la liste +```C + (3) tmp->suivant = crt->suivant; + (4) crt->suivant = tmp; + return lst; +``` + +## 3. Extraction d'un élément dans une liste triée + +Voici l'entête de la procédure : `liste extraire(liste lst,int val);` + +Si la liste est vide, on retourne la liste vide. + +Ensuite, on déplace deux pointeurs prec et crt à travers la liste jusqu'à ce que : `prec->n < val <= crt->n` + +On utilise une boucle: +```C + while (NULL != crt && val > crt->n) { + prec = crt; + crt = crt->suivant; + } +``` + +Il faut à nouveau considérer plusieurs cas. + +### La valeur à retirer est supérieure à la dernière valeur de la liste. + +Ceci équivaut à: `crt == NULL` ou `prec->suivant == NULL` + +On retourne la liste inchangée. + +Par exemple, pour `val = 30` + + + +### La valeur à retirer n'est pas celle dans l'élément pointé par `crt`. + +Ceci équivaut à: `val < crt->n` + +On retourne la liste inchangée. + +Par exemple, pour `val = 9` + + + +ou pour val = 1 + + + +### La valeur à retirer est celle dans l'élément pointé par `crt`. + +Ceci équivaut à: `val == crt->n` + +#### La valeur à retirer est en début de liste. + +Ceci équivaut à: `crt == prec` + +On doit déplacer la tête de liste : lst = crt->suivant; + +Par exemple, pour `val = 3` + + + +#### La valeur à retirer n'est pas en début de liste. + +On doit raccrocher l'élément pointé par prec à celui suivant `crt`: `prec->suivant = crt->suivant;` + +Par exemple, pour `val = 12` + + + +ou pour `val = 21` + + + +Finalement, on libère la mémoire de l'élément pointé par `crt`: `free(crt);` + + + +## 4. Recherche dans une liste triée + +La fonction recherche retourne un pointeur sur l'élément qui contient la valeur recherchée ou un pointeur `NULL` si la valeur est absente de la liste triée. + +Voici l'entête de la procédure : `element* recherche(liste lst,int val);` + +On considère d'abord la fonction utilitaire `position` qui retourne un pointeur sur l'élément avant la +position d'insertion d'une valeur ou un pointeur `NULL` s'il s'agit de la tête de liste. +```C + element* position(liste lst,int val) { + element* pos = lst; + if (est_vide(lst) || val <= lst->n) { + pos = NULL; + } else { + while (NULL != pos->suivant && val > pos->suivant->n) { + pos = pos->suivant; + } + } + return pos; + } +``` + +Par exemple, pour val = 1 ou 3 + + + +et pour val = 29 + + + +et finalement pour val = 10 ou 12 + + + +Ainsi, la fonction de recherche s'écrit simplement : +```C + element* recherche(liste lst,int val) { + element* pos = position(lst,val); + if (est_vide(lst)) { + return NULL; + } + if (NULL == pos && val == lst->n) { + return lst; + } else if (NULL != pos->suivant && val == pos->suivant->n) { + return pos->suivant; + } else { + return NULL; + } + } +``` + +## Exercice + +Ecrire directement la fonction `recherche` sans utiliser la fonction `position`. +Faire les dessins illustrant les différents cas possibles. + + + + + diff --git a/lessons/figures/fig_1st_element_sorted_list_extract.png b/lessons/figures/fig_1st_element_sorted_list_extract.png new file mode 100644 index 0000000000000000000000000000000000000000..02057f27d58980d2f99a9cb3b5235e2e879ae993 GIT binary patch literal 9227 zcmeAS@N?(olHy`uVBq!ia0y~yV7kM=z|h3O#K6Gt>q5r_1_lP^VkgfK4i1jn5B(o7 zFeos1x;TbZ%z1max<okjpZ$mB0jG34q^B`8$IQ~dl6>WGUW8+?rkTd{15GWvoCJ<A z>~ia0{c>GGz?6a%(=NTmrw>-d?0UIL=V97ovD}2fMY)+b7Wt(fUGXA+!fl1^np2E8 za_j4RT5fpHGMnskX<vMOfzjlX#`B*kzO^<!e`fNf8#g={7#J9)T=RViaw7wWqXr`b zLjy}=0Eo+}82XZF(!BG}rS0qXTna7WtgNiGoA3WE?P7Cbvz$-ai-Ud+>l&9x{}WEw 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+typedef element* liste; + +// Crée une liste vide +liste liste_creer() { + return NULL; +} + +// Teste si la liste vide +bool liste_est_vide(liste lst) { + return NULL == lst; +} + +// Retourne un pointeur sur l'élement avant l'emplacement d'insertion; +// ce pointeur est nul si la liste est vide ou si l'insertion est en tête de liste +element* position(liste lst,int val) { + element* pos = lst; + if (liste_est_vide(lst) || val <= lst->n) { + pos = NULL; + } else { + while (NULL != pos->suivant && val > pos->suivant->n) { + pos = pos->suivant; + } + } + return pos; +} + +// Insère un élément dans la liste triée et retourne la liste mise à jour +liste liste_inserer(liste lst,int val) { + element* tmp = malloc(sizeof(element)); + tmp->n = val; + element* crt = position(lst,val); + if (NULL == crt) { // insertion dans une liste vide ou en tête de liste + tmp->suivant = lst; + lst = tmp; + } else { // insertion au milieu ou en fin de liste + tmp->suivant = crt->suivant; + crt->suivant = tmp; + } + return lst; +} + +// Extrait un élément avec la valeur <val> et retourne la liste mise à jour; +// la liste est inchangée si elle est initialement vide +// ou si la valeur est absente +liste liste_extraire(liste lst,int val) { + element *crt = lst, *prec = lst; + // boucle pour placer <val>: prec->n < val <= crt->n + while (NULL != crt && val > crt->n) { + prec = crt; + crt = crt->suivant; + } + // liste non-vide et <val> présente de la liste + if (NULL != crt && val == crt->n) { + if (crt == prec) { // extraction en début de liste + lst = lst->suivant; + } else { // extraction en milieu ou fin de liste + prec->suivant = crt->suivant; + } + free(crt); + } + return lst; +} + +// Retourne un pointeur sur l'élément qui contient <val> ou un pointeur nul +// si la liste est vide ou la valeur absente +element* liste_recherche(liste lst,int val) { + // à compléter + return NULL; +} + +// Imprime le contenu de la liste +void print(liste lst) { + element* crt = lst; + while (NULL != crt) { + printf("%d ",crt->n); + crt = crt->suivant; + } +} + +int main(int argc, char** argv) { + liste lst = liste_creer(); + char str[20]; + do { + printf("Insert: "); + scanf("%s", str); + if (0 == strcmp("quit",str)) break; + lst = liste_inserer(lst,atoi(str)); + print(lst); + printf("\n"); + } while (true); + do { + printf("Extract: "); + scanf("%s", str); + if (0 == strcmp("quit",str)) break; + lst = liste_extraire(lst,atoi(str)); + print(lst); + printf("\n"); + } while (true); + return 0; +} + diff --git a/source_codes/sorted_lists/sorted_list_partiel.c b/source_codes/sorted_lists/sorted_list_partiel.c new file mode 100644 index 0000000..773e80f --- /dev/null +++ b/source_codes/sorted_lists/sorted_list_partiel.c @@ -0,0 +1,103 @@ +#include <stdio.h> +#include <stdlib.h> +#include <assert.h> +#include <stdbool.h> + +typedef struct _element { + int n; + struct _element* suivant; +} element; +typedef element* liste; + +// Crée une liste vide +liste liste_creer() { + return NULL; +} + +// Teste si la liste vide +bool liste_est_vide(liste lst) { + return NULL == lst; +} + +// Retourne un pointeur sur l'élement avant l'emplacement d'insertion; +// ce pointeur est nul si la liste est vide ou si l'insertion est en tête de liste +element* position(liste lst,int val) { + element* pos = lst; + if (liste_est_vide(lst) || val <= lst->n) { + pos = NULL; + } else { + while (NULL != pos->suivant && val > pos->suivant->n) { + pos = pos->suivant; + } + } + return pos; +} + +// Insère un élément dans la liste triée et retourne la liste mise à jour +liste liste_inserer(liste lst,int val) { + element* tmp = malloc(sizeof(element)); + tmp->n = val; + element* pos = position(lst,val); + if (NULL == pos) { // insertion dans une liste vide ou en tête de liste + // à compléter + } else { // insertion au milieu ou en fin de liste + // à compléter + } + return lst; +} + +// Extrait un élément avec la valeur <val> et retourne la liste mise à jour; +// la liste est inchangée si elle est initialement vide +// ou si la valeur est absente +liste liste_extraire(liste lst,int val) { + element* prec = lst; + element* crt = lst; + // boucle pour placer <val>: prec->n < val <= crt->n + // à compléter + + // liste non-vide et <val> présente de la liste + if (NULL != crt && val == crt->n) { + if (crt == prec) { // extraction en début de liste + lst = lst->suivant; + } else { // extraction en milieu ou fin de liste + prec->suivant = crt->suivant; + } + free(crt); + } + return lst; +} + +// Retourne un pointeur sur l'élément qui contient <val> ou un pointeur nul +// si la liste est vide ou la valeur absente +element* liste_recherche(liste lst,int val) { + // à compléter + return NULL; +} + +// Imprime le contenu de la liste +void print(liste lst) { + //à compléter +} + +int main(int argc, char** argv) { + liste lst = liste_creer(); + char str[20]; + do { + printf("Insert: "); + scanf("%s", str); + if (0 == strcmp("quit",str)) break; + lst = liste_inserer(lst,atoi(str)); + print(lst); + printf("\n"); + } while (true); + do { + printf("Extract: "); + scanf("%s", str); + if (0 == strcmp("quit",str)) break; + lst = liste_extraire(lst,atoi(str)); + print(lst); + printf("\n"); + } while (true); + return 0; +} + -- GitLab