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Verified Commit 394e0378 authored by orestis.malaspin's avatar orestis.malaspin
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added search

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...@@ -416,10 +416,23 @@ Une liste chaînée triée est: ...@@ -416,10 +416,23 @@ Une liste chaînée triée est:
# Les listes triées # Les listes triées
## Quelle structure de données? ## Quel but?
* Permet de retrouver rapidement un élément.
* Utile pour la recherche de plus court chemin dans des graphes.
* Ordonnancement de processus par degré de priorité.
## Comment?
* Les implémentations les plus efficaces se basent sur les tableaux.
* Possibles aussi avec des listes chaînées.
# Les listes triées
## Quelle structure de données dans notre cas?
Une liste chaînée bien sûr!
Une liste chaînée bien sûr (oui c'est pour vous entraîner)!
```C ```C
typedef struct _element { // chaque élément typedef struct _element { // chaque élément
...@@ -614,19 +627,81 @@ element* sorted_list_search(sorted_list list, int val); ...@@ -614,19 +627,81 @@ element* sorted_list_search(sorted_list list, int val);
. . . . . .
```C ```C
element* recherche(liste lst,int val) { element* sorted_list_search(sorted_list list, int val) {
element* pos = position(lst,val); // search for element smaller than val
if (est_vide(lst)) { element* pos = sorted_list_position(list, val);
return NULL; if (NULL == pos && val == list->data) {
return list; // first element contains val
} else if (NULL != pos->next && val == pos->next->data) {
return pos->next; // non-first element contains val
} else {
return NULL; // well... val's not here
}
} }
if (NULL == pos && val == lst->n) { ```
return lst;
} else if (NULL != pos->suivant && val == pos->suivant->n) { # La recherche
return pos->suivant;
## La fonction `sorted_list_position`
```C
element* sorted_list_position(sorted_list list, int val);
```
![Trois exemples de retour de la fonction `sorted_list_position()`.](figs/sorted_list_position.svg)
# La recherche
## Exercice: implémenter
```C
element* sorted_list_position(sorted_list list, int val);
```
. . .
```C
element* sorted_list_position(sorted_list list, int val) {
element* pos = list;
if (sorted_list_is_empty(list) || val <= list->data) {
pos = NULL;
} else { } else {
return NULL; while (NULL != pos->next && val > pos->next>data) {
pos = pos->next;
}
} }
return pos;
} }
``` ```
# Exercice: recherche sans position # Complexité de la liste chaînée triée
## L'insertion?
. . .
$$
\mathcal{O}(N).
$$
## L'extraction?
. . .
$$
\mathcal{O}(N).
$$
## La recherche?
. . .
$$
\mathcal{O}(N).
$$
# Liste doublement chaînée
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style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10.5833px;line-height:1.25;font-family:monospace;-inkscape-font-specification:monospace;letter-spacing:0px;word-spacing:0px;stroke-width:0.264583"
x="-96.908218"
y="125.1735"
id="text3066"><tspan
sodipodi:role="line"
id="tspan3064"
style="stroke-width:0.264583"
x="-96.908218"
y="125.1735">pour val = 29</tspan></text>
<text
xml:space="preserve"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10.5833px;line-height:1.25;font-family:monospace;-inkscape-font-specification:monospace;letter-spacing:0px;word-spacing:0px;stroke-width:0.264583"
x="-96.908218"
y="182.89594"
id="text5886"><tspan
sodipodi:role="line"
id="tspan5884"
style="stroke-width:0.264583"
x="-96.908218"
y="182.89594">pour val = 10 ou val = 12</tspan></text>
<text
xml:space="preserve"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10.5833px;line-height:1.25;font-family:monospace;-inkscape-font-specification:monospace;letter-spacing:0px;word-spacing:0px;stroke-width:0.264583"
x="-96.908218"
y="71.00132"
id="text8888"><tspan
sodipodi:role="line"
id="tspan8886"
style="stroke-width:0.264583"
x="-96.908218"
y="71.00132">pour val = 1</tspan></text>
</g>
</svg>
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