diff --git a/slides/cours_11.md b/slides/cours_11.md index 4e83e85e0cf230e13509bebcbb5e67c3b6c46925..0a34ccfad09156f973344b6b8edcd915c5c1c8eb 100644 --- a/slides/cours_11.md +++ b/slides/cours_11.md @@ -416,10 +416,23 @@ Une liste chaînée triée est: # 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 typedef struct _element { // chaque élément @@ -614,19 +627,81 @@ element* sorted_list_search(sorted_list list, int val); . . . ```C -element* recherche(liste lst,int val) { - element* pos = position(lst,val); - if (est_vide(lst)) { - return NULL; +element* sorted_list_search(sorted_list list, int val) { + // search for element smaller than val + element* pos = sorted_list_position(list, val); + 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) { - return pos->suivant; +} +``` + +# La recherche + +## La fonction `sorted_list_position` + +```C +element* sorted_list_position(sorted_list list, int val); +``` + + + +# 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 { - 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 + + + diff --git a/slides/figs/sorted_list_position.svg b/slides/figs/sorted_list_position.svg new file mode 100644 index 0000000000000000000000000000000000000000..0c4f328ebe12997793545291a0e4d9a0ca5fd5f3 --- /dev/null +++ b/slides/figs/sorted_list_position.svg @@ -0,0 +1,1202 @@ +<?xml version="1.0" encoding="UTF-8" standalone="no"?> +<!-- Created with Inkscape (http://www.inkscape.org/) --> + +<svg + width="400.57916mm" + height="207.96249mm" + viewBox="0 0 400.57916 207.96249" + version="1.1" + id="svg5" + inkscape:version="1.1.1 (3bf5ae0, 2021-09-20)" + 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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>