From 38564913cd5177a80e2c488bcf01436f606f1640 Mon Sep 17 00:00:00 2001 From: dartoisl Date: Tue, 14 Mar 2023 16:28:15 +0100 Subject: [PATCH] TP4 --- TP/TP4.md | 73 ++++++++++++++++++++++++++++++++++++++++++++++++ TP/dijsktra.png | Bin 0 -> 68691 bytes TP/prim.png | Bin 0 -> 87240 bytes 3 files changed, 73 insertions(+) create mode 100644 TP/TP4.md create mode 100644 TP/dijsktra.png create mode 100644 TP/prim.png diff --git a/TP/TP4.md b/TP/TP4.md new file mode 100644 index 0000000..4d94fc9 --- /dev/null +++ b/TP/TP4.md @@ -0,0 +1,73 @@ +TP Graphes 4 : Plus Court Chemin et Arbre Recouvrant Minimal +============ + +Le TP est prévu pour être fait en utilisant le codage des graphes à l'aide de matrices d'adjacence. +Pour plus de clarté, vous pouvez utiliser un nouveau fichier, en copiant les structures et fonctions nécessaires depuis les TPs précédants. + + +- - - - - +Exercice 0 : Graphes valués +---------- + +Nous avons enrichi nos graphes avec une valuation des arêtes. + +**Question :** + +Comment intégrer cela à notre structure de données ? + + +Quel fonction(s) faut-il modifier pour prendre en compte cet enrichissement ? + +**Question :** + +Créez un nouveau fichier graphesvalues.c contenant la structure et les primitives nécessaires à la manipulation des graphes valués. + + +- - - - - +Exercice 1 : Algorithme de Dijkstra +---------- + + + +L'algorithme de Dijkstra renvoie deux données : la fonction d donnant la distance minimale entre la source et un sommet, et la fonction père donnant la direction à prendre pour atteindre cette distance minimale. + +**Question :** + +Une fonction des sommets vers un entier (ou un autre sommet) sera représentée par un tableau où la case i contient la valeur de la fonction pour i. + +Le C ne permettant de renvoyer qu'une structure de données, comment permettre de renvoyer les deux fonctions ? + +**Question :** + +Implémentez l'algorithme de Dijsktra, que je redonne ci-dessous : + +[Algorithme de Dijkstra](dijkstra.png) + + +**Question :** + +Testez votre algorithme en reprenant le graphes des frontières avec des valuation de votre choix. +Vérifier à la main que l'algorithme effectue les bons calculs. + + + +- - - - - +Exercice 2 : Algorithme de Prim +---------- + +Pour simplifier l'implémentation, on se contentera d'afficher sur la sortie standard les arêtes sélectionnées. On renverra tout de même la valuation totale de l'arbre couvrant. + +[Algorithme de Prim](prim.png) + + +**Question (optionnelle) :** + +Comme pour Dijkstra, l'ensemble des sommets atteint sera représenté par un tableau binaire. +Ecrivez une fonction `void selecArete(graphe g,int* atteint,int* x,int* y);` +qui trouve et dans le graphe g l'arête de poids minimale entre un sommet atteint et un sommet non atteint. Le résultat est stocké dans les arguments pointés x et y selon la nomenclature de l'algorithme. + +**Question :** +Implémentez l'algorithme de Prim en vous aidant de la fonction de la question précédente, ou directement. + +**Question :** +Testez et vérifiez votre implémentation sur un exemple, au hasard le graphe des frontières. \ No newline at end of file diff --git a/TP/dijsktra.png b/TP/dijsktra.png new file mode 100644 index 0000000000000000000000000000000000000000..5bfae8d98364234c106cb88d96f772a83616a792 GIT binary patch literal 68691 zcmbTd1yq&ayDhu{=>{oD0YO2!yF*G)xcSv`~UE6d2 z=bZ0+_l$GLWef%z*!x}UUGKBjGoLx<6RxTvhmG+B0|J3yzmk`J1A!pI!1oCn3iu0d z)&o2Efo?Ca;{<`=biuz7;+b*CArKnKD`^RJ_tf2aH}$uZNT`Q)k_7S)iSx(pB5ln( z3prMLZhE%R2`kER9KVkx6B?*iwv;Y4nmff_OAES0L~}^UU!rXggXmkuo{v;?aEdwuW z4!%F6R)s3CQu-h3tI5jBsrw<{!f~>Bhl(nhRzs1hcrU6`0ufQFVu3OZ=#%r0`dane}iubvs%~3bu15s-#ymbqTrdiT|sv=p>s+Ir273F zo}%S|w2WdT=e|aJZhoH0eT0TP#UTZ+CehKJR*vfQcwT9v3|OCc_P@Bt@?Si@yqbi4 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