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 </office:styles>
 <office:automatic-styles>
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   <text:p text:style-name="P4"/>
   <text:p text:style-name="P9">Rendu TP3 ALGO</text:p>
   <text:p text:style-name="P5"/>
   <text:p text:style-name="P5"/>
   <text:p text:style-name="P6">Lien vers le code source: <text:span text:style-name="T3">https://gricad-gitlab.univ-grenoble-alpes.fr/amessega/tp3-ALGO</text:span></text:p>
   <text:p text:style-name="P5"/>
   <text:p text:style-name="P7">Idées de fonctions principaux:</text:p>
   <text:p text:style-name="P5"/>
   <text:p text:style-name="P10"><text:span text:style-name="T17">dijkstra </text:span>:on commence par initialiser les distances des sommets à une valeur infinie. Ensuite, on initialise la distance du sommet de départ à zéro et on le met dans une file de priorité. On boucle tant que la file n&apos;est pas vide, en extrayant chaque fois le sommet avec la plus petite distance actuelle. Pour chaque arc sortant de ce sommet, si le sommet de destination n&apos;a pas encore été visité ou si une distance plus courte a été trouvée, on met à jour sa distance et on l&apos;ajoute à la file. Enfin, on affiche les distances les plus courtes trouvées pour chaque sommet.</text:p>
   <text:p text:style-name="P11"><text:s/></text:p>
   <text:p text:style-name="P11"/>
   <text:p text:style-name="P11"><text:span text:style-name="T17">Elementaire </text:span>:on cherche d&apos;abord le premier sommet du chemin dans le graphe. Si ce sommet n&apos;est pas trouvé, on affiche un message d&apos;erreur et on retourne 0. Ensuite, on parcourt les arcs du chemin pour vérifier s&apos;il y a des répétitions de sommets. Si on trouve un sommet répété, on affiche un message d&apos;erreur et on retourne 0. Sinon, on retourne 1, indiquant que le chemin est élémentaire.</text:p>
   <text:p text:style-name="P12"/>
   <text:p text:style-name="P10"><text:span text:style-name="T17">Simple :</text:span>on alloue dynamiquement un tableau pour suivre les poids des arcs déjà parcourus. Ensuite, on parcourt les arcs du chemin donné. Si on trouve un poids d&apos;arc déjà présent dans le tableau, on libère la mémoire allouée et on retourne 0. Sinon, on ajoute le poids de l&apos;arc au tableau et on continue. Une fois la vérification terminée, on libère la mémoire allouée pour le tableau et on retourne 1, indiquant que le chemin est simple.</text:p>
   <text:p text:style-name="P10"/>
   <text:p text:style-name="P10"/>
   <text:p text:style-name="P10"><text:span text:style-name="T18">E</text:span><text:span text:style-name="T17">ulerien </text:span>:on commence par déterminer le nombre total d&apos;arcs dans le graphe. Ensuite, on compte le nombre d&apos;arcs dans le chemin donné. Si le nombre d&apos;arcs dans le chemin est égal au nombre d&apos;arcs dans le graphe, on retourne vrai, sinon on retourne faux.</text:p>
   <text:p text:style-name="P10"/>
   <text:p text:style-name="P11"><text:span text:style-name="T17">Graphe_eulerien </text:span>:on parcourt chaque sommet du graphe. Pour chaque sommet, on calcule son degré sortant. Si on trouve un sommet avec un degré sortant impair, on retourne faux, indiquant que le graphe n&apos;est pas eulerien. Sinon, si tous les sommets ont un degré sortant pair, on retourne vrai, signifiant que le graphe est eulerien.</text:p>
   <text:p text:style-name="P11"/>
   <text:p text:style-name="P13">Graphe_hamiltonien :</text:p>
   <text:p text:style-name="P11">on commence par vérifier si le graphe est vide. Ensuite, on parcourt chaque sommet du graphe. Pour chaque sommet, on initialise les couleurs des sommets. Si on trouve un chemin hamiltonien à partir du sommet actuel, on retourne vrai. Sinon, si aucun chemin hamiltonien n&apos;est trouvé, on retourne faux.</text:p>
   <text:p text:style-name="P11"/>
   <text:p text:style-name="P11"><text:soft-page-break/><text:span text:style-name="T17">Distance :</text:span>, on cherche d&apos;abord les sommets x et y dans le graphe. Si l&apos;un des sommets n&apos;est pas trouvé, on affiche un message d&apos;erreur et on retourne -1. Ensuite, on initialise les couleurs des sommets et les distances à partir du sommet de départ x en utilisant l&apos;algorithme de Dijkstra. On parcourt le graphe en mettant à jour les distances jusqu&apos;à ce qu&apos;on atteigne le sommet y ou que tous les chemins possibles aient été explorés. Si le sommet y est atteint, on retourne la distance jusqu&apos;à ce sommet. Sinon, si aucun chemin n&apos;est trouvé, on affiche un message d&apos;erreur et on retourne -1.</text:p>
   <text:p text:style-name="P11"/>
   <text:p text:style-name="P11"><text:span text:style-name="T17">Excentricite :</text:span>on cherche d&apos;abord le sommet n dans le graphe. Si le sommet n&apos;est pas trouvé, on affiche un message d&apos;erreur et on retourne -1. Ensuite, on initialise les couleurs des sommets et les distances à partir du sommet n en utilisant l&apos;algorithme de Dijkstra. On parcourt le graphe en mettant à jour les distances jusqu&apos;à ce que la file de priorité soit vide. Pendant ce processus, on met à jour l&apos;excentricité maximale si une distance plus grande est trouvée. Enfin, on retourne l&apos;excentricité maximale trouvée.</text:p>
   <text:p text:style-name="P11"/>
   <text:p text:style-name="P3"><text:span text:style-name="T15">Diametre </text:span><text:span text:style-name="T13">:on parcourt chaque sommet du graphe. Pour chaque sommet, on calcule son excentricité en utilisant la fonction « </text:span><text:span text:style-name="Source_20_Text"><text:span text:style-name="T13">excentricite »</text:span></text:span><text:span text:style-name="T13">. On met à jour le diamètre maximal si une excentricité plus grande est trouvée. Enfin, on retourne le diamètre maximal trouvé parmi tous les sommets du graphe.</text:span></text:p>
   <text:p text:style-name="P10"/>
   <text:p text:style-name="P10"><text:span text:style-name="T17">Afficher_profondeur </text:span>:On initialise d&apos;abord les couleurs des sommets, puis on cherche le sommet de départ, et enfin on lance récursivement le parcours en profondeur, affichant les sommets visités dans l&apos;ordre.</text:p>
   <text:p text:style-name="P10"/>
   <text:p text:style-name="P2"><text:span text:style-name="T15">Afficher_graphe_largeur:</text:span><text:span text:style-name="T13">On a laissé cette fonction à la fin pour l’implémenter, avec le parcours profondeur, sous prétexte qu’elle était facile, mais on a bien galéré à la coder. On a essayé avec une file à priorité</text:span><text:span text:style-name="T14"> au début,</text:span><text:span text:style-name="T13"> comme on a utilisé une file à priorité dans la plupart des fonctions, et aussi avec une file normale, mais on n&apos;a pas réussi à la coder comme il le faut. Il existe un petit bug de pointeur qu’on n&apos;a pas réussi à trouver.</text:span></text:p>
  </office:text>
 </office:body>
</office:document>