From 3c48f975b2fc3e8e020cf98b5009922177b2cd25 Mon Sep 17 00:00:00 2001 From: Klafyvel Date: Tue, 9 Jan 2018 17:53:28 +0100 Subject: [PATCH] =?UTF-8?q?S=C3=A9ance=20du=209/01?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- compte_rendu/compte_rendu.aux | 6 + compte_rendu/compte_rendu.lof | 1 + compte_rendu/compte_rendu.pdf | Bin 0 -> 44951 bytes compte_rendu/compte_rendu.synctex.gz | Bin 0 -> 4014 bytes compte_rendu/compte_rendu.tex | 25 ++ compte_rendu/compte_rendu.toc | 2 + compte_rendu/images/3_2_carburant.png | Bin 0 -> 25624 bytes compte_rendu/images/3_2_temps.png | Bin 0 -> 25349 bytes compte_rendu/images/3_4_chemin.png | Bin 0 -> 27078 bytes compte_rendu/images/3_5_liste.png | Bin 0 -> 27076 bytes compte_rendu/images/3_5_tas.png | Bin 0 -> 26925 bytes compte_rendu/images/3_6.png | Bin 0 -> 41373 bytes compte_rendu/images/dijkstra_lin.png | Bin 0 -> 27648 bytes compte_rendu/images/dijkstra_log.png | Bin 0 -> 24083 bytes .../{ => images}/gabriel_vs_delaunay.png | Bin compte_rendu/{ => images}/reseau_naif.png | Bin compte_rendu/{ => images}/reseau_naif_log.png | Bin .../{ => images}/reseau_vs_reseauRapide.png | Bin .../reseau_vs_reseauRapide_log.png | Bin graphe.py | 156 ++++++++++- graphique.py | 4 +- tas.py | 248 +++++++++--------- test.py | 126 ++++++++- 23 files changed, 434 insertions(+), 134 deletions(-) create mode 100644 compte_rendu/compte_rendu.aux create mode 100644 compte_rendu/compte_rendu.lof create mode 100644 compte_rendu/compte_rendu.pdf create mode 100644 compte_rendu/compte_rendu.synctex.gz create mode 100644 compte_rendu/compte_rendu.toc create mode 100644 compte_rendu/images/3_2_carburant.png create mode 100644 compte_rendu/images/3_2_temps.png create mode 100644 compte_rendu/images/3_4_chemin.png create mode 100644 compte_rendu/images/3_5_liste.png create mode 100644 compte_rendu/images/3_5_tas.png create mode 100644 compte_rendu/images/3_6.png create mode 100644 compte_rendu/images/dijkstra_lin.png create mode 100644 compte_rendu/images/dijkstra_log.png rename compte_rendu/{ => images}/gabriel_vs_delaunay.png (100%) rename compte_rendu/{ => images}/reseau_naif.png (100%) rename compte_rendu/{ => images}/reseau_naif_log.png (100%) rename compte_rendu/{ => images}/reseau_vs_reseauRapide.png (100%) rename compte_rendu/{ => images}/reseau_vs_reseauRapide_log.png (100%) diff --git a/compte_rendu/compte_rendu.aux b/compte_rendu/compte_rendu.aux new file mode 100644 index 0000000..06c79ac --- /dev/null +++ b/compte_rendu/compte_rendu.aux @@ -0,0 +1,6 @@ +\relax +\select@language{french} +\@writefile{toc}{\select@language{french}} +\@writefile{lof}{\select@language{french}} +\@writefile{lot}{\select@language{french}} +\@writefile{toc}{\contentsline {part}{I\hspace {1em}Objectifs de ce TL}{3}} diff --git a/compte_rendu/compte_rendu.lof b/compte_rendu/compte_rendu.lof new file mode 100644 index 0000000..6ddbdcd --- /dev/null +++ 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break - elt.index = self.__deplace(parent, elt.index) - self.__deplace(elt, elt.index) - - def actualise(self, elt): - assert isinstance(elt, Tas.Element) - elt.priorite = self.fonctionPriorite(elt.valeur) - self.__promeut(elt) - - def ajoute(self, valeur): - elt = Tas.Element(valeur, self.fonctionPriorite(valeur), len(self.L)) - self.L.append(elt) - self.__promeut(elt) - return elt - - def empty(self): - return len(self.L) == 0 - - def pop(self): - n = len(self.L) - if(n == 0): - return None - - tete = self.L[0] - elt = self.L[n - 1] - elt.index = 0 - - while True: - filsGauche = self.__fils_gauche(elt) - filsDroit = self.__fils_droit(elt) - plusPrioritaire = elt - if(filsGauche != None and filsGauche.priorite > plusPrioritaire.priorite): - plusPrioritaire = filsGauche - if(filsDroit != None and filsDroit.priorite > plusPrioritaire.priorite): - plusPrioritaire = filsDroit - elt.index = self.__deplace(plusPrioritaire, elt.index) - if(plusPrioritaire is elt): - break - self.L.pop() - return tete.valeur + def __init__(self, fonctionPriorite): + self.L = [] + self.fonctionPriorite = fonctionPriorite + + def __str__(self): + s = "[" + for elt in self.L: + s += " " + str(elt) + s += "]" + return s + + def __parent(self, elt): + if(elt.index == 0): + return None + else: + return self.L[(elt.index - 1) // 2] + + def __fils_gauche(self, elt): + i = 2 * elt.index + 1 + if(i < len(self.L)): + return self.L[i] + else: + return None + + def __fils_droit(self, elt): + i = 2 * elt.index + 2 + if(i < len(self.L)): + return self.L[i] + else: + return None + + def __deplace(self, elt, index): + assert isinstance(elt, Tas.Element) + ancien = elt.index + self.L[index] = elt + elt.index = index + return ancien + + def __promeut(self, elt): + while(True): + parent = self.__parent(elt) + if(parent == None): + break + if(parent.priorite >= elt.priorite): + break + elt.index = self.__deplace(parent, elt.index) + self.__deplace(elt, elt.index) + + def actualise(self, elt): + assert isinstance(elt, Tas.Element) + elt.priorite = self.fonctionPriorite(elt.valeur) + self.__promeut(elt) + + def ajoute(self, valeur): + elt = Tas.Element(valeur, self.fonctionPriorite(valeur), len(self.L)) + self.L.append(elt) + self.__promeut(elt) + return elt + + def empty(self): + return len(self.L) == 0 + + def pop(self): + n = len(self.L) + if(n == 0): + return None + + tete = self.L[0] + elt = self.L[n - 1] + elt.index = 0 + + while True: + filsGauche = self.__fils_gauche(elt) + filsDroit = self.__fils_droit(elt) + plusPrioritaire = elt + if(filsGauche != None and filsGauche.priorite > plusPrioritaire.priorite): + plusPrioritaire = filsGauche + if(filsDroit != None and filsDroit.priorite > plusPrioritaire.priorite): + plusPrioritaire = filsDroit + elt.index = self.__deplace(plusPrioritaire, elt.index) + if(plusPrioritaire is elt): + break + self.L.pop() + return tete.valeur ######################################### # Exemple d'utilisatio de la classe Tas # # Tri de tâches par ordre chronologique # ######################################### + class Tache: - '''Tache devant être effectuée avant une date limite''' - def __init__(self, jour, nom): - self.jour = jour - self.nom = nom - # Cet attribut servira à accueillir la clé du tas - self.cle = None - - def __str__(self): - return self.nom + " ({})".format(self.jour) - + '''Tache devant être effectuée avant une date limite''' + + def __init__(self, jour, nom): + self.jour = jour + self.nom = nom + # Cet attribut servira à accueillir la clé du tas + self.cle = None + + def __str__(self): + return self.nom + " ({})".format(self.jour) + + if __name__ == "__main__": - - # Le niveau de priorité d'un événement x est -x.jour : on trie donc les événements par ordre chronologique - def calculePriorite(tache): - return -tache.jour - - # On crée un tas dont les éléments sont des événements triés par ordre chronologique - T = Tas(calculePriorite) - - # Ajoute des événements au tas - evts = [ Tache(5, "T1"), Tache(10, "T2"), Tache(5, "T3"), Tache(3, "T4")] - for evt in evts: - evt.cle = T.ajoute(evt) - - # Supposons que la tache 2 devienne soudain assez urgente - evts[1].jour = 4 - T.actualise(evts[1].cle) - - # Retirons dans l'ordre chronologie les éléments du tas - while(not T.empty()): - print(T.pop()) - - + + # Le niveau de priorité d'un événement x est -x.jour : on trie donc les événements par ordre chronologique + def calculePriorite(tache): + return -tache.jour + + # On crée un tas dont les éléments sont des événements triés par ordre chronologique + T = Tas(calculePriorite) + + # Ajoute des événements au tas + evts = [Tache(5, "T1"), Tache(10, "T2"), Tache(5, "T3"), Tache(3, "T4")] + for evt in evts: + evt.cle = T.ajoute(evt) + + # Supposons que la tache 2 devienne soudain assez urgente + evts[1].jour = 4 + T.actualise(evts[1].cle) + + # Retirons dans l'ordre chronologie les éléments du tas + while(not T.empty()): + print(T.pop()) diff --git a/test.py b/test.py index 7a3e89b..78b43e5 100644 --- a/test.py +++ b/test.py @@ -1,3 +1,12 @@ +"""Test des fonctions du TL. + +Pour tester la question x_y : `python3 test.py x_y`. + +Donc pour la question 3_4 : `python3 test.py 3_4`. +""" + +import sys + import graphe import graphique import copy @@ -5,7 +14,6 @@ import numpy as np import matplotlib.pyplot as pl import time - def creerGrapheFigure1(): """ Crée le graphe de la figure 1 """ g = graphe.Graphe("Graphe de la figure 1") @@ -159,7 +167,115 @@ def testQuestion2_9(): pl.show() +def testQuestion3_1(): + """Trace le plus court chemin avec dijkstra.""" + g = graphe.pointsAleatoires(30, 30) + g.renomme("Dijkstra") + graphe.reseauRapide(g) + g.dijkstra(g.sommets[0]) + g.traceArbreDesChemins() + graphique.affiche(g, (0, 0), 10.) + + +def testQuestion3_2(): + """Trace le plus court chemin avec dijkstra.""" + g = graphe.pointsAleatoires(30, 30) + g.renomme("Dijkstra") + + graphe.reseauRapide(g) + g.fixeTempsCommeCout() + g.dijkstra(g.sommets[0]) + g.traceArbreDesChemins() + g.renomme("Temps") + graphique.affiche(g, (0, 0), 10., blocage=False) + g.fixeCarburantCommeCout() + g.dijkstra(g.sommets[0]) + g.traceArbreDesChemins() + g.renomme("Carburant") + graphique.affiche(g, (0, 0), 10.) + + +def testQuestion3_3(): + """Mesure le temps d'exécution de Dijkstra.""" + prepare = lambda p : graphe.reseauRapide(graphe.pointsAleatoires(p, 100)) + valeurs_n = list(map(lambda x: int(x), np.logspace(1, 4, 10))) + temps = chronometre(graphe.Graphe.dijkstra, prepare, valeurs_n) + pl.close('all') + pl.title("Temps d'exécution en fonction de la taille du graphe.") + pl.plot(valeurs_n, temps, label='reseau') + pl.legend(loc='best') + pl.xlabel("n") + pl.ylabel("temps") + pl.show() + pl.title("Temps d'exécution en fonction de la taille du graphe.") + pl.loglog(valeurs_n, temps, label='reseau') + pl.legend(loc='best') + pl.xlabel("n") + pl.ylabel("temps") + pl.show() + + +def testQuestion3_4(): + """Trace le plus court chemin avec dijkstra.""" + g = graphe.pointsAleatoires(30, 30) + g.renomme("Plus court chemin") + + graphe.reseauRapide(g) + g.fixeTempsCommeCout() + g.dijkstra(g.sommets[0]) + c = g.cheminOptimal(g.sommets[-1]) + g.colorieChemin(c, (0.,1.,0.)) + g.renomme("Temps") + graphique.affiche(g, (0, 0), 10.) + + +def testQuestion3_5(): + """Trace le plus court chemin avec dijkstra.""" + g = graphe.pointsAleatoires(30, 30) + g.fixeTempsCommeCout() + + graphe.reseauRapide(g) + g.dijkstra(g.sommets[0]) + g.traceArbreDesChemins() + g.renomme("Liste") + graphique.affiche(g, (0, 0), 10., blocage=False) + g.dijkstraAvecTas(g.sommets[0]) + g.traceArbreDesChemins() + g.renomme("Tas") + graphique.affiche(g, (0, 0), 10.) + + +def testQuestion3_6(): + """Compare Dijkstra avec et sans tas.""" + prepare = lambda p : graphe.reseauRapide(graphe.pointsAleatoires(p, 10)) + valeurs_n = list(map(lambda x: int(x), np.logspace(1, 3, 10))) + temps1 = chronometre(graphe.Graphe.dijkstra, prepare, valeurs_n) + temps2 = chronometre(graphe.Graphe.dijkstraAvecTas, prepare, valeurs_n) + pl.close('all') + pl.title("Comparaison du temps d'exécution de `dijkstra` et `dijkstraAvecTas`.") + pl.plot(valeurs_n, temps1, label='Dijkstra') + pl.plot(valeurs_n, temps2, label='Dijkstra avec tas') + pl.legend(loc='best') + pl.xlabel("n") + pl.ylabel("temps") + pl.show() + pl.title("Comparaison du temps d'exécution de `reseau` et `reseauRapide`.") + pl.loglog(valeurs_n, temps1, label='Dijkstra') + pl.loglog(valeurs_n, temps2, label='Dijkstra avec tas') + pl.legend(loc='best') + pl.xlabel("n") + pl.ylabel("temps") + pl.show() + + +if __name__ == '__main__': + n = sys.argv[1] + if n in ('--help', '-h'): + print(__doc__) + else: + print('Question ', n) + locals()['testQuestion'+n]() # testQuestion1_2() # testQuestion1_3() # testQuestion1_4() @@ -169,4 +285,10 @@ def testQuestion2_9(): # testQuestion2_6() # testQuestion2_7() # testQuestion2_8() -testQuestion2_9() +# testQuestion2_9() +# testQuestion3_1() +# testQuestion3_2() +# testQuestion3_3() +# testQuestion3_4() +# testQuestion3_5() +# testQuestion3_6()