From 37755824eab52784a3af80c434dcf5b9a6e16af5 Mon Sep 17 00:00:00 2001 From: Klafyvel Date: Tue, 23 Jan 2018 17:57:53 +0100 Subject: [PATCH] =?UTF-8?q?S=C3=A9ance=20du=2023=20janvier?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- compte_rendu/compte_rendu.aux | 13 ++-- compte_rendu/compte_rendu.lof | 2 + compte_rendu/compte_rendu.pdf | Bin 97627 -> 143500 bytes compte_rendu/compte_rendu.synctex.gz | Bin 13868 -> 16950 bytes compte_rendu/compte_rendu.tex | 30 ++++++++- compte_rendu/compte_rendu.toc | 9 +-- compte_rendu/images/2_5.png | Bin 0 -> 36053 bytes compte_rendu/images/2_6_lin.png | Bin 0 -> 23978 bytes compte_rendu/images/4_6.png | Bin 0 -> 38639 bytes compte_rendu/images/4_7_cout.png | Bin 0 -> 18955 bytes compte_rendu/images/4_7_graphe.png | Bin 0 -> 40604 bytes compte_rendu/images/4_8_simple.png | Bin 0 -> 42352 bytes compte_rendu/images/4_9.png | Bin 0 -> 31269 bytes graphe.py | 91 ++++++++++++++++++++++++--- stack.py | 22 +++++++ test.py | 82 +++++++++++++++++++++++- 16 files changed, 232 insertions(+), 17 deletions(-) create mode 100644 compte_rendu/images/2_5.png create mode 100644 compte_rendu/images/2_6_lin.png create mode 100644 compte_rendu/images/4_6.png create mode 100644 compte_rendu/images/4_7_cout.png create mode 100644 compte_rendu/images/4_7_graphe.png create mode 100644 compte_rendu/images/4_8_simple.png create mode 100644 compte_rendu/images/4_9.png create mode 100644 stack.py diff --git a/compte_rendu/compte_rendu.aux b/compte_rendu/compte_rendu.aux index f42c506..24abad9 100644 --- a/compte_rendu/compte_rendu.aux +++ b/compte_rendu/compte_rendu.aux @@ -12,7 +12,12 @@ \newlabel{eq:condArete}{{1}{3}} \@writefile{toc}{\contentsline {paragraph}{preuve :}{3}} \@writefile{toc}{\contentsline {section}{\numberline {2}Mise en pratique : graphe de Gabriel et de voisinage relatif}{3}} -\@writefile{toc}{\contentsline {section}{\numberline {3}Triangulation de Delaunay}{4}} -\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Pratique}{4}} -\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Aspect théorique}{4}} -\@writefile{toc}{\contentsline {part}{III\hspace {1em}Algorithme de Dijkstra pour la recherche du plus court chemin}{4}} +\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Création de graphe de Gabriel et de voisinage relatif}{3}} +\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Graphe de gabriel\relax }}{4}} +\newlabel{fig:2_4_gabriel}{{2}{4}} +\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Graphe de voisinage realtif\relax }}{5}} +\newlabel{fig:2_4_gvr}{{3}{5}} +\@writefile{toc}{\contentsline {section}{\numberline {3}Triangulation de Delaunay}{6}} +\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Pratique}{6}} +\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Aspect théorique}{6}} +\@writefile{toc}{\contentsline {part}{III\hspace {1em}Algorithme 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Graphe.Cout.TEMPS + self.cout = Graphe.Cout.TEMPS self.arrivee = None def renomme(self, nom): @@ -55,6 +56,8 @@ class Graphe: """ a = Arete(s1, s2, longueur, v_moyenne, self) self.aretes.append(a) + s1.aretes.add(a) + s2.aretes.add(a) return a def n(self): @@ -303,18 +306,19 @@ class Graphe: minCout = sys.float_info.max matrice = self.matriceCout(tournee) cout = 0 - visite = [False]*len(tournee) + visite = [False] * len(tournee) visite[0] = True itineraire = [0] + def backtrack(): nonlocal meilleurItineraire, minCout, matrice, cout, visite, itineraire if cout < minCout: - if len(itineraire)==len(tournee): + if len(itineraire) == len(tournee): if cout + matrice[0, itineraire[-1]] < minCout: minCout = cout + matrice[0, itineraire[-1]] meilleurItineraire = [tournee[x] for x in itineraire] else: - for i,sommet_visite in enumerate(visite): + for i, sommet_visite in enumerate(visite): if not sommet_visite: visite[i] = True indicePrec = itineraire[-1] @@ -328,12 +332,82 @@ class Graphe: return minCout, meilleurItineraire def traceItineraire(self, itineraire): - for i,x in enumerate(itineraire): + for i, x in enumerate(itineraire): x.nom = "s" + str(i) - suivant = itineraire[(i+1)%len(itineraire)] - c,_ = self.astar(x, suivant) + suivant = itineraire[(i + 1) % len(itineraire)] + c, _ = self.astar(x, suivant) self.colorieChemin(c, (0.8, 0.1, 0.8)) + def Prim(self): + for s in self.sommets: + s.selection = False + for a in self.aretes: + a.selection = False + aretes = tas.Tas(lambda x: -x.cout) + for a in self.sommets[0].aretes: + aretes.ajoute(a) + self.sommets[0].selection = True + arbre = [] + ptot = 0 + while not aretes.empty(): + a = aretes.pop() + s1, s2 = a.s1, a.s2 + if not s1.selection or not s2.selection: + a.selection = True + ptot += a.cout + if not s1.selection: + s1.selection = True + for a_1 in s1.aretes: + aretes.ajoute(a_1) + if not s2.selection: + s2.selection = True + for a_2 in s2.aretes: + aretes.ajoute(a_2) + return ptot + + def colorieSelection(self, couleur=(0.1, 0.6, 0.2)): + """Colorie les sommets et arêtes avec le drapeau `selection` à True.""" + for s in self.sommets: + if s.selection: + s.couleur = couleur + for s in self.aretes: + if s.selection: + s.couleur = couleur + + def grapheDeCout(self, tournee): + g = Graphe("Graphe de cout de " + self.nom) + for s in tournee: + s_a = g.ajouteSommet(s.x(), s.y()) + s_a.image = s + s.image = s_a + + for i, s in enumerate(g.sommets): + self.dijkstraAvecTas(s.image) + for s_v in g.sommets[i:]: + d = sum((a.cout for a in self.cheminOptimal(s_v.image))) + g.connecte(s, s_v, d, 1) + return g + + def tourneeApproximative(self, tournee): + g_cout = self.grapheDeCout(tournee) + g_cout.Prim() + pile = stack.Stack() + pile.add(tournee[0].image) + tournee[0].image.selection = False + chemin = [tournee[0]] + while not pile.empty(): + actuel = pile.pop() + fils = list(filter(lambda x: x.selection, actuel.aretes)) + if fils: + a = fils.pop() + a.selection = False + nouveau = a.voisin(actuel) + nouveau.selection = False + chemin.append(nouveau.image) + pile.add(actuel) + pile.add(nouveau) + return chemin + class Sommet: """Implémente un sommet de graphe.""" @@ -352,6 +426,8 @@ class Sommet: self.cumul = None self.precedent = None self.graphe = graphe + self.selection = False + self.image = None @property def minCumulRestant(self): @@ -409,6 +485,7 @@ class Arete: self.v_moyenne = v_moyenne self.couleur = couleur self.graph = graph + self.selection = False def voisin(self, s): """Retourne le sommet voisin de s dans l'arête. diff --git a/stack.py b/stack.py new file mode 100644 index 0000000..0d76c59 --- /dev/null +++ b/stack.py @@ -0,0 +1,22 @@ +class Stack: + class StackElem: + def __init__(self, elt, prec): + self.elt = elt + self.prec = prec + + def __init__(self, elts=[]): + self.first = None + for e in elts: + self.add(e) + + def add(self, e): + se = self.StackElem(e, self.first) + self.first = se + + def pop(self): + e = self.first.elt + self.first = self.first.prec + return e + + def empty(self): + return self.first is None diff --git a/test.py b/test.py index aae843c..ce81b39 100644 --- a/test.py +++ b/test.py @@ -6,6 +6,7 @@ Donc pour la question 3_4 : `python3 test.py 3_4`. """ import sys +import random import graphe import graphique @@ -101,7 +102,7 @@ def chronometre(fonctionTest, fonctionPreparation, parametres): def testQuestion2_6(): """Mesure la performance de graphe.reseau""" prepare = lambda p : graphe.pointsAleatoires(p, 10) - valeurs_n = np.arange(1, 200) + valeurs_n = list(map(int, np.logspace(1, 2.7, 100))) temps = chronometre(graphe.reseau, prepare, valeurs_n) pl.close('all') pl.title("Mesure du temps d'exécution de `reseau`.") @@ -347,6 +348,85 @@ def testQuestion4_2(): graphique.affiche(g, (0, 0), 10.) +def testQuestion4_3(): + """Mesure le temps de calcul.""" + g = graphe.reseauRapide(graphe.pointsAleatoires(1000, 1000)) + prepare = lambda p : random.sample(g.sommets, p) + valeurs_n = list(map(int, np.linspace(1, 15, 10))) + temps = chronometre(g.voyageurDeCommerceNaif, prepare, valeurs_n) + pl.close('all') + pl.title("Temps d'exécution pour le voyageur de commerce.") + pl.plot(valeurs_n, temps) + pl.xlabel("n (nombre de points de la tournée)") + pl.ylabel("temps") + pl.show() + pl.title("Temps d'exécution pour le voyageur de commerce.") + pl.loglog(valeurs_n, temps) + pl.xlabel("n (nombre de points de la tournée)") + pl.ylabel("temps") + pl.show() + + +def testQuestion4_6(): + g = graphe.pointsAleatoires(30, 30) + + graphe.reseauRapide(g) + g.fixeTempsCommeCout() + g.renomme("Algorithme de Prim (cout=temps)") + p = g.Prim() + print("Poids de prim:", p) + g.colorieSelection() + graphique.affiche(g, (0, 0), 10.) + + +def testQuestion4_7(): + g = graphe.pointsAleatoires(30, 30) + + graphe.reseauRapide(g) + g.fixeTempsCommeCout() + g.renomme("Graphe de test (cout=temps)") + tournee = [g.sommets[i] for i in (0, 1, 2, 7)] + g1 = g.grapheDeCout(tournee) + graphique.affiche(g, (0, 0), 10., blocage=False) + graphique.affiche(g1, (0, 0), 10.) + + +def testQuestion4_8(): + g = graphe.pointsAleatoires(30, 30) + + graphe.reseauRapide(g) + g.fixeTempsCommeCout() + g.renomme("Graphe de test (cout=temps)") + g1 = copy.deepcopy(g) + print("Tournée 0, 1, 2, 7") + tournee = [g.sommets[i] for i in (0, 1, 2, 7)] + iti = g.tourneeApproximative(tournee) + g.traceItineraire(iti) + tournee = [g1.sommets[i] for i in (0, 1, 2, 7)] + cout,iti = g1.voyageurDeCommerceNaif(tournee) + g1.traceItineraire(iti) + graphique.affiche(g, (0, 0), 10., blocage=False) + graphique.affiche(g1, (0, 0), 10.) + + +def testQuestion4_9(): + """Mesure le temps de calcul.""" + g = graphe.reseauRapide(graphe.pointsAleatoires(1000, 1000)) + prepare = lambda p : random.sample(g.sommets, p) + valeurs_n = list(map(int, np.logspace(1, 2, 30))) + temps = chronometre(g.tourneeApproximative, prepare, valeurs_n) + pl.close('all') + pl.title("Temps d'exécution pour le voyageur de commerce approximatif.") + pl.plot(valeurs_n, temps) + pl.xlabel("n (nombre de points de la tournée)") + pl.ylabel("temps") + pl.show() + pl.title("Temps d'exécution pour le voyageur de commerce approximatif.") + pl.loglog(valeurs_n, temps) + pl.xlabel("n (nombre de points de la tournée)") + pl.ylabel("temps") + pl.show() + if __name__ == '__main__': n = sys.argv[1] if n in ('--help', '-h'):