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Lille <http://portail.fil.univ-lille1.fr>_ +:date: janvier 2017 +:dernières révisions: février 2018, février 2019 + +Analyse empirique des tris + +""" +from random import shuffle +from typing import Callable +from compare import compare +from ap_decorators import count +from tris import * +from functools import cmp_to_key + +################################################ +# ANALYSE EMPIRIQUE DES TRIS # +################################################ + +# ajout d'un compteur à la fonction compare +compare = count(compare) + +def analyser_tri(tri: Callable[[list[T], Callable[[T, T], int]], NoneType], + nbre_essais: int, + taille: int) -> float: + """ + renvoie: le nombre moyen de comparaisons effectuées par l'algo tri + pour trier des listes de taille t, la moyenne étant calculée + sur n listes aléatoires. + précondition: n > 0, t >= 0, la fonc + """ + res = 0 + for i in range(nbre_essais): + compare.counter = 0 + l = [k for k in range(taille)] + shuffle(l) + tri(l, compare) + res += compare.counter + return res / nbre_essais + +def tri_sort(l:list[int], cmp): + """à_remplacer_par_ce_que_fait_la_fonction + + Précondition : + Exemple(s) : + $$$ + + """ + l.sort(key = cmp_to_key(cmp)) + + +if (__name__ == '__main__'): + from matplotlib import pyplot as plt + + # Calcul de nombres moyens de comparaison pour des listes + # de tailles comprises entre 0 et TAILLE_MAX + NB_ESSAIS = 50 + TAILLE_MAX = 100 + c_select = [0.0] * (TAILLE_MAX + 1) + c_insert = [0.0] * (TAILLE_MAX + 1) + c_sort = [0.0] * (TAILLE_MAX + 1) + + for t in range(TAILLE_MAX + 1): + c_select[t] = analyser_tri(tri_select, 1, t) + # inutile de moyenner pour le tri par sélection + c_insert[t] = analyser_tri(tri_insert, NB_ESSAIS, t) + c_sort[t] = analyser_tri(tri_sort, NB_ESSAIS, t) + + # Sauvegarde des données calculées dans un fichier au format CSV + prem_ligne = 'taille;"tri séléction";"tri insertion"\n' + ligne = '{:3d};{:8.2f};{:8.2f}\n' + with open('analyse_tris.csv', 'wt', encoding='utf8') as sortie: + sortie.write(prem_ligne) + for t in range(TAILLE_MAX + 1): + sortie.write(ligne.format(t, + c_select[t], + c_insert[t])) + + # Représentation graphique + plt.plot(list(range(TAILLE_MAX + 1)), c_select, 'b.', label='Tri sélection') + plt.plot(list(range(TAILLE_MAX + 1)), c_insert, 'r.', label='Tri insertion') + plt.plot(list(range(TAILLE_MAX + 1)), c_sort, 'g.', label='Tri sort') + plt.title('Tris : nbre de comparaisons') + plt.legend() + plt.xlabel('n = taille des listes') + plt.ylabel('c(n) = nbre de comparaisons') + plt.savefig('tris_nbcomp.png') + plt.show() + + diff --git a/Tp07/tris_nbcomp.png b/Tp07/tris_nbcomp.png index a2ce8bdaaad372e005af87d22e90db36c52fb421..d1437223e647c02958e0b2f80200baade2d587cf 100644 GIT binary patch literal 29781 zcmeAS@N?(olHy`uVBq!ia0y~yU}|7sV0^&A#=yW}dhyN^1_lPp64!{5;QX|b^2DN4 z2H(Vzf}H%4oXjMJvecsD%=|oKJqtZ!9fgdNl7eC@ef?ax0=@jAbp7McB7zwh7&r?& zB8wRq_!B{xafSWzOa_MHL!K^<Ar*7p-Yt&^alg&>q1w?(Ct^hto2cmSrdEl?8xyZ* 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