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| 1 | # -*- coding: utf-8 -*- | |
| 2 | ||
| 3 | from support import * | |
| 4 | ||
| 5 | # EXERCICE 1 | |
| 6 | ||
| 7 | G = {
| |
| 8 | "A" : { "F" : 35, "C" : 5 },
| |
| 9 | "F" : { "G" : 13 },
| |
| 10 | "G" : { },
| |
| 11 | "E" : { "G" : 14 },
| |
| 12 | "B" : { "E" : 15, "C" : 9 },
| |
| 13 | "D" : { "A" : 3, "B" : 12 },
| |
| 14 | "C" : { "F" : 8, "E" : 10 }
| |
| 15 | } | |
| 16 | ||
| 17 | # [v for v in G["A"]] represente l'ensemble des sommets relies à A. | |
| 18 | print(str([v for v in G["A"]])) | |
| 19 | ||
| 20 | # EXERCICE 2 | |
| 21 | ||
| 22 | infini = float("inf")
| |
| 23 | ||
| 24 | def BFS(G, r, distance = False): | |
| 25 | global infini | |
| 26 | Couleur, Pere, Dist = dict(), dict(), dict() | |
| 27 | F = creer_file() | |
| 28 | for u in G: | |
| 29 | Couleur[u] = "Blanc" | |
| 30 | Pere[u] = None | |
| 31 | Dist[u] = infini | |
| 32 | enfiler(F, r) | |
| 33 | Couleur[r] = "Gris" | |
| 34 | Dist[r] = 0 | |
| 35 | while not est_vide(F): | |
| 36 | u = tete(F) | |
| 37 | for v in G[u]: | |
| 38 | if Couleur[v] == "Blanc": | |
| 39 | Couleur[v] = "Gris" | |
| 40 | Dist[v] = Dist[u] + 1 * (1 - distance) + G[u][v] * distance | |
| 41 | Pere[v] = u | |
| 42 | enfiler(F, v) | |
| 43 | defiler(F) | |
| 44 | Couleur[u] = "Noir" | |
| 45 | return Dist | |
| 46 | ||
| 47 | # Sans utiliser la vraie distance (distance en arcs) | |
| 48 | print(str(BFS(G, "A"))) | |
| 49 | print(str(BFS(G, "D"))) | |
| 50 | # L'algorithme ne donnera plus la vraie distance la plus courte : | |
| 51 | print(str(BFS(G, "D", True))) | |
| 52 | ||
| 53 | # EXERCICE 3 | |
| 54 | ||
| 55 | def DFS(G, r): | |
| 56 | P = creer_pile() | |
| 57 | marque = {}
| |
| 58 | parcours = [] | |
| 59 | for u in G: | |
| 60 | marque[u] = False | |
| 61 | empiler(P, r) | |
| 62 | while not est_vide(P): | |
| 63 | u = sommet(P) | |
| 64 | desempiler(P) | |
| 65 | if not marque[u]: | |
| 66 | marque[u] = True | |
| 67 | parcours.append(u) | |
| 68 | for v in G[u]: | |
| 69 | if not marque[v]: | |
| 70 | empiler(P, v) | |
| 71 | return parcours | |
| 72 | ||
| 73 | # Affichage du parcours en profondeur | |
| 74 | print(str(DFS(G, "A"))) | |
| 75 | print(str(DFS(G, "D"))) | |
| 76 | ||
| 77 | # EXERCICE 4 | |
| 78 | ||
| 79 | def creerMatrice(G): | |
| 80 | import numpy as np | |
| 81 | liste = [] | |
| 82 | for i in range(len(G.keys())): | |
| 83 | temp = [] | |
| 84 | for j in range(len(G.keys())): | |
| 85 | temp.append(infini) | |
| 86 | liste.append(temp) | |
| 87 | sortedKeys = list(G.keys()) | |
| 88 | sortedKeys.sort() | |
| 89 | for i, e in enumerate(sortedKeys): | |
| 90 | liste[i][i] = 0 | |
| 91 | for j, v in enumerate(sortedKeys): | |
| 92 | if G[e].get(v, -1) != -1: | |
| 93 | liste[i][j] = G[e][v] | |
| 94 | return np.array(liste) | |
| 95 | ||
| 96 | import numpy as np | |
| 97 | ||
| 98 | def init_distances_min(n): | |
| 99 | global infini | |
| 100 | liste = [[0 if i == j else infini for j in range(n)] for i in range(n)] | |
| 101 | return np.array(liste) | |
| 102 | ||
| 103 | def iterations(distances, distances_min): | |
| 104 | retourne = [] | |
| 105 | global infini | |
| 106 | for i in range(len(distances)): | |
| 107 | temp = [] | |
| 108 | for j in range(len(distances)): | |
| 109 | temp.append(infini) | |
| 110 | retourne.append(temp) | |
| 111 | ||
| 112 | for i in range(len(distances)): | |
| 113 | for j in range(len(distances)): | |
| 114 | retourne[i][j] = min(distances_min[i][j], min([distances[i][t] + distances_min[t][j] for t in range(len(G))])) | |
| 115 | ||
| 116 | return np.array(retourne) | |
| 117 | ||
| 118 | def utiliserIterations(G): | |
| 119 | distances = creerMatrice(G) | |
| 120 | t = init_distances_min(len(G)) | |
| 121 | for i in range(len(G)): | |
| 122 | t = iterations(distances, t) | |
| 123 | return t | |
| 124 | ||
| 125 | def itineraire_min(G, A, B): | |
| 126 | carte = utiliserIterations(G) |
