SNT Seconde — Chapitre 6 : Localisation, cartographie et mobilité

c = 300000      # vitesse de la lumiere en km/s

altitude = 20200
duree = altitude / c
print(f"Duree du trajet : {duree:.4f} s")

def distance(duree):
    return c * duree

print(f"Satellite a {distance(0.0712):.0f} km")
erreur = distance(0.000001) * 1000
print(f"Erreur d'une microseconde : {erreur:.0f} m")

def en_degres(valeur, nb_chiffres_degres):
    degres = int(valeur[:nb_chiffres_degres])
    minutes = float(valeur[nb_chiffres_degres:])
    return degres + minutes / 60

def decoder(trame):
    champs = trame.split(",")
    heure = champs[1]
    print(f"Heure : {heure[0:2]} h {heure[2:4]} min {heure[4:6]} s (UTC)")
    lat = en_degres(champs[2], 2)
    if champs[3] == "S":
        lat = -lat
    lon = en_degres(champs[4], 3)
    if champs[5] == "W":
        lon = -lon
    print(f"Latitude : {lat:.4f} - Longitude : {lon:.4f}")
    print(f"Altitude : {champs[9]} m - {int(champs[7])} satellites")

decoder("$GPGGA,143512.00,4851.5040,N,00217.6700,E,1,08,0.9,35.0,M,46.9,M,,*5C")
decoder("$GPGGA,170834.00,4322.0710,S,07027.4560,W,1,07,1.2,612.0,M,30.1,M,,*6D")

import math

def distance_km(lat1, lon1, lat2, lon2):
    p1 = math.radians(lat1)
    p2 = math.radians(lat2)
    dp = math.radians(lat2 - lat1)
    dl = math.radians(lon2 - lon1)
    h = math.sin(dp / 2) ** 2 + math.cos(p1) * math.cos(p2) * math.sin(dl / 2) ** 2
    return 2 * 6371 * math.asin(math.sqrt(h))

paris = (48.8566, 2.3522)
lyon = (45.7640, 4.8357)
marseille = (43.2965, 5.3698)
print(f"Paris - Lyon : {distance_km(paris[0], paris[1], lyon[0], lyon[1]):.0f} km")
d = distance_km(paris[0], paris[1], marseille[0], marseille[1])
print(f"Paris - Marseille : {d:.0f} km")
print(f"La route est plus longue de {(775 - d) / d * 100:.0f} %")

routes = {
    "A": {"B": 7, "C": 9},
    "B": {"A": 7, "C": 3, "D": 7},
    "C": {"A": 9, "B": 3, "D": 6, "E": 11},
    "D": {"B": 7, "C": 6, "E": 2, "F": 9},
    "E": {"C": 11, "D": 2, "F": 4},
    "F": {"D": 9, "E": 4},
}

def longueur(chemin):
    total = 0
    for i in range(len(chemin) - 1):
        if chemin[i + 1] not in routes[chemin[i]]:
            return None
        total = total + routes[chemin[i]][chemin[i + 1]]
    return total

itineraires = [["A", "B", "D", "F"], ["A", "C", "E", "F"], ["A", "B", "D", "E", "F"], ["A", "C", "D", "E", "F"]]
meilleur = itineraires[0]
for chemin in itineraires:
    print(" -> ".join(chemin), ":", longueur(chemin), "min")
    if longueur(chemin) < longueur(meilleur):
        meilleur = chemin
print("Le plus court :", " -> ".join(meilleur))
print(longueur(["A", "D"]))

routes = {
    "A": {"B": 7, "C": 9},
    "B": {"A": 7, "C": 3, "D": 7},
    "C": {"A": 9, "B": 3, "D": 6, "E": 11},
    "D": {"B": 7, "C": 6, "E": 2, "F": 9},
    "E": {"C": 11, "D": 2, "F": 4},
    "F": {"D": 9, "E": 4},
}

def dijkstra(depart):
    infini = 1000000
    dist = {}
    for s in routes:
        dist[s] = infini
    dist[depart] = 0
    fixes = []
    while len(fixes) < len(routes):
        u = None
        for s in routes:
            if s not in fixes and (u is None or dist[s] < dist[u]):
                u = s
        fixes.append(u)
        for v in routes[u]:
            duree = routes[u][v]
            if dist[u] + duree < dist[v]:
                dist[v] = dist[u] + duree
    return dist

print("Depuis A :", dijkstra("A"))
print("Depuis F :", dijkstra("F"))