Projet_Boites/Probas.py

from random import random
from math import floor, sqrt
from statistics import mean, variance
# from matplotlib import pyplot

def simulate_NFBP(N):
    """
    Tries to simulate T_i, V_i and H_n for N boxes of random size.
    """
    i = 0  # Nombre de boites
    R = [0]  # Remplissage de la i-eme boite
    T = [0]  # Nombre de paquets de la i-eme boite
    V = [0]  # Taille du premier paquet de la i-eme boite
    H = []  # Rang de la boite contenant le n-ieme paquet
    for n in range(N):
        size = random()
        if R[i] + size >= 1:
            # Il y n'y a plus de la place dans la boite pour le paquet.
            # On passe à la boite suivante (qu'on initialise)
            i += 1
            R.append(0)
            T.append(0)
            V.append(0)
        R[i] += size
        T[i] += 1
        if V[i] == 0:
            # C'est le premier paquet de la boite
            V[i] = size
        H.append(i)

    return {
        "i": i,
        "R": R,
        "T": T,
        "V": V,
        "H": H
    }


def stats_NFBP(R, N):
    """
    Runs R runs of NFBP (for N packages) and studies distribution, variance, mean...
    """
    print("Running {} NFBP simulations with {} packages".format(R, N))
    I = []
    H = [[] for _ in range(N)]  # List of empty lists

    for i in range(R):
        sim = simulate_NFBP(N)
        I.append(sim["i"])
        for n in range(N):
            H[n].append(sim["H"][n])

    print("Mean number of boxes : {} (variance {})".format(mean(I), variance(I)))

    for n in range(N):
        print("Mean H_{} : {} (variance {})".format(n, mean(H[n]), variance(H[n])))

def stats_NFBP_iter(R, N):
    """
    Runs R runs of NFBP (for N packages) and studies distribution, variance, mean...
    Calculates stats during runtime instead of after to avoid excessive memory usage.
    """
    print("Running {} NFBP simulations with {} packages".format(R, N))
    ISum = 0
    IVarianceSum = 0
    HSum = [0 for _ in range(N)]
    HSumVariance = [0 for _ in range(N)]

    for i in range(R):
        sim = simulate_NFBP(N)
        ISum += sim["i"]
        IVarianceSum += sim["i"]**2
        for n in range(N):
            HSum[n] += sim["H"][n]
            HSumVariance[n] += sim["H"][n]**2

    I = ISum/R
    IVariance = sqrt(IVarianceSum/(R-1) - I**2)

    print("Mean number of boxes : {} (variance {})".format(I, IVariance))
    for n in range(n):
        Hn = HSum[n]/R
        HVariance = sqrt(HSumVariance[n]/(R-1) - Hn**2)
        print("Index of box containing the {}th package (H_{}) : {} (variance {})".format(n, n, Hn, HVariance))

def simulate_NFDBP(N):
    """
    Tries to simulate T_i, V_i and H_n for N boxes of random size.
    """
    i = 0  # Nombre de boites
    R = [0]  # Remplissage de la i-eme boite
    T = [0]  # Nombre de paquets de la i-eme boite
    V = [0]  # Taille du premier paquet de la i-eme boite
    H = []  # Rang de la boite contenant le n-ieme paquet
    for n in range(N):
        size = random()
        R[i] += size
        T[i] += 1
        if R[i] + size >= 1:
            # Il y n'y a plus de la place dans la boite pour le paquet.
            # On passe à la boite suivante (qu'on initialise)
            i += 1
            R.append(0)
            T.append(0)
            V.append(0)

        if V[i] == 0:
            # C'est le premier paquet de la boite
            V[i] = size
        H.append(i)

    return {
        "i": i,
        "R": R,
        "T": T,
        "V": V,
        "H": H
    }


def stats_NFDBP(R, N):
    """
    Runs R runs of NFDBP (for N packages) and studies distribution, variance, mean...
    """
    print("Running {} NFDBP simulations with {} packages".format(R, N))
    I = []
    H = [[] for _ in range(N)]  # List of empty lists
    Tmean=[]
    for i in range(R):
        sim = simulate_NFDBP(N)
        I.append(sim["i"])
        for n in range(N):
            H[n].append(sim["H"][n])

        for k in range(sim["i"]):
            # for o in range(sim["i"]):
                Tmean+=sim["T"]
    print("Mean number of boxes : {} (variance {})".format(mean(I), variance(I)))

    for n in range(N):
        print("Mean H_{} : {} (variance {})".format(n, mean(H[n]), variance(H[n])))
    for k in range(int(mean(I))+1):
        print(Tmean[7])
       # print("Mean T_{} : {} (variance {})".format(k, mean(Tmean[k]), variance(Tmean[k])))

N = 10 ** 1
sim = simulate_NFBP(N)

print("Simulation NFBP pour {} packaets. Contenu des boites :".format(N))
for j in range(sim["i"] + 1):
    remplissage = floor(sim["R"][j] * 100)
    print("Boite {} : Rempli à {} % avec {} paquets. Taille du premier paquet : {}".format(j, remplissage, sim["T"][j],
                                                                                           sim["V"][j]))

print()
stats_NFBP(10 ** 4, 10)

N = 10 ** 1
sim = simulate_NFDBP(N)
print("Simulation NFDBP pour {} packaets. Contenu des boites :".format(N))
for j in range(sim["i"] + 1):
    remplissage = floor(sim["R"][j] * 100)
    print("Boite {} : Rempli à {} % avec {} paquets. Taille du premier paquet : {}".format(j, remplissage,
                                                                                               sim["T"][j],
                                                                                               sim["V"][j]))

print()
stats_NFDBP(10 ** 4, 10)
stats_NFBP_iter(10**6, 10)

#
# pyplot.plot([1, 2, 4, 4, 2, 1], color = 'red', linestyle = 'dashed', linewidth = 2,
#   markerfacecolor = 'blue', markersize = 5)
# pyplot.ylim(0, 5)
# pyplot.title('Un exemple')