#!/usr/bin/python3
from random import random
from math import floor, sqrt
from statistics import mean, variance
from matplotlib import pyplot as plt
from pylab import *
import numpy as np

def simulate_NFBP(N):
    """
    Tries to simulate T_i, V_i and H_n for N packages 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.
    """
    P=R*N
    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)]
    Sum_T=[0 for _ in range(10)]
    Sum_V=[]
    Sum_H=[]
    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
        T=sim['T']
        for i in range(5):
            T.append(0)
        Sum_T=[x+y for x,y in zip(Sum_T,T)]
        Sum_H=Sum_H+sim['H']
        for k in range(sim['i']):
            #we use round to approximate variations of continuous variable V
            Sum_V.append(round(sim['V'][k],2))
    Sum_T=[x/R for x in Sum_T]
    print(Sum_T)
    I = ISum/R
    IVariance = sqrt(IVarianceSum/(R-1) - I**2)
    print("Mean number of boxes : {} (variance {})".format(I, IVariance),'\n')
    print(" {} * {} iterations of T".format(R,N),'\n')
   
#Plotting
    #matplotlib.stairs(Sum_T,bins=[0,1,2,3,4])
    #ax.hist(Sum_T, bins=8, edgecolor='k', density=True, label='Valeurs empiriques')
    #ax.set(xlim=(0, 8), xticks=np.arange(1, 8),
    #ylim=(0, 500), yticks=np.linspace(0, 56, 9))
    #plot:
    #fig = plt.subplots()
    fig = plt.figure()
    #T plot
    x =  np.arange(7)
    print(x)
    ax = fig.add_subplot(221)
    ax.bar(x,Sum_T, width=1, edgecolor="white", linewidth=0.7)
  # ax.hist(Sum_T, bins=6, linewidth=0.5, edgecolor="white", label='Empirical values')
    ax.set(xlim=(0, 10), xticks=np.arange(0, 10),ylim=(0,10), yticks=np.linspace(0, 10, 1))
    ax.set_title('T histogram for {} packages (Number of packages in each box)'.format(P))
    ax.legend()
    #V plot
    bx = fig.add_subplot(222) 
    bx.hist(Sum_V, bins=10, linewidth=0.5, edgecolor="white", label='Empirical values')
    bx.set(xlim=(0, 1), xticks=np.arange(0, 1),ylim=(0, 1000), yticks=np.linspace(0, 1000, 9))
    bx.set_title('V histogram for {} packages (first package size of each box)'.format(P))
    bx.legend()
    #H plot
    cx = fig.add_subplot(223) 
    cx.hist(Sum_H, bins=10, linewidth=0.5, edgecolor="white", label='Empirical values')
    cx.set(xlim=(0, 10), xticks=np.arange(0, 10),ylim=(0, 2000), yticks=np.linspace(0, 2000, 9))
    cx.set_title('H histogram for {} packages'.format(P))
    cx.legend()
    plt.show() 
    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 packages 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))
    P=N*R
    I = []
    H = [[] for _ in range(N)]  # List of empty lists
    Tmean=[]
    T=[]
    Sum_T=[]
    #First iteration to use zip after
    sim=simulate_NFDBP(N)
    Sum_T=sim["T"]
    for i in range(R):
        sim = simulate_NFDBP(N)
        I.append(sim["i"])
        for n in range(N):
            H[n].append(sim["H"][n])
        T=sim["T"]
        for k in range(10):
            Sum_T.append(0)
        for k in range(sim["i"]):
                Tmean.append(T[k])
        Sum_T=[x+y for x,y in zip(Sum_T,sim["T"])]
    print(Sum_T)
    print(sum(Sum_T))
    print(P)
    Sum_T=[x*100/(sum(Sum_T)) for x in Sum_T]
    print(Sum_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])))
    print("Mean T_{} : {} (variance {})".format(k, mean(Tmean), variance(Tmean)))

#Plotting
    fig, ax = plt.subplots()
    #T plot
    x = 0.5 + np.arange(8)
    x=x.tolist()
    print(type(x))
    print(x)
    ax.bar(x, Sum_T, width=1, edgecolor="white", linewidth=0.5)
    ax.set(xlim=(0, 10), xticks=np.arange(0, 10),ylim=(0, 25), yticks=np.linspace(0, 25, 9))
    ax.set_title('Repartition of packets in each box percents for {} packages '.format(P))
    ax.legend()
    plt.show()


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 ** 3, 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_NFBP_iter(10**3, 10)
#stats_NFDBP(10 ** 3, 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')
#show()