#!/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
import matplotlib.pyplot as pt

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(N)]
    Sum_V=[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
        T=sim['T']
        V=sim['V']
        for i in range(N):
            T.append(0)
            V.append(0)
        Sum_T=[x+y for x,y in zip(Sum_T,T)]
        Sum_V=[x+y for x,y in zip(Sum_V,V)]
            #we use round to approximate variations of continuous variable V
       # Sum_V=  round(sim['V'],2))
    Sum_T=[x/R for x in Sum_T]
    Sum_V=[round(x/R,2) for x in Sum_V]
    print(Sum_V)
    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')
    
    for n in range(N):
        Hn = HSum[n]/R # moyenne
        HVariance = sqrt(HSumVariance[n]/(R-1) - Hn**2) # Variance
        print("Index of box containing the {}th package (H_{}) : {} (variance {})".format(n, n, Hn, HVariance))
    HSum=[x/R for x in HSum]
    print(HSum)
#Plotting
    fig = plt.figure()
    #T plot
    x =  np.arange(N)
    print(x)
    ax = fig.add_subplot(221)
    ax.bar(x,Sum_T, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red')
    ax.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,3), yticks=np.linspace(0, 3, 5))
    ax.set_ylabel('Items')
    ax.set_xlabel('Boxes (1-{})'.format(N))
    ax.set_title('T histogram for {} packages (Number of packages in each box)'.format(P))
    ax.legend(loc='upper left',title='Legend')
    #V plot
    bx = fig.add_subplot(222) 
    bx.bar(x,Sum_V, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='orange')
    bx.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0, 1), yticks=np.linspace(0, 1, 10))
    bx.set_ylabel('First item size')
    bx.set_xlabel('Boxes (1-{})'.format(N))
    bx.set_title('V histogram for {} packages (first package size of each box)'.format(P))
    bx.legend(loc='upper left',title='Legend')
    #H plot
    #We will simulate this part for a asymptotic study
    cx = fig.add_subplot(223)
    cx.bar(x,HSum, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='green')
    cx.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0, 10), yticks=np.linspace(0, N, 5))
    cx.set_ylabel('Box ranking of n-item')
    cx.set_xlabel('n-item (1-{})'.format(N))
    cx.set_title('H histogram for {} packages'.format(P))
    xb=linspace(0,N,10)
    yb=Hn*xb/10
    wb=HVariance*xb/10
    cx.plot(xb,yb,label='Theoretical E(Hn)',color='brown')
    cx.plot(xb,wb,label='Theoretical V(Hn)',color='purple')
    cx.legend(loc='upper left',title='Legend')
    plt.show() 

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,t_i):
    """
    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
    T=[]
    Tk=[[] for _ in range(N)]
    Ti=[]
    #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])
            Tk[n].append(sim["T"][n])
        T=sim["T"]
        Ti.append(sim["T"])
        for k in range(N):
            Sum_T.append(0)
            T.append(0)
        Sum_T=[x+y for x,y in zip(Sum_T,T)]
    Sum_T=[x/R for x in Sum_T] #Experimental [Ti=k]
    Sum_T=[x*100/(sum(Sum_T)) for x in Sum_T] #Pourcentage de la repartition des items 
    print(Tk)
    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(Sum_T), variance(Sum_T)))

#Plotting
    fig = plt.figure()
    #T plot
    x =  np.arange(N)
    print(x)
    ax = fig.add_subplot(121)
    ax.bar(x,Sum_T, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red')
    ax.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,3), yticks=np.linspace(0, 3, 5))
    ax.set_ylabel('Items')
    ax.set_xlabel('Boxes (1-{})'.format(N))
    ax.set_title('T histogram for {} packages (Number of packages in each box)'.format(P))
    ax.legend(loc='upper left',title='Legend')
    plt.show()

    #Mathematical P(Ti=k) plot
    x =  np.arange(N)
    print(x)
    ax = fig.add_subplot(122)
    ax.hist(x,Sum_T, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red')
    ax.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,3), yticks=np.linspace(0, 3, 5))
    ax.set_ylabel('Items')
    ax.set_xlabel('Boxes (1-{})'.format(N))
    ax.set_title('T histogram for {} packages (Number of packages in each box)'.format(P))
    ax.legend(loc='upper left',title='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()