#!/usr/bin/python3
from random import random
from math import floor, sqrt,factorial
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 items 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
    }


# unused
def stats_NFBP(R, N):
    """
    Runs R runs of NFBP (for N items) and studies distribution, variance, mean...
    """
    print("Running {} NFBP simulations with {} items".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 bins : {} (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 items) and studies distribution, variance, mean...
    Calculates stats during runtime instead of after to avoid excessive memory usage.
    """
    P=R*N  # Total number of items
    print("## Running {} NFBP simulations with {} items".format(R, N))
    # number of bins
    ISum = 0  
    IVarianceSum = 0
    # index of the bin containing the n-th item
    HSum = [0 for _ in range(N)] 
    HSumVariance = [0 for _ in range(N)]
    # number of items in the i-th bin
    Sum_T=[0 for _ in range(N)]
    # size of the first item in the i-th bin
    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']
        # ensure that T, V have the same length as Sum_T, Sum_V
        for i in range(N - sim['i']):
            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)]

    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 bins : {} (variance {})".format(I, IVariance),'\n')
    # TODO clarify line below
    print(" {} * {} iterations of T".format(R,N),'\n')
    
    for n in range(min(N, 10)):
        Hn = HSum[n]/R # moyenne
        HVariance = sqrt(HSumVariance[n]/(R-1) - Hn**2) # Variance
        print("Index of bin containing the {}th item (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('Bins (1-{})'.format(N))
    ax.set_title('T histogram for {} items (Number of items in each bin)'.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('Bins (1-{})'.format(N))
    bx.set_title('V histogram for {} items (first item size of each bin)'.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('Bin ranking of n-item')
    cx.set_xlabel('n-item (1-{})'.format(N))
    cx.set_title('H histogram for {} items'.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 items of random size.
    Next Fit Dual Bin Packing : bins should overflow
    """
    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 items) and studies distribution, variance, mean...
    """
    print("## Running {} NFDBP simulations with {} items".format(R, N))
    P=N*R  # Total number of items
    I = [] 
    H = [[] for _ in range(N)]  # List of empty lists
    T=[]
    Tk=[[] for _ in range(N)]
    Ti=[]
    T_maths=[]
    #First iteration to use zip after
    sim=simulate_NFDBP(N)
    Sum_T=[0 for _ in range(N)]
    for i in range(R):
        sim = simulate_NFDBP(N)
        I.append(sim["i"])
        for k in range(N):
            T.append(0)
            T=sim["T"]
        for n in range(N):
            H[n].append(sim["H"][n])
            Tk[n].append(sim["T"][n])
        Ti.append(sim["T"])
        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("Mean number of bins : {} (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)))
    #Loi math
    for u in range(N):
        u=u+2
        T_maths.append(1/(factorial(u-1))-1/factorial(u))
    E=0
    sigma2=0
    # print(T_maths)
    for p in range(len(T_maths)):
        E=E+(p+1)*T_maths[p]
        sigma2=((T_maths[p]-E)**2)/(len(T_maths)-1)
    print("Mathematical values : Empiric mean T_{} : {} Variance {})".format(t_i, E, sqrt(sigma2)))
    T_maths=[x*100 for x in T_maths]
    #Plotting
    fig = plt.figure()
    #T plot
    x =  np.arange(N)
    print(x)
    print(Sum_T)
    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=(0,20), yticks=np.linspace(0, 20, 2))
    ax.set_ylabel('Items(n) in %')
    ax.set_xlabel('Bins (1-{})'.format(N))
    ax.set_title('Items percentage for each bin and {} items (Number of items in each bin)'.format(P))
    ax.legend(loc='upper left',title='Legend')

    #Mathematical P(Ti=k) plot. It shows the Ti(t_i) law with the probability of each number of items.
    print(len(Tk[t_i]))
    bx = fig.add_subplot(222)
    bx.hist(Tk[t_i],bins=10, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red')
    bx.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,len(Tk[t_i])), yticks=np.linspace(0, 1, 1))
    bx.set_ylabel('P(T{}=i)'.format(t_i))
    bx.set_xlabel('Bins i=(1-{}) in %'.format(N))
    bx.set_title('T{} histogram for {} items (Number of items in each bin)'.format(t_i,P))
    bx.legend(loc='upper left',title='Legend')

    #Loi mathematique
    print(T_maths)
    cx = fig.add_subplot(224)
    cx.bar(x,T_maths, width=1,label='Theoretical values', edgecolor="blue", linewidth=0.7,color='red')
    cx.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,100), yticks=np.linspace(0, 100, 10))
    cx.set_ylabel('P(T{}=i)'.format(t_i))
    cx.set_xlabel('Bins i=(1-{})'.format(N))
    cx.set_title('Theoretical T{} values in %'.format(t_i))
    cx.legend(loc='upper left',title='Legend')
    plt.show()

# unused
def basic_demo():
    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]))

stats_NFBP_iter(10**3, 10)
print('\n\n')
stats_NFDBP(10 ** 3, 10,1)