#!/usr/bin/env python3
import random
import numpy as np
import matplotlib.pyplot as plt


class Question:
    def __init__(self,i=1, l=0, n=''):
        self.name=n
        self.level=l
        self.number=i
    def __enter__(self):
        print('\n' + (self.level*2)*' ' + f"-> {self.number}. : {self.name} -- Début")
        return self
    def __exit__(self, exc_type, exc_value, exc_traceback):
        print((self.level*2)*' ' + f"<- {self.number}. : {self.name} -- Fin\n") 
with Question(1):
    def tirer(n):
        item = 0
        for _ in range(n):
            if random.random()<.5:
                item +=1
        return item

    def proportion(n , N, k):
        s = 0
        for i in range(N):
            if tirer(n) == k:
                s += 1
        return s/N
    print('proportion(10, 100, 1) :', proportion(10, 100, 5))
    n = 10
    N = 100
    plt.figure(0)
    x = np.asarray(range(n+1))
    y = np.asarray([proportion(n, N, k) for k in x])
    plt.plot(x, y)
    
    
    def binom(k, n):
        return np.math.factorial(n)/(np.math.factorial(k)*np.math.factorial(n-k))
    plt.figure(1)
    x = np.asarray(range(n+1))
    y = np.asarray([binom(k, n) for k in x])
    plt.plot(x, y)
    
    #Version avec une proportion p : 
    def tirer2(n, p):
        item = 0
        for _ in range(n):
            if random.random()<p:
                item +=1
        return item

    def proportion2(n, p, N, k):
        s = 0
        for i in range(N):
            if tirer2(n, p) == k:
                s += 1
        return s/N
    
    p = .3
    print('proportion2(10, p, 100, 1) :', proportion2(10, p, 100, 5))
    n = 10
    N = 100
    plt.figure(2)
    x = np.asarray(range(n+1))
    y = np.asarray([proportion2(n, p, N, k) for k in x])
    plt.plot(x, y)
    
    
    def prop(k, n, p):
        return binom(k, n) * (p**k) * (1-p)**(n-k)
    plt.figure(3)
    x = np.asarray(range(n+1))
    y = np.asarray([prop(k, n, p) for k in x])
    plt.plot(x, y)
plt.show()