import matplotlib.pyplot as plt
import numpy as np
import numpy.random as rd
import numpy.linalg as al

def markov_avec_matrice (n, M, x0) :
    X = np.zeros(n)
    X[0]= x0
    for k in range(n-1) :
        X[k+1]= np.random.choice(a=list(range(len(M))), p=M[int(X[k]), :])
    return X




## Évolution d'une maladie, Programmes à trous.
    

#def Exemple(n): 
#    X=np.zeros(n)
#    X[0]=1
#    for k in range(n-1) :
#        if X[k] == 1 :
#            X[k+1] = np.random.choice(a=[1,2,3], p=[1/2,1/2,0])
#        elif X[k] == 2 :
#            X[k+1] = np.random.choice(a=[1,2,3], p=[0,1/5,4/5])
#        else :
#            X[k+1] = np.random.choice(a=[1,2,3], p=[1/10,0,9/10])
#    return X

#y=Exemple(100)
#
#plt.plot(y)
#plt.show()
    
#U=np.zeros(100)
#for k in range (100):
#    U[k]=Exemple(1000)[999];
#    
#
#frequ = np.zeros(3)
#for j in range(3):
#    for k in range(len(U)):
#        if U[k] == j+1 :
#            frequ[j]=frequ[j]+1
#           
#            
#plt.bar([1,2,3],frequ, width=0.1)
#plt.show()
    

### Question 3
#    
#A=np.array([[1/2,1/2,0],[0,1/5,4/5],[1/10,0,9/10]])
#B=al.matrix_power(A,1000)
#
#u0=[1,0,0]
#
#prob = np.dot(u0,B)
#print(prob)
#    
#
#
### Question 4
#
##
##    
#def Example_bis(n):
#    return markov_avec_matrice(n,A,0)
#
#plt.plot(Example_bis(100))

    

def google(n): 
    X=np.zeros(n)
    X[0]=rd.randint(1,4)
    for k in range(n-1) :
        if X[k] == 1 :
            X[k+1] = np.random.choice(a=[1,2,3], p=[1/3,1/3,1/3])
        elif X[k] == 2 :
            X[k+1] = np.random.choice(a=[1,2,3], p=[1/7,5/7,1/7])
        else :
            X[k+1] = np.random.choice(a=[1,2,3], p=[1/12,7/12,4/12])
    return X
    

#U=np.zeros(1000)
#for k in range (1000):
#    U[k]=google(1000)[999];
#    
#
#frequ = np.zeros(3)
#for j in range(3):
#    for k in range(len(U)):
#        if U[k] == j+1 :
#            frequ[j]=frequ[j]+1
#           
#            
#plt.bar([1,2,3],frequ, width=0.1)
    

def google2(n): 
    X=np.zeros(n)
    X[0]=rd.randint(1,6)
    for k in range(n-1) :
        if X[k] == 1 :
            if rd.random()<=0.15:
                X[k+1]=rd.randint(1,6)
            else :
                X[k+1]=rd.choice(a=[2,3,5],p=[1/3,1/3,1/3])
        elif X[k] == 2 :
            if rd.random()<=0.15:
                X[k+1]=rd.randint(1,6)
            else :
                X[k+1]=rd.choice(a=[1,4],p=[1/2,1/2])
        elif X[k] == 3 :
            if rd.random()<=0.15:
                X[k+1]=rd.randint(1,6)
            else :
                X[k+1]=rd.choice(a=[2,5],p=[1/2,1/2])
        elif X[k] == 4 :
            if rd.random()<=0.15:
                X[k+1]=rd.randint(1,6)
            else :
                X[k+1]=rd.choice(a=[2,5],p=[1/2,1/2])
        else :
            if rd.random()<=0.15:
                X[k+1]=rd.randint(1,6)
            else :
                X[k+1]=2
    return X


U=np.zeros(1000)
for k in range (1000):
    U[k]=google2(1000)[999];
    

frequ = np.zeros(5)
for j in range(5):
    for k in range(len(U)):
        if U[k] == j+1 :
            frequ[j]=frequ[j]+1
           
            
plt.bar([1,2,3,4,5],frequ, width=0.1)





plt.show()