Problem02.py

# The function below returns the first prime divisor of an integer:
def firstDivisor(n):
    if (n == 0 or n == 1):
        return 1
    for i in range(2,n+1):
        if n%i == 0:
            break
    return i

# This function returns the list of prime factors of an integer:
def listOfDivisor(n):
    l=[1]
    m=n
    while m!=1:
        l.append(firstDivisor(m))
        m=m//firstDivisor(m)
    return l[1:]

#the function removes repeated numbers in a given list
def noRepeat(l):
    M=[l[0]]
    for i in range(1,len(l)):
        if not (l[i] in l[:i]):
            M.append(l[i])
    return M

# The following function returns the p-adic valuation of an integer, where p is a prime number
def counter(n):
    l = listOfDivisor(n)
    M = noRepeat(l)
    K = []
    for i in M:
        K.append(l.count(i))
    return K

# This increment function proposes an increment method to browse a list, it will help us to
# determine the divisors of an integer
def incr(l,K):
    i=0
    while l[i] == K[i]:
        if i < len(l)-1:
            i = i+1
        else:
            break
    l[i] = l[i]+1
    for j in range(i):
        l[j]=0
    return l

# The following function will help us calculate the number of divisors of an integer
def prod(l):
    p=1
    for i in range(len(l)):
        p=p*(1+l[i])
    return p

# The following function is a sort function of a given list
def sortList(l):
    L=l[:]
    for i in range(len(l)-1):
        for j in range(i+1,len(l)):
            k = i
            if L[j] < L[k]:
                k = j
        m = l[i]
        L[k] = L[i]
        L[i] = L[k]
    return L

# The main function: gives the list of positive divisors of an integer given as input
def division(n):
    l = listOfDivisor(n)
    M = noRepeat(l)
    K = counter(n)
    D = [1]
    L = [0 for i in range(len(K))]
    for i in range(prod(K)-1):
        d = 1
        Y = incr(L,K)
        for i in range(len(M)):
            d = d*(M[i]**Y[i])
        D.append(d)
    return sortList(D)

# approche2 : 
def integer_to_badique(n,b):
    L = []
    m = n
    while (m // b > 1):
        L = L + [m % b]
        m = m // b
    return L

def distance(L1, L2):
    l1 = L1[:]
    l2 = L2[:]
    list_distance = []
    length1, length2 = len(L1), len(L2)
    if (length1 > length2):
        l2.extend([0 for i in range(length1 - length2)])
    
    if (length2 > length1):
        l1.extend([0 for i in range(length2 - length1)])
    for i in range (max(length1,length2)):
        list_distance.append(abs(l1[i] - l2[i]))
    return list_distance