def divisors(n):
    return [div for div in range(1,n) if n % div == 0]

from math import ceil
def divisors2(n):
    divs = [1]
    for m in range(2, ceil(n ** 0.5)):#1 and n**0.5 will be handled separately. why?
        if n % m == 0:
            divs += [m, n // m]
    if n % n ** 0.5 == 0:
        divs += [int(n ** 0.5)]
    return divs

print(divisors(36))
print(sorted(divisors2(36)))

import time
help(time.clock)

print(time.clock()) 
print(time.clock())

n = 1234567890
tic = time.clock()
divisors(n)
toc = time.clock()
print("divisors: ",(toc-tic))
tic = time.clock()
divisors2(n)
toc = time.clock()
print("divisors2:",(toc-tic))

x_bin = "11110"
x_bin = x_bin[::-1] # reverse it so that LSB is on the left for the iteration
x_dec = 0
for k in range(len(x_bin)):
    bit = int(x_bin[k])
    print(k,bit)
    x_dec += bit * 2**k
print(x_dec)

x_dec = 42
x_bin = ''
while x_dec > 0:
    bit = x_dec % 2
    x_bin = str(bit) + x_bin
    x_dec = x_dec // 2
print(x_bin)

bin(42)

int('101010',2)

hex(42)

int('2a',16)

def convert_base(n,b):
    '''convert_base(integer, integer) -> string
    Return the textual representation of n (decimal) in base 2 <= b <= 10.
    '''
    result = ''
    while n > 0:
        digit = n % b
        n = n // b
        print(digit)
        result = str(digit) + result
    return result

convert_base(23,12)

1+12+12**2

convert_base(10,16)

def convert_base(n,b):
    '''convert_base(integer, integer) -> string
    Return the textual representation of n (decimal) in base 2 <= b <= 10.
    '''
    assert 2 <= b <= 36
    
    if n == 0:
        result = '0'
    elif n < 0:
        result = '-'
    else:
        result = ''
    n = abs(n)
    while n > 0:
        digit = n % b
        n = n // b
        # str(digit) only works for b <= 10
        result = '0123456789abcdefghijklmnopqrstuvwxyz'[digit] + result 
    return result

convert_base(23,12)

convert_base(10,6)

convert_base(10,16)

convert_base(40,32)

convert_base(0,5)

convert_base(100,55)