"""

Project Euler Problem 24

========================

A permutation is an ordered arrangement of objects. For example, 3124 is

one possible permutation of the digits 1, 2, 3 and 4. If all of the

permutations are listed numerically or alphabetically, we call it

lexicographic order. The lexicographic permutations of 0, 1 and 2 are:

012 021 102 120 201 210

What is the millionth lexicographic permutation of the digits 0, 1, 2, 3,

4, 5, 6, 7, 8 and 9?

"""

import euler_utils as utils

digits = [chr(i+48) for i in range(0,10)]

count = 0

permutation = []

for position in range(9,0,-1):

#we could have just divided here, it will straightaway give us the index

factorial = utils.factorial_of(position)

for i in range(len(digits)):

count += factorial

if count >= 1000000:

count -= factorial

permutation.append(digits[i])

digits.remove(digits[i])

break

permutation = permutation + digits

print ''.join(permutation)