millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9

nth_lexographic_permutation.py

from math import factorial


numbers = list(range(10))
nth_perm = 1000000
total_numbers = len(numbers)
num = ''


def get_factorial_divisor(factorial, dividend):
	quotient = dividend // factorial
	remainder = dividend % factorial
	if remainder == 0:
		quotient -= 1
		remainder = dividend % (quotient * factorial)
	return quotient, remainder


for i in range(total_numbers - 1, 0, -1):
	ifactorial = factorial(i)
	quotient, nth_perm = get_factorial_divisor(ifactorial, nth_perm)
	num += str(numbers.pop(quotient))
num += str(numbers[0])
print(num)