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51 lines (39 loc) · 1.33 KB
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#!/usr/bin/env python
# coding=utf-8
# Python Script
#
# Copyleft © Manoel Vilela
#
#
"""
Lexicographic permutations
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?
"""
def factorial(n):
return 1 if n < 1 else n * factorial(n - 1)
# let the entry of element number of the sorted element
def problem24(element):
from string import digits
answer = ''
nums = list(digits)
while len(nums) != 0:
# calculate the periodic of the unitary decimal actual
factor_num = factorial(len(nums) - 1)
# verify which must be the number of digit actual
order = element//factor_num
if element % factor_num != 0:
order = element//factor_num + 1
# keep only the rest of periodicity, whose we say which number is.
order %= len(nums)
# insert the value on final of string
answer += nums.pop(order - 1)
return answer
print(problem24(10 ** 6))