Project Euler Problem 24

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?

# 在0-9十个数字全排列组成的数字中，从小到大的第1百万个数是多少?

# 思路：因为是从小到大排序，可以逐次从最高位开始寻找

# 以0开头的有9！个，以1开头的有9！个，所以第一位数是2

# 以20开头有8！个，...，第二位是7

# ...

from math import factorial as fac

nth = 1000000
num = [0,1,2,3,4,5,6,7,8,9]
zones = [fac(x) for x in range(9,-1,-1)]
nth -= 1

str1 = ''
for i in range(10):
    zone = nth // zones[i]
    nth = nth % zones[i]
    str1 += str(num[zone])
    num.remove(num[zone])
print(int(str1))

# 1 millionth :2783915460