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