60. Permutation Sequence

The set [1,2,3,...,n] contains a total of n! unique permutations.

By listing and labeling all of the permutations in order, we get the following sequence for n = 3:

1. "123"
2. "132"
3. "213"
4. "231"
5. "312"
6. "321"

Given n and k, return the _k_th permutation sequence.

Note:

• Given n will be between 1 and 9 inclusive.
• Given k will be between 1 and n! inclusive.

Example 1:

Input: n = 3, k = 3
Output: "213"

Example 2:

Input: n = 4, k = 9
Output: "2314"

Code:

class Solution(object):
    def getPermutation(self, n, k):
        """
        :type n: int
        :type k: int
        :rtype: str
        """
        import math
        numbers = range(1, n+1)
        permutation = ''
        k -= 1
        while n > 0:
            n -= 1
            # get the index of current digit
            index, k = divmod(k, math.factorial(n))  # 阶乘y
            permutation += str(numbers[index])
            # remove handled number
            numbers.remove(numbers[index])

        return permutation