Permutation Sequence

Problem: Permutation Sequence

It's actually a math problem. For permutations of n numbers, they are grouped into n groups size of (n-1)!. Based on this property, we can get the permutation we want quickly.

Code in Python:

class Solution(object):
    def getPermutation(self, n, k):
        """
        :type n: int
        :type k: int
        :rtype: str
        """
        ans, nums = "", [x for x in range(1,n+1)]
        for i in xrange(n-1, -1, -1):
            index, k = (k-1)/math.factorial(i), k%math.factorial(i)
            ans += str(nums[index])
            nums.pop(index)
        return ans