60. Permutation Sequence

problem description

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 kth 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"

algorithm thought

n个数排列有n!种情况，如果数字是1-n，那么1开头的排列会有(n-1)!个。同理可以退出，如果需要找第k个排列，第一个字符我们是可以确定的。然后利用递归的思路，一直将数字推出。

code