Permutation Sequence

Medium

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:

"123"
"132"
"213"
"231"
"312"
"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"

3 * 2 * 1 4 * 3 * 2 * 1

0000 === 1 0010 === 2 0100 === 3 0110 === 4 0200 === 5 0210 === 6 1000 === 7 1010 === 8 1100 === 9 2000 === 13 3000 === 19

17

2110

1234 1243 1324 1342 1423 1432 2134 2143 2314 ==== 9

1 2 6

123 213

001000