Permutation Sequence [leetcode]

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 (ie, for n = 3):

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

Given n and k, return the kth permutation sequence.

string getPermutation(int n, int k) {
        string content;
        vector<int> left;
        int factor = 1;
        for (int i = 1; i <= n; i++)
        {
            left.push_back('0' + i);
            factor *= i;
        }
        int i = n;
        k--;
        while (i)
        {
            factor /= (i--);
            content += left[k / factor];
            left.erase(left.begin() + k/factor);
            k -= k / factor * factor;
        }
        return content;
    }