Leetcode 60. Permutation Sequence

class Solution {
public:
    string getPermutation(int n, int k) {
        string result;
        int factorial[n + 1] = {0};
        factorial[0] = 1;
        for(int i = 1; i <= n; i++) {
            factorial[i] = factorial[i - 1] * i;
        }
        vector<int> nums;
        for(int i = 1; i <=n; i++) {
            nums.push_back(i);
        }
        for(int i = n; i > 0; i--) {
            int remainder = k % factorial[i - 1];
            int quotient = k / factorial[i - 1];
            if(remainder) {
                quotient++;
            }
            result += to_string(nums[quotient - 1]);
            nums.erase(nums.begin() + quotient - 1);
            k %= factorial[i - 1];
            if(k == 0) {
                k = factorial[i - 1];
            }
        }
        return result;
    }
};