LeetCode 60. Permutation Sequence

class Solution {
    public String getPermutation(int n, int k) {
        StringBuilder permutation = new StringBuilder();
        Map<Integer, Integer> numsMap = updateMap(getOrderedNumsUpToN(n));

        for (int i = 0; i < n; i++) {
            int nSize = n - i;
            int s; // section number
            int nFact = factorial(nSize);
            int r = factorial(nSize - 1);

            s = (int) Math.ceil((float) k / r);
            permutation.append(numsMap.get(s));

            numsMap.remove(s);
            List<Integer> values = new ArrayList<Integer>(numsMap.values());
            Collections.sort(values);
            numsMap = updateMap(values);

            k = k - (s - 1) * r;
        }

        return permutation.toString();
    }

    public int factorial(int number) {
        int result = 1;
        for (int factor = 2; factor <= number; factor++) {
            result *= factor;
        }
        return result;
    }

    public List<Integer> getOrderedNumsUpToN(int n) {
        List<Integer> nums = new ArrayList<Integer>();
        for (int i = 1; i <= n; i++) {
            nums.add(i);
        }
        return nums;
    }

    public static Map<Integer, Integer> updateMap(List<Integer> values) {
        Map<Integer, Integer> numsMap = new HashMap<Integer, Integer>();
        for (int i = 1; i <= values.size(); i++) {
            numsMap.put(i, values.get(i - 1));
        }
        return numsMap;
    }
}