Leetcode #254. Factor Combinations

[yokostan]

If we iterate in [2, n]:

class Solution {
    public List<List<Integer>> getFactors(int n) {
        List<List<Integer>> res = new ArrayList<List<Integer>>();
        if (n <= 3) return res;

        backtrack(n, 2, res, new ArrayList<Integer>());

        return res;
    }

    private void backtrack(int n, int start, List<List<Integer>> res, ArrayList<Integer> list) {
        if (n <= 1) {
            if (list.size() > 1) res.add(new ArrayList<Integer>(list));
            return ;
        }
        for (int i = start; i <= n; i++) {
            if (n % i == 0) {
                list.add(i);
                backtrack(n / i, i, res, list);
                list.remove(list.size() - 1);
            }
        }
    }
}

If we iterate in [2, sqrt(n)] it's even faster:

class Solution {
    public List<List<Integer>> getFactors(int n) {
        List<List<Integer>> res = new ArrayList<List<Integer>>();
        if (n <= 3) return res;

        backtrack(n, 2, res, new ArrayList<Integer>());

        return res;
    }

    private void backtrack(int n, int start, List<List<Integer>> res, ArrayList<Integer> list) {
        for (int i = start; i * i <= n; i++) {
            if (n % i == 0) {
                list.add(i);
                list.add(n / i);
                res.add(new ArrayList<>(list));
                list.remove(list.size() - 1);
                backtrack(n / i, i, res, list);
                list.remove(list.size() - 1);
            }
        }
    }
}