[LC] 254. Factor Combinations

Numbers can be regarded as product of its factors. For example,

8 = 2 x 2 x 2;
  = 2 x 4.

Write a function that takes an integer n and return all possible combinations of its factors.

Note:

1. You may assume that n is always positive.
2. Factors should be greater than 1 and less than n.

Example 1:

Input: 1
Output: []

Example 2:

Input: 37
Output:[]

Example 3:

Input: 12
Output:
[
  [2, 6],
  [2, 2, 3],
  [3, 4]
]

Example 4:

Input: 32
Output:
[
  [2, 16],
  [2, 2, 8],
  [2, 2, 2, 4],
  [2, 2, 2, 2, 2],
  [2, 4, 4],
  [4, 8]
]

class Solution {
    public List<List<Integer>> getFactors(int n) {
        List<List<Integer>> res = new ArrayList<>();
        helper(res, new ArrayList<>(), n, 2);
        return res;
    }
    
    private void helper(List<List<Integer>> res, List<Integer> list, int n, int start) {
        if (n == 1) {
            // exclude the self case
            if (list.size() > 1) {
                res.add(new ArrayList<>(list));
                return;
            }
        }
        for (int i = start; i <= n; i++) {
            if (n % i == 0) {
                list.add(i);
                helper(res, list, n / i, i);
                list.remove(list.size() - 1);
            }
        }
    }
}

class Solution {
    public List<List<Integer>> getFactors(int n) {
        List<Integer> factors = new ArrayList<>();
        for (int i = 2; i * i <= n; i++) {
            if (n % i == 0) {
                factors.add(i);
                if (i * i != n) {
                    factors.add(n / i);
                }
            }
        }
        // Collections.sort(factors);
        // System.out.println(factors);
        List<List<Integer>> res = new ArrayList<>();
        dfs(res, factors, new ArrayList<Integer>(), 1, n, 0);
        return res;
    }
    
        private void dfs(List<List<Integer>> res, List<Integer> factors, List<Integer> list, int cur, int n, int index) {
        if (cur > n) {
            return;
        }
        if (cur == n) {
            if (list.size() > 1) {
                res.add(new ArrayList<>(list));                
            }
            return;
        }
        // System.out.println(index);
        for (int i = index; i < factors.size(); i++) {
            list.add(factors.get(i));
            dfs(res, factors, list, cur * factors.get(i), n, i);
            list.remove(list.size() - 1);
        }
    }
}