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]
]



// other 

public List<List<Integer>> getFactors(int n) {
    List<List<Integer>> result = new ArrayList<List<Integer>>();
    helper(result, new ArrayList<Integer>(), n, 2);
    return result;
}

public void helper(List<List<Integer>> result, List<Integer> item, int n, int start){
    if (n <= 1) {
        if (item.size() > 1) {
            result.add(new ArrayList<Integer>(item));
        }
        return;
    }
    
    for (int i = start; i <= n; ++i) {
        if (n % i == 0) {
            item.add(i);
            helper(result, item, n/i, i);
            item.remove(item.size()-1);
        }
    }
}

 

public List<List<Integer>> getFactors(int n) {
    List<List<Integer>> res = new LinkedList<>();
    backtrack(2, n, new LinkedList<>(), res);
    return res;
}

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

 

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