Leetcode 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.

 

Examples: 
input: 1
output: 

[]

input: 37
output: 

[]

input: 12
output:

[
  [2, 6],
  [2, 2, 3],
  [3, 4]
]

input: 32
output:

[
  [2, 16],
  [2, 2, 8],
  [2, 2, 2, 4],
  [2, 2, 2, 2, 2],
  [2, 4, 4],
  [4, 8]
]

 

 

 

public class Solution {
    public IList<IList<int>> GetFactors(int n) {
        var results = new List<IList<int>>();
        DFS(n, new List<int>(), results);
        return results;
    }
    
    private void DFS(int cur, IList<int> candidate, IList<IList<int>> results)
    {
        int start = candidate.Count == 0 ? 2 : candidate[candidate.Count - 1];
        for (int i = start; i <= Math.Sqrt(cur); i++)
        {
            if (cur % i == 0)
            {
                var tmp = new List<int>(candidate);
                tmp.Add(i);
                tmp.Add(cur / i);
                results.Add(tmp);

                // can further split
                if (cur / i >= 4)
                {
                    candidate.Add(i);
                    DFS(cur / i, candidate, results);
                    candidate.RemoveAt(candidate.Count - 1);
                }
            }
        }
    }
}