254. Factor Combinations

• Difficulty: Medium

• Topics: Backtracking

• Similar Questions:

  • Combination Sum

Problem:

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]
]

Solutions:

class Solution {
public:
    vector<vector<int>> getFactors(int n) {
        vector<int> path;
        vector<vector<int>> ret;

        for (int i = 2; n / i >= i; ++i) {
            if (n % i == 0) {
                path.push_back(i);
                helper(n/i, i, path, ret);
                path.pop_back();
            }
        }
        return ret;
    }

private:
    void helper(int n, int factor, vector<int>& path, vector<vector<int>>& ret) {
        if (factor > n) return;

        for (int i = factor; i <= n / i; ++i) {
            if (n % i == 0) {
                path.push_back(i);
                helper(n / i, i, path, ret);
                path.pop_back();
            }
        }

        path.push_back(n); // the number itself should be considered!
        ret.push_back(path);
        path.pop_back(); // pop back!
    }

};