[leetcode]254. Factor Combinations因式组合

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]
]

 

题意：

给定正整数n，返回所有乘积等于n的不同组合(除了n = n)。为避免重复，所有乘数单调递增。

 

思路：

backtracking

 

代码：

class Solution {
    public List<List<Integer>> getFactors(int n) {
        List<List<Integer>> res = new ArrayList<>();
        helper(res, new ArrayList<>(), n, 2);
        return res;
    }
    
    public void helper(List<List<Integer>> res, List<Integer> list, int n, int start){
        if(n == 1){
            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);
            }
        }
    }
}