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# 254    Factor Combinations

## 254. [Factor Combinations](https://leetcode.com/problems/factor-combinations/description/)

## 1. Question

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 integernand 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]
]
```

## 2. Implementation

**(1) Backtracking**

```java
class Solution {
    public List<List<Integer>> getFactors(int n) {
        List<List<Integer>> res = new ArrayList<>();
        List<Integer> factors = new ArrayList<>();
        recGetFactors(2, n, factors, res);
        return res;
    }

    public void recGetFactors(int factor, int curNum, List<Integer> factors, List<List<Integer>> res) {
        if (curNum == 1 && factors.size() > 1) {
            res.add(new ArrayList<>(factors));
            return;
        }

        for (int i = factor; i <= curNum; i++) {
            if (curNum % i == 0)  {
                factors.add(i);
                recGetFactors(i, curNum / i, factors, res);
                factors.remove(factors.size() - 1);
            }
        }
    }
}
```

## 3. Time & Space Complexity

时间复杂度O((logn)! \* n ^ (logn)),对于数n，它有大约logn个约数， 具体解析见<https://www.jiuzhang.com/qa/5224/> 空间复杂度O(logn)，等于约数的个数