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]
]
```

254. Factor Combinations
``````struct Solution;

impl Solution {
fn get_factors(n: i32) -> Vec<Vec<i32>> {
let mut cur = vec![];
let mut res = vec![];
Self::dfs(2, n, &mut cur, &mut res);
res
}

fn dfs(start: i32, n: i32, cur: &mut Vec<i32>, all: &mut Vec<Vec<i32>>) {
if n == 1 {
if cur.len() > 1 {
all.push(cur.to_vec());
}
} else {
for i in start..=n {
if n % i == 0 {
cur.push(i);
Self::dfs(i, n / i, cur, all);
cur.pop();
}
}
}
}
}

#[test]
fn test() {
let n = 1;
let res: Vec<Vec<i32>> = vec![];
assert_eq!(Solution::get_factors(n), res);
let n = 37;
let res: Vec<Vec<i32>> = vec![];
assert_eq!(Solution::get_factors(n), res);
let n = 12;
let mut res: Vec<Vec<i32>> = vec_vec_i32![[2, 6], [2, 2, 3], [3, 4]];
let mut ans = Solution::get_factors(n);
res.sort();
ans.sort();
assert_eq!(ans, res);
let n = 32;
let mut res: Vec<Vec<i32>> = vec_vec_i32![
[2, 16],
[2, 2, 8],
[2, 2, 2, 4],
[2, 2, 2, 2, 2],
[2, 4, 4],
[4, 8]
];
let mut ans = Solution::get_factors(n);
res.sort();
ans.sort();
assert_eq!(ans, res);
}
``````