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);
}
}
}
}

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