254 Factor Combinations

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. 1.
    You may assume that n is always positive.
  2. 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
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