254 Factor Combinations

254. Factor Combinations​
1. Question
Numbers can be regarded as product of its factors. For example,
1
8 = 2 x 2 x 2;
2
  = 2 x 4.
Copied!
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:
1
[
2
  [2, 6],
3
  [2, 2, 3],
4
  [3, 4]
5
]
Copied!
input:32
output:
1
[
2
  [2, 16],
3
  [2, 2, 8],
4
  [2, 2, 2, 4],
5
  [2, 2, 2, 2, 2],
6
  [2, 4, 4],
7
  [4, 8]
8
]
Copied!
2. Implementation
(1) Backtracking
1
class Solution {
2
    public List<List<Integer>> getFactors(int n) {
3
        List<List<Integer>> res = new ArrayList<>();
4
        List<Integer> factors = new ArrayList<>();
5
        recGetFactors(2, n, factors, res);
6
        return res;
7
    }
8
​
9
    public void recGetFactors(int factor, int curNum, List<Integer> factors, List<List<Integer>> res) {
10
        if (curNum == 1 && factors.size() > 1) {
11
            res.add(new ArrayList<>(factors));
12
            return;
13
        }
14
​
15
        for (int i = factor; i <= curNum; i++) {
16
            if (curNum % i == 0)  {
17
                factors.add(i);
18
                recGetFactors(i, curNum / i, factors, res);
19
                factors.remove(factors.size() - 1);
20
            }
21
        }
22
    }
23
}
Copied!
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

216 Combination Sum III

267 Palindrome Permutation II

Last modified 2yr ago

Copy link

Contents

254. Factor Combinations

1. Question

2. Implementation

3. Time & Space Complexity

254. Factor Combinations​

1. Question

2. Implementation

3. Time & Space Complexity

254. Factor Combinations