254. Factor Combinations

254 - Factor Combinations

Total Accepted: 9165 Total Submissions: 25833 Difficulty: Medium

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:
You may assume that n is always positive.
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]
]

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思路

这题和combination sum 比较类似。还是用backtrack方法来做。
factor的范围是 从 [2, 3, 4, ..., n] ，我们用一个变量pos，来记录每次起始factor。然后在backtrack里面递归执行。最后把验证过的factor加入result里面。

public class Solution {
    public List> getFactors(int n) {
         List> res = new ArrayList>();
         if (n < 2) return res;
         backtrack(n, 2, new ArrayList(), res);
         return res;
    }
    
    public void backtrack(int n, int pos,  List cur, List> res) {
        if ( n == 1) {
            if (cur.size() > 1 ) {
                res.add(new ArrayList(cur));
            }
            
        }
        
        for (int i = pos; i <= n; i++) {
            if (n % i == 0) {
                cur.add(i);
                backtrack(n/i,  i ,cur, res);
                cur.remove(cur.size() - 1); 
            }
           
        }
     }
}