Leetcode 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.

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]
]

解法一：

先求出所有的factor，在用DFS。注意由于答案中的factor都是升序排列，所以在往line里加入数字时先判断一下要加入line的数字是不是>=里面最后一个（如果有的话）。 或者先对factor.sort()，然后每次取得时候从 factors[i:]里面取，这样也可以保证每个解都是递增数列。

 class Solution(object):
     def getFactors(self, n):
         """
         :type n: int
         :rtype: List[List[int]]
         """
         res = []
         line = []
         factors = []
         for i in range(2,int(math.sqrt(n))+1):
             if n%i == 0 and i< math.sqrt(n):
                 factors.append(i)
                 factors.append(n/i)
             elif n == i*i:
                 factors.append(i)
         if not factors:
             return []
         self.DFS(factors, n, res, line)
         return res

     def DFS(self, nums, target, res, line):
         if target == 1:
             res.append([x for x in line])
             return 

         if target > 1:
             for elem in nums:
                 if target % elem == 0 and (not line or line and elem >= line[-1]):
                     line.append(elem)
                     self.DFS(nums, target/elem, res, line)
                     line.pop()