Factor Combinations

Factor Combinations

Problem:

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. Each combination's factors must be sorted ascending, for example: The factors of 2 and 6 is [2, 6], not [6, 2].
2. You may assume that n is always positive.
3. Factors should be greater than 1 and less than n.

 public class Solution {
     public List<List<Integer>> getFactors(int n) {
         List<List<Integer>> listAll = new ArrayList<>();
         if (n < ) return listAll;
         List<Integer> list = factors(n);

         helper(n, , , list, listAll, new ArrayList<Integer>());
         return listAll;
     }

     public void helper(int n, long value, int index, List<Integer> list, List<List<Integer>> listAll, List<Integer> temp) {
         if (index >= list.size() || value >= n) return;

         int curValue = list.get(index);
         temp.add(curValue);
         value *= curValue;

         if (n == value) {
             listAll.add(new ArrayList<Integer>(temp));
         }

         helper(n, value, index, list, listAll, temp);
         value /= curValue;
         temp.remove(temp.size() - );
         helper(n, value, index + , list, listAll, temp);
     }

     public List<Integer> factors(int n) {
         List<Integer> list = new ArrayList<>();
         for (int i = ; i <= (n + ) / ; i++) {
             if (n % i == ) {
                 list.add(i);
             }
         }
         return list;
     }
 }

上面代码其实可以用另下面这种方法，原理一样。

 public class Solution {
   public List<List<Integer>> getFactors(int n) {
       List<List<Integer>> result = new ArrayList<>();
       List<Integer> list = new ArrayList<>();
       helper(, , n, result, list);
       return result;
   }

   public void helper(int start, int product, int n, List<List<Integer>> result, List<Integer> curr) {
       if (start > n || product > n) return;

       if (product == n) {
           List<Integer> t = new ArrayList<>(curr);
           result.add(t);
       }

       for (int i = start; i <= n / ; i++) {
           if(i * product > n) break;
           if (n % i == ) {
               curr.add(i);
               helper(i, i * product, n, result, curr);
               curr.remove(curr.size() - );
           }
       }
   }
 }