*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:

Each combination's factors must be sorted ascending, for example: The factors of 2 and 6 is

[2, 6]

, not

[6, 2]

.

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]
]

快速解法：

public class Solution {
public List<List<Integer>> getFactors(int n) {
List<List<Integer>> result = new ArrayList<List<Integer>>();
helper(result, new ArrayList<Integer>(), n, -1);
return result;
}

public void helper(List<List<Integer>> result, List<Integer> item, int n, int start){
if (start != -1) {
item.add(n);
result.add(new ArrayList<Integer>(item));
item.remove(item.size() - 1);
}

for (int i = Math.max(start,2); i <= Math.sqrt(n); ++i) {
if (n % i == 0) {
item.add(i);
helper(result, item, n/i, i);
item.remove(item.size()-1);
}
}
}
}

请忽略一下解法

什么破方法慢死！recursion的解法：

public class Solution {
public List<List<Integer>> getFactors(int n) {
List<List<Integer>> result = new ArrayList<List<Integer>>();
helper(result, new ArrayList<Integer>(), n, 2);
return result;
}

public void helper(List<List<Integer>> result, List<Integer> item, int n, int start){
if (n <= 1) {
if (item.size() > 1) {
result.add(new ArrayList<Integer>(item));
System.out.println("add item to result");
}
return;
}

for (int i = start; i <= n; ++i) {
if (n % i == 0) {
item.add(i);
System.out.println("item");
System.out.println(item);
helper(result, item, n/i, i);
item.remove(item.size()-1);
System.out.println("removed item");
System.out.println(item);
}
}
}
}

运行结果：

test case n=8

item
[2]
item
[2, 2]
item
[2, 2, 2]
add to result
removed item
[2, 2]
removed item
[2]
item
[2, 4]
add to result
removed item
[2]
removed item
[]item
[4]
removed item
[]item
[8]
removed item
[]

结果：

Your answer

[[2,2,2],[2,4]]

Expected answer

[[2,4],[2,2,2]]

reference：https://leetcode.com/discuss/51250/my-recursive-dfs-java-solution