Question
Formatted question description: https://leetcode.ca/all/254.html
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:
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]
]
Algorithm
Iterate from 2 to n. If the current number i is divisible by n, it means that i is a factor of n. Store it in a onePath list, and then recursively call n/i. At this time, do not traverse from 2. It traverses from i to n/i, and the condition for stopping is when n is equal to 1, if there is a factor in onePath at this time, store this combination in the result.
Pitfall
Need to avoid case: n=32, and only 32 in this list, add check
if (onePath.size() > 1)
Code
Java
import java.util.ArrayList;
import java.util.List;
public class Factor_Combinations {
public static void main(String[] args) {
Factor_Combinations out = new Factor_Combinations();
Solution s = out.new Solution();
System.out.println(s.getFactors(32));
}
public class Solution {
List<List<Integer>> result = new ArrayList<>();
public List<List<Integer>> getFactors(int n) {
if (n <= 3) {
return result;
}
dfs(2, n, new ArrayList<Integer>());
return result;
}
private void dfs(int start, int target, ArrayList<Integer> onePath) {
if (target <= 1) {
if (onePath.size() > 1) { // to avoid case: n=32, and only 32 in this list
result.add(new ArrayList<Integer>(onePath));
}
return;
}
// start is always 2, can be removed, and hardcode to 2
for (int i = start; i <= target; i++) { // note: <=, eg: i=2, target=2
if (target % i == 0) {
onePath.add(i);
dfs(i, target / i, onePath); // not i+1, but i => example: 32, then 2,2,2...
onePath.remove(onePath.size() - 1);
}
}
}
}
}