[LeetCode] Combination Sum III

Combination Sum III

Find all possible combinations of k numbers that add up to a number n, given that only numbers from 1 to 9 can be used and each combination should be a unique set of numbers.

Ensure that numbers within the set are sorted in ascending order.

Example 1:

Input:  k = 3,  n = 7

Output: 

[[1,2,4]]

Example 2:

Input:  k = 3,  n = 9

Output: 

[[1,2,6], [1,3,5], [2,3,4]]

Credits:
Special thanks to @mithmatt for adding this problem and creating all test cases.

Solution: Recursion.
Let combinationSum3(int k, int n, int i) denotes that we solve this problem using numbers from i to 9. Then all we need to do is to call combinationSum3(k, n, 1).

There are two cases, depending whether we use i or not, where 1 <= i <= 9. And then we solve the problem recursively using updated values of k, n, and i.

public class Solution {
    private List<List<Integer>> combinationSum3(int k, int n, int i) {
        ArrayList<List<Integer>> list = 
            new ArrayList<List<Integer>>();
        if (i > 9 || k < 1 || n < i) {
            return list;
        }
        
        if (k == 1 && n == i) {
            ArrayList<Integer> l = new ArrayList<Integer>();
            l.add(i);
            list.add(l);
            return list;
        }
        
        List<List<Integer>> l1 = combinationSum3(k, n, i + 1);
        list.addAll(l1);
        List<List<Integer>> l2 = combinationSum3(k - 1, n - i, i + 1);
        for (List<Integer> ll : l2) {
            ArrayList<Integer> l = new ArrayList<Integer>();
            l.add(i);
            l.addAll(ll);
            list.add(l);
        }
        return list;
    }
    
    public List<List<Integer>> combinationSum3(int k, int n) {
        return combinationSum3(k, n, 1);
    }
}