Combination Sum III

Problem

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.

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]]

Solution

Typical Backtracking Solution

public class Solution {
    public List<List<Integer>> combinationSum3(int k, int n) {
        List<List<Integer>> res = new ArrayList<>();
        helper(res, new ArrayList<>(), 1, k, n);
        return res;
    }

    private void helper(List<List<Integer>> res, List<Integer> list, int start, int k, int n) {
        if (list.size() == k && n == 0) {
            res.add(new ArrayList<>(list));
            return;
        }

        for (int i = start; i <= 9; i++) {
            list.add(i);
            helper(res, list, i + 1, k, n - i);
            list.remove(list.size() - 1);
        }
    }
}

Analysis

Typical backtracking solution
In the helper() method, we have a for loop starting from start until the 9 as problem required
Notice that we only add current list to our res if list.size() == k && n == 0