[LeetCode] 216. 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.

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]]

Thought process:
DFS + backtracking.

Solution:

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class Solution {
    public List<List<Integer>> combinationSum3(int k, int n) {
        List<List<Integer>> combinations = new ArrayList<>();
        combinationSum3(k, n, 1, new ArrayList<>(), combinations);
        return combinations;
    }
    
    private void combinationSum3(int k, int n, int start, List<Integer> combination, List<List<Integer>> combinations) {
        if (combination.size() == k) {
            if (n == 0) {
                combinations.add(new ArrayList<>(combination));
            }
            return;
        }
        
        for (int i = start; i <= 9; i++) {
            combination.add(i);
            combinationSum3(k, n - i, i + 1, combination, combinations);
            combination.remove(combination.size() - 1);
        }
    }
}

Time complexity: O(9 choose k).
Location: Philadelphia, PA, USA

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