# 216     Combination Sum III

## 216. [Combination Sum III](https://leetcode.com/problems/combination-sum-iii/description/)

## 1. Question

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]]
```

## 2. Implementation

**(1) Backtracking**

```java
class Solution {
    public List<List<Integer>> combinationSum3(int k, int n) {
        List<List<Integer>> res = new ArrayList<>();
        List<Integer> combinations = new ArrayList<>();
        getCombinations(1, 0, k, n, combinations, res);
        return res;
    }

    public void getCombinations(int start, int sum, int k, int target, List<Integer> combinations, List<List<Integer>> res) {
        if (sum > target) {
            return;
        }

        if (k == 0 && sum == target) {
            res.add(new ArrayList<>(combinations));
            return;
        }

        for (int i = start; i <= 9; i++) {
            combinations.add(i);
            getCombinations(i + 1, sum + i, k - 1, target, combinations, res);
            combinations.remove(combinations.size() - 1);
        }
    }
}
```

## 3. Time & Space Complexity

**Backtracking:** 时间复杂度O(n^k), 根据组合公式得到，空间复杂度O(n^k)