### 216.Combination_Sum_III

Find all valid combinations of k numbers that sum up to n such that the following conditions are true:

• Only numbers 1 through 9 are used.
• `Each number is used at most once`.

Return a list of all possible valid combinations. The list must not contain the same combination twice, and the combinations may be returned in any order.

Example 1:

``````Input: k = 3, n = 7
Output: [[1,2,4]]

Explanation:
1 + 2 + 4 = 7
There are no other valid combinations.``````

Example 2:

``````Input: k = 3, n = 9
Output: [[1,2,6],[1,3,5],[2,3,4]]

Explanation:
1 + 2 + 6 = 9
1 + 3 + 5 = 9
2 + 3 + 4 = 9
There are no other valid combinations.``````

Example 3:

``````Input: k = 4, n = 1
Output: []

Explanation: There are no valid combinations. [1,2,1] is not valid because 1 is used twice.``````

Example 4:

``````Input: k = 3, n = 2
Output: []

Explanation: There are no valid combinations.``````

Example 5:

``````Input: k = 9, n = 45
Output: [[1,2,3,4,5,6,7,8,9]]

Explanation:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
​​​​​​​There are no other valid combinations.``````

Constraints:

• 2 <= k <= 9
• 1 <= n <= 60

### Analyze

``````/**
* @param {number} k
* @param {number} n
* @return {number[][]}
*/
var combinationSum3 = function(k, n) {
const result = []

recursive(k, n, 1, [], result)
return result
};

var recursive = function(k, n, start, temp, result) {
if (n < 0 || temp.length > k) return
if (n === 0 && temp.length === k) {
result.push([...temp])
return
}

for (let i = start; i <= 9; i++) {
temp.push(i)
n = n - i
recursive(k, n, i + 1, temp, result)
n = n + i
temp.pop()
}
}``````

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