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

# @lc code=start
using LeetCode

function combination_sum3(k::Int, n::Int)
    function combination_sum3(k::Int, n::Int, s::Int)::Vector{Vector{Int}}
        if s + k - 1 > 9 || sum(s:(s + k - 1)) > n
            return []
        elseif k == 1 && s == n
            return [[n]]
        end
        choose_s = combination_sum3(k - 1, n - s, s + 1)
        notchoose_s = combination_sum3(k, n, s + 1)
        return [[[s, cs...] for cs in choose_s]..., notchoose_s...]
    end
    return combination_sum3(k, n, 1)
end
# @lc code=end

combination_sum3 (generic function with 1 method)

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