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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. Using 4 different numbers in the range [1,9], the smallest sum we can get is 1+2+3+4 = 10 and since 10 > 1, there are no valid combination.

Constraints:

  • 2 <= k <= 9
  • 1 <= n <= 60

Solutions (Rust)

1. Solution

implSolution{pubfncombination_sum3(k:i32,n:i32) -> Vec<Vec<i32>>{letmut x:i32 = (1 << k) - 1;letmut ret = vec![];while x < (1 << 9){let comb = (1..=9).filter(|&digit| (1 << (digit - 1))& x != 0).collect::<Vec<i32>>();if comb.iter().sum::<i32>() == n { ret.push(comb);} x += (x & -x) + (1 << ((x >> x.trailing_zeros()).trailing_ones() - 1)) - 1;} ret }}
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