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

从题目 Each number is used at most once 得知, 该题属于组合问题。

/**
 * @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()
  }
}

Sister Title

39、40