一、题目

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

二、题解

class Solution {
public:vector<vector<int>> res;vector<int> tmp;void backtracking(int k,int n,int startIndex){if(tmp.size() == k){int sum = 0;for(int i = 0;i < tmp.size();i++) sum += tmp[i];if(sum == n) res.push_back(tmp);return;}for(int i = startIndex;i <= 9 - (k - tmp.size()) + 1;i++){tmp.push_back(i);backtracking(k,n,i+1);tmp.pop_back();}}vector<vector<int>> combinationSum3(int k, int n) {backtracking(k,n,1);return res;}
};