combination-sum-iii.md

216. Combination Sum III

Medium

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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

Solution:

class Solution {
public:
    vector<vector<int>> combinationSum3(int k, int n) {
        vector<vector<int>> ans;
        vector<int> comb;
        combination(ans,comb,k,1,n);
        return ans;
    }
    void combination(vector<vector<int>> &ans,vector<int> &comb,int &k,int st,int n){
        if(comb.size()==k){
            if(!n)
                ans.push_back(comb);
            return;
        }
        for(int i=st;i<10;i++){
            comb.push_back(i);
            combination(ans,comb,k,i+1,n-i);
            comb.pop_back();
        }
    }
};