216. Combination Sum III

Problem Statement

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

Intuition

Approach 1:
Make an array of 1 to 9

Thus Maintaining a state of number of tries we will pick up numbers

Video Links

Approach 1:

C++

class Solution {
public:
    vector<vector<int>> ans;
    vector<int> temp;
    void find_comb(int index, int target, int tries){
        if(index == 10){
            if(target == 0 and tries == 0)
                ans.push_back(temp);
            return ;
        }

        find_comb(index+1, target, tries);
        if(index <= target){
            temp.push_back(index);
            find_comb(index+1, target-index, tries-1);
            temp.pop_back();
        }
    }

    vector<vector<int>> combinationSum3(int k, int n) {
        find_comb(1, n, k);

        return ans;
    }
};

Approach 2:

C++

Approach 3:

C++

Approach 4:

C++