# Combination Sum IIII in C++

Consider we have to generate all possible combinations of k numbers that add up to a number n, given that only numbers from 1 to 9 can be used. Each combination should be a unique set of numbers. All numbers should be positive, and the solution must not contain duplicate combinations. So if k = 3 and n = 9, then the possible combinations are [[1,2,6],[1,3,5],[2,3,4]]

To solve this, we will follow these steps −

• Suppose we will solve this using forming a method called solve. This will be recursive method, this will take k, n, temp array, and start. the start is initially 1

• if n = 0

• if size of temp = k, then insert temp into res and return

• for i := start to minimum of 9 and n

• insert i into temp

• solve(k, n – i, temp, i + 1)

• delete the last element from temp

• The main method will be like

• create one blank vector called temp

• solve(k, n, temp)

• return res

## Example

Let us see the following implementation to get better understanding −

class Solution {
public:
vector < vector <int> > res;
void solve(int k, int n, vector <int> temp, int start = 1){
if(n == 0){
if(temp.size() == k){
res.push_back(temp);
}
return;
}
for(int i = start ; i <= min(9, n); i++){
temp.push_back(i);
solve(k, n - i, temp, i + 1);
temp.pop_back();
}
}
vector<vector<int>> combinationSum3(int k, int n) {
res.clear();
vector <int> temp;
solve(k, n, temp);
return res;
}
};

## Input

3
9

## Output

[[1,2,6],[1,3,5],[2,3,4]]
Published on 05-Feb-2020 10:07:39