# Combinations in C++

Suppose we have two integers n and k. We have to find all possible combinations of k numbers out of 1 ... n. So if n = 4 and k = 2, then the combinations will be [[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]]

To solve this, we will follow these steps −

• We will use recursive function to solve this. the function solve() is taking n, k, temp array and start. The start is initially 1. This will act like
• if size of temp array = k, then insert temp into res array, and return
• for i := start to n,
• insert i into temp
• solve(n, k, temp, i + 1)
• remove one element from the end of temp
• call the solve function like solve(n, k, [])
• return res

## Example

Let us see the following implementation to get a better understanding −

Live Demo

#include <bits/stdc++.h>
using namespace std;
void print_vector(vector<vector<int> > v){
cout << "[";
for(int i = 0; i<v.size(); i++){
cout << "[";
for(int j = 0; j <v[i].size(); j++){
cout << v[i][j] << ", ";
}
cout << "],";
}
cout << "]"<<endl;
}
class Solution {
public:
vector < vector <int> > res;
void solve(int n, int k, vector <int> temp, int start = 1){
if(temp.size() == k){
res.push_back(temp);
return;
}
for(int i = start; i <= n; i++){
temp.push_back(i);
solve(n, k, temp, i + 1);
temp.pop_back();
}
}
vector<vector<int> > combine(int n, int k) {
res.clear();
vector <int> temp;
solve(n ,k, temp);
return res;
}
};
main(){
Solution ob;
print_vector(ob.combine(5,3));
}

## Input

5
3

## Output

[[1,2,3],[1,2,4],[1,2,5],[1,3,4],[1,3,5],[1,4,5],[2,3,4],[2,3,5],[2,4,5],[3,4,5]]