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Make all combinations of size k
  • Difficulty Level : Medium
  • Last Updated : 23 Aug, 2017

Given two numbers n and k and you have to find all possible combination of k numbers from 1…n.

Examples:

Input : n = 4 
        k = 2
Output : 1 2 
         1 3 
         1 4 
         2 3 
         2 4 
         3 4 

Input : n = 5 
        k = 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 

We have discussed one approach in below post.

Print all possible combinations of r elements in a given array of size n



In this, we use DFS based approach. We want all numbers from 1 to n. We first push all numbers from 1 to k in tmp_vector and as soon as k is equal to 0, we push all numbers from tmp_vector to ans_vector. After this we remove the last element from tmp_vector and make make all remaining combination.




// C++ program to print all combinations of size
// k of elements in set 1..n
#include <bits/stdc++.h>
using namespace std;
  
void makeCombiUtil(vector<vector<int> >& ans,
    vector<int>& tmp, int n, int left, int k)
{
    // Pushing this vector to a vector of vector
    if (k == 0) {
        ans.push_back(tmp);
        return;
    }
  
    // i iterates from left to n. First time
    // left will be 1
    for (int i = left; i <= n; ++i)
    {
        tmp.push_back(i);
        makeCombiUtil(ans, tmp, n, i + 1, k - 1);
  
        // Popping out last inserted element
        // from the vector
        tmp.pop_back();
    }
}
  
// Prints all combinations of size k of numbers
// from 1 to n.
vector<vector<int> > makeCombi(int n, int k)
{
    vector<vector<int> > ans;
    vector<int> tmp;
    makeCombiUtil(ans, tmp, n, 1, k);
    return ans;
}
  
// Driver code
int main()
{
    // given number
    int n = 5;
    int k = 3;
    vector<vector<int> > ans = makeCombi(n, k);
    for (int i = 0; i < ans.size(); i++) {
        for (int j = 0; j < ans[i].size(); j++) {
            cout << ans.at(i).at(j) << " ";
        }
        cout << endl;
    }
    return 0;
}

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 

This article is contributed by Roshni Agarwal. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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