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Make all combinations of size k

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  • Difficulty Level : Medium
  • Last Updated : 11 Jul, 2022
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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 the 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 all remaining combination.
 

C++




// 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;
}

Java




// Java program to print all combinations of size
// k of elements in set 1..n
import java.util.*;
public class Main
{
    static Vector<Vector<Integer>> ans = new Vector<Vector<Integer>>();
    static Vector<Integer> tmp = new Vector<Integer>();
       
    static void makeCombiUtil(int n, int left, int k)
    {
       
        // Pushing this vector to a vector of vector
        if (k == 0) {
            ans.add(tmp);
            for(int i = 0; i < tmp.size(); i++)
            {
                System.out.print(tmp.get(i) + " ");
            }
            System.out.println();
            return;
        }
  
        // i iterates from left to n. First time
        // left will be 1
        for (int i = left; i <= n; ++i)
        {
            tmp.add(i);
            makeCombiUtil(n, i + 1, k - 1);
  
            // Popping out last inserted element
            // from the vector
            tmp.remove(tmp.size() - 1);
        }
    }
  
    // Prints all combinations of size k of numbers
    // from 1 to n.
    static Vector<Vector<Integer>> makeCombi(int n, int k)
    {
        makeCombiUtil(n, 1, k);
        return ans;
    }
     
    public static void main(String[] args)
    {
       
        // given number
        int n = 5;
        int k = 3;
        ans = makeCombi(n, k);
    }
}
 
// This code is contributed by suresh07.

Python3




# Python3 program to print all combinations of size
# k of elements in set 1..n
ans = []
tmp = []
 
def makeCombiUtil(n, left, k):
    # Pushing this vector to a vector of vector
    if (k == 0):
        ans.append(tmp)
        for i in range(len(tmp)):
            print(tmp[i], end = " ")
        print()
        return
 
    # i iterates from left to n. First time
    # left will be 1
    for i in range(left, n + 1):
        tmp.append(i)
        makeCombiUtil(n, i + 1, k - 1)
 
        # Popping out last inserted element
        # from the vector
        tmp.pop()
 
# Prints all combinations of size k of numbers
# from 1 to n.
def makeCombi(n, k):
    makeCombiUtil(n, 1, k)
    return ans
  
# given number
n = 5
k = 3
ans = makeCombi(n, k)
 
# This code is contributed by divyeshrabadiya07.

C#




// C# program to print all combinations of size
// k of elements in set 1..n
using System;
using System.Collections.Generic;
class GFG {
     
    static List<List<int>> ans = new List<List<int>>();
    static List<int> tmp = new List<int>();
       
    static void makeCombiUtil(int n, int left, int k)
    {
       
        // Pushing this vector to a vector of vector
        if (k == 0) {
            ans.Add(tmp);
            for(int i = 0; i < tmp.Count; i++)
            {
                Console.Write(tmp[i] + " ");
            }
            Console.WriteLine();
            return;
        }
  
        // i iterates from left to n. First time
        // left will be 1
        for (int i = left; i <= n; ++i)
        {
            tmp.Add(i);
            makeCombiUtil(n, i + 1, k - 1);
  
            // Popping out last inserted element
            // from the vector
            tmp.RemoveAt(tmp.Count - 1);
        }
    }
  
    // Prints all combinations of size k of numbers
    // from 1 to n.
    static List<List<int>> makeCombi(int n, int k)
    {
        makeCombiUtil(n, 1, k);
        return ans;
    }
 
  static void Main()
  {
     
    // given number
    int n = 5;
    int k = 3;
    ans = makeCombi(n, k);
  }
}
 
// This code is contributed by rameshtravel07.

Javascript




<script>
    // Javascript program to print all combinations of size
    // k of elements in set 1..n
    let ans = [];
      let tmp = [];
         
    function makeCombiUtil(n, left, k)
    {
        // Pushing this vector to a vector of vector
        if (k == 0) {
            ans.push(tmp);
            for(let i = 0; i < tmp.length; i++)
            {
                document.write(tmp[i] + " ");
            }
            document.write("</br>");
            return;
        }
 
        // i iterates from left to n. First time
        // left will be 1
        for (let i = left; i <= n; ++i)
        {
            tmp.push(i);
            makeCombiUtil(n, i + 1, k - 1);
 
            // Popping out last inserted element
            // from the vector
            tmp.pop();
        }
    }
 
    // Prints all combinations of size k of numbers
    // from 1 to n.
    function makeCombi(n, k)
    {
        makeCombiUtil(n, 1, k);
        return ans;
    }
     
    // given number
    let n = 5;
    let k = 3;
    ans = makeCombi(n, k);
 
// This code is contributed by divyesh072019.
</script>

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 

Time Complexity:  O((nCk)*k), where nCk is all possible subsets and k to copy subsets into ans vector.

Space Complexity: O((nCk)*k), to store all n C k subset in the ans vector of size k.

This article is contributed by Roshni Agarwal. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@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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