Make all combinations of size k

11 Jul, 2022
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 nIn 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++
Java
Python3
C#
Javascript
// 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 codeint 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 program to print all combinations of size// k of elements in set 1..nimport 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 program to print all combinations of size# k of elements in set 1..nans = []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 numbern = 5k = 3ans = makeCombi(n, k) # This code is contributed by divyeshrabadiya07.
// C# program to print all combinations of size// k of elements in set 1..nusing 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.
<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.
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kunal6203
divyesh072019
divyeshrabadiya07
rameshtravel07
suresh07
isha307
DFS
Combinatorial
DFS
Combinatorial
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