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

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