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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