# Combinations

## Problem

Given two integers n and k, return all possible combinations of k numbers chosen from the range [1, n].

You may return the answer in any order.

Example 1:

```
Input: n = 4, k = 2
Output: [[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]]
Explanation: There are 4 choose 2 = 6 total combinations.
Note that combinations are unordered, i.e., [1,2] and [2,1] are considered to be the same combination.
```

Example 2:

```
Input: n = 1, k = 1
Output: [[1]]
Explanation: There is 1 choose 1 = 1 total combination.
```

Constraints:

- 1 <= n <= 20
- 1 <= k <= n

## Solution

Time: O(n! / (n - k)!) Space: O(n)

```
class Solution {
public List<List<Integer>> combine(int n, int k) {
var ans = new ArrayList<List<Integer>>();
solve(n, k, 1, List.of(), ans);
return ans;
}
public void solve(int n, int k, int x, List<Integer> curr, List<List<Integer>> ans) {
if (k == 0) {
ans.add(curr);
return;
}
// choose one from n
for (var i = x; i <= n; i++) {
var copy = new ArrayList<>(curr);
copy.add(i);
solve(n, k - 1, i + 1, copy, ans);
}
}
}
```