# 000077-Combinations

### Problem

https://leetcode.com/problems/combinations/description/

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

backtracking problem

```python
class Solution:
    def combine(self, n: int, k: int) -> List[List[int]]:
        res = []
        def helper(idx, temp):
            if len(temp) > k: 
                return
            
            if len(temp) == k:
                res.append(temp[:])
                return
            for i in range(idx, n+1):
                temp.append(i)
                helper(i+1, temp)
                temp.pop() # backtracking
       
        helper(1, []) 
        
        return res
```
